Mathematics College

## Answers

**Answer 1**

The average **force** associated with the particle impacting the walls is 2mv²/t.

The average force associated with a particle bouncing elastically in one **dimension** between two walls can be calculated by considering the time it takes to make a round trip.

Let's assume that the **velocity **of the particle after the impact is equal to its velocity before the impact but in the opposite direction.

Let's call the time it takes for the particle to make a complete round trip from one wall to the other and back t. Then, the distance traveled by the particle at this time is 2vt. The force exerted on the particle during each impact is equal to its change in **momentum**, which is 2mv/t, where m is the mass of the particle.

Since the particle maintains its **kinetic energy** after the impact, its velocity remains constant. Hence, the time t taken for a round trip is proportional to the square root of the initial velocity. Thus, the average force can be expressed as:

F = (2mv²)/(2vt) = mv²/t

The average force exerted on the walls is then equal to 2F, since the force exerted on one wall is equal and opposite to the force exerted on the other wall.

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## Related Questions

assume that an int variable pos, as well as the strings line and clause, have already been declared. write a sequence of statements that finds the first comma in line, and assigns to clause the portion of line up to, but not including the comma.

### Answers

You can describe the solution in **natural language** as follows:

Find the **position** of the first comma in the **string line**.If a comma is found, store its position in the** variable** pos.Store the portion of the string line up to but not including the comma in the** variable clause**.

If you want to used **Java Programming** here the syntax code:

int commaIndex = line.indexOf(",");

if (commaIndex != -1) {

pos = commaIndex;

clause = line.substring(0, commaIndex);

}

String Comma Split

The solution of finding the position of the first comma in a string and then storing the portion of the string up to but not including the comma in a separate variable is a **general technique** that can be applied to many different types of problems.

It's a common task in **string processing** and is useful when you need to break down a string into smaller, more manageable parts.

For example, you could use this technique to parse a CSV file, extract the first name and last name from a full name, or split a URL into its component parts. The exact application will depend on the specific problem you are trying to solve, but this solution can be a useful building block in many different contexts.

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noah is a statistician who is trying to understand the statistical properties of blackjack, a game where all players receive two cards, one face down and one face up, and can either hit (draw another card) or stay when it is their turn. the goal is to obtain cards whose value is greater than the dealer's hand, but without going over 21. dealers always stay if the value of their hand is more than 16, so the game is algorithmic and can be simulated using a computer program. noah uses a computer program to simulate dealing 21 pairs of cards, where each pair is from a fully-stocked and shuffled deck of 52 playing cards. the result in terms of the total card value of each pair is included below. use excel to create a dot plot of the dataset. using the dot plot, determine how many of the starting hands the dealer would have to stay. blackjack starting hand 17 20 15 17 11 20 10 18 7 helpcopy to clipboarddownload csv

### Answers

Here is one way to **create** a **dot plot** in Excel:

Enter the data into a column in **Excel**.

Go to the Insert tab and select **Scatter** from the Charts group.

Select the Scatter with only **Markers chart** type and click OK.

The dot plot will be created, with each **data point** represented by a dot on the chart.

To determine how many of the starting hands the dealer would have to stay, we need to count the **number** of starting hands that have a total card value of 17 or higher. Based on the data, there are 6 starting hands that have a value of 17 or higher: 17, 20, 15, 17, 20, and 18. So, the dealer would have to stay for 6 of the 21 s**tarting hands**.

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Write an equation for the nth term of the geometric sequence

Then find an

### Answers

Answer:

Equation: x(n)=2*4^(n-1)

a6=2048

Step-by-step explanation:

Take note that the common ratio is 4 because 2*4=8, 8*4=32, 32*4=128, and so on...

We will use the equation (n) = ar^(n-1) where n

represents the nth term, r stands for the common ratio, and "a" stands for the first term. We use (n-1) because ar^O is for the 1st term

Given the first term is a=2, the common ratio is F=4, then we have the equation x(n)=2*4^(n-1)

So, 128*4=512 would be the 5th term, and the 6th term would be 512*4=2048

So a6=2048

Simon and his friends have 27 pieces of candy. They split them up evenly and each person gets 9 pieces. How many people are there? Select the correct equation and solve for p....

Question 6 options:

27 = 9p; p = 3

9 = 27 - p; p = 18

p/27 = 9; p = 3

9 + p = 27; p = 18

### Answers

**Answer:**

The correct equation and solution for the number of people (p) is:

p/9 = 27/9; p = 27/9 * 9/1 = 27

So there are 27 people.

**Step-by-step explanation:**

**Answer:**

p/27 = 9;p = 3

**Step-by-step explanation:**

thats the answer

Determine the vertex and direction of opening of the parabola for the following quadratic equation: y = x2 - 10 x + 7

### Answers

The **vertex **of the parabola is (5, -18) and the direction of the opening of the parabola is opens upwards.

What is Parabola?

A parabola is a** two dimensional **figure on a plane which is U shaped and any point on the parabola is at an equal distance from a fixed point called **focus **and a fixed line called directrix.

Equation of a parabola is a **quadratic equation**.

Standard equation of the parabola is,

a(x - h)² + k, where (h, k) is the vertex.

From the quadratic equation ax² + bx + c, h = - (b/2a) and k = c - (b²/4a)

Given quadratic equation is y = x² - 10x + 7.

a = 1, b = -10 and c = 7.

h = - (b/2a) = - (-10 / 2) = 5

k = c - (b²/4a) = 7 - ((-10)² / 4) = 7 - (100/4) = 7 - 25 = -18

The vertex is (h, k) = (5, -18).

In the quadratic equation, ax² + bx + c, if the leading coefficient, a, is positive, the parabola opens upward and if a is **negative**, the parabola opens downward.

Here a = 1.

Parabola opens upward.

Hence the parabola opens **upward **with vertex (5, -18).

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Suppose your waiting time in minutes for the Caltrain in the morning is uniformly distributed on [0, 5], whereas waiting time in the evening is uniformly distributed on [0, 10]. Each waiting time is independent of all other waiting times.

(a) If you take the Caltrain each morning and each evening for 5 days in a row, what is your total expected waiting time?

(b) What is the variance of your total waiting time?

(c) What is the expected value of the difference between the total evening waiting time and the total morning waiting time over all 5 days?

(d) What is the variance of the difference between the total evening waiting time and the total morning waiting time over all 5 days?

### Answers

a)The total expected waiting time is** 37.5 minutes**.

b)The total variance is **52.05 minutes^2**.

c)The expected value of the difference between the total evening waiting time and the total morning waiting time over all 5 days is **12.5 minutes**.

d)The variance of the difference between the total evening waiting time and the total morning waiting time over all 5 days is **28.95 minutes^2.**

(a) To find the expected waiting time for the Caltrain in the morning, we calculate the expected value of the **uniform distribution** on [0, 5], which is (0 + 5) / 2 = 2.5 minutes. In the evening, the expected value of the uniform distribution on [0, 10] is (0 + 10) / 2 = 5 minutes.

So, the total expected waiting time for one morning and one evening trip is 2.5 + 5 = 7.5 minutes. For 5 days in a row, the total expected waiting time is 5 * 7.5 = 37.5 minutes.

(b) The **variance of the waiting time **for one morning trip is (5 - 0)^2 / 12 = 25 / 12 = 2.08. The variance of the waiting time for one evening trip is (10 - 0)^2 / 12 = 100 / 12 = 8.33. The total variance of the waiting time for one morning and one evening trip is 2.08 + 8.33 = 10.41. For 5 days in a row, the total variance is 5 * 10.41 = 52.05 minutes^2.

(c) The **expected value **of the difference between the total evening waiting time and the total morning waiting time over all 5 days is 5 * (5 - 2.5) = 12.5 minutes.

(d) The **variance **of the difference between the total evening waiting time and the total morning waiting time over all 5 days is 5 * (8.33 - 2.08) = 28.95 minutes^2.

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Carlo has 200 ml of a 35% alcohol hand sanitizer. Rita has 150 ml of an 85% alcohol hand sanitizer. They mix the sanitizers together in an effort to achieve a 60% concentration of alcohol. What is the concentration of alcohol in the new mixture? (Round your answer to one decimal place.)

### Answers

**Answer:**

**Step-by-step explanation:**

CDC recommends washing hands with soap and water whenever possible because handwashing reduces the amounts of all types of germs and chemicals on hands. But if soap and water are not available, using a hand sanitizer with at least 60% alcohol can help you avoid getting sick and spreading germs to others. The guidance for effective handwashing and use of hand sanitizer in community settings was developed based on data from a number of studies.

Use the figures on the left to complete the statement.

Triangle GHI is congruent to triangle

.

### Answers

By applying the **congruent triangles** concept, it can be concluded ΔGHI is congruent to ΔJKL.

**Congruent triangles** are two or more triangles that are exactly the **same shape** and **size **as one another. So, the triangles will remain exactly the same when rotated, reversed, or even folded.

The properties of congruent triangles:

if ΔABC ≅ ΔEFG then:

AB = EF

BC = FG

∠A = ∠E

∠B = ∠F

Now we look at the attached image:

Because GH ≠ MN, we don't need to check the other properties to conclude that ΔGHI and ΔMNP are not congruent.

Because GH = JK, HI = KL, ∠G = ∠J, and ∠H = ∠K, then we can conclude that ΔGHI ≅ ΔJKL

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Based on historical data, three hospital trauma centers in ontario have 50, 30, and 20 percent of cases. the probability of a case resulting in a malpractice lawsuit in each of the three hospitals is .001,.005, and .008 respectively. if the malpractice suit is filled, what is the probability that it originated in hospital 2?

### Answers

The **probability** that the malpractice suit if filled and it is from **hospital** B is 0.42.

What is probability?

It is the chance of an event to occur from a total number of **outcomes**.

The formula for probability is given as:

**Probability** = Number of required events / Total number of outcomes.

We have,

**Hospital A:**

Probability of the hospital having the case.

P(A) = 50

Probability of case resulting in malpractice in hospital A.

P(M/A) =0.001

**Hospital B:**

The probability of the hospital having the case

P(B) = 30

Probability of case resulting in malpractice in hospital B

P(M/B) =0.005

**Hospital C:**

Probability of the hospital having the case.

P(C) = 20

Probability of case resulting in malpractice in hospital C.

P(M/C) = 0.008

Now,

Using **Baye's** **theorem.**

P(A/M) = P(M/A)P(A) / [ P(M/A)P(A) + P(M/B)P(B) + P(M/C)P(C) }

The **probability** that the malpractice suit if filled and it is from **hospital** B.

P(B/M) = P(M/B)P(B) / [ P(M/A)P(A) + P(M/B)P(B) + P(M/C)P(C) }

**Substituting** the values.

P(B/M)

= (0.005 x 30) / [ 0.001 x 50 + 0.005 x 30 + 0.008 x 20 ]

= 0.15 / [ 0.05 + 0.15 + 0.16 ]

= 0.15 / 0.36

= 0.42

Thus,

The **probability** that the malpractice suit from **hospital** B is 0.42.

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a square park has an area of 8100 square meters. question 1 part a write an equation that can be used to determine the side length ss, in meters, of the park. enter the correct answer in the box.

### Answers

The **equation **is s² = 8100, where s is the side length of the** square park** in meters.

The **area** of a square is given by the formula A = s², where s is the length of one side. If we know the area of a square, we can determine the length of one side by taking the **square root** of the area.

In this case, the area of the park is given as 8100 square meters, so we can write an equation to determine the side length, s, as follows:

s² = 8100

which can be rearranged as:

s= √8100

Taking the square root of 8100 gives a side length of approximately** 90.044 meters**.

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If the measure of Z equals 136°, then what is the measure of T?

### Answers

The measure of angle ∠T is equivalent to **40°**.

What are angles?

In Euclidean geometry, an **angle** is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the **vertex** of the angle.

Given is the measure of **∠Z = 136°**.

We can write -

∠T + ∠Z = 180°

∠T = 180° - ∠Z

∠T = 180° - 136°

∠T = 40°

Therefore, the measure of angle ∠T is equivalent to **40°**.

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Find the volume of a right rectangular prism that has a base area of 112 square feet and a height of 4 1/2

### Answers

The volume of the right rectangular prism is **504 cubic feet.**

To find the **volume** of a right rectangular prism with a base area of 112 square feet and a height of 4½ feet, we can use the formula:

**Volume = Base Area x Height**

First, we need to convert the height to feet and inches or decimal feet:

4½ feet = 4.5 feet

Now we can **substitute** the given values into the formula and calculate the volume:

Volume = 112 square feet x 4.5 feet

Volume = 504 cubic feet

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recall that the variance of a list is defined as the mean squared deviation from average, and that the standard deviation (sd) of the list is the square root of the variance (data 8, chapter 14.2).

### Answers

The **variance** of a list of n numbers is calculated as the mean of the squared deviations from the mean, and the standard **deviation** is the square root of the variance. The formula for variance is given by:

Variance = Σ (x - μ)^2 / n

Where x is a given data point, μ is the **mean** of the data, and n is the number of data points. The standard deviation is then given by the square root of the variance:

Standard deviation = √Variance

The standard deviation is a **measure** of how spread out the data is, with a larger standard deviation indicating that the data is more spread out, and a smaller standard deviation indicating that the data is more tightly **clustered** around the mean.

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Select each graph that shows a function and its inverse.

### Answers

The procedure to find the **Inverse** of a function is mentioned above.

**What is inverse of a function?**

In mathematics, the** inverse function **of a function f is a function that undoes the operation of f. The inverse of f exists if and only if f is **bijective**.

Given is the function and its inverse.

Since the function and their graphs are not given, we will learn how to find the **inverse** of a function. The steps are mentioned below.

**Procedure **(to find inverse function)** - **

**Inverse** of a function can be calculated by following the steps mentioned below -

Step 1 - Replace 'y' with 'x' and vice - versa.

Step 2 - Rewrite the equation by solving for 'y'.

Step 3 - Replace 'y' with f⁻¹(x).

Hence, the procedure to find the **Inverse** of a function is mentioned above.

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**Answer: Correct answer is A and D**

**Step-by-step explanation:**

can someone solve this with answers? no work needed

### Answers

The amount that is **present **after 11 **minutes **is 261.2 mg.

What is the correct equation?

Exponential growth is a type of growth that occurs when a quantity increases at a rate proportional to its current value. It is characterized by a constant growth rate, which leads to rapid increase in the quantity over time.

We can see that the correct **equation **of the process would have the general form of; P = Poe^rt

P= amount at time t

Po = **Initial **amount

r = rate of growth

t = time taken

Thus;

2(Po) = Poe^7r

2 = e^7r

r = ln2/7

r = 0.099

For 11 minutes we would have that;

P= 87.9e^0.099*11

P = 261.2 mg

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A box of candy hearts contains 52 hearts of which 19 are white, 10 are tan, 7 are

pink, 3 are purple, 5 are yellow, 2 are orange, and 6 are green. If you select 8 pieces

of candy randomly from the box, without replacement, find the probability that

(a) Two of the hearts are white.

(b) At least two hearts are white.

(c) Two are white, two are tan, one is pink, one is yellow, and two are green.

### Answers

(a) The **probability **that two of the hearts are white is 0.25167

(b) The probability that **at least **two **hearts **are white is 0.87369

(c) The probability that two are white, two are **tan**, one is pink, one is **yellow**, and two are **green **is 0.00537

(a) The probability of selecting **2 white hearts **from a **total **of 8 pieces of candy is given by -

C(19,2) / C(52,8) = 171 / 14,311 = 0.25167

(b) The probability of selecting **at least 2 white hearts** from a total of 8 pieces of candy is given by -

1 - (C(19,0) * C(33,8) + C(19,1) * C(33,7)) / C(52,8) = 1 - (1 * 56,717 + 19 * 4,221) / 14,311 = 0.87369

(c) The probability of selecting 2 **white**, 2 tan, 1 **pink**, 1 **yellow**, and 2 **green **hearts from a total of 8 pieces of **candy **is given by -

C(19,2) * C(10,2) * C(7,1) * C(5,1) * C(6,2) / C(52,8) = 171 * 45 * 7 * 5 * 15 / 14,311 = 0.00537

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In a lab experiment, 830 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 28 hours. How many bacteria would there be after 13 hours, to the nearest whole number?

### Answers

**After **13 hours, there will be 1145 bacteria, with their number **doubling **every 28 **hours**.

What is the formula for exponential growth and exponential decaying function?

The **exponential **growth formula is y = y0.e (kt).

The formula for exponential **decay **is y = y₀.e^(-kt).

We may apply the formula, to **double **the rate of bacterial growth.

[tex]y_f=y_0*2^\frac{t_r}{t}[/tex], where [tex]y_f[/tex] represents the final **population**, [tex]y_0[/tex] is the initial population, [tex]t_r[/tex] is the **period **of time we must estimate, and [tex]t[/tex] represents the time rate growth.

Thus, based on the information provided, the **quantity **of bacteria after 13 hours will be,

[tex]y_f=830*2\frac{13}{28} \\\\y_f=830*1.38\\\\y_f=1144.86[/tex]

or 1145 **bacterias**.

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Angles of ploygons

find the value of x

### Answers

The requried **measure **of the x in the **polygon **is given as x = 16.

What is the angle?

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of **orientation **and this **measure **is known as the angle.

here,

The sum of the exterior angle of the polygon is equal to 180.

5x + 12 + 9x + 1 + 10x - 37 = 360

24x - 24 = 360

x = 360/24 +1

x = 15 + 1

x = 16

Thus, the requried **measure **of the x in the **polygon **is given as x = 16.

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3. A plumber charges $65 for any part of the first hour of a repair call and $45 for every additional hour. What is the Linear Equation for this?

### Answers

**Answer:**

Y=45X+65

**Step-by-step explanation:**

are the following matrices symmetric, skew-symmetric, or orthogonal? find the spectrum of each, thereby illustrating theorems 1 and 5. show your work in det

### Answers

This matrix is not **symmetric,** **skew-symmetric, **or orthogonal and the eigenvalues of the matrix are: λ = (1 + √65) / 2 and λ = (1 - √65) / 2

To determine if it is **orthogonal,** we can check if it satisfies the condition for orthogonality, which is that its transpose is equal to its inverse.

The transpose of the matrix [1 4 -4 1] is:

[1 -4 4 1]

To find the inverse, we need to calculate the determinant of the matrix and the adjugate of the matrix. The determinant is:

(1)(1) - (4)(-4) = 1 + 16 = 17

The **adjugate** is:

[1 -4 -4 1]

So, the inverse of the matrix is:

[1/17 -4/17 -4/17 1/17]

The transpose of the matrix is not equal to its inverse, so this matrix is not orthogonal.

The spectrum of this matrix can be found by finding its **eigenvalues**. To do this, we solve for the values of λ that satisfy the characteristic equation:

det(A - λI) = 0

where A is the matrix [1 4 -4 1] and I is the identity matrix.

The determinant of A - λI is:

[1-λ 4 -4 1-λ]

[(1-λ)(1-λ) - (4)(-4) = (1-λ)^2 + 16]

So, we need to find the values of λ that satisfy:

(1-λ)^2 + 16 = 0

This equation can be solved using the **quadratic formula:**

λ = (-b ± √(b^2 - 4ac)) / 2a

where a = 1, b = -1, and c = -16.

So,

λ = (-(-1) ± √((-1)^2 - 4(1)(-16))) / 2(1)

λ = (1 ± √(1 + 64)) / 2

λ = (1 ± √65) / 2

So, the eigenvalues of the matrix are:

λ = (1 + √65) / 2 and λ = (1 - √65) / 2

These are the eigenvalues of the matrix and make up its spectrum.

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The question is incomplete; the complete question is:

Are the following matrices symmetric, skew-symmetric, or orthogonal? Find the spectrum of each, thereby illustrating and Theorems 1 and 5. Show your work in detail. [1 4 -4 1]

A bus and a train leave a station at the same time,t = 0. The graph shows the bus’s distance to the next station over time. The train moves more quickly than the bus. Write an equation of a function that could represent the train’s distance to the next station.

### Answers

An **equation of a function** that could represent the train’s distance to the next station. y = (5/2)x + 20

Since the bus and train are both at the **station** at time 0, the **y-intercept **for the new equation is 20. That is one point on the new graph: (0,20) The question said that the train travels faster, that means it spends less time getting to the next station. The **existing graph** shows the bus got to the next station in 10 minutes, so maybe the train got there in 8 minutes. So** another point** on the graph is (8,0) We can use a slope formula to calculate the slope of a new line. Or just count squares on the graph (se image) to find the **slope**. Slope tells how steep a line is, whether the line is going up or down, but also the slope is like directions how to get from one point to another **point** on the line.

All you need to write an **equation is the slope,** m and the y-intercept, b and fill those two **numbers** into the formula y=mx+b Here slope is 5/2 and y-intercept is 20. So you get

y=(5/2)x +20

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Hello my name is Clyde how are you doing today I have a math problem that I just can't figure out the problem is 6 over 45

### Answers

2/15 is the **simplified** form of 6/45

What is Division?

A division is a process of **splitting** a specific amount into equal parts.

we have to find the **value** of six over forty five

6 over 45

The number six and forty five both are **divided** by three

When 6 is divided by three we get two.

When** forty five **divide by three we get 15

So that 6 over 45 is 2 by 15

6/45

2/15

Hence, 2/15 is the **simplified** form of 6/45.

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Which point is a solution of the system of linear equations? x − 3y = 4 y = −3x + 2 (1, 1) (1, −1) (−1, 1) (−1, −1)

### Answers

**Answer:**

**Step-by-step explanation:**

The solution to the system of linear equation, x - 3y = 4 and y = - 3x + 2 is (1, -1).

How to solve linear equation?

A linear equation is an equation in which the highest power of the variable is always 1.

Therefore, the point of the solution of the system of linear equation is represented as follows:

x - 3y = 4

y = - 3x + 2

substitute the value of y in equation(i)

x - 3(-3x + 2) = 4

x + 9x - 6 = 4

10x - 6 = 4

10x = 4 + 6

10x = 10

divide both sides of the equation by 10

x = 10 / 10

x = 1

Therefore,

1 - 3y = 4

- 3y = 4 - 1

- 3y = 3

divide both sides of the equation by - 3

y = 3 / - 3

y = -1

Therefore, the solution of the equation is (1, -1)

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Which sum is equal to the expression

-5x³+2x²+9x+2?

(x²+2)²

A. A + Bx+C

x²+2 (x²+2)²

B. A + Bx+C

(x²+2)²(x²+2)²

C. Ax+B + Cx + D

x²+2 (x²+2)²

D. Ax + B + Cx+D

(x²+2)² (x²+2)²

Answer is C

### Answers

**Answer:5x **

**3**

** +2x **

**2**

** +9x+2?×(x **

**2**

** +2) **

**2**

**Step-by-step explanation:**

What is the solution to the system of equations that Darren graphed?

Make sure you write the solution as an (x,y) ordered pair.

### Answers

For the graph of system of **linear equations **the solution in **order pair** is (2,2).

**What is a linear equation?**

A **linear equation** is one that has a degree of 1 as its maximum value. No variable in a **linear equation**, thus, has an **exponent** greater than 1. A** linear equation's** graph will always be a straight line.

The first line drawn by Darren moves from **third quadrant **to **first quadrant**.

The second line drawn by Darren also moves from **third quadrant **to **first quadrant**.

Both the lines **intersect **at a point in the** first quadrant**.

The point of **intersection** is the solution to the **system of linear equations**.

The point of intersection is (2,2).

Therefore, the solution is (2,2).

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For the functions f(x)=5x−3 and g(x)=3x^2−5x, find (f(g(x)).

### Answers

**Answer:**

15x^2 -25x -3

**Step-by-step explanation:**

f(x)=5x−3 and g(x)=3x^2−5x, find **(f(g(x))**.

Substitute g(x) for x in the function f(x)

5(3x^2−5x) -3

Distribute

15x^2 -25x -3

Find X then solve the right triangle. AB=4x; BC= 2x+8. x=? AB=? BC=?AC=? m

### Answers

**Answer:**

**Step-by-step explanation:**

To find the value of x, we can use the information given in the problem. We have AB = 4x and BC = 2x + 8.

Using the Pythagorean theorem, we can find the length of AC. The theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse).

So, AC^2 = AB^2 + BC^2.

Substituting the values, we get:

AC^2 = (4x)^2 + (2x + 8)^2.

Expanding the squares, we get:

AC^2 = 16x^2 + 16x^2 + 64x + 64.

Combining like terms, we get:

AC^2 = 32x^2 + 64x + 64.

Solving for x, we can use the information that AB = 14 inches. So, 4x = 14 and x = 3.5.

Now that we have the value of x, we can find the lengths of AB, BC, and AC.

AB = 4x = 4 * 3.5 = 14 inches

BC = 2x + 8 = 2 * 3.5 + 8 = 13 inches

And finally, using the Pythagorean theorem, we can find the length of AC:

AC = √(32x^2 + 64x + 64) = √(32 * 3.5^2 + 64 * 3.5 + 64) = √(588).

So, the length of AC is approximately 24.33 inches.

The final answer is x = 3.5, AB = 14 inches, BC = 13 inches, and AC = 24.33 inches.

list seven advantages that aluminum parallel-flow plate-and-fin evaporator has over a standard round copper tube plate-and-fin evaporator.

### Answers

The **aluminum** parallel-flow plate-and-fin **evaporator** has several key advantages over the **standard **round copper tube** plate-and-fin evaporator **are **Lighter Weight,** Improved** Heat Transfer Efficiency.**

An evaporator is a device used in air **conditioning **and refrigeration systems to remove heat from the **refrigerant**, which helps to cool down the air. There are two main types of evaporators: the aluminum parallel-flow plate-and-fin **evaporator **and the standard round copper tube plate-and-fin evaporator.

The parallel-flow design of the **aluminum** evaporator provides a larger surface area for heat transfer, which results in more efficient cooling. This means that less **energy **is required to achieve the same cooling effect.

**Reduced Pressure Drop:** The parallel-flow design also reduces the pressure drop in the refrigerant, which can improve the overall efficiency of the air conditioning or **refrigeration **system.

Aluminum is lighter than copper, which makes the aluminum evaporator easier to handle and install. This can be especially important in large air **conditioning **or refrigeration systems where weight and handling can be a significant concern.

Increased Durability: Aluminum is a more durable material than copper, which means that the aluminum evaporator is less likely to **suffer **from corrosion or other types of damage over time.

**Better Resistance to Leakage:** The parallel-flow design of the aluminum evaporator provides a tighter seal, which reduces the risk of refrigerant leakage. This helps to maintain the efficiency of the air conditioning or refrigeration system.

Lower Maintenance Costs: The increased **durability **and better resistance to leakage of the aluminum evaporator can help to lower maintenance costs over time.

Improved Environmental Performance: The improved efficiency and reduced pressure drop of the aluminum evaporator can help to lower the energy **consumption **of the air conditioning or refrigeration system. This can result in a reduction in greenhouse gas emissions and other environmental impacts.

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The function P(t) = -5t2 + 70t + 600 models a company's profit in thousands of dollars, where t is the

number of years since 1990.

a) In what year will the company reach its maximum profit?

b) What is the company's max profit?

c) How much money will the company have in 2002²

### Answers

**Answer:**

a) The maximum profit occurs at the vertex of the parabola, which has an x-value of -b/2a. In this case, the function is P(t) = -5t^2 + 70t + 600, so a = -5 and b = 70. Therefore, the vertex occurs at t = -b/2a = -70/(2*(-5)) = 7. The number 7 represents the number of years after 1990, so the company will reach its maximum profit in 1997.

b) To find the maximum profit, we need to evaluate the function at the x-value of the vertex. In this case, the vertex occurs at t = 7, so the maximum profit is P(7) = -5(7)^2 + 70(7) + 600 = $745,000.

c) To find the profit in 2002^2, we need to find the value of t that corresponds to the year 2002^2. 2002^2 = 4008004, which is 14 years after 1990. Therefore, we need to find P(14). P(t) = -5t^2 + 70t + 600, so P(14) = -5(14)^2 + 70(14) + 600 = $680.

This is the first quadrant graph for an even function

The function is increasing for:

A)-3B)-7C)-9

The point:

A)(-5,8)

B)(-5,-8)

C)(5,-8)

Lies on the graph of the function.

### Answers

The **solution** is, the** function** is increasing for: (0,0) to (3,9)

What is function?

**Function**, in mathematics, an **expression**, rule, or law that defines a relationship between one **variable** (the independent variable) and another **variable**.

here, we have,

from the given **graph** we get,

the function is ** increasing** for:

(0,0) to (3,9)

Hence, The **solution** is, the** function** is increasing for: (0,0) to (3,9).

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