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zaharov [31]
3 years ago
12

Consider a solid spherical ball made of wood. Suppose a hole is bored (drilled) vertically through the center of the ball and th

e resulting solid has a height of 8 inches. What is the volume of the resulting solid?
Mathematics
1 answer:
lbvjy [14]3 years ago
5 0

Answer:

The volume of solid is 268.08 inches cube.

Step-by-step explanation:

The solid spherical ball has height 8 inches that means the diameter of the sphere is 8 inches. So, the radius will be the half of diameter. Thus, radius is 4 inches.

Now use below formula to find the volume of solid sphere.

Volume = \frac{4}{3}\pi r^{2} \\Volume = \frac{4}{3}\pi (4)^{2} \\Volume = 268.08 \ in^{3}

Therefore, the volume of solid is 268.08 inches cube.

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ABC has side lenths 20, 24, and 31. Do the side lenghts form a Pythagorean triple?
Brut [27]
No they don't.
Phythagorean triple is when the sum of the squares of two numbers is equal to the square of another number.

20^2 + 24^2 = 400 + 576 = 976
31^2 = 961

20^2 + 24^2 should have been equal to 31^2 but that's not the case. So, the side's length don't form a triple.

Hope it helped!
4 0
3 years ago
PLEASE HELP PLEASE WILL MARK BRAINLY
Shtirlitz [24]

Answer:

Every 18 miles he uses 3 gallons

divide this:

18 ÷ 3 = 6 miles per gallon

30 miles = 30 ÷ 6 = 5 gallons

7 gallons = 7 x 6 = 42 miles

48 miles = 48 ÷ 6 = 8 gallons

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8 0
2 years ago
Read 2 more answers
General solutions of sin(x-90)+cos(x+270)=-1<br> {both 90 and 270 are in degrees}
mixer [17]

Answer:

\left[\begin{array}{l}x=2\pi k,\ \ k\in Z\\ \\x=-\dfrac{\pi }{2}+2\pi k,\ k\in Z\end{array}\right.

Step-by-step explanation:

Given:

\sin (x-90^{\circ})+\cos(x+270^{\circ})=-1

First, note that

\sin (x-90^{\circ})=-\cos x\\ \\\cos(x+270^{\circ})=\sin x

So, the equation is

-\cos x+\sin x= -1

Multiply this equation by \frac{\sqrt{2}}{2}:

-\dfrac{\sqrt{2}}{2}\cos x+\dfrac{\sqrt{2}}{2}\sin x= -\dfrac{\sqrt{2}}{2}\\ \\\dfrac{\sqrt{2}}{2}\cos x-\dfrac{\sqrt{2}}{2}\sin x=\dfrac{\sqrt{2}}{2}\\ \\\cos 45^{\circ}\cos x-\sin 45^{\circ}\sin x=\dfrac{\sqrt{2}}{2}\\ \\\cos (x+45^{\circ})=\dfrac{\sqrt{2}}{2}

The general solution is

x+45^{\circ}=\pm \arccos \left(\dfrac{\sqrt{2}}{2}\right)+2\pi k,\ \ k\in Z\\ \\x+\dfrac{\pi }{4}=\pm \dfrac{\pi }{4}+2\pi k,\ \ k\in Z\\ \\x=-\dfrac{\pi }{4}\pm \dfrac{\pi }{4}+2\pi k,\ \ k\in Z\\ \\\left[\begin{array}{l}x=2\pi k,\ \ k\in Z\\ \\x=-\dfrac{\pi }{2}+2\pi k,\ k\in Z\end{array}\right.

4 0
3 years ago
3x+9<br> -------- how do I solve this?<br> 4x+12
Reptile [31]
Put common terms in evidence and simplify:

\boxed{\frac{3x+9}{4x+12}=\frac{3(x+3)}{4(x+3)}=\frac{3}{4}}
5 0
3 years ago
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Which equation is equivalent to y-34=x(x-12)
egoroff_w [7]
The final answer is:
y - 34 = x2 - 12x
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3 years ago
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