The length l of a rectangle is decreasing at a rate of 3 cm/sec while the width w is increasing at a rate of 3 cm/sec. When l=5 cm and w=12 cm, find the rates of change of the area, the perimeter, and the lengths of the diagonals of the rectangle. Determine which of these quantities are increasing, decreasing, or constant.
a) The rate of changes of the area of the rectangle is _______ cm^2/sec
Is the area increasing, decreasing, or constant?
b) The rate of change of the perimeter of the rectangle is ____ cm/sec.
Is the perimeter increasing, decreasing, or constant?
c) The rate of change of the length of the diagonals of the rectangle is ____ cm/sec.
Is the length of the diagonals increasing, decreasing, or constant.

Answers

Answer 1

Answer:

1) dA/dt = -21 cm²/s and Area is decreasing

2)dP/dt = 0 and perimeter is constant

3) dD/dt = 21/13 cm/s and diagonal is increasing

Step-by-step explanation:

We are given that;

length l of a rectangle is decreasing at a rate of 3 cm/sec.

Thus, dl/dt = -3 cm/sec

Also, the width w is increasing at a rate of 3 cm/sec. Thus;

dw/dt = 3 cm/sec

When l=5 cm and w=12 cm;

A) Area is given by the formula;

A = lw

The rate at which area is increasing is;

dA/dt = l(dw/dt) + w(dl/dt)

Plugging in the relevant values;

dA/dt = 5(3) + 12(-3)

dA/dt = 15 - 36

dA/dt = -21 cm²/s

This is less than 0.thus, A is decreasing.

B) Formula for perimeter is;

P = 2l + 2w

rate of change of perimeter is;

dP/dt = 2(dw/dt) + 2(dl/dt)

Plugging in the relevant values, we have;

dP/dt = 2(-3) + 2(3)

dP/dt = 0

Thus,Perimeter is constant

C) the length of the diagonal of a rectangle is given by;

D = √(w² + l²)

Rate of change of diagonal is;

dD/dt = [2w(dw/dt) + 2l(dl/dt)]/(2√(w² + l²))

2 will cancel out in numerator and denominator to give;

dD/dt = [w(dw/dt) + l(dl/dt)]/(√(w² + l²))

Plugging in the relevant values gives;

dD/dt = [12(3) + 5(-3)]/(√(12² + 5²))

dD/dt = (36 - 15)/13

dD/dt = 21/13 cm/s

This is greater than 0.

Thus, diagonal is increasing.


Related Questions

find the surface area of the cereal box of 30x20x5​

Answers

Answer:

1700 units squared

Step-by-step explanation:

Answer:

ITS 3000

Step-by-step explanation:

It was found that an unknown solid had a density of 20 g/cm3 and a volume of 30 cm3. Determine the mass of the solid.

Answers

Answer:

30

Step-by-step explanation:

The mass of the solid is 600 grams if the unknown solid had a density of 20 g/cm3 and a volume of 30 cm3

What is density?

It is defined as the mass-to-volume ratio. The density indicates the object's density and is represented by the symbol. The density is measured in kilograms per cubic meter.

It is given that:

It was found that an unknown solid had a density of 20 g/cm3 and a volume of 30 cm3

As we know, from the definition of density:the mass-to-volume ratio

Density = mass/volume

mass = densityxvolume

mass =20x30

mass = 600 grams

Thus, the mass of the solid is 600 grams if the unknown solid had a density of 20 g/cm3 and a volume of 30 cm3

Learn more about the density here:

brainly.com/question/952755

#SPJ2

8-4x for x = 9
The expression equals I

Answers

Answer:

- 28

Step-by-step explanation:

Step 1:

8 - 4x        Equation

Step 2:

8 - 4 ( 9 )     Input x value

Step 3:

8 - 36        Multiply

Answer:

- 28          Subtract

Hope This Helps :)

-28..............................

Meg's Bakery sells the following items.
• one cinnamon roll for $2.50 or four for $10.00
• one pie for $12.50 or two pies for $22.00
• a dozen brownies for $9.00
A. Determine if there is a proportional relationship between cinnamon rolls and the cost of cinnamon rolls. If there is determine the unit rate.

Answers

Answer:

it is $2.50 multiplied by 4

Step-by-step explanation:

this is because for every 1 cinnamon roll it is $2.50 and if you multiply that by 4 you get $10, or how much it costs for 1 roll

HEEELPPPPP PPLS The second side of a triangle is 8 inches less than the first side. The third side is 14 inches more than the first side. The perimeter of the triangle is 78 inches. Find each side of the triangle.

Answers

Answer: ):

Step-by-step explanation:

Answer:

second side is 16

third side is 38

Step-by-step explanation:

x + (x - 8) + (x + 14) = 78

3x + 6 = 78

3x = 78 - 6

3 x = 72

x = 72/3

x = 24

24 + (24 - 8) + (24 + 14) = 78

24 + 16 + 38 = 78

Solve for g: 19 > 2(g + 7.9).

Answers

Answer: g < 1 3/5

Step-by-step explanation:

first, i removed the parentheses.

19 > 2g + 15.8

then, i moved the terms.

-2g > 15.8 - 19

the, i calculated that.

-2g > -3.2

finally, i divided both sides.

g < 1.6

the alternative form is g < 1 3/5

(basically, the second answer)

can u pls help me with this question ​

Answers

Answer:

5

Step-by-step explanation:

Let me know if I am wrong

9 correct : 15 questions = 45 correct: q questions
please help me ​

Answers

Answer: it should be 75

Step-by-step explanation:

9 times 5 is 45 so 15 times 5 should be 75

A proportional relationship is graphed on the coordinate plane. The line that represents the relationship passes through points (0,0) and (5,10). What is the unit rate of the proportional relationship?

Answers

Answer:

Step-by-step explanation:

HELLPPPP

what 0.05% in as a decimal and a mixed number in simplest form

Answers

deimal: 0.05% / 100 = 0.0005

mixed number: 5/10000

-19 + 4k - 15k - k -9

Answers

Answer:

Let's simplify step-by-step.

−19+4k−15k−k−9

=−19+4k+−15k+−k+−9

Combine Like Terms:

=−19+4k+−15k+−k+−9

=(4k+−15k+−k)+(−19+−9)

=−12k+−28

Answer:

=−12k−28

Step-by-step explanation:

Please explain the relationship between a hypothesis and an experiment.

Answers

Answer:

A hypothesis is "is a suggested solution for an unexplained occurrence that does not fit into current accepted scientific theory. The basic idea of a hypothesis is that there is no pre-determined outcome.". And an experiment is "is defined as to try out something new or to test a theory. An example of experiment is when you try out a new hair style. An example of experiment is when you use test tubes and chemicals in a lab to complete a project and to try to better understand chemical reactions.".

Find the slope given the following ordered pairs (6,11) and (8,19)

Answers

Answer:

4

Step-by-step explanation:

solved it

Answer:

m = 4

Step-by-step explanation:

m = (y2 - y1) / (x2-x1)

Given points (6,11) and (8,19) Let y2 = 19, y1 = 11, x2 = 8, and x1 = 6

Subbing in

m = (19-11)/(8-6) = 8/2 = 4

So, the slope is 4

x^3-y^3 how to solve?

Answers

Answer:

x^(3)-y^(3)

Step-by-step explanation:

can someone help me on this

Answers

Answer:

1) Reflections just change the signs of the coordinates, so (1.5, -2) and (-1 and 1/2, 2) are reflections of each other. Also (1.75, -4) and (-1 and 3/4, 4)

2) From left to right: -1.75, -3/4, 1/4, 0.75, 1 and 1/2.

Remember that each 1/4 = 0.25, so this could help you work out fractions and decimals.

Answer:

First question answer: D  Second Question answer: (lowest to highest) -1.75, -3/4, 1/4, 0.75, and 1 1/2

Step-by-step explanation:

write 5/6 - 7/9 in simplest form

Answers

9514 1404 393

Answer:

  1/18

Step-by-step explanation:

18 is a suitable denominator for both fractions:

  5/6 = 15/18

  7/9 = 14/18

Then the difference is ...

  5/6 -7/9 = 15/18 -14/18 = (15 -14)/18 = 1/18

Find the Values of X and Y in the diagram. PLZ HELP

Answers

Answer: x is 47, y is 75

Step-by-step explanation:

A .14kg baseball is dropped from rest. It has a momentum of .78kg x m/s just before it lands on the ground. For what amount of time was the ball in the air?

Answers

Answer

what r the options? a b c d?????

i wuld say it is 2.5

Step-by-step explanation:

Write an equation in slope intercept form with the slope as 1/3 and the point (-3,4)

Answers

Answer:

[tex]y = \frac{1}{3}x + 5[/tex]

Step-by-step explanation:

Slope (m) = 1/3

(-3 , 4)

y - y1 = m(x -x1)

y - 4 = (1/3) (x - [-3])

[tex]y - 4 = \frac{1}{3}(x + 3)\\\\y - 4 = \frac{1}{3}x + \frac{1}{3}*3\\\\y - 4 = \frac{1}{3}x + 1\\\\ y = \frac{1}{3}x + 1 + 4\\\\ y = \frac{1}{3}x + 5[/tex]

A proportional relationship between y and x When x5, ym
What is the constant of proportionality, K?
Enter your answer as a simplified or improper fraction in the box
k -

Answers

Answer:

-7/5

Step-by-step explanation:

Answer:

-7/5

Step-by-step explanation:

What is the answer for 2m + 3m + 8 + 6

Answers

Answer:

5m+14

Step-by-step explanation:

8 times the difference between a number and 6 is equal to 4 times the number.
What is the number?
OA. 12
OB. 4
OC. 16
OD. 48

Answers

Answer:

it's either A (12) or B(4) but I think it's 12

Step-by-step explanation:

if we make it into an equation, we get

8(x-6)=4x

8x-48=4x

-48=-4x

-12=-x

x=12

the reason why it might be 4 as well is if we switch the order

8(6-x)=4x

48-8x=4x

48=12x

x=4

So both of those could be correct, but I'm thinking that because they said between a number and 6, then x goes first, so therefore, I think it is 12

Miguel ate 1/4 of a pizza in 1/2 of an hour. How much pizza will Miguel eat in one hour?

Answers

Answer:

he will eat 2/4 or 1/2 in 1 hour

Step-by-step explanation:

How do I solve this?

Answers

Answer:

The answer is 7.5

Step-by-step explanation:

3x+18=9x−27

3x+18−9x=9x−27−9x

−6x+18=−27

−6x+18−18=−27−18

−6x=−45

−6x /−6 = −45 /−6

x =  15 /2  which is equal to 7.5 as a decimal.  

Last month you spent ​$30 on clothing. This month you spent 150​% of what you spent last month. Set up a proportion to model this situation. How much did you spend this​ month?
You spent ​$*blank* this month.​

Answers

Answer:

$45

Step-by-step explanation:

x=1.5(30)

x=45

Select ALL the terms that are like 5b2

.
Question 4 options:


12b2



5


5b


10b2

Answers

Answer:

12b2 10b2

Step-by-step explanation:

$43 shirt; 6% tax Please Help!!

Answers

Answer:

tax is 2.58

Step-by-step explanation:

Answer:

.06 times 43 is $2.53 in tax

Step-by-step explanation:

Ms. Hartt burns 300 calories when she runs for 1 hour. If Ms. Hartt runs 5 hours in a week how many calories would she burn?

Answers

Answer: If Ms. Hartt burns 300 calories in 1 hour, and runs 5 hours in a week, she burns 1,500 calories in a week.

Explanation: 300 x 5 = 1,500

plz help me im struggling hard​

Answers

Answer:

0.20 × 65 is what you would do for the second

Step-by-step explanation:

btw listen to yungblud

Note that the cost for the rent is a function of the amount of the miles you drove. Let's call that [tex]C(m)[/tex].

Also note that the amount you pay will linearly increase, in other words, the increase in cost will always be the same for each mile. This tells us that our function is indeed a line, a first order polynomial of the form [tex]C(m) = am+b[/tex]

What would happen if you were to rent a truck and not drive it at all? You would pay only the one-time fee.

Therefore, [tex]C(0)=55[/tex]

So, [tex]C(m) = am + 50[/tex]

The cost will increase by $0.20 for each mile, wich tells us that [tex]a=0.20[/tex]

Finally, our expression is [tex]\boxed{C(m) = 0.2m+55}[/tex]

If we want to know how much would you pay if you drove 65 miles, we want to know what [tex]C(65)[/tex] is.

By plugging [tex]m=65[/tex] in the expression, we get

[tex]C(65) =68[/tex]

So you would pay $68

PLS HELP WILL GIVE BRAINLIEST
How can parents that dont have a O blood type still have a O blood type baby???

Answers

Answer: While a child could have the same blood type as one of his/her parents, it doesn’t always happen that way.

Step-by-step explanation:

For example, parents with AB and O blood types can either have children with blood type A or blood type B. These two types are definitely different than parents’ blood types!

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