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o-na [289]
3 years ago
11

Write down an (in)equality which describes the solid ball of radius 8 centered at (−10,10,−7). it should have a form like x2 y2

(z−2)2−4>
Mathematics
2 answers:
natali 33 [55]3 years ago
8 0

The equation of a sphere (I mean only the surface) is

(x-x_0)^2 + (y-y_0)^2 + (z-z_0)^2 = r^2

where (x_0,y_0,z_0) is the center of its sphere, and r is its radius. This equation simply menas "consider the points who are exactly r units away from the center".

So, if instead of the sphere surface we want the solid ball, we need to consider all the points whose distance from the center is less than or equal to the radius. So, the equation becomes

(x+10)^2 + (y-10)^2 + (z+7)^2 \leq 64

Contact [7]3 years ago
5 0

A sphere centered at (h, j, k) with radius r has equation

... (x-h)² + (y-j)² + (z-k)² = r²

A solid ball with the same center will have any radius up to r. Your ball has equation

... (x +10)² +(y -10)² +(z +7)² ≤ 64

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3 years ago
Please help with this question!! I need serious help!!
asambeis [7]

Answer:

<h2>The circumference is multipled by 4.</h2>

Step-by-step explanation:

The formula of an area of a circle"

A=\pi r^2

The formula of a circumference of a circle:

C=2\pi r

The area multipled by 16:

16A=16\pi r^2\\\\16A=\pi(4^2r^2)\\\\16A=\pi(4r)^2

The radius has increased fourfold, therefore:

C'=2\pi(4r)=4(2\pi r)=4C

The circumference is multipled by 4.

You can calculate the area and check the circumference:

r=11.6\ in\\\\A=\pi(11.6)^2=132.56\pi\\\\16A=(16)(134.56\pi)=2152.96\pi\ in^2

Calculate the radius:

\pi r^2=2152.96\pi             <em>divide both sides by π</em>

r^2=2152.96\to r=\sqrt{2152.96}\\\\r=46.4\ in

Calculate the circumference of both circles:

r=11.6\ in\\\\C=2\pi(11.6)=23.2\pi\ in

r=46.4\ in\\\\C'=2\pi(46.4)=92.8\pi\ in

\dfrac{C'}{C}=\dfrac{92.8\pi}{23.2\pi}=4\to C'=4C

5 0
3 years ago
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