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2 years ago

I definitely need help, big time. What's the step by step solution to this math problem -(80/-10)^2?

Mathematics

2 answers:

mojhsa [17]2 years ago

6 0

The final answer is -64

Yanka [14]2 years ago

3 0

$\: \: \: ( { \frac{80}{ - 10}) }^{2} = {?}$

$= - { (\frac{80}{ - 10})} \times - ( \frac{80}{ - 10} )$

$= \frac{64}{1}$

$= 64 \: is \: the \: answer$

hope it helps you

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Find the standard equation of a sphere that has diameter with the end points given below. (3,-2,4) (7,12,4)

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The standard equation of the sphere is $(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53$

Step-by-step explanation:

From the question, the end point are (3,-2,4) and (7,12,4)

Since we know the end points of the diameter, we can determine the center (midpoint of the two end points) of the sphere.

The midpoint can be calculated thus

Midpoint = $(\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})$

Let the first endpoint be represented as $(x_{1}, y_{1}, z_{1})$ and the second endpoint be $(x_{2}, y_{2}, z_{2})$ .

Hence,

Midpoint = $(\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})$

Midpoint = $(\frac{3 + 7 }{2}, \frac{-2+12 }{2}, \frac{4 + 4 }{2})$

Midpoint = $(\frac{10 }{2}, \frac{10}{2}, \frac{8 }{2})\\$

Midpoint = $(5, 5, 4)$

This is the center of the sphere.

Now, we will determine the distance (diameter) of the sphere

The distance is given by

$d = \sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} + (z_{2}- z_{1})^{2} }$

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To find the radius, r

From $Radius = \frac{Diameter}{2}$

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Now, we can write the standard equation of the sphere since we know the center and the radius

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$(x-h)^{2} + (y-k)^{2} + (z-l)^{2} = r^{2}$

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$(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = \sqrt{(53} )^{2}$

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