Find the equation of the sphere if one of its diameters has endpoints (4, 2, -9) and (6, 6, -3) which has been normalized so that the coefficient of x2 is 1.

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(Expand to obtain an equivalent expression for the sphere: )

Step-by-step explanation:

Apply the Pythagorean Theorem to find the distance between these two endpoints:

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Since the two endpoints form a diameter of the sphere, the distance between them would be equal to the diameter of the sphere. The radius of a sphere is one-half of its diameter. In this case, that would be equal to:

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In a sphere, the midpoint of every diameter would be the center of the sphere. Each component of the midpoint of a segment (such as the diameter in this question) is equal to the arithmetic mean of that component of the two endpoints. In other words, the midpoint of a segment between and would be:

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In this case, the midpoint of the diameter, which is the same as the center of the sphere, would be at:

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The equation for a sphere of radius and center would be:

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In this case, the equation would be:

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Simplify to obtain:

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Expand the squares and simplify to obtain:

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6,250

step-by-step explanation:

to get the area, multiply 360 by 160.(57,600)

to find out how many bags of fertilizer it will take, first figure out how many square feet one bag can hold. divide 1000 by 8(125) to get the unit rate(how many square feet one pound of fertilizer can hold)and multiply it by 50(6250). if i haven't made a mistake, that is the answer.

step-by-step explanation: