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4 years ago

The product of a number and four is at most -10

1 answer:

6 0

The product (multiply) of a number (x) and four (4) is at most (≤) -10.

4x ≤ -10

To solve this, divide both sides by 4

x ≤ -2 $\frac{1}{2}$

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A ball of radius 15 has a round hole of radius 5 drilled through its center. Find the volume of the resulting solid. Hint: The u

OverLord2011 [107]

Answer:

The volume of the ball with the drilled hole is:

$\displaystyle\frac{8000\pi\sqrt{2}}{3}$

Step-by-step explanation:

See attached a sketch of the region that is revolved about the y-axis to produce the upper half of the ball. Notice the function y is the equation of a circle centered at the origin with radius 15:

$x^2+y^2=15^2\to y=\sqrt{225-x^2}$

Then we set the integral for the volume by using shell method:

$\displaystyle\int_5^{15}2\pi x\sqrt{225-x^2}dx$

That can be solved by substitution:

$u=225-x^2\to du=-2xdx$

The limits of integration also change:

For x=5: $u=225-5^2=200$

For x=15: $u=225-15^2=0$

So the integral becomes:

$\displaystyle -\int_{200}^{0}\pi \sqrt{u}du$

If we flip the limits we also get rid of the minus in front, and writing the root as an exponent we get:

$\displaystyle \int_{0}^{200}\pi u^{1/2}du$

Then applying the basic rule we get:

$\displaystyle\frac{2\pi}{3}u^{3/2}\Bigg|_0^{200}=\frac{2\pi(200\sqrt{200})}{3}=\frac{400\pi(10)\sqrt{2}}{3}=\frac{4000\pi\sqrt{2}}{3}$

Since that is just half of the solid, we multiply by 2 to get the complete volume:

$\displaystyle\frac{2\cdot4000\pi\sqrt{2}}{3}$

$=\displaystyle\frac{8000\pi\sqrt{2}}{3}$

5 0

4 years ago

Betty can travel 61 centimeters in 5 minutes. Please calculate Betty's rate of speed. (round to 2 decimal places)

iren [92.7K]

Answer:

61/5= 12.2 centimeters per minute

Step-by-step explanation:

8 0

3 years ago

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A martial artist is practicing breaking 5 boards. He is able to break a board with probability 0.8. (a) What is the probability

konstantin123 [22]

Answer:

(a) = 0.32 or 8/25

(b) = 0.48 or 12/25

Step-by-step explanation:

(a):

0.8 x 2/5

8/10 x 4/10

(8 x 4) / (10 x 10)

(32) / (100)

0.32 or 8/25

(b):

0.8 x 3/5

8/10 x 6/10

(8 x 6) / (10 x 10)

(48) / (100)

0.48 or 12/25

(c):

0.8 x 5

8/10 x 50/10

(8 x 50) / (10 x 10)

(400) / (100)

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4 years ago

A 4-meter ladder is placed against a wall so that it reaches a height of 3.7 m. To the nearest tenth of a meter, how far away fr

Ne4ueva [31]

Answer:

I have no idea im so sry jcfksafjehalcbhjoEwo

Step-by-step explanation:

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3 years ago

What is the relationship between the following two sequences?

solmaris [256]

Answer:

The terms in sequence 2 are half as large as the terms in sequence 1.

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3 years ago

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