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3 years ago

Which of the following represents the set in words X|x

Mathematics

1 answer:

docker41 [41]3 years ago

8 0

Answer:

My skills are playing soccer, learning fast, being sociable, playing basketball, etc. and my family: my mother and my sister.

Step-by-step explanation:

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The radius of a right circular cylinder is increasing at the rate of 7 in./sec, while the height is decreasing at the rate of 6

Arlecino [84]

Answer:

$\approx \bold{6544\ in^3/sec}$

Step-by-step explanation:

Given:

Rate of change of radius of cylinder:

$\dfrac{dr}{dt} = +7\ in/sec$

(This is increasing rate so positive)

Rate of change of height of cylinder:

$\dfrac{dh}{dt} = -6\ in/sec$

(This is decreasing rate so negative)

To find:

Rate of change of volume when r = 20 inches and h = 16 inches.

Solution:

First of all, let us have a look at the formula for Volume:

$V = \pi r^2h$

Differentiating it w.r.to 't':

$\dfrac{dV}{dt} = \dfrac{d}{dt}(\pi r^2h)$

Let us have a look at the formula:

$1.\ \dfrac{d}{dx} (C.f(x)) = C\dfrac{d(f(x))}{dx} \ \ \ (\text{C is a constant})\\2.\ \dfrac{d}{dx} (f(x).g(x)) = f(x)\dfrac{d}{dx} (g(x))+g(x)\dfrac{d}{dx} (f(x))$

$3.\ \dfrac{dx^n}{dx} = nx^{n-1}$

Applying the two formula for the above differentiation:

$\Rightarrow \dfrac{dV}{dt} = \pi\dfrac{d}{dt}( r^2h)\\\Rightarrow \dfrac{dV}{dt} = \pi h\dfrac{d }{dt}( r^2)+\pi r^2\dfrac{dh }{dt}\\\Rightarrow \dfrac{dV}{dt} = \pi h\times 2r \dfrac{dr }{dt}+\pi r^2\dfrac{dh }{dt}$

Now, putting the values:

$\Rightarrow \dfrac{dV}{dt} = \pi \times 16\times 2\times 20 \times 7+\pi\times 20^2\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 22 \times 16\times 2\times 20 +3.14\times 400\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 14080 -7536\\\Rightarrow \dfrac{dV}{dt} \approx \bold{6544\ in^3/sec}$

So, the answer is: $\approx \bold{6544\ in^3/sec}$

3 0

3 years ago

10 multiplied by 1/5

Bingel [31]

10* (1/5)
= 10/5
= 2

The final answer is 2~

6 0

4 years ago

Read 2 more answers

7 yd 4 yd 18 yd 11 yd 14 yd

Dima020 [189]

Answer:

????????????

Step-by-step explanation:

8 0

3 years ago

I need help I do not get it please help

zhenek [66]

The first fraction is 4 over 6, right? hopefully it is, i cant really see.
Basically, you can divide 4 and 6 by the same number, they have factors in common. They're both multiples of 2. if you divide them both by 2, you get 2 over 3, which is the exact same amount as 4 over 6, it's just written in a simpler way. the first answer is 2 over 3.

What numbers can both 10 and 15 be divided by? give it a try.

4 0

3 years ago

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Sofia takes 10mg of a medicine whose concentration in blood decreases by a factor of one half every day. Let t be the number of

adelina 88 [10]

Answer:

$L = 10(\frac{1}{2} )^{t-4}$

Step-by-step explanation:

If t is the number of days since Sofia took the medication of 10 mg, then the amount of medication in her system after t days will be $S = 10(\frac{1}{2} )^{t}$ .

So, the concentration of medicine in blood decreases by a factor of one half every day.

If we count the number of days from today and Lexi takes 10 mg of the same medicine four days later then the amount of medicine left on her body after t days will be $L = 10(\frac{1}{2} )^{t-4}$ . (Answer)

3 0

3 years ago

Read 2 more answers