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3 years ago

Is my answer correct? If not, please tell me the correct answer and explain. Thanks in advance!

Mathematics

1 answer:

Marat540 [252]3 years ago

7 0

Unfortunately, you are incorrect because the answer is D. It makes no sense for him to make profit out of selling nothing, so A,B, and C are wrong, and D is correct because it's the only answer that says he can profit if he sells 100 DVDs.

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A filter filled with liquid is in the shape of a vertex-down cone with a height of 9 inches and a diameter of 6 inches at its op

Alina [70]

Answer: Level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.

Step-by-step explanation:

Since we have given that

Height = 9 inches

Diameter = 6 inches

Radius = 3 inches

So, $\dfrac{r}{h}=\dfrac{3}{9}=\dfrac{1}{3}\\\\r=\dfrac{1}{3}h$

Volume of cone is given by

$V=\dfrac{1}{3}\pi r^2h\\\\V=\dfrac{1}{3}\pi \dfrac{1}{9}h^2\times h\\\\V=\dfrac{1}{27}\pi h^3$

By differentiating with respect to time t, we get that

$\dfrac{dv}{dt}=\dfrac{1}{27}\pi \times 3\times h^2\dfrac{dh}{dt}=\dfrac{1}{9}\pi h^2\dfrac{dh}{dt}$

Now, the liquid drips out the bottom of the filter at the constant rate of 4 cubic inches per second, ie $\dfrac{dv}{dt}=-4\ in^3$

and h = 2 inches deep.

$-4=\dfrac{1}{9}\times \pi\times (2)^2\dfrac{dh}{dt}\\\\-9\pi =\dfrac{dh}{dt}\\\\-28.28=\dfrac{dh}{dt}$

Hence, level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.

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3 years ago

Solve the following proportion problem for x: 14/3x=20/x-5

Butoxors [25]

14 20

---- = ----- cross multiply

3x x-5

14(x-5) = 3x (20)

14x - 70 = 60x

-14x -14x

-70 = 36x

/36 /36

-70/36 = x

-35/18 = x

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3 years ago

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sukhopar [10]

Answer:

2x+6=-8(x>=-7), 2x+3<9(x<3), 2x-4<=-8(x<=-2), -x-8>=-5(x<=-3), x+-4<=-3(x<=1)

Step-by-step explanation:

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Archy [21]

Answer:

Step-by-step explanation:

The *period* of a function is the length it takes before it repeats. Usually, the period of the sine function is 2π; it takes a full rotation around the unit circle for it to repeat. When we replace the input x with -2x, this does a few things:

- Changes the rotation direction

- Makes the rotation go twice as fast

If we rotate around the unit circle twice as fast, it’ll take us half of 2π, or just π to complete a cycle.

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3 years ago

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m_a_m_a [10]

Answer:

Step-by-step explanation:

A=πr2

= (3.14)(27)2

= 2289.06

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