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2 years ago

Find the volume of a cylinder if the radius is 12 inches and the height is 17 inches

Mathematics

1 answer:

Alex Ar [27]2 years ago

3 0

Answer:

Volume of the cylinder = $7686.72\,inches^3$

Step-by-step explanation:

Radius(r) of the cylinder= $12\,inches$

Height(h) of the cylinder= $17\,inches$

Volume of a cylinder is :

$\pi \times r^2\times h$

As,

$\pi =\dfrac{22}{7}=3.14$

Volume is:

$=3.14\times (12\times 12)\times 17\\\\=3.14\times 144 \times 17\\\\=3.14\times 2448\\\\=7686.72\,inches^3$

The volume of the cylinder is: $7686.72\,inches^3$

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Consider the curve defined by the equation y=6x2+14x. Set up an integral that represents the length of curve from the point (−2,

torisob [31]

Answer:

32.66 units

Step-by-step explanation:

We are given that

$y=6x^2+14x$

Point A=(-2,-4) and point B=(1,20)

Differentiate w.r. t x

$\frac{dy}{dx}=12x+14$

We know that length of curve

$s=\int_{a}^{b}\sqrt{1+(\frac{dy}{dx})^2}dx$

We have a=-2 and b=1

Using the formula

Length of curve= $s=\int_{-2}^{1}\sqrt{1+(12x+14)^2}dx$

Using substitution method

Substitute t=12x+14

Differentiate w.r t. x

$dt=12dx$

$dx=\frac{1}{12}dt$

Length of curve= $s=\frac{1}{12}\int_{-2}^{1}\sqrt{1+t^2}dt$

We know that

$\sqrt{x^2+a^2}dx=\frac{x\sqrt {x^2+a^2}}{2}+\frac{1}{2}\ln(x+\sqrt {x^2+a^2})+C$

By using the formula

Length of curve= $s=\frac{1}{12}[\frac{t}{2}\sqrt{1+t^2}+\frac{1}{2}ln(t+\sqrt{1+t^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}[\frac{12x+14}{2}\sqrt{1+(12x+14)^2}+\frac{1}{2}ln(12x+14+\sqrt{1+(12x+14)^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}(\frac{(12+14)\sqrt{1+(26)^2}}{2}+\frac{1}{2}ln(26+\sqrt{1+(26)^2})-\frac{12(-2)+14}{2}\sqrt{1+(-10)^2}-\frac{1}{2}ln(-10+\sqrt{1+(-10)^2})$

Length of curve= $s=\frac{1}{12}(13\sqrt{677}+\frac{1}{2}ln(26+\sqrt{677})+5\sqrt{101}-\frac{1}{2}ln(-10+\sqrt{101})$

Length of curve= $s=32.66$

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2 years ago

Which of the following functions are solutions of the differential equation y'' + y = 3 sin x? (select all that apply)

DiKsa [7]

Answer:

Step-by-step explanation:

We must compute the derivatives and check if the equation is satisfied.

A. $y'=(3\sin x)'=3\cos x$ . Differentiate again to get $y''=(3\cos x)'=-3\sin x$ , then $y''+y=-3\sin x+3\sin x=0\neq 3\sin x$ so this choice of y doesn't solve the equation.

B. $y'=3\sin x+3x\cos x-5\cosx +5x\sin x=(5x+3)\sin x+(3x-5)\cos x$ and $y''=5\sin x+(5x+3)\cos x+3\cos x-(3x-5)\sin x=(10-3x)\sin x+(5x+6)\cos x$ , then $y''+y=10\sin x+6\cos x\neq 3\sin x$ so y is not a solution

C. $y'=\frac{-3}{2}\cos x+\frac{3}{2}x\sin x$ hence $y''=\frac{3}{2}\sin x+\frac{3}{2}\sin x+\frac{3}{2}x\cos x=3\sin x+\frac{3}{2}x\cos x$ . Then $y''+y=3\sin x+\frac{3}{2}x\cos x-\frac{3}{2}x\cos x=3\sin x$ so y is a solution.

D. $y'=-3\sin x$ and $y''=-3\cos x$ , then $y''+y=0$ thus y isn't a solution

E. $y'=\frac{3}{2}\sin x+\frac{3}{2}x\cos x$ hence $y''=\frac{3}{2}\cos x+\frac{3}{2}\cos x-\frac{3}{2}x\sin x=3\cos x-\frac{3}{2}x\cos x$ . Then $y''+y=3\cos x-\frac{3}{2}x\cos x-\frac{3}{2}x\cos x=3\cos x\neq 3\sin x$ then y is not a solution.

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2 years ago

Q5.) Use the model to determine when the population of the country will be 827 million.

Aneli [31]

The country population would be 827 million in about 20 years.

This can be found by replacing "t" with 20 and solving. The solution would be about 8273.28 million. Thus meaning in about 20 years, the population would be 827 million.

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2 years ago

Now, use your research to decide which business is the best choice for this community. Explain your choice in two to three sente

MA_775_DIABLO [31]

Answer:

The business which offers services needed by the citizens of the community, and which is most profitable. That is the best business.

Step-by-step explanation:

You didn't state which community you are referring to. However, the business that is best for any community is a business which offers services mostly needed by the citizens of the community, and which is most profitable.

9 0

2 years ago

Read 2 more answers

Suppose there is a 1.1 Fahrenheit a drop in temperature for every thousand feet that an airplane climbs into the sky and the tem

Mashutka [201]

Answer:

45.8 degrees

Step-by-step explanation:

We know that the temp before take off is 57.9

We also know the temp decreases every 1,000 feet so

if we are 11,000 feet in the air and divide that 11000/1000=11

We know that the temp drops 11 times

11x1.1=12.1

57.9-12.1=45.8 degrees

3 0

2 years ago