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2 years ago

This function can be used to determine the number of bacteria in a culture h hours after the culture was started.

Mathematics

1 answer:

dimulka [17.4K]2 years ago

3 0

Answer:

The statement means that after 2 hours, there are 90 bacteria in the culture.

Step-by-step explanation:

The number of bacteria after x hours is given by the function states in the exercise. We have that f(x) will be the number of bacteria after x hours.

Which statement best describes the meaning of the equation f(2) = 90 ?

The statement means that after 2 hours, there are 90 bacteria in the culture.

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The radius of a cone is decreasing at a constant rate of 7 inches per second, and the volume is decreasing at a rate of 948 cubi

inessss [21]

Answer:

The height of cone is decreasing at a rate of 0.085131 inch per second.

Step-by-step explanation:

We are given the following information in the question:

The radius of a cone is decreasing at a constant rate.

$\displaystyle\frac{dr}{dt} = -7\text{ inch per second}$

The volume is decreasing at a constant rate.

$\displaystyle\frac{dV}{dt} = -948\text{ cubic inch per second}$

Instant radius = 99 inch

Instant Volume = 525 cubic inches

We have to find the rate of change of height with respect to time.

Volume of cone =

$V = \displaystyle\frac{1}{3}\pi r^2 h$

Instant volume =

$525 = \displaystyle\frac{1}{3}\pi r^2h = \frac{1}{3}\pi (99)^2h\\\\\text{Instant heigth} = h = \frac{525\times 3}{\pi(99)^2}$

Differentiating with respect to t,

$\displaystyle\frac{dV}{dt} = \frac{1}{3}\pi \bigg(2r\frac{dr}{dt}h + r^2\frac{dh}{dt}\bigg)$

Putting all the values, we get,

$\displaystyle\frac{dV}{dt} = \frac{1}{3}\pi \bigg(2r\frac{dr}{dt}h + r^2\frac{dh}{dt}\bigg)\\\\-948 = \frac{1}{3}\pi\bigg(2(99)(-7)(\frac{525\times 3}{\pi(99)^2}) + (99)(99)\frac{dh}{dt}\bigg)\\\\\frac{-948\times 3}{\pi} + \frac{2\times 7\times 525\times 3}{99\times \pi} = (99)^2\frac{dh}{dt}\\\\\frac{1}{(99)^2}\bigg(\frac{-948\times 3}{\pi} + \frac{2\times 7\times 525\times 3}{99\times \pi}\bigg) = \frac{dh}{dt}\\\\\frac{dh}{dt} = -0.085131$

Thus, the height of cone is decreasing at a rate of 0.085131 inch per second.

3 0

2 years ago

How much do you need to subtract from 87/10 to make 8

Brut [27]

Answer:

You would have to subtract 7/10

Step-by-step explanation:

87/10 - 7/10 would equal 8

3 0

2 years ago

Translate (x-2, y+D) then rotate 90° counterclockwise (-1, 1)

IgorLugansk [536]

Answer:

By taking (-1, 1) and translating it left by 2 and up by D we have (-3, 1+D)

Rotating 90° counterclockwise puts a negative on your y-coordinate and switches the x and y-coordinates.

Final answer:

(-1-D, -3)

Your well wisher :-)

7 0

2 years ago

What is 44 times 54 and show how you can write your work down?

____ [38]

Answer:

44 x 55= 2420 because 44 x 5=220, so 44 x 55 will equal 2,420

4 0

1 year ago

Read 2 more answers

3 drinks and 2 pretzels costs $16, but 5 drinks and 5 pretzels costs $31.25. What is the price of one pretzel?

sweet [91]

(3d + 2p = 16)5
(5d + 5p = 31.25)3
Make them same d value
15d + 10p = 80
15d + 15p = 93.75
Subtract both (elimination)
-5p = -13.75
Divide by -5
p = 2.75
Answer: $2.75 per pretzel

6 0

2 years ago