Mathematics High School

## Answers

**Answer 1**

(x2 + y2) dv e , where e lies between the **spheres** x2 + y2 + z2 = 1 and x2 + y2 + z2 = 25 and V = 1666,13×π **Vol units**

We need solve this problem; it is necessary determine the **integrations limits** first.

V = 1666,13×π vol units

In order to express the information in **spherical coordinates**, we have:

x = ρ×cosθ×sinφ

y = ρ×sinθ×sinφ

z = ρ×cosφ

and dV = ρ²×sinφ×dρ×dθ×dφ

0 ≤ φ ≤ π

0 ≤ θ ≤ 2×π

x² + y² + z² = 25 and x² + y² + z² = 1 are two concentric spheres with **center** at the origin and **radius** 5 and 1 respectively.

According to that: 1 ≤ ρ ≤ 5

V = ∫ (x² + y²)× dV

V = ∫ (x² + y²) × ρ²×sinφ×dρ×dθ×dφ

V = ∫ ( ρ²×cos²θ×sin²φ + ρ²×sin²θ×sin²φ ) ×ρ²×sinφ×dρ×dθ×dφ

V = ∫ [ ρ²×sin²φ (cos²θ + sin²θ) ×ρ²×sinφ×dρ×dθ×dφ

V = ∫ [ ρ²×sin²φ×ρ²×sinφ×dρ×dθ×dφ

V = ∫ [ ρ⁴×sin³φ×dρ×dθ×dφ

V = ∫₁⁵ρ⁴×dρ ×∫dθ ×∫sin³φ×dφ

V = ρ⁵/5 |₁⁵×∫dθ ×∫sin³φ×dφ

ρ⁵/5 |₁⁵ = 5⁵/5 - 1⁵/5 = 3125 / 5 - 1/5 = 3124/5

V = 3124/5× θ |₀²π×∫sin³φ×dφ

θ |₀²π = 2×π - 0

V = 3124/5× (2×π) ×∫sin³φ×dφ

∫sin³φ×dφ [ 0 y π ] = 4/3

V = 3124/5× (2×π) ×4/3

V = 1666,13×π **Vol units**

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## Related Questions

derive the formula for the volume of a frustum where the base radii are r1 and r2 and the height is h. (idea: think of the side as a linear function).

### Answers

The **formula** is V = (1/3)πh(r2^2 + r1r2 + r1^2).

How we can derive the formula of the volume of a frustum where base radii are r1 and r2 and height is h?

The **frustum **can be thought of as a **combination** of a smaller cone with radius r1 and height h1, and a larger cone with radius r2 and height h2, where h1 + h2 = h.

The **volume** of the smaller cone is (1/3)πr1^2h1, and the volume of the larger **cone** is (1/3)πr2^2h2. To find the volume of the frustum, we need to **subtract **the volume of the smaller cone from the volume of the larger cone.

First, we can use similar **triangles **to find the relationship between h1, h2, r1, and r2. The triangles formed by connecting the centers of the **bases **of the cones and the top point of the frustum are similar, so we have:

h1 / r1 = h2 / r2

**Solving** for h1, we get:

h1 = h(r1 / (r1 + r2))

**Similarly**, we can find h2:

h2 = h(r2 / (r1 + r2))

Now we can substitute these **expressions** into the formulas for the volumes of the cones:

V1 = (1/3)πr1^2h1 = (1/3)πr1^2h(r1 / (r1 + r2))V2 = (1/3)πr2^2h2 = (1/3)πr2^2h(r2 / (r1 + r2))

The volume of the frustum is then:

V = V2 - V1 = (1/3)πr2^2h(r2 / (r1 + r2)) - (1/3)πr1^2h(r1 / (r1 + r2))

**Simplifying **this expression, we get:

V = (1/3)πh(r2^2 + r1r2 + r1^2)

This is the formula for the volume of a frustum with base radii r1 and r2 and height h.

The volume of a frustum can be **found **by subtracting the volume of the smaller cone from the volume of the larger cone.

We can use similar triangles to find the **relationship** between the heights and radii of the cones, and then **substitute **these expressions into the formulas for the volumes of the cones.

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00

13 of 23

<

p(z)=32400(0.71)²

8 9

10 11 12 13 14 15 16 17

The value of a car purchased in 2018 can be modeled by the

function below where z is the number of years since the car was

purchased.

>

I

Fin

Explain what the growth or decay factor you identified in the

previous question means in this situation.

B

### Answers

**Answer:**

the car's estimated value in 2021 is approximately $16,080.72, which is about 49.7% (100% - 29% x 3) of its original value in 2018.

**Step-by-step explanation:**

The growth or decay factor identified in the previous question (which is 0.71 in this case) represents the rate of depreciation of the car's value over time. In other words, the factor indicates the percentage of the original value that remains after each year.

Since the factor is less than 1 (0.71 is less than 1), this means that the car's value decreases over time. Specifically, the car loses approximately 29% (100% - 71%) of its value each year according to the given function.

For example, if the car was purchased in 2018 and we want to find its estimated value in 2021 (which is 3 years later), we can substitute z = 3 into the function:

p(3) = 32400(0.71)^2 ≈ 16,080.72

This means that the car's estimated value in 2021 is approximately $16,080.72, which is about 49.7% (100% - 29% x 3) of its original value in 2018.

a strategy this student could use to prevent the same error in the future. A bag of apples comes with three red apples and one green apples. Use r to represent the total cost of the red apples and g to represent the cost of the green apples. Write and simplify an expression that represent the total cost of 7 bags of apples. Incorrect Work/Solution Identify and Explain the Error

### Answers

**Step-by-step explanation:**

r = red apples, g = green apples, t = total

3r + g = t

7(3r + g = t)

21r + 7g = 7t

The cost of the apples was not included in the question, but you can multiply the total of one bag by 7, or the cost of the individual apples by the values above.

I need to show my work please help me

### Answers

Five and one half of the antialiasing

Which of the following local anesthetics is safest to use for dental treatment for a pregnant woman?

a. Mepivacaine

b. Lidocaine

c. Articaine

d. Bupivacaine

### Answers

The safest **local anesthetic** to use for dental treatment for a pregnant woman is Lidocaine. therefore, option b. Lidocaine correct.

Local anesthetics are **substances **that cause temporary loss of sensation in a limited area of the body, particularly pain. They do not impact consciousness. A wide range of these compounds are utilized in clinical practice, each with its distinct advantages and disadvantages.

They may be** delivered** by a variety of routes, including **injection**, topical application, or infiltration.Local anesthetics are useful for surgeries, dental procedures, and some kinds of pain relief.

During pregnancy, most local anesthetics used in dentistry are considered safe. Local anesthetics used in dentistry, such as lidocaine, bupivacaine, and articaine, are not teratogenic, mutagenic, or carcinogenic.In addition, lidocaine is the most often used local anesthetic for dental treatment in pregnant women due to its rapid onset and short duration of action, as well as its **excellent** efficacy and safety profile.

However, the American Dental Association advises against the use of Articaine for dental procedures during pregnancy due to a lack of **adequate **data. Articaine, a pregnancy category C drug, has been linked to a slightly higher incidence of adverse effects in animal models.

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Write tan 15° in the form √a-1 /√ а+1, Where a Є N.

### Answers

tan (15°)=2-[tex]\sqrt{3[/tex]

Analyze the responses of Franklin D. Roosevelt's administration to the problems of the Great Depression. How effective were the responses? How did they change the role of the federal government?

### Answers

**Franklin **D. Roosevelt's **administration **responded to the problems of the Great Depression through a series of measures known as the New Deal.

The New Deal included programs such as the **Civilian **Conservation Corps, the Works Progress Administration, and the Social Security Act, which aimed to create jobs, stimulate economic growth, and provide social welfare benefits to those in need.

Overall, the New Deal was effective in providing immediate relief to millions of Americans suffering from the economic downturn. It also helped to stabilize the banking system and regulate the stock market through the creation of institutions such as the **Federal **Deposit Insurance Corporation and the Securities and Exchange Commission.

However, the New Deal did not completely end the Great Depression and it took the country's entry into World War II to fully revive the **economy**.

The New Deal also changed the role of the federal government by greatly expanding its authority and responsibilities. The government became more involved in providing **social **welfare benefits and regulating the economy. This shift in the government's role has continued to shape American politics and policy to this day.

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Eight to the power of 3X divided by eight to the power of 2X plus one equals eight to the power of nine. what X value makes this equation true?

### Answers

The value of X that makes the equation true is X = 9. The given equation is [tex]8^(3X)/(8^(2X)+1) = 8^9[/tex]. To solve for X, we can use the properties of **exponents **to simplify the **equation**.

First, we can use the rule that [tex]a^(b+c)[/tex]=[tex]a^b * a^c[/tex] to rewrite the **denominator **as [tex]8^(2X)[/tex] + 1 =[tex]8^(2X) * 8^0[/tex]. Then we can use the **rule **that [tex]a^0[/tex]= 1 to **simplify **this to [tex]8^(2X) * 1 = 8^(2X)[/tex].

So the equation becomes[tex]8^(3X) / 8^(2X) = 8^(9)[/tex].

Next, we can use the rule that [tex]a^(b-c) = a^b / a^c[/tex] to simplify the left-hand side of the equation to [tex]8^(3X-2X) = 8^(X)[/tex].

So the **equation **now becomes [tex]8^X = 8^9[/tex].

Finally, we can use the rule that if[tex]a^x = a^y[/tex], then x = y to conclude that X = 9.

Therefore, the value of X that makes the equation true is X = 9.

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thelma and david built a recycling bin with a volume of 576 cubic feet. the bin is a rectangular prism with a base 12 feet long and 6 feet wide. a rectangular box measuring 12 feet by 6 feet by h feet. what is the height, h of the bin?

### Answers

The volume of the recycling bin is given as 576 cubic feet. We know that the bin is a rectangular prism with a base of 12 feet by 6 feet. So, we can use the formula for the volume of a rectangular prism to find the height:

**Volume of rectangular prism = base area x height**

**In this case, the base area is 12 feet x 6 feet = 72 square feet. So, we have:**

**576 cubic feet = 72 square feet x height**

**Dividing both sides by 72 square feet, we get:**

**height = 576 cubic feet / 72 square feet**

**Simplifying this expression, we get:**

**height = 8 feet**

**Therefore, the height of the bin is 8 feet.**

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What is the value of x

### Answers

The **value of x**, considering the similar triangles, is given as follows:

x = 15.

What are similar triangles?

Similar triangles are triangles that share these **two features **listed as follows:

Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.

The two triangles in this problem are similar, considering the bisection, hence the **proportional relationship** for the side lengths is given as follows:

9/15 = x/25

9/15 = 0.6, hence we apply cross multiplication to obtain the** value of x **as follows:

x = 0.6 x 25

x = 15.

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The Jelly Bean jar has a radius

of 6.2 cm and a height of 18.3

cm.

What would be a reasonable

lower limit for the number of

jelly beans in the jar?

### Answers

A reasonable **lower limit** for the number of jelly beans in the** jar** is about 13,098.

**What is the** **lower limit?**

To estimate the lower limit for the number of **jelly beans** in the jar, we need to calculate the volume of the jar and divide it by the volume of a single jelly bean. This will give us an estimate of the maximum number of jelly beans that can fit in the jar.

The** volume** of a right circular cylinder, such as the jelly bean jar, is given by the formula V = πr²h, where r is the radius and h is the height.

In this case, the radius is 6.2 cm and the height is 18.3 cm, so the volume of the jar is:

V = π(6.2 cm)²(18.3 cm) ≈ 6791.9 cm³

Now, we need to estimate the volume of a single jelly bean. Let's assume that a jelly bean is approximately a sphere with a radius of 0.5 cm. Then, the volume of a single jelly bean would be:

V_jelly bean = (4/3)π(0.5 cm)³ ≈ 0.52 cm³

Finally, we can estimate the lower limit for the number of jelly beans in the jar by dividing the volume of the jar by the volume of a single jelly bean:

Number of jelly beans ≈ V_jar / V_jelly bean ≈ 6791.9 cm³ / 0.52 cm³ ≈ 13098.1

Therefore, a reasonable lower limit for the number of jelly beans in the jar is about 13,098.

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A cow is tethered to one corner of a square barn, 10 feet by 10 feet, with a rope 100ft long. What is the maximum grazing area for the cow. I know that the answer is 31,145.15 ft squared. I figured out that the left side of the circle has an area of 49348feet. the other semicircular shape - it is not a true semicircle- is split up into three four areas. a quarter circle on the bottom right, sector on the upper right a sector on the right side and a triangle between those two sectors.

### Answers

When a cow is tethered to one **corner** of a square barn, 10 feet by 10 feet, with a rope 100 feet long, the maximum grazing** area** for the cow is 31,145.15 feet squared.

The left side of the circle has an area of 49348 feet.

The other **semicircular** shape is split up into three or four areas. A quarter circle on the bottom right, a sector on the upper right, a sector on the right side, and a triangle between those two sectors.

Therefore, the area of the **quarter circle **on the bottom right is given by:

πr² / 4 = (22/7) × (100/4)² / 4 = 1963.34 ft²

The area of the two sectors is given by: 2πr² / 8 = 2 × (22/7) × (100/8)² / 4 = 1570.80 ft²

The area of the triangle is given by: 1/2 × base × height = 1/2 × 25 × 75 = 937.5 ft²

Therefore, the area of the semicircle is: 1963.34 + 1570.80 + 1570.80 + 937.5 = 6042.44 ft2. The maximum grazing area of the cow is the total area of the square barn minus the ungrazed area of the semicircle.

The area of the square barn is 10 by 10 feet, or 100 ft2.

Therefore, the maximum grazing **area** of the cow is:

100 - 6042.44 = 31,145.15 ft².

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In an increasing-cost industry, where the entry of new firms causes an increase in per-unit costs, a ______ is necessary to induce more production.

### Answers

**Answer: In an increasing-cost industry, where the entry of new firms causes an increase in per-unit costs, a higher price is necessary to induce more production.**

**As new firms enter the industry, they increase the demand for the factors of production, such as labor and raw materials, which leads to an increase in their prices. This increase in input costs results in higher per-unit costs for all firms in the industry, as they have to pay more to produce the same quantity of output.**

**To maintain profits and induce more production, firms must increase their prices to cover the higher per-unit costs. This higher price, in turn, encourages existing firms to increase production and new firms to enter the market, which further increases the demand for factors of production and drives up costs. This cycle continues until the market reaches a new equilibrium where the higher price reflects the higher per-unit costs of production.**

**Step-by-step explanation:**

A. -4/5 + 3/10

B. 2 and 5/8 - 1 and 1/3

Show work. Please help!

### Answers

The solutions to the **equations** A. -4/5 + 3/10 and B. 2 and 5/8 - 1 and 1/3 are -5/10 and 43/24, respectively.

What is equation?

An equation is a mathematical statement that expresses two **expressions**, such as numbers, variables or functions, connected by an equal sign (=). By solving the equation, you can determine the **value** of the variables. Equations can be used to model and solve real-world problems.

A. -4/5 + 3/10

To solve this equation, the fractions must first be converted to the same denominator. The least common denominator of 5 and 10 is 10. Therefore, -4/5 becomes -8/10 and 3/10 stays the same.

-8/10 + 3/10

Now, the equation can be solved by combining the like terms.

-8/10 + 3/10 = -5/10

Therefore, the answer is -5/10.

B. 2 and 5/8 - 1 and 1/3

This equation can be solved by first converting the mixed numbers to improper fractions.

2 and 5/8 = 21/8 and 1 and 1/3 = 5/3

Now, the equation can be solved by combining the like terms.

21/8 - 5/3 = 63/24 - 20/24 = 43/24

Therefore, the answer is 43/24.

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Complete questions as follows-

Solve for A. -4/5 + 3/10

B. 2 and 5/8 - 1 and 1/3

Show work. Please help!

9. State whether the equation represents exponential growth, exponential decay, or neither. (1 point)

y = 2.0.68*

O Exponential growth

O Exponential decay

Oneither

### Answers

Answer:

A. Exponential groth

Step-by-step explanation:

in an experiment, a 6-sided die is rolled until a 6 appears when the experiment ends. what is the sample space for this experiment? let bn denote the event that n rolls are required to complete the experiment. with p the probability of success, establish the probability distribution for bn

### Answers

The** probability distribution** for bn is:

n | P(bn)

1 | 1/6

2 | (5/6)(1/6)

3 | (5/6)^2(1/6)

4 | (5/6)^3*(1/6)

... | ...

k | (5/6)^(k-1)*(1/6)

... | ...

where k can be any **positive integer**. Note that this is a geometric distribution with p=1/6.

The **sample space** for this experiment consists of the sequence of rolls required to obtain the first 6. For example, if a 6 appears on the first roll, then the sample space consists of the single element {6}. If a 6 does not appear on the first roll, then the sample space consists of all possible sequences of rolls that do not include a 6 until the final roll, which is a 6.

More formally, we can represent the sample space as follows:

S = {6, (not 6)(6), (not 6)(not 6)(6), (not 6)(not 6)(not 6)(6), ...}

where (not 6) represents any roll that is not a 6, and each element of the sample space consists of a** sequence** of (not 6) rolls followed by a 6.

Now, let bn denote the event that n rolls are required to complete the experiment, i.e., the experiment ends with a 6 on the nth roll. The probability of success on any roll is 1/6, and the probability of failure (i.e., rolling a number other than 6) is 5/6. Therefore, the probability of requiring exactly n rolls to obtain the first 6 is:

P(bn) = (5/6)^(n-1) * (1/6)

This is because we must roll a non-6 number on the first n-1 rolls (with **probability** 5/6 for each roll), and then roll a 6 on the nth roll (with probability 1/6).

Therefore, the** probability distribution** for bn is:

n | P(bn)

1 | 1/6

2 | (5/6)(1/6)

3 | (5/6)^2(1/6)

4 | (5/6)^3*(1/6)

... | ...

k | (5/6)^(k-1)*(1/6)

... | ...

where k can be any positive integer. Note that this is a geometric distribution with p=1/6.

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determine whether each sequence below converges or diverges. if the sequence converges, find its limit. carefully show your work! (a) an

### Answers

The given **sequence **converges to zero

**Why a sequence converges to 0?**

The given sequence is {an}n = 1∞ = 1/ (n + 3).

The task is to find whether the sequence converges or diverges.

If it converges, then we have to determine the **limit** of the given sequence.

The general term of the sequence is given by,

an = 1/ (n + 3) ...[1]

The given sequence is

{an}n = 1∞ = 1/ (n + 3).

For the given sequence, let us check whether it is converging or diverging.

To determine if the sequence converges or **diverges**, we take the limit of the sequence.

Let, L = limit of sequence.

Then,

lim n→∞an = lim n→∞1/ (n + 3)

Put n = ∞ in [1].

an = 1/ (n + 3)an = 1/ (∞ + 3) = 0L = 0.

Hence,

lim n→∞an = 0.

Since limit exists, we can say that the sequence is convergent.

If the sequence is **convergent**, then we can find its limit.

To find the limit of the sequence, we can directly write the value of the limit.

L = 0.

Hence, the given sequence converges to zero.

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Lakshman Lal owned property worth 60,000. He gave 75% of his property to his

wife) 15% to his son and the remaining to charity. What amounts were received by

his wife and son?

### Answers

**The amount received by Wife is** **45000.**

**The amount received by Son is 9000.**

The total amount is 60000.

The amount given to the wife is 75% of 60000 i.e.,

60000*75/100=45000

The amount given to the son is 15% of 60000 i.e.,

60000*15/100=9000

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On Tuesday, Naomi tests Code Quest with a different group of players. The dot plot shows the time it takes them to complete the puzzle what is the mean of the times

### Answers

The **mean** time it takes for this group of players to complete the **puzzle** is 16 seconds.

**What is the mean of the time?**

To find the mean of the times, we need to add up all the **times **and divide by the** total** number of times.

The times are: 10, 12, 18, 20, 20

To find the sum, we add these times:

10 + 12 + 18 + 20 + 20 = 80

The total number of times is 5.

Now, we divide the sum by the total number of times:

80 / 5 = 16

Therefore, the mean time it takes for this group of players to complete the puzzle is 16 seconds.

**What is puzzle?**

A puzzle is a game, toy, or problem that challenges a person's intellectual or physical **abilities**. Puzzles come in various forms and can be made of different materials, such as cardboard,** wood**, metal, or plastic. Some common types of puzzles include jigsaw puzzles, crossword puzzles, Sudoku, Rubik's cube, and brain teasers. Puzzles are often used for entertainment, education, or cognitive development, and they can be enjoyed by people of all ages.

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let f(x)=g(x)/2x^2-32, where g(x) is a polynomial

### Answers

The **function** f(x) is defined as the ratio of a polynomial g(x) divided by a quadratic expression 2x2-32.

What is **function**?

A function is a set of instructions or code that performs a specific task when it is called or invoked. It is a **subprogram** that can be used in other programs. Functions are also known as procedures, routines, subroutines, and methods. They are essential for making code more organized and reusable. Functions can be used to perform repetitive tasks, or tasks that would be difficult to write out in one program. They can also be used to break down a larger program into smaller, more manageable parts. When used properly, functions can make code easier to read, debug, and maintain.

The form of the polynomial g(x) is not specified, but it can be any polynomial of any degree.

For example, if g(x) is a **linear polynomial** of the form ax+b, then f(x) would be of the form (ax+b)/(2x2-32).

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In the context of operant conditioning, which of the following scenarios best exemplifies negative reinforcement? A. Drake no longer cuts class now that his parents have confiscated his iPhone.

B. Maria buys a particular brand of cereal to get two boxes for the price of one.

C. Nate no longer arrives late at work following a reprimand from his boss.

D. Vanna fastens her seatbelt as soon as she gets in her car to stop the annoying alert sound.

### Answers

The scenario that best exemplifies **negative reinforcement **in operant conditioning is* "Vanna fastens her seatbelt as soon as she gets in her car to stop the annoying alert sound"*. Thus, Option D is correct.

Negative reinforcement involves the removal of an aversive stimulus to increase the likelihood of a behavior occurring in the future.

In this scenario, Vanna fastens her seatbelt to remove the aversive stimulus of the annoying alert sound, which increases the likelihood of her fastening her seatbelt in the future. The other scenarios involve either punishment (confiscation of phone, reprimand from boss) or **positive reinforcement **(getting two boxes of cereal for the price of one), which are different from negative reinforcement.

Overall, negative **reinforcement **involves removing something unpleasant to increase the likelihood of a behavior occurring again in the future. It is important to note that negative reinforcement is not the same as punishment, which involves adding something unpleasant to decrease the likelihood of a behavior occurring again in the future.

Option D holds true.

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Melissa deposited $1200 in a certificate of deposit account that earns 3.2% interest applied at the end of each

year. Which of the following calculations would correctly predict the amount of money in

y in Melissa's account

at the end of four years?

### Answers

Since Melissa deposited $1,200 in a certificate of deposit account that earns 3.2% interest applied at the end of each year, the correct calculation predicting the amount of money, y, (**future value**) in Melissa's account at the end of four years is 3) 1200(1.032)⁴.

What is the future value?

The **future value** represents the present value or investment **compounded** at an interest rate into the future.

The future value can be computed using the **future value formula**, FV = P (1 + r)^n, as follows:

FV = 1200(1.032)⁴

= $1,361.13

The **future value** can also be computed using an **online finance calculator** as follows:

N (# of periods) = 4 years

I/Y (Interest per year) = 3.2%

PV (Present Value) = $1,200

PMT (Periodic Payment) = $0

Results:

**Future Value** (FV) = $1,361.13

Total Interest = $161.13

Thus, we can conclude that Melissa's CD account will be worth a **future value** of $1,361.13 in four years.

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If 12 men can do a work in 20 days, in how many days will 8 men complete the same work?

### Answers

**Answer: 30 days**

**Step-by-step explanation:**

Answer:

30 days

Step-by-step explanation:

Formula: 12×20=N÷8=N

12(men) 8(men)

______ ______

N 20(days)

12×20=240

240÷8=30 days can 8 men complete the same work

Let $f$ be a function such that $f(x+y) = x + f(y)$ for any two real numbers $x$ and $y$.

If $f(0) = 2$, then what is $f(2021)?$

### Answers

Given:

f(0) = 2

So first of all, we let x = 2021, y = 0:

Then, F(2021) = 2021 + f(0)

Since f(0) = 2, then f(2021) = 2021 + 2 = 2023.

To add, the process that relates an input to an output is called a function.

There are always three main parts of a function, namely:

Input

The Relationship

The Output

The classic way of writing a function is "f(x) = ... ".

What goes into the function is put inside parentheses () after the name of the function: So, f(x) shows us the function is called "f", and "x" goes in.

What a function does with the input can be usually seen as:

f(x) = x2 reveals to us that function "f" takes "x" and squares it.

Please answer the question to the file i have attached below

### Answers

The **function** for Bank A with **annual** compounding is [tex]A (t) = 1 x (1 + 0.021)^t.[/tex]

This function states that the **balance** of Kimiyo's account after t years is equal to her initial investment of $1 multiplied by 1 plus the annual interest rate of 2.1% raised to the power of t years. This calculation will show the **amount** of money Kimiyo will have in her savings account after t years.The function for Bank B with quarterly compounding is [tex]A (t) = 1 x (1 + 0.008)^4t.[/tex] This function states that the balance of Kimiyo's account after t years is equal to her initial **investment** of $1 multiplied by 1 plus the quarterly interest rate of 0.8% raised to the power of 4t years. This calculation is done by taking the number of years, t, and multiplying it by 4, as there are four quarters in a year. This will show the amount of money Kimiyo will have in her savings account after t years.For example, if Kimiyo invests $1 in Bank A with an annual **interest** rate of 2.1%, then after 3 years, her balance would be [tex]A (3) = 1 x (1 + 0.021)^3 = 1.06631[/tex]. This means that Kimiyo would have $1.07 in her savings account after 3 years.

Similarly, if Kimiyo invests $1 in Bank B with a quarterly interest rate of 0.8%, then after 3 years, her balance would be [tex]A (3) = 1 x (1 + 0.008)^12 = 1.06631.[/tex] This means that Kimiyo would also have $1.07 in her **savings** account after 3 years.

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HELP ME PLS!!!

Enlarge shape A by scale factor 3 with centre of enlargement (-7, -8).

What are the coordinates of the vertices of the image?

### Answers

A' (-16, 1), B' (-13, -17), C' (-16, -23), and D' are the **coordinates **of the image's vertices after increasing form A by a scale factor of 3, with the center of expansion (-7, -8) (-22, -17)

What is the procedure for scaling up?

Scale factor = Dimension of the new shape Dimension of the old shape is the **fundamental formula** used to calculate it. Scale factor = Larger figure dimensions is how the formula is written. If the original figure is expanded, smaller figure dimensions.

To enlarge shape A by a scale factor of 3 with the center of enlargement (-7, -8),

Here are the coordinates of the **vertices **of shape A and their corresponding images after enlargement:

Vertex A: (-9, -5)

Image of A: (-16, 1)

Vertex B: (-4, -5)

Image of B: (-13, -17)

Vertex C: (-4, -9)

Image of C: (-16, -23)

Vertex D: (-9, -9)

Image of D: (-22, -17)

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Find the form of (but do not solve for any coefficients in) the appropriate particular solution Y for the differential equation y" + 9y = x cos(3.0) 3x using the Method of Undetermined Coefficients (primes indicate derivatives with respect to x). In your answer, give undetermined coefficients as A, B, etc. Y (x +A). (B cos(3x) + C sin (3x)) =

### Answers

The appropriate particular solution Y for the given **differential equation** y" + 9y = x cos(3x) using the Method of Undetermined Coefficients is Y = (Ax + B) cos(3x) + (Cx + D) sin(3x).

To use the Method of Undetermined Coefficients, we assume a particular form of the solution that has the same form as the **non-homogeneous** term in the differential equation. In this case, the non-homogeneous term is x cos(3x).

Since cos(3x) and sin(3x) are solutions to the homogeneous equation y" + 9y = 0, we need to add an extra factor of x to our guess for the particular solution to ensure **linear** independence.

Therefore, we guess that the particular solution has the form Y = (Ax + B) cos(3x) + (Cx + D) sin(3x).

Taking the first and second **derivatives** of Y, we get:

Y' = (3A + Cx + D) sin(3x) + (Ax + B) (-3sin(3x))

Y'' = (9A - 9Bx + 6C) cos(3x) + (6D - 9Cx) sin(3x)

Substituting these expressions for Y, Y', and Y'' into the differential equation, we get:

(9A - 9Bx + 6C) cos(3x) + (6D - 9Cx) sin(3x) + 9[(Ax + B) cos(3x) + (Cx + D) sin(3x)] = x cos(3x)

Simplifying this equation, we get:

(9A + 6D) cos(3x) + (6C - 9B) sin(3x) = x cos(3x)

Since cos(3x) and sin(3x) are linearly independent, we can equate the **coefficients** of cos(3x) and sin(3x) separately to get a system of equations:

9A + 6D = 0

6C - 9B = 1

Solving this **system of equations**, we get:

A = -2/27

B = -1/27

C = 1/18

D = 0

Therefore, the particular solution is:

Y = (-2/27 x - 1/27) cos(3x) + (1/18 x) sin(3x)

Simplifying further, we get:

Y = -(2x + 3) cos(3x) + (3x) sin(3x)

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End item A is made by assembling 2 parts of B and 4 parts of C. Part C is made from 3 parts of D and 2 parts of E. Gross requirements for end item A are 100 units.

What is the net requirement for part C?

### Answers

End item A is made by assembling 2 parts of B and 4 parts of C. Part C is made from 3 parts of D and 2 parts of E. Gross requirements for end item A are 100 units.Thus, the **net requirement** for part C is -900 units.

The net requirement for part C can be **calculated** as follows:

We can calculate the** total number** of part C required as:

4 (parts of C) × 100 (units of end item A) = 400 (units of part C)

Now, let's calculate the **gross **requirements for parts D and E which are used to **manufacture** part C.

Part C = 3 parts of D + 2 parts of E 100 units of part C will require:

3 (parts of D) × 100 (units of part C) = 300 (units of part D)2 (parts of E) × 100 (units of part C)

= 200 (units of part E)

Therefore, the net requirement for **part C **will be:

Gross requirement for part C - Total parts of C required= 400 - (3 × 300 + 2 * 200)

= 400 - (900 + 400)

= 400 - 1300

= - 900 units

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Find the average value of f over the given rectangle. F(x, y) = 2x2y, R has vertices (−2, 0), (−2, 5), (2, 5), (2, 0)

### Answers

The **average value** of f(x,y) = 2x²y over the given **rectangle** R is approximately 6.42.

To find the average value of f(x,y) = 2x²y over the given rectangle R with vertices (-2,0), (-2,5), (2,5), and (2,0), we need to **integrate** f over R and divide by the area of R.

First, we can find the area of R using the formula for the **area** of a rectangle, which is length times width. The length of R is 4 units and the width is 5 units, so the area of R is 4 × 5 = 20 square units.

Next, we can integrate f(x,y) over R by setting up a double integral of f over R, which is ∫∫R 2x²y dA.

We can evaluate this double integral using iterated integration. First, we integrate with respect to y from 0 to 5: ∫[tex]0^5[/tex] 2x²y dy = x²(5²) = 25x².

Next, we integrate with respect to x from -2 to 2: ∫-2² 25x² dx = (25/3)(2³ - (-2)³) = 128.33.

Finally, we divide the value of the **double** **integral** by the area of R to get the average value of f over R: (1/20)(128.33) = 6.42.

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8) Part C

Classify the following mixtures as homogeneous or heterogeneous. Drag the appropriate items to their respective bins.

1)steel

2)vodka

3)compost

4)honey

5)fruit salad

Part B

Classify each of the following substances as an element, a compound, or a mixture. Drag the appropriate items to their respective bins.

1) soft drink

2) hydrogen peroxide, HOOH

3)boron nitride, BN

4) argon, Ar

5) copper, Cu

### Answers

Part C:

1) Steel - **Homogeneous**

2) Vodka - Homogeneous

3) Compost - Heterogeneous

4) Honey - Homogeneous

5) Fruit Salad - Heterogeneous

Part B:

1) Soft drink - **Mixture**

2) Hydrogen peroxide, HOOH - **Compound**

3) Boron nitride, BN - Compound

4) Argon, Ar - **Element**

5) Copper, Cu - Element

To classify the following mixtures as **homogeneous **or **heterogeneous**, we need to drag the appropriate items to their respective bins.

1) Steel - Homogeneous

2) Vodka - Homogeneous

3) Compost - Heterogeneous

4) Honey - Homogeneous

5) Fruit salad - Heterogeneous

To classify each of the following **substances **as an element, a compound, or a **mixture**, we need to drag the appropriate items to their respective bins.

1) Soft drink - Mixture

2) Hydrogen peroxide, HOOH - Compound

3) Boron nitride, BN - Compound

4) Argon, Ar - **Element**

5) Copper, Cu - Element

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