Suppose y = sqrt 2x+1, where x and y are functions of t.
(a) If dx/dt = 9, find dy/dt when x = 4.
(b) If dy/dt = 3, find dx/dt when x = 40.

Answers

Answer 1

If y = √(2x + 1), then differentiating both sides implicitly with respect to t gives

dy/dt = 1/2 • 1/√(2x + 1) • 2 • dx/dt = 1/√(2x + 1) • dx/dt

(a) If dx/dt = 9 and x = 4, then

dy/dt = 1/√(2•4 + 1) • 9

dy/dt = 1/√(8 + 1) • 9

dy/dt = 1/√9 • 9

dy/dt = 9/3

dy/dt = 3

(b) If dy/dt = 3 and x = 40, then

3 = 1/√(2•40 + 1) • dx/dt

3 = 1/√(80 + 1) • dx/dt

3 = 1/√81 • dx/dt

3 = 1/9 • dx/dt

dx/dt = 27


Related Questions

According to the food label on a box cookies, each box has 16
servings and each sering contains 4 cookies. The weight of the
ba of cookies is Kilogroms. What is the weight of each
cooke?

Answers

I cant help you but I can give you the equation: 16 x 4 x weight per cookie = answer

Step-by-step explanation:

did you forget to write the whole question?

A new hotel was built with r rooms. The first weekend it was open, 3/5 of them were reserved. Which of the following expressions represents the number of rooms which were reserved?

A r-3/5
B r x 3/5
C r+3/5
D ÷3/5

PLEASE HELP ITS STUDY ISLAND

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Answer:

c r/ 3/5

Step-by-step explanation:

i think

david has x nickels and y dimes

Answers

You have to find out what x and y our first

A man flies a kite 354 feet in the air when he runs out of string, what is the angle of elevation if he had 200 yards of string to begin with

Answers

Answer:

Step-by-step explanation:

Assuming the string is straight (it will not be so due to gravity and wind load)

θ arcsin(354 / (200(3)) = 36°

expand 6(7+11x)
,,,,​

Answers

Answer:

It would be 41+66x

Step-by-step explanation:

1. Write the equation of a horizontal line that passes through the point (–2, 2). x = –2 y = –2 y = 2 x = 2

Answers

Answer:

x = 2

Step-by-step explanation:

The given point is (-2, 2).  A horizontal line passing through this point is x = 2.

The school football team is hosting a fundraiser dinner. Tickets are $20 for adults, $15 for seniors, and $6 for children. The expression 20a + 15s + 6c represents the total sales for a adult, s senior tickets, and c child tickets. Mariel sold 6 adult, 4 senior, and 8 child tickets.

20a + 15s + 6c = 20 (6) + 15 (4) + 6 (8) = ? + ? + ?

Answers

20(6) + 15(4) + 6(8)
120 + 60 + 48
228

What is the midline of the function y=19cos(9x+3)+34 ?
plss help mee

Answers

Factor out the horizontal stretch,

Midline of y=cosx is 0

This graph is shifted 34 units up

Midline is 34

The midline of the function is y = 34.

What is a function?

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The midline of a periodic function is the horizontal line that divides the graph of the function into two equal parts.

For a cosine function of the form y = A cos(Bx - C) + D, the midline is given by the equation y = D.

In this case, the function is y = 19cos(9x+3)+34, so the midline is given by the constant term, which is D = 34.

Therefore,

The midline of the function is y = 34.

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Please hurry I have to do it in 2 minutes

Answers

Answer:

[tex]w-0.15 = 0.25[/tex]

Step-by-step explanation:

Does anyone know this?

Answers

Answer:

I think 7.6 i remember i had something like this  

Step-by-step explanation:

Solve by factoring
Y^2+5y+6=0

•-3
•4,8
•2,3
•-4,3

Answers

Step-by-step explanation:

y²+5y+6=0

y²+2y+3y+6=0

y(y+2)+3(y+2)=0

(y+2)(y+3)=0

:. y=2,3

option C.

hope this helps you.

Answer:

Step-by-step explanation:

Y^2+5y+6=0

5^2 - 4*2*6

25-48

23 i

-5 +4.79i =>   -0.21  =>      0.5i

2*2                     4

-5 +4.79i =>   -9.79  =>      2.44i

2*2                     4

A person is running a distance race at a constant rate. What time will they finish the race what information would you need to be able to solve the problem?

Answers

Answer:

you need the distance they're running and the pace they are running at.

Solve for X. 22 = 10x Simplify your answer as much as possible. x = 음. 6 08 ?​

Answers

Answer:

x=11/5

Step-by-step explanation:

isolate x

22/10 = 10x/10

22/10 = x

simplify

11/5 = x

can someone pls help me … I really need help

Answers

Answer:

It's the last one!

Step-by-step explanation:

Jeremy can row 2/3 of a mile in 1/2 hour how long will it take him to row 1 mile?

Answers

Answer:

It takes 3/4 of an hour to go 1 mile

Step-by-step explanation:

You can do this by setting up a proportion and by using decimals for some fractions

2/3 = 0.66667 Miles

1/2 = 0.5  hours

0.66667/0.5 = 1/x                         Cross multiply

0.66667 * x = 0.5 * 1                     Simplify

0.66667 * x = 0.5                         Divide both sides by 0.66667

x = 0.5 / 0.66667

x =  0.74999625                           Notice when rounded this is 0.75

x = 0.75                                         Now notice that 0.75 as a fraction is 3/4

x = 3/4

Jeremy can row 2/3 of a mile in 1/2 hour then it will take him 3/4 hour to row 1 mile.

If Jeremy can row 2/3 of a mile in 1/2 hour, then the time it takes him to row 1 mile can be found by setting up a proportion:

(2/3 mile) / (1/2 hour) = 1 mile / (x hours)

Cross-multiply:

(2/3) × x = 1 × (1/2)

Now solve for x:

x = (1/2) / (2/3)

x = 3/4

So, it will take Jeremy 3/4 of an hour (or 45 minutes) to row 1 mile.

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I WILL GIVE BRAINLIST IF ALL ANSWERED CORRECTLY
Injured runners train on a special track at a rehabilitation center. The track is a square with a half circle on its left and right sides. The area of the square is 128 square feet. What is the length of the track? Use the table to help you answer the questions.

Square 11.02 11.12 11.22 11.32 11.42 11.52
Value 121.0 123.2 125.4 127.7 130.0 132.3
Square 11.62 11.72 11.82 11.92 12.02
Value 134.6 136.9 139.2 141.6 144.0

1. Fill in the blanks to complete the description of the track. (2 points)
The track has ____ sides of the square and the distance around ____ complete circle(s).















2. The length of one side of the square is the square root of its area. Use the table to find the approximate length of one side of the square. Explain how you used the table to find this information. (2 points)















3. Use your answers above to find the total length of the part of the track that is made up of sides of the square. (2 points)















4. The circumference of (distance around) a circle is π times the diameter, or C = πd. A side of the square is the diameter of each half circle.
In your answer to question 1, you gave the number of complete circles included in the track. Use this answer and C = πd to find the approximate length of the circular part of the track to the nearest tenth of a foot. Use 3.14 for π and show your work. (2 points)















5. Find the approximate length of the track, including the straight and circular sections. (2 points)

Answers

Answer:

The length of the track is approximately 51.7 ft

The track has three sides of the square and the distance round a half of a complete circle

Step-by-step explanation:

The given track shape and measurements are;

The shape on the left side of the track  = Square

The shape on the right side of the track  = Half circle

The area of the square on the the left side of the track  = 128 square feet

Therefore, from the area, A, of a square of side length, s, which is s × s, and letting the side length of the square = s, we have;

Area of the square portion of the track = s × s = s² = 128 ft²

Therefore, s = √(128 ft²) = 8·√(2) ft.

Whereby the side length of the square is bounded by the diameter of the half circle, we have;

Length of the diameter of the half circle = s = 8·√(2) ft.

The length of the perimeter of the half circle = π·D/2 = π × 8·√(2)/2 = π × 4·√(2) ≈ 17.77 ft.

The perimeter of the track, which is the length of the track is made up of the three sides of the square opposite to the half circle and the circumference of the half circle.

Therefore;

The length of the track = 3 × 8·√(2) ft + π × 4·√(2) ft. = 4·√2×(π+6) ≈ 51.7 ft

The length of the track ≈ 51.7 ft

Which gives;

The track has three sides of the square and the distance round a half of a complete circle.

(9x+3)5 i really need help with this pleaseeee

Answers

Answer:

1/15

Step-by-step explanation:

Thats my guess I think its that though.

Answer: 3

Step-by-step explanation:

PEMDAS

55. H(x) = – 3x² + 6x
=

Answers

Answer:

Well this is a function/ quadratic question.

So using this info we can make this into a standard form for quadratics which is

ax^2+bx+c=0

In this case c is 0 and we cna just make everything else equal to zero so.

-3x^2+6x=0

Now with this we can use the quadratic formula

-b±√(b²-4ac)/(2a)

So pluggin everything in

X=-6±√(6²-4(-3)0)/(2(-3))

Now we solve

36/-6

or -6

Now we just do

-6±-6

x= -12

x= 0

These are your answers

x=-12

x=0

NEED HELP ASAP! TYSM IF YOU DO

Which of the following equations represents the greatest value of x?

Equation 1
x^2 = 17
Equation 2
x^2 = 26
Equation 3
x^3 = 64
Equation 4
x^3 = 27

Answers

Answer:

Equation 2 represents the greatest value of x!

Step-by-step explanation:

Let's solve each equation for x.

Equation 1; x = 4.1 (about)

Equation 2: x = 5 (about)

Equation 3: x = 4 (exact)

Equation 4: x = 3 (exact)

Hope this helps. :)

Equation 2
Hopes this helped love

the following points lies in the solution set of the system of inequalities shown graphed below?
A. (1, 0)
B. (2, 2)
C. (-4, 0)
D. (2, -4)

Answers

Option C would be the correct answer :)

Simpson office furniture pays Tom Russell a $2490 monthly salary plus a 9% commission on merchandise he sells each month .Assume Tom's sales were $88,000 for last month.​

Answers

Answer:

Amount Tom was paid for his sales last month 88,000 x9%= $7920.00

Step-by-step explanation:

HELP IF CORRECT WILL GIVE BRAINLIEST (if you are trying to play around i will report u u-u)

Answers

Answer:

synthetic.

Step-by-step explanation:

I don't know how to give a step by step.

Answer:

Well I don't have the previous reading stated in the question obviously, but fossil fuels are natural resources. They form from decomposing plants and animals and are mainly found in the Earth's crust. These fuels are made of hydrogen and carbon which can be burned for energy.

solve pls brainliest

Answers

Answer:

Mixed Number = 2 9/10

Improper Fraction = 29/10

Step-by-step explanation:

Mixed Number = 29/10 = 2 9/10

Improper Fraction = 29/10

A Gardner has 1 1/4 cubic feet of soil available for filling pots. Each pot will need 2/5 cubic foot to be filled. What is the greatest number of pots that the gardener fill

Answers

The greatest number of pots that can be filled is 3.

In order to determine the greatest number of pots that can be filled, the quantity of soil available would be divided by the capacity of each pot.

Number of pots that can be filled = 1 1/4 ÷ 2/5

= 5/4  ÷ 2/5

= 5/4 x 5/2 = 25/8 = 3 1/8

Thus, the greatest number of pots that can be filled is 3.

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Suppose you roll a pair of six-sided dice and add their totals, What is the probability that the sum of the numbers on your dice is a number other than 11

Answers

Answer:

17/18

Step-by-step explanation:

total number of outcomes=6×6=36

favorable outcomes for a total of 11=56,65

number of favorable items for a total of 11=2

P(a total of 11)=2/36=1/18

P(for a total other than 11=1-1/18=(18-1)/(18)=17/18

how do i do 3 5/6 - 2 7/15?

Answers

Answer:

don't know don't know don't know don't know don't know don't know don't know

Step-by-step explanation:

don't know don't know don't know don't know don't know don't know don't know don't

Which is the best estimate of the product 3,780 × 2?

Answers

Answer:

8000

Step-by-step explanation:

bru,h does anyone know this?

Answers

Answer:

The width is 410ft and the length is 780ft

Write a story that can be representd by the equation y=x+1/5x

Answers

Answer:

I sorry but I don't get this question

A vendor sells burgers and cookies. A customer buys 2 burgersand 2 cookies for $7.50. Another customer buys 4 burgers and 3 cookies for $13.75. Find the cost of each item.

Answers

Answer:

The burgers cost $2.50 and the cookies cost $1.25.

Step-by-step explanation:

Let b represent burgers and c represent cookies.

2b + 2c = 7.50

4b + 3c = 13.75

Step 1: Use one of the two equations and isolate one of the variables.

2b + 2c = 7.50

      - 2c    -2c

[tex]\frac{2}{2}[/tex]b = [tex]\frac{7.50}{2}[/tex] - [tex]\frac{2}{2}[/tex]c

b =  3.75 - c

Step 2: Plug what you get for b into the second equation.

4(3.75 - c) + 3c = 13.75

15 - 4c + 3c = 13.75

15 - 1c = 13.75

Step 3: Isolate the variable and solve for c.

15 - 1c = 13.75

-15        -15

[tex]-\frac{1}{1}[/tex]c = [tex]\frac{-1.25}{-1}[/tex]

c = 1.25 ← price for cookies

Step 4: Plug in what you have for c into one of the previous equations and solve for b.

2b + 2(1.25) = 7.50

2b + 2.50 = 7.50

     - 2.50   -2.50

[tex]\frac{2}{2}[/tex]b = [tex]\frac{5}{2}[/tex]

b = 2.50 ← price for burgers

Now you know the cost of each item:

The burgers cost $2.50 and the cookies cost $1.25.

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