The length of a rectangle is given by 6t + 5 and its height is √t, where t is time in seconds and the dimensions are in centimeters. Find the rate of change of the area with respect to time.
A'(t) =???​

Answers

Answer 1

MARK AS BRAINLIST

Step-by-step explanation:

L = 6t+5

H = √t

A = L*H

= (6t+5) *√t = 6t√t + 5√t

A'(t) = 6t * 1/2*√t + √t * 6 + 5/2*√t

= 6t/2√t + 6√t + 5/2√t

Answer 2

Expression for the rate of change of the area with respect to time will be,

A' = [tex]9t^{\frac{1}{2}}+\frac{5}{2}t^{-\frac{1}{2}}[/tex] cm per second

It's given in the question,

Length of a rectangle is given by the expression

      (6t + 5) cm

Width or height of the rectangle is given by the expression,

       [tex]\sqrt{t}[/tex] cm

Area of the rectangle is given by,

Area = Length × Height

A = (6t + 5)(√t)

A = [tex]6t^{\frac{3}{2}}+5t^\frac{1}{2}[/tex]

Now find the derivative of area (A) with respect to time (t).

[tex]\frac{dA}{dt}=\frac{d}{dt}(6t^{\frac{3}{2}}+5t^\frac{1}{2})[/tex]

A' = [tex](6\times \frac{3}{2})t^\frac{1}{2}+\frac{5}{2} t^{-\frac{1}{2}}[/tex]

A' = [tex]9t^{\frac{1}{2}}+\frac{5}{2}t^{-\frac{1}{2}}[/tex]

     Therefore, expression for the rate of change of the area will be,

A' = [tex]9t^{\frac{1}{2}}+\frac{5}{2}t^{-\frac{1}{2}}[/tex]

Learn more,

https://brainly.com/question/12596049?


Related Questions

Look at the picture to see question plz help quickly and step by step

Answers

Answer: 16.6

Step-by-step explanation:

Which one?
A. B. C. or D? ​

Answers

Answer:

I think that the answer is D

Step-by-step explanation:

​can someone help me solve this system. thanks
2y = 6
3(x + y) = 12

Answers

Answer

y=3   x=1

Step-by-step explanation:

3(x+3)=12

3x+9=12

subtract 9 from both sides to get...

3x=3

divide 3 from both sides to get...

x=1

Step-by-step explanation:

this is very easy

2y=6

y=2/6=3

so ,

3(x+y)=12

3x+3y=12

3x+3+3=12

3x+9=12

3x=12-9

3x=3

x=3/3

x=1

22+54=y+16 whats the answer

Answers

Answer:

y=60 or 60=y

Step-by-step explanation:

22+54= 76

76=y+16

60=y or the other way around

Ethan builds two different kinds of chairs, rockers and swivels. It takes him 3 hours to build a rocker and requires 2 oz of stain. It takes him 2 hours to build a swivel chair and requires 8 oz of stain. Ethan has 56 oz of stain available and he can only work up to 24 hours. He makes $12 profit on each rocker and $10 profit on each swivel chair. 1. Since there cannot be negative chairs, create two constraints to represent this. 2.Create a constraint for the hours it takes to build the chairs. 3. Create a constraint for the stain it takes for the chairs. PLEASE HELP

Answers

Answer:

(1) [tex]x\geq 0\; \text {and}\;y\geq 0[/tex]

(2) [tex]3x + 2y\leq[/tex] 24

(3) [tex]x+4y\leq 28[/tex]

Step-by-step explanation:

Let x and y be the numbers of rockers and swivels made by Ethan.

(1) Since the number of chairs can't be negative. So,

x\geq0 and y\geq 0 are the two constraints.

(2) He can work a maximum of 24 hours.

The time required to make 1 rocker chair and 1 swivels chair are 3 hr and 2 hr respectively.

So, the time required to make x rocker chair = 3x hr

and the time required to make y swivel chair = 2y hr.

The total time required is  3x + 2y hr which can't be more than the available time, 24 hr.

So, the required constraint is

[tex]3x + 2y\leq 24[/tex]

(3) Similarly,

As 1 rocker chair requires 2 oz strain and 1 swivel chair required 8 ox strain.

So, to make x rocker chair 2x oz required and make y swivel chair 8y oz required which can't be more than the available oz, 56.

So, the required constraint is

[tex]2x + 8y\leq 56[/tex]

[tex]\Rightarrow x+4y\leq 28.[/tex]

HELP PLEASE HS GEOMETRY 50 POINTS!!!!!

Answers

Answer: 1,6,3,8

Step-by-step explanation: that one, and its opposite and the other one is the same

Answer:

1, 3, and 8

Step-by-step explanation:

You should know this because, 88 degrees and 2 are in a straight line which there means that 2 would be 92 degrees. So every length would be slightly shorter or longer than the other. As you can observe 1, 3, and 8 other than 6 are all the ones that are slightly shorter than their counterpart 2, 4, 5, and 7. Which means that 1, 3, and 8 all equal 88 degrees just like 6.

what is the answer to 6y * 88 = 88 * 6y

Answers

Answer:

0 or No solutions

Step-by-step explanation:

hope this helps!

which is the best estimate of -14 1/9 × -2 9/10 ​

Answers

Answer: 42

Step-by-step explanation:

-14 1/9 would round to -14

-2 9/10 would round to -3

-14 x -3= 42

A scale drawing of a rectangular park is 5 inches wide and 7 inches long. The actual park is 280 yards long. What is the area?

Answers

Answer:

315

Step-by-step explanation:

5 x 7 = 35

280 + 35 = 315

There sth answer

Answer:7 inches → 280 yards

1 inch → 280 ÷ 7 = 40 yards

5 inches → 40 x 5 = 200 yards

Area = 280 x 200 = 56 000 yards

hope this help btw i am 12

Step-by-step explanation:

1+2x6+7= -13
where do i have to put the parenthesis so its correct

Answers

Answer:

you have to but it back 2 times

Step-by-step explanation:

ir is because it should be back 2 rimes

¡¡ANSWER MY QUESTION FIRST¡¡

Can you help me with these questions, please?

Answers

Answer:

∠5 = 70°

∠8 = 130°

Step-by-step explanation:

Since ∠5 and ∠1 are equal they will both equal 70°

Since ∠6 and ∠8 are also equal they will both equal 130°

Hope this helps

Plz mark brainliest

can someone PLEASE help me on this PLEASE.
The given table of values represents a linear equation. What is the slope?

Answers

Answer:

2

Step-by-step explanation:

slope=∆y/∆x

slope=(9-7)÷(3-2)

slope= 2.

i need help answering the questions using distributive property. i already know the answers 3. will give brainliest.

Answers

Answer:

Hello

Step-by-step explanation:

by what i understood the awnser should be c

An aircraft factory manufactures airplane engines. The unit cost (the cost in dollars to make each airplane engine) depends on the number of engines made. If engines are made, then the unit cost is given by the function . What is the minimum unit cost?C(x)=x^2-520x+73458

Answers

Answer:

Minimum unit cost = 5,858

Step-by-step explanation:

Given the function : C(x)=x^2−520x+73458

To find the minimum unit cost :

Take the derivative of C(x) with respect to x

dC/dx = 2x - 520

Set = 0

2x - 520

2x = 520

x = 260

To minimize unit cost, 260 engines must be produced

Hence, minimum unit cost will be :

C(x)=x^2−520x+73458

Put x = 260

C(260) = 260^2−520(260) + 73458

= 5,858

Given m||n, find the value of x.

Answers

Answer:

27 degrees

Step-by-step explanation:

the 27 degrees

Answer:

27°

Step-by-step explanation:

X and 27° are both alternate interior angles (on opposite sides of the transversal, between the two parallel lines), which makes them congruent! So they are both 27°.

A restaurant charged Ms. Smith $120 for dinner,
while at dinner she met with a friend and they had a
great conversation about the 25 animals at the zoo.
When dinner was over she left a 15% tip. How much
was the tip amount?

Answers

The tip amount is $18. The total bill would be $138

can somebody help me pleaseee ?? it’s due soon & im stuck .

Answers

Answer:

a. lenqth=32 , width=2

b. m∠p=100  m∠Q=50  m∠R=30

c. XY=20  YZ=12

d.m∠1=90    m∠2=90

Step-by-step explanation:

a. the area of a rectangle is length×width so to find the possible sizes for L and W we need to list the factors (multiplication of two numbers to get 64) of 64, which are,

1  AND  64   (this answer is suitable but it's better to choose another

one if available for more accuracy)

2  AND  32  (this is a good answer to use)

4  AND 16   (this one already used in the question)

8   AND  8   (this answer will be wrong as the sizes need to be different because it's a rectangle but it will be good for square)

SO we will choose 2 AND 32 for the answer and we can put them in any order we want.

b. first of all acute angles are angles measured less than 90 degrees. so to have at least one angle not acute we use measures up to 90 degrees.

I will put one answer as 100 degrees (note you can use any number above 90 to not be an acute angle) and the other answers will be two numbers add up to be 80 degrees (and again you can choose any numbers for that).

c. the two answers should add up to be 32 so for this counterexample we can choose any two numbers to have the sum of 32 (remember that 16+16 already chosen in the question.

d. two supplementary angles are two angles add up to be 180 degrees so for this question we need to find two angles sum to 180 and not obtuse (that mean 90 degrees or less) and the only answer can appear is 90+90=180.  

do you guys know this by any chance

Answers

Answer:

[tex]10^{17}[/tex]

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the

10

10

. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

What is the range of the function in this table x 1 2 3 4 Y 2 4 3 2

Answers

Answer:

(2, 4, 3)

Step-by-step explanation:

Range = Y

If f(x) = -2 cos x, findf(-300 º). Do not use a calculator.

Answers

Answer:

- 1

Step-by-step explanation:

Using the trigonometric identity

cos(- x) = cosx and exact value cos60° = [tex]\frac{1}{2}[/tex]

Given

f(x) = - 2cosx , then

f(- 300° )

= - 2cos(- 300)°

= - 2cos(300)°

= - 2cos(360 - 300)°

= - 2cos60°

= - 2 × [tex]\frac{1}{2}[/tex]

= - 1

What is the constant RATIO (how do you you multiply ) of the exponential curve that passes through the points (0, 3) and (5, 96) ?

Answers

Answer:

The answer is 1.788

Step-by-step explanation:

What is the solution to 8x - 3(2x - 4) = 3x - 18?

Answers

Answer:

X=30

Step-by-step explanation:

The answer is X=30

How do you write 8.43 × 10^-4 in standard form?

Answers

Answer:

0.000843

Step-by-step explanation:

simplify the expression:

8.43 × 0.0001

now simplify:

0.000843

If you find my answer helpful

Pls consider marking my answer as Brainliest! It would mean a lot!


A 20 gallon tank is full. How many gallons are in the tank?

Answers

Answer:

20???

Step-by-step explanation:

20 gallons because it is full and the most that can be filled up is 20 gallons

Name the subset(s) of real numbers to which the number belongs.
−1.57

A. integer only
B. rational only
C. irrational and rational
D. rational and integer

Answers

it’s b- rational (i think)

help me plzzzzzzzzzzz

Answers

1. √8, π, 4
2. 5, π+ 2, 17/3,
3. -2, √2 , 1.7
4. 3/2, √5, 2.5
5. √13, 3.7, π + 1
6. √5/2, π - 2, 5/4

Apologies if I got some wrong

You work in a grocery store warehouse recording shipments. A driver delivers 25 crates of strawberries for distribution. A store calls needing seven crates of strawberries. After you fill this order, how many crates of strawberries are available for other stores?

Answers

Answer:

18 crates

Step-by-step explanation:

Data provided in the question

The Number of  strawberries for distribution delivered is 25 crated

Now he seven crates is required

So the remaining crates left is

= 25 - 7

= 18 crates

hence, after filling the order the number of order crates of strawberries is 18 crates and the same is to be considered

Write each equation/inequality in slope-intercept form.
y- 5 = 1/3 (x-6)

Answers

Answer:

Your answer is: y = 1/3x + 3

Use the formula y = mx + b

Step-by-step explanation:

Hope this helped : )

Find the distance between V (4.4) and X (5.8). Round to the nearest tenth, if necessary. about units​

Answers

Answer:

V= 5 X=6

Step-by-step explanation:

X^2+ 17x+91=0
Help please!!

Answers

Answer:

x^2+17x+91=0

a = 1; b = 17; c = +91;

Δ = b2-4ac

Δ = 172-4·1·91

Δ = -75

Delta is less than zero, so there is no solution for the equation

Step-by-step explanation:

Other Questions
Name the subset(s) of real numbers to which the number belongs.1.57 A. integer only B. rational only C. irrational and rational D. rational and integer What is the range of the function in this table x 1 2 3 4 Y 2 4 3 2 Given m||n, find the value of x. Kyle invested $ 500 and received $ 650 after three years. What had been the interest rate? A person has a mass of 1000g and an acceleration of 20 m/s/s. What is the force on the person After settling a legal dispute, Frank must chose one of two settlementpayment options. He can either receive an immediate lump sum payment of$250,000, or he can receive an installment payment package with annualpayments of $25,500 spread out over a span of 10 years. Which would likelybe more beneficial to him, and why?A. The installment package would be better because it would preventhim from spending all of his money immediately.B. The immediate payment would be better because it is moremoney overall.C. The immediate payment would be better because he could use themoney immediately to invest it in a safe, low return account.D. The installment package would be better because he'll have moremoney in 10 years than with the lump sum. Which one? A. B. C. or D? Is anyone willing to answer this question I cant do it which is the best estimate of -14 1/9 -2 9/10 3/4x-4=5/6Rewrite so it doesnt have any fraction 118/13= 59/zwhat is the answer?? How does the description of Madame Carambeaus house in paragraphs 1-2 contribute to the meaning of the passage? Its music someone please help which answer option best evaluates how well the following summary reflects the original passage? Scientists have changed the model of the atom as they have gathered new evidence. One of the atomic models is shown below. A purple center outlined in black with two concentric black circles around the center, the inner circle having 2 small green balls on it and the outer circle having 8 small green balls on it. What experimental evidence led scientists to change from the previous model to this one? A few of the positive particles aimed at a gold foil seemed to bounce back. The colors of light emitted from heated atoms had very specific energies. Experiments with water vapor showed that elements combine in specific proportions. Cathode rays were bent in the same way whenever a magnet was brought near them. PLS ANSWER HURRY!!!!!Does an animal's ability to recognize themselves in a mirror mean that they are self-aware and/ or have a self-concept? Explain? If the mass of Earth were increased by a factor of 8.00 , by how many times would the force between Earth and the Sun increase? You work in a grocery store warehouse recording shipments. A driver delivers 25 crates of strawberries for distribution. A store calls needing seven crates of strawberries. After you fill this order, how many crates of strawberries are available for other stores? The adjusted trial balance of Gary Cooper Co. as of December 31, 2014, contains the following. GARY COOPER CO. ADJUSTED TRIAL BALANCE DECEMBER 31, 2020 Debit Credit Cash $20,892 Accounts Receivable 8,340 Prepaid Rent 3,700 Equipment 19,470 Accumulated Depreciation-Equipment $6,315 Notes Payable 7,120 Accounts Payable 6,892 Common Stock 21,420 Retained Earnings 12,730 Dividends 4,420 Service Revenue 13,010 Salaries and Wages Expense 8,260 Rent Expense 2,154 Depreciation Expense 251 Interest Expense 189 Interest Payable 189 $67,676 $67,676Instructions: (a) Prepare an income statement. (b) Prepare a statement of retained earnings. (c) Prepare a classified balance sheet. I GIVE BRAINLY. Makoa is reading a book about Abraham LincolnWhich text feature would Makoa use to help him find the meaning of the word "emancipation"?O glossarytable of contentsindexpronunciation guide