a rectangle has a length of 1 inches and a width of 6 inches whose sides are changing. the length is increasing by 4 in/sec and the width is shrinking at 2 in/sec. what is the rate of change of the perimeter?

Answers

Answer 1

The rate of change of the perimeter of a rectangle is 4 in/sec.

What is the perimeter of a rectangle?

The whole length of the outline is referred to as the perimeter of a two-dimensional shape. We add the lengths of all four corners of a rectangle to find its perimeter. Since the opposite sides of a rectangle are always equal, we must determine the length and width of the rectangle in order to determine its perimeter. The rectangle's perimeter can be expressed as twice the sum of its length and width.

Given, the length of a rectangle, L = 1 inches

width of a rectangle, W = 6 inches

rate of increasing length, dL/dt = +4 in/sec

rate of decreasing width, dW/dt = -2 in/sec

Now, the perimeter of a rectangle is given by

P = 2L + 2W

Then, the rate of change of the perimeter is

dP/dt = 2 * ( dL/dt) + 2*(dW/dt )

= 2*(+4) + 2*(-2)

= 8-4

= 4 in/sec

Hence, the rate of change of the perimeter is 4 in/sec.

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Related Questions

Kaleb deleted 20 songs from his MP3 player. If the ratio of songs he deleted to songs he
kept was 10:3, how many songs did he originally have on his MP3 player?

Answers

If he deleted 10 songs to every 3 he kept, then he originally had 26 songs

Can someone check this plsss

Answers

Um I’m sorry I don’t know I just need points but good luck :)

a group of n people plays a game. each person puts their name on a slip of paper in a hat, and then picks a name randomly from the hat (without replacement). what is the standard ceviation of the number x of people who pick their own name (assume n≥2)?

Answers

Given that each individual has a [tex]\frac{1}{n}[/tex] chance of receiving their own name, we may indicate whether or not person I received their own name by using a sequence of n identically distributed Bernoulli random variables with

[tex]P=\frac{1}{n}[/tex] .

The total number of people who received their own name is the sum of these Bernoullis. The linearity of expectation causes the expected value of the sum to equal the sum of their respective expected values.

Since each summand has expected value [tex]\frac{1}{n}[/tex] and there are n of them, the expected value is one.

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help me for math..........

Answers

Answer:

A) -20

Step-by-step explanation:

[tex]4y(4y-4)-4(-4y+5+4y^2)\\\\16y^2-16y + 16y-20-16y^2\\\\-20\\[/tex]

What are advantages and disadvanteges when using percent to measure change?

Answers

Answer:

Step-by-step explanation:

Percentages are a powerful way to compare samples with different numbers of observations. By standardising measures using a scale of 0 to 100, samples can be compared quickly and easily. Any graph of the data, however, must include the full range of 0 to 100 to ensure that false impressions are not created.

let e1 be the event that the second coin comes up tails and e2 be the event that two, and not three, heads come up in a row. drag the probability values from the right column and drop them in the corresponding events of left column.

Answers

EVENT 1 has a probability value of 0.5.

EVENT 2 has a probability value of 0.5.

There is an equal chance of getting a HEAD or a TAIL when flipping a fair coin.

A coin has two faces: Head and Tail, and the total probability is always 1

1/2 = 0.5 is the likelihood of getting a head.

1/2 = 0.5 is the probability of receiving a tail.

When the coin is tossed for the first time, E1 is the event when TAIL comes up.

When the coin is tossed a second time, E2 represents the circumstance in which HEAD appears.

EVENT 1 has a probability value of 0.5.

EVENT 2 has a probability value of 0.5.

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kennedy needs to order some new supplies for the restaurant where she works. the restaurant needs at least 512 spoons. there are currently 264 spoons. of each set on sale contains 6 spoons, what is the minimum number of sets of spoons kennedy should buy?

Answers

Kennedy needs purchase at least 42 sets of spoons.

Explain the term inequality of numbers?An algebraic expression with two values that are not equal is represented by an inequality. A sign of inequality can be used to show that one of the two variables is larger than, greater than or comparable to, less than, or equal to another value.

The minimum set of spoons needed in the restaurant = 512 spoons.

Available spoons = 264.

Each set on the sale has 6 spoons.

Let the minimum number of spoon set required be 'x'.

Then,

6x + 264 ≥ 512

Solving the in equality.

6x ≥ 512 - 264

6x ≥ 248

x ≥ 248/6

x ≥ 41.33

Thus, Kennedy needs purchase at least 42 sets of spoons.

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Graph each function and identify its domain, range, intercepts, asymptotes, and holes.

Thank you! :)

Answers

Answer: The domain is : (-∞,5)∪(5,∞)

there is no x intercepts

y-intercept= (0,-29/5)

asymptotes= x=5, no horizantal, oblique y=x-5

there is no holes

range= (-∞,-4]∪[4,∞)

Step-by-step explanation:

read the first five results and summarize the models they describe. choose one you find interesting, and determine how it is similar to the nist sp 800-100 model. how is it different?

Answers

Answer: Both the National Institute of Standards and Technology (NIST)

Step-by-step explanation:

Jack took Diane out to dinner to celebrate her birthday. The total bill for the dinner was $62.80. Jack wants to tip the waiter exactly 15%. How much will Jack tip the waiter?

Answers

The amount of the tip that Jack gave to the waiter will be $9.42.

What is the percentage?

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Jack took Diane out to supper to praise her birthday. The all out bill for the supper was $62.80. Jack needs to tip the server precisely 15%.

The amount of the tip will be given as,

⇒ 15% of $62.8

⇒ 0.15 x $62.8

⇒ $9.42

The amount of the tip that Jack gave to the waiter will be $9.42.

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omg please help me with the ones with the red dot t’s for my math geometry class

Answers

12x is the correct answernj think

Study the pattern in the table. Tell whether the relationship between x and y is linear, exponential, or neither, and explain your answer. If the relationship is linear or
exponential, write an equation for it.

Answers

Answer:
6. y = 2·2^x — exponential
7. y = (1/16)·4^x — exponential
8. neither
9. neither
Step-by-step explanation:
First of all, no table with an entry for 0 will be an inverse relation. When the ratio of one term to the next is a constant, the function is exponential. When the difference from one term to the next is a constant, the function is linear.
Here, some tricks are thrown in. The first two (6 and 7) are exponential functions. The common ratios are 2 and 4, respectively. The multiplier is the value of the function when x=0.
6. y = 2·2^x
7. y = (1/16)·4^x
8. The table for function 8 is that of what is known as a harmonic sequence. The denominator increases linearly. It is a kind of an inverse function, but not the kind we normally call an inverse function.
y = 1/(x+1)
9. The function is not obviously linear, inverse, or exponential. The 6 points can always be described by a polynomial of degree n-1, where n is the number of points. The 5th-degree polynomial that fits these points is tedious to find, but can be found to be ...
y = (120 + 103702x - 213975x^2 + 149665x^3 - 42225 x^4 + 4393x^5)/120
Since the function is not of one of the kinds listed, you are under no obligation to write an equation for it.

The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of people who appear on the list that are actually caught. Step 2 of 2: Suppose a sample of 782 suspected criminals is drawn. Of these people. 273 were captured. Using the data, construct the 98% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list. Round your answers to three decimal places.

Answers

The confidence interval is (0.309, 0.389).

Calculate a 98% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list.

Sample size, n = 782

Sample proportion, p = x/n = 0.349105

Confidence level, 1 - α = 98% = 0.98 Implies

Level of significance, α = 0.02

At α = 0.02, the two-tailed critical value from the z-table, Zα/2 = 2.33

Then, the 98% confidence interval is,

It gives, 0.309≤ p ≤0.389

Lower endpoint = 0.309

Upper endpoint = 0.389

We are 98% confident that the proportion of all suspected criminals who were captured is within the confidence interval. If we were to take a large number of random samples of size 782, 98% of the resulting confidence intervals would contain the true proportion of all suspected criminals who were captured.

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what solution value does not satisfy the compound inequality x – 7 < 17 or –6x > 36? question 2 options: a) x

Answers

The solution of compound inequalities is -6 < x < 24.

A compound inequality is a sentence that contains two inequality statements connected by the words "or" or "and." The conjunction "and" denotes that both statements of the compound sentence are true at the same time. It is the intersection or overlap of the solution sets for the individual statements. "Or" indicates that the entire compound sentence is true if either statement is true. It is the union or combination of the solution sets for each individual statement. A conjunction is a compound inequality that contains the word "and."

Inequalities are expressions that do not have an equal sign between them.

Given,

X - 7<17or-6x>36

First,

x - 7 < 17

x < 17 + 7

x < 24

Similarly,

-6x >36

x < [tex]\frac{-36}{6}[/tex]

x < -6

Thus, compound inequality's solution is -6 < x < 24

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a researcher writes down in a notebook the arrival times of different city buses at a bus stop during different weather conditions. which kind of study is this?

Answers

The times that buses arrive at bus stops in various cities and in various climates are noted by a researcher in a notebook. This study is an observational one. Here option D is the correct answer.

It is an observation because it involves systematically noting people's actions, things, and occurrences without engaging in conversation or other interactions. In observational studies, the impact of a risk factor, diagnostic test, therapy, or other intervention is observed without an attempt to alter who is or is not exposed to it.

Two categories of observational studies are cohort studies and case-control studies. It cannot be a single-blind experiment, nor can it be a double-blind experiment since it is not an experiment.

Single-blind refers to a subject or an assessor. When a study is double-blind, neither the patient nor the outcome evaluator is aware of who received the prescription. It is not a survey because it relies on interviews with a representative sample of people as the main way of gathering data.

Complete question:

A researcher writes down in a notebook the arrival times of different city buses at a bus stop during different weather conditions. Which kind of study is this?

A - observational

B - survey

C - single-blind experiment

D - double-blind experiment

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How can the triangles be proven similar by the SSS similarity theorem?

Answers

Answer:

I Think its b

Step-by-step explanation:

(show that the ratio UV_XY and WV_ZY are equivalent.)

*3rd thing*

if it is wrong (which i dont think it is) then show me a study guide or some way to learn more about it, hope this helps

Find the measure of A:
A
15x
31x-2

Answers

Answer:

Step-by-step explanation:

Triangles add up to 180.

Your known sides are: 15x, 31x-2, and 90 (the square on the corner of the angle tells you that it's a right angle or 90 degrees.)

First make an equation to find X

this looks like: 15x+31x-2+90=180

I just added the sides we know and set them to equal 180. Because triangles add up to 180.

Now solve this by first combining like terms

15x+31x-2+90=180 (do the numbers with x's) so 15x+31x

46x-2+90=180 (now combine the numbers without X's) so -2+90

46x+88=180 (now since 88 is positive, do the opposite and subtract it from 180. This is because 180 is on the other side of the = sign.)

46x=92 (now since 46x means 46 times x, you do the opposite of multiplication and divide 92 by 46.

This gives you x=2

Now the last thing you need to do is solve for angle A

Angle A says "15x" so you can substitute our x value (2) for the x

This looks like 15(2) 15 times 2 is 30

so 30 should be your answer

5. the chi-square test for goodness of fit - no difference from a known population suppose you are reading a study conducted in the year 2000 about welfare recipients in the united states. the authors report the following frequency data on the household size of the 1,844 welfare recipients in their random sample: observed frequencies household size 5-or-more-person 4-person 3-person 2-person 1-person 203 277 301 550 513 you wonder if welfare recipients tend to live in different-sized households than the us population at large. you obtain the following data from the 2000 census: percent distribution of us households by size household size 5-or-more-person 4-person 3-person 2-person 1-person 10.83% 14.20% 16.53% 32.63% 25.81% [source: hobbs f., & Stoops, N. (2002). Census 2000 special reports: Demographic trends in [Source: the 20th century. U.S. Census Bureau.] You use a chi-square test for goodness of fit to see how well the sample of welfare recipients fits the census data. What is the most appropriate null hypothesis? O The distribution of household sizes among welfare recipients is the same as that provided by the census data. The distribution of household sizes among welfare recipients is equal across the five household-size categories. O The distribution of household sizes among welfare recipients is different from that provided by the census data. O The distribution of household sizes among welfare recipients is not equal across the five household-size categories. Fill in the missing values in the following table indicating the expected frequencies in each category for a sample size of 1,844, if the null hypothesis is true: Expected Frequencies Household Size 5-or-more-person 4-person 3-person 2-person 1-person 475.94 304.81 601.70 The chi-square statistic has been calculated for you: x2 = 8.31. The distribution of the chi-square statistic has degrees of freedom. Use the following Distributions tool to find the critical value. Chi-Square Distribution Degrees of Freedom = 4 4 10 11 12 13 14 With the level of significance a = .01, the critical value is Because the chi-square statistic x2 is the critical value, you the null hypothesis. Therefore, you conclude that the proportions of welfare recipients in the five household-size categories differ from the corresponding proportions for all U.S. households.

Answers

The confidence interval for the given ANOVA test to calculate the average typing speed be, (144.83 , 155.17) and the margin of error of the poll be, ±5.17

On Subtracting 1 from your sample size, we get

150 – 1 = 149.

On Subtracting confidence level from 1, and then divide by two.

(1 – .95) / 2 = 0.025

Now, df = 149 and α = 0.025

from the table at df = 149 we got 2.262.

Divide your sample standard deviation by the square root of your sample size.

28 / √(150) = 2.28

Now, 2.262 × 2.28 = 5.17

So, the confidence interval be,

(150 - 5.17 , 150 + 5.17) = (144.83 , 155.17)

Hence, the confidence interval for the given ANOVA test to calculate the average typing speed be, (144.83 , 155.17) and the margin of error of the poll be, ±5.17

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help me with math pls im almost done with it for the week...................

Answers

The expression (5/3)x + (5/9)y is equivalent to the given expression. which is the correct answer would be an option (A).

What is the algebraic expression?

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

The expression is given in the question as:

(2/3)x - (4/9)y + x + y

Rearrange the terms in the above expression,

(2/3)x + x - (4/9)y + y

Combine the likewise terms,

(5/3)x + (5/9)y

Therefore, the expression (5/3)x + (5/9)y is equivalent to the given expression.

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An investment of $9,875 earns 4. 8% interest compounded monthly over 12 years. Approximately how much interest is earned on the investment?.

Answers

Using the compound interest formula, we know that $7,672 is the interest on investments earned.

What is compound interest?

The yearly interest rate is raised to the number of compound periods minus one, and the starting principal amount is multiplied by both of these factors.

The resulting value is subsequently deducted from the loan's entire original amount.

So, interest earned on investment:

A = 9,875 (1 + 0.048/12)^ 12(12)

A = $ 15,547

Interest on investments is the money received:

= $ 15,547 - $ 9,875

= $ 7,672

Therefore, using the compound interest formula, we know that $7,672 is the interest on investments earned.

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Complete question:

An investment of $9,875 earns 4.8% interest compounded monthly over 12 years. approximately how much interest is earned on the investment?

a. $4,740

b. $7,458

c. $7,672

d. $17,567

PLS HELP ASAP!!!! 35pts!!

Answers

The hypotenuse - leg congruency can be applied in both right triangles.

How to find congruent triangles?

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

If the hypotenuse and a side of a right- angled triangle is equivalent to the hypotenuse and a side of the second right- angled triangle, then the two right triangles are said to be congruent by RHS rule.

In other words, if the hypotenuse and a leg of a right triangle are each congruent with the corresponding hypotenuse and leg of another right triangle, then the triangles are congruent.

Hence, the legs of the right triangle are congruent and one of the legs are congruent.

Therefore, the hypotenuse - leg congruency can be applied.

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What is the range of this relation?

Answers

-2, -1, 5, 7, 8 is the range
range is the y-values

my question is how do you write a simplified expression that is equivalent to 7/8+3/8x-1/4y+3/4y-1/2?

Answers

the answer is 3x/8 + y/2 + 3/8

Answer:

1/8(3x+4y+3)

Step-by-step explanation:

Show your work 0.4(20-10m) = 2.5 -2m -12.5

Answers

Answer:

give the guy under me a brainlist lol

Step-by-step explanation:

Hope this helps you

Given: Triangle ABC is isosceles with A as the vertex angle and segment AD bisects segment BC,
Prove: Segment AD bisects angle BAC.

Answers

Answer:

PAy Attention Triangle

Step-by-step explanation:

Triangle ABC is isolated True

a square in the x-y plane in free space has a point charge of q at comer (a/2,a/2) and the comer (a/2,-a/2) and a point charge of -q at (-a/2, a/2) and (-a/2, -a/2). a) find the electric potential at any point along the x-axis. b) evaluate v at x

Answers

Electrical potential at any point along the x-axis is V = Q/2πε0(1/R1 − 1/R3) and V at x is Vx = 0.55Q/πε0a

Given info,

A square in the x-y plane in free space has a point charge of q at comer (a/2,a/2) and the comer (a/2,-a/2) and a point charge of -q at (-a/2, a/2) and (-a/2, -a/2).

Let,

V = Q/4πε0R1 + Q/4πε0R2 + −Q/4πε0R3 + −Q/4πε0R4

= Q/2πε0(1/R1 − 1/R3)

With,

R1 = √[(x - a/2)² + (a/2)²]

R3 = √[(x + a/2)² + (a/2)²]

At x = a/2,

R1 = a/2

R3 = a√5/2

Vx = 0.55Q/πε0a.

Therefore, Electrical potential is V = Q/2πε0(1/R1 − 1/R3) and V at x is Vx = 0.55Q/πε0a

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Drew painted his uncle's barn on Saturday. It took him 8 hours to paint the whole barn, and his uncle paid him 224 dollars for his work. What was Drew's pay rate, in dollars per hour?

Answers

Answer:

$28/hour

Step-by-step explanation:

224 ÷ 8 = 28

When two pipes fill a pool together, they can finish in 4 hours. If one of the pipes fills half the pool then the other takes over and finishes filling the pool, it will take them 9 hours. How long will it take each pipe to fill the pool if it were working alone?
How many hours for one pipe to fill the pool? How many hours for the other pipe to fill the pool?

Answers

One pipe takes 6 hours to fill the pool and the other takes 12 hours.

Pipe A fills 1/x of the pool per hour, and Pipe B fills 1/y of the pool per hour. In other words, A takes x hours to fill the pool and B takes y hours to fill the pool.

Together, they fill 1/x + 1/y of the pool per hour. So, 4 hours times that rate should equal 1 full pool, since together they take 4 hours to fill the pool. That gives you your first equation:

4(1/x + 1/y) = 1

You're also told that if one pipe fills half the pool and the other takes over to fill the rest, it will take 9 hours. We don't know how long Pipe A works, so call that number of hours t. Pipe B must work for 9 - t hours.

So, Pipe A, working for t hours, fills half the pool:

t(1/x) = 1/2

And Pipe B, working for 9 - t hours, fills half the pool:

(9-t)(1/y) = 1/2

You now have a system of three equations (because this is an exceptionally complicated pipe-filling-pool problem):

4(1/x + 1/y) = 1

t(1/x) = 1/2

(9-t)(1/y) = 1/2

Solve for t in that second equation, then plug it into the third equation:

t(1/x) = 1/2

t = x(1/2)

t = x/2

(9 - x/2)(1/y) = 1/2

Now you've got a system of two equations:

4(1/x + 1/y) = 1

(9 - x/2)(1/y) = 1/2

Solve for y in the second equation, then plug that into the first equation:

(9 - x/2)(1/y) = 1/2

(9 - x/2) = y(1/2)

2(9 - x/2) = y

18 - x = y (this is a really nice-looking form of that equation; we'll use it again later)

4(1/x + 1/y) = 1

4(1/x + 1/(18-x)) = 1

4/x + 4/(18-x) = 1

(4(18-x))/(x(18-x)) + (4x)/(x(18-x)) = 1

(4(18-x) + 4x)/(x(18-x)) = 1

4(18-x) + 4x = x(18-x)

72 - 4x + 4x = 18x - x2

72 = 18x - x2

x2 - 18x + 72 = 0

(x - 6)(x - 12) = 0

x - 6 = 0 OR x - 12 = 0

x = 6 OR x = 12

So, Pipe A takes either x = 6 or x = 12 hours to fill the pool alone.

When Pipe A takes 6 hours to fill the pool, Pipe B takes 12. When Pipe A takes 12 hours to fill the pool, Pipe B takes 6.

These cases are equivalent, since the original problem makes no distinction between the pipes.

Hence, one pipe takes 6 hours to fill the pool and the other takes 12 hours.

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write a different expression to model sean's order.eveluate not expressions to check that they are equivlent .How many cupcakes does sean have

Answers

The expression that represents the orders is 12 * (5 + 3.5)

Another expression is 12 * 8.5 The total order is 102

How to determine the expression for Sean's purchase?

From the question, we have the following parameters that can be used in our computation:

Number of cupcakes in a box = 12Number of boxes ordered for his sister’s graduation party = 5Number of boxes ordered for the Variety Show party = 3.5

The above parameters mean that:

Expression for Sean's purchase = Number of cupcakes in a box * (Number of boxes ordered for his sister’s graduation party + Number of boxes ordered for the Variety Show party)

Substitute the known values in the above equation, so, we have the following representation

Expression for Sean's purchase = 12 * (5 + 3.5)

Hence, the expression is 12 * (5 + 3.5)

A different expression

In (a), we have

Expression = 12 * (5 + 3.5)

Evaluate the sum

Expression = 12 * 8.5

Evaluate

Expression = 102

This means that the total number of box is 102

Answers

The change in her investment, due to the lost money is $112

How to determine the amount of money lost to the investment?

From the question, we have the following parameters that can be used in our solution:

Rate of loss = $4 per day

Duration = 4 weeks

From the above parameter, we can calculate the amount of money lost to the investment using:

Amount lost = Duration * Rate of loss

Substitute the known values in the above equation

So, we have the following equation

Amount = 4 weeks * $4

Convert weeks to days

Amount = 28 * $4

Evaluate the quotient

Amount = $112

Hence, the amount is $112