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4 years ago

What's the difference between an ABSOLUTE extrema and a RELATIVE extrema? ...?

1 answer:

3 0

Absolute Extrema. If a function has an absolute maximum at x = b , then f (b) is the largest value that f can attain. Similarly, if a function has an absolute minimum at x = b , then f (b) is the smallest value that f can attain.

The strategy for tracking the sign of the derivative is useful for more than determining where a function is increasing or decreasing. It is also useful for locating the relative extrema of a function. At a relative extrema, a function changes from increasing to decreasing or decreasing to increasing.


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Helium is pumped into a spherical balloon at a rate of 3 cubic feet per second. How fast is the radius increasing after 2 minute

Arisa [49]

Answer:

The rate of change of radius is 0.0530 ft/sec.

Step-by-step explanation:

Given : Helium is pumped into a spherical balloon at a rate of 3 cubic feet per second.

To find : How fast is the radius increasing after 2 minutes?

Solution :

The volume of the sphere is $V=\frac{4}{3}\pi r^3$

Differentiating w.r.t. r,

$\frac{dV}{dr}=4\pi r^2$

We have given, Helium is pumped into a spherical balloon at a rate of 3 cubic feet per second.

i.e. $\frac{dV}{dt}=3$

Integrate w.r.t. t,

$V=3t+C$

Assuming V=0 when t=0 then C=0

So, $\frac{4}{3}\pi r^3=3t$

$r^3=\frac{t}{4\pi}$

$r=\sqrt[3]{\frac{t}{4\pi}}$

Now, we apply chain rule

i.e. $\frac{dV}{dt}=\frac{dV}{dr}\cdot \frac{dr}{dt}$

$3=4\pi(\frac{t}{4\pi})^{\frac{2}{3}}\cdot \frac{dr}{dt}$

The radius increasing after 2 minutes i.e. at $t=2\times 60=120$

$3=4\pi(\frac{120}{4\pi})^{\frac{2}{3}})\cdot \frac{dr}{dt}$

$3=56.56\cdot \frac{dr}{dt}$

$\frac{dr}{dt}=\frac{3}{56.56}$

$\frac{dr}{dt}=0.0530$

Therefore, the rate of change of radius is 0.0530 ft/sec.

8 0

3 years ago

Find the missing side

arlik [135]

Answer:

12.94811641 =x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj/ hyp

cos 44 = x /18

18 cos 44 =x

12.94811641 =x

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3 years ago

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Will mark brainlist

vladimir2022 [97]

Answer:

n-17

Step-by-step explanation:

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4 years ago

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Apply the Distributive Property -8(a + b -c)

mel-nik [20]

Answer:

-8a -8b + 8c

Step-by-step explanation:

-8(a + b - c)

-8 x a is -8a

-8 x b is -8b

-8 x -c is 8c

-8a -8b + 8c

I Hope That This Helps! :)

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3 years ago

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You are using the equation 4(p – 7) = 44 to determine how many pictures can be saved at one time to the photo stream on your cel

REY [17]

You would first distribute the 4 in the parenthesis and then you would add 7 to both sides and whatever you get you will have to divide it by 4 to find p. I hope that this hepls.

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