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]

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Related Questions

50 points plus Brainnlest for right answer

What is the equation?
What should you replace for each given variable?
What should you solve for?

Answers

Equations: 60x + 3000 = 3,000, 600 + 150y = 3000

X: 20

Y: 10

You should solve for x & y

Q1: 0, it's already filled up to the max of 3000 pounds.

Q2: 16, 60 times 10 is 600. 3000-600 = 2400. 2400/150 = 16

I hope this helped, ask if you need more help :)

Rasu made some chocolate milk. She added 3 tsp. Of cocoa mix with 2 cups of milk. Farah also made some chocolate milk. She added 5 tsp. Of cocoa mix to 3 cups of milk. Which mixture is more chocolatey flavored (stronger chocolate flavor)? Explain your reasoning.

Answers

The correct answer is Farah's mixture

Explanation:

In this situation, how strong chocolate flavor is in the mix depends on the ratio of ingredients as more cocoa leads to a stronger chocolate flavor.

Rasu:

Her ratio was 3 teaspoons of cocoa mix and 2 cups of milk. This can be expressed as 3:2  or [tex]\frac{3}{2}[/tex]. Also, this can be simplified by dividing the amount of cocoa into the amount of milk 3 ÷ 2 = 1.5. This means for each cup of milk Rasu added 1.5 teaspoons of cocoa.

Farah:

The ratio was 5 teaspoons of cocoa mix and 3 cups of milk. So, the ratio is 5 : 3 or [tex]\frac{5}{3}[/tex], which is equal to 1.6. This implies for each cup of milk Farah added 1.6 teaspoons of cocoa. This ratio of cocoa vs milk is higher in Farah, which means he added more cocoa, and her mix would have a stronger chocolate flavor.

how to find the sequence



X. Y

0. 0
1. 1.5
2. 4
3. 7.5
4. 12​

Answers

Answer:

they add one half to each number

Which one is the right answer

Answers

Answer:

90 degrees

Step-by-step explanation:

if you add a line from point B to point D, you will make a square and all sides are equal to 90 degrees.

use angle 3 and 4 which equal 90. divide that by 2 and each side is equal to 45. since we know that all sides are equal, angle 3 is equal to angle 2. so from here you add 45 + 45 and get 90 degrees.

HOPE THIS HELPS. can i have brainliest please?

Worth 30 points.

Show all work to solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.

the square root of x minus 3 plus five equals x.

Picture of question and equation attached.

Answers

Answer:

x=7 valid solution

x=4 extraneous solution

Step-by-step explanation:

sqrt( x-3) +5 = x

Subtract 5 from each side

sqrt( x-3) +5 -5= x-5

sqrt( x-3)  = x-5

Square each side

(sqrt( x-3))^2 = (x-5)^2

Foil the right side ( x-5)(x-5) =x^2 -5x-5x+25 = x^2 -10x+25

x-3 = x^2 -10x+25

Subtract x from each side

-3 = x^2 -10x -x+25

Add 3 to each side

0 = x^2 -11x +25 +3

0 = x^2 -11x+28

Factor

0 = (x-7)(x-4)

Using the zero product property

x-7 =0  x-4=0

x=7  x=4

Check the solutions

sqrt( x-3) +5 = x

x=7

sqrt( 7-3) +5 = 7

sqrt(4) +5 = 7

2 +5 = 7  valid solution

x=4

sqrt( 4-3) +5 = 4

sqrt(1) +5 = 4

1 +5 = 4    not true   extraneous solution

Which set of side lengths form a right triangle?
a.) 2 inches, 3 inches, 4 inches
b.) 6 inches, 8 inches, 10 inches
c.) 8 inches, 9 inches, 11 inches
d.) 10 inches, 12 inches, 13 inches

Answers

It is c So yea it is c for sure if I get it wrong I’m dumb than

Consider the equation 3x+10=2x+10. Does this equation have one solution, infinitely many solutions, or no solutions? Explain your answer.

Answers

Answer:

One solution:  x = 0

Step-by-step explanation:

Starting with 3x+10=2x+10,

subtract 2x from both sides.  We get x + 10 = 10, or x = 0.  This equation has ONE solution, x = 0.

7. 2y + 13.2 =78
у =

Answers

Step-by-step explanation:

I hope it will help you here's the answer

Which graph shows a system with no solutions? Graph A Graph B Graph C y= 2r-1 2y 4x-2 A. Graph C OB. Graph B C. Graph A​

Answers

Answer:

graph b

Step-by-step explanation:

A store is marking down the price of a television 25% from the original price of $250 which expression can be used to find the markdown price

Answers

Answer:

62.5%

Step-by-step explanation:

Thw price markdown will be 62.5%

Answer a I think

Step-by-step explanation:

determine the unit rate for each ratio.
The gas station charges $180 for 3 hours of work. How much
they charge for 1 hour of work?

Answers

Answer:

$60

Step-by-step explanation:

180/3 = 60

I hope this helps :)

Answer:60 per hour

Step-by-step explanation: you divide 180 by 3

Jordan get a $10 allowance and works a job that pays $7.00 per hour. Alex gets a $20 allowance and works a job that pays $6.50 per hour. If they both work the same number of hours each week, how many hours would they need to work to have the same amount of money for the week?

Answers

Answer:

20 hours

Step-by-step explanation:

Let x = number of hours

Jordan

Allowance = $10

Pay per hour = $7

Total = 10 + 7x

Alex

Allowance = $20

Pay per hour = $6.50

Total = 20 + 6.50x

Equate total of Jordan and Alex earnings

10 + 7x = 20 + 6.50x

Collect like terms

10 - 20 = 6.50x - 7x

-10 = - 0.5x

Divide both sides by - 0.5

x = -10 / -0.5

= 20

x = 20 hours

Jordan and Alex will both work for 20 hours to have the same amount of money in a week

the value X = −3 and Y = 6.
what would be the answer to this
4y−3x =

Answers

Answer:

15

Step-by-step explanation:

First we would want to plug the x value given -3 into x in the equation then we want to plug the y value given 6 in the equation then solve.

4(6) - 3(-3) = ?

4 x 6 = 24

-3 x -3 = 9

24 - 9 = 15

Hope this helps

What is the slope of a line parallel to the line whose equation is 6x-y=1. Fully reduce your answer.

Answers

Answer:

0, -1

1, 5

(Hope it helped)

Answer:

I believe the slope is 6  

Step-by-step explanation:

6x - y = 1

- y = - 6x + 1

-1 ( - y = - 6x + 1)

y = 6x + 1

6 = slope

All shirts are the same price. Which deal is cheaper per shirt?
A) Buy 2 shirts and get 25% off.
B) Buy 3 shirts and save 30%.

Answers

Answer:

The answer of this question is option A

Let’s say each shirt is $10.

If I buy 2 shirts for $20 and get 25% off, I will have spent $15. This would come out to $7.50 per shirt.

If I buy 3 shirts for $30 and get 30% off, i will have spent $21. Which is $7 per shirt.

The answer is option B

Gloria and her friends love the Caramel Macchiato at Black Rock Coffee.

If she pays $19.05 for 4 macchiato’s and she adds a bagel for $1.25, how much is 1 macchiato?

Gloria still wants her macchiato and
bagel but decides to buy another
macchiato for her friend.
How much does she owe?

Answers

See attachment for math work and answer.

Which one?
A or B? ​

Answers

The answer is A

Multiplying an even number of negative terms makes the product positive -4x-6 will be 4x6 so we multiply all of them to get the answer.
3x6x4x6= 432

if X = 5 then 3( 2X - 4) - X

Answers

Answer:

13

Step-by-step explanation:

Answer:

well if you're looking for the answer, it is: 13

Step-by-step explanation:

I don’t get it . I need help please!

Answers

Answer:

You need to solve it like a rectangle

Scale 1cm = 30Yd

Formula = A=lxw

Length = 7x30=210yd

Height = 4x30=120yd

Answer 120x210= 25,200 sq. yd.

Right, make sense?

Answer:

25200 square yards

Step-by-step explanation:

Reminder: the area of a parallelogram is its length times its height. In that case, it would be 4cm*7cm.

But you have to remember that 1 cm represents 30 yards, so you have to multiply everything by 30 first, and then solve:

4*30 yards * 7*30 yards

= 120 yards * 210 yards

= 25200 square yards.

solve x²-24x+14=0 by completing the square. what are the solutions​

Answers

Answer:

x=±√130+12

I believe :-)

TRUE OR FALSE
Angle BAH and angle DAG form linear pair.

Answers

Answer:

false

Step-by-step explanation:

The answer is TRUE ANGLE BAH AND ANGLE DAG ARE A FORM OF A LINEAR PAIR

6) Which of the following expressions are equivalent to 40x + 30y? Choose ALL that apply.
5x(8 + 6)
5(8x + 6y)
10(40x + 30y)
10(4x + 3y)
2y(20x + 15)
2(20x + 15y)

Answers

Answer:

5(8x + 6y), 10(4x + 3y), 2(20x + 15y)

Step-by-step explanation:

(5x *8) + (5x *6) = 40x + 30x no

(5 * 8x) + (5 *6y) = 40x + 30y yes

10*40x + 10*30y = 400x + 300y no

10*4x + 10*3y = 40x + 30y yes

2y *20x + 2y*15 = 40xy + 30y no

2*20x + 2*15y = 40x + 30y yes

The expressions that are equivalent to (40x + 30y) is (10(4x + 3y)) and (2(20x + 15y)) and this can be determined by using the arithmetic operations.

Given :

Expression  --  (40x + 30y)

The following steps can be used in order to determine the expressions that are equivalent to (40x + 30y):

Step 1 - The arithmetic operations can be used in order to determine the expressions that are equivalent to (40x + 30y).

Step 2 - Take the 10 common in the given expression.

= 40x + 30y

= 10(4x + 3y)

Step 3 - Also can take 2 common in the given expression.

= 40x + 30y

= 2(20x + 15y)

Therefore, the correct option is D) and F).

For more information, refer to the link given below:

https://brainly.com/question/25834626

What four consecutive integers have a sum of 90?

Answers

Answer:

x, x+1, x+2, x+3.

Step-by-step explanation:

I took the test

Answer:

21 + 22 + 23 +24 = 90

Step-by-step explanation:

Let's represent this with x:

x+x1+x+2+x+3 = 90

Group the x's together

4x+6 = 90

subtract 6 on both sides

4x=84

x=84/4

x= 21

ft. = 4.8 yd.
How many feet is it

Answers

The answer is 14.4 feet


(3 + zi) (3 + 4i) - (3 + zi) (3 - 2i)
Express in simplest a+bi form

Answers

Answer:

Step-by-step explanation:

9+12i+3zi+4zi²-(9-6i+3zi-2zi²)

= 9+12i+3zi+4zi²-9+6i-3zi+2zi²

= 18i+6zi²

= i(18+6zi) or 6i(3+zi)

i hope this is the anwer you're looking for

10m - 8n^2
(if m = 2 and 11 = -3)

Answers

Answer: -52

Explanation:
If you plug in the variable answers the equation is 20-8•-3^2 then do the exponent so, 20-8•9, then multiply so 20-72 which is -52.

The solution of the equation when m = 2 and 11 = -3 will be - 52.

What is a solution to a system of equations?

For a solution to be solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs,

So solution to a system is the intersection of all its equation at single point(as we need common point, which is going to be intersection of course)(this can be one or many, or sometimes none)

We have been given; 10m - 8n^2

(if m = 2 and 11 = -3)

If we plug in the variable

the equation is 20 - 8(-3)^2

Now, do the exponent

So, 20 - 8^9,

Then multiply

20-72 = -52.

Therefore, the solution of the equation when m = 2 and 11 = -3 will be - 52.

Learn more about finding the solution graphically here:

https://brainly.com/question/26254258

#SPJ2

How to solve 240=-16 Equation

Answers

no idea

Step-by-step explanation:

u can use google for this if u r in hurry

I am guessing that we are divided?

So

240:-16=-15
Answer: -15

If this was not about dividing comment on this answer and tell me what its about more in detail and I’ll be more then happy to answer this question for you.


A baker makes 4 apple pies and 9 chocolate cream pies what is the ratio

Answers

The ratio of apple pies to chocolate cream pies is 1:2.25 (apple:chocolate) since there are 9 chocolate and 4 apple, i divided 9/4 and got 2.25, meaning that 2.25 chocolate cream pies will be made by the time 1 apple pie is made.

simply the following (z⁵)²​

Answers

Answer:

Z^10

Step-by-step explanation:

Answer:

multiply 5*2=10

your answer will be =z^10

Step-by-step explanation:

walking at a speed of 12 feet per second. How many feet per hour is this? *

Answers

Answer:

43200 feet per hour

Step-by-step explanation:

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