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Chapter 10: Q 30 (page 789)

Find the equation of a sphere with center (4, -2, -3) and radius 3.

Short Answer

Expert verified

The required equation is ${(x - 4)}^{2} + {(y + 2)}^{2} + {(z + 3)}^{2} = 9$

Step by step solution

Given information

A sphere with center (4,-2,-3) and radius 3.

Finding the equation

The equation of sphere may be written as:

${(x - 4)}^{2} + {(y + 2)}^{2} + {(z + 3)}^{2} = 3^{2}$

Simplify:

${(x - 4)}^{2} + {(y + 2)}^{2} + {(z + 3)}^{2} = 9$

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Most popular questions from this chapter

Find $||v||$ and find the unit vector in the direction of $v$ .

$v = (3, - 4)$

Use the definition of the derivative to find $f'$ for each function $f$ in Exercises 39-54

$f (x) = \frac{1}{\sqrt{2 x + 1}}$

In Exercises 20-23, find the dot product of the given pairs of vectors and the angle between the two vectors.

$u = <1, 2>, v = <3, 5>$

In Exercises 20-23, find the dot product of the given pairs of vectors and the angle between the two vectors.

$u = <3, - 1, 2>, v = <- 4, - 6, 3>$

Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.

(a) True or False: The sum formulas in Theorem 4.4 can be applied only to sums whose starting index value is $k = 1$ .

(b) True or False: $\sum_{k = 0}^{n} \frac{1}{k + 1} + \sum_{k = 1}^{n} k^{2}$ is equal to $\sum_{k = 0}^{n} \frac{k^{3} + k^{2} + 1}{k + 1}$ .

(c) True or False: $\sum_{k = 1}^{n} \frac{1}{k + 1} + \sum_{k = 0}^{n} k^{2}$ is equal to $\sum_{k = 1}^{n} \frac{k^{3} + k^{2} + 1}{k + 1}$ .

(d) True or False: $(\sum_{k = 1}^{n} \frac{1}{k + 1}) (\sum_{k = 1}^{n} k^{2})$ is equal to $\sum_{k = 1}^{n} \frac{k^{2}}{k + 1}$ .

(e) True or False: $\sum_{k = 0}^{m} \sqrt{k} + \sum_{k = m}^{n} \sqrt{k}$ is equal to $\sum_{k = 0}^{n} \sqrt{k}$ .

(f) True or False: $\sum_{k = 0}^{n} a_{k} = - a_{0} - a_{n} + \sum_{k = 1}^{n - 1} a_{k}$ .

(g) True or False: ${(\sum_{k = 1}^{10} a_{k})}^{2} = \sum_{k = 1}^{10} a_{k}^{2}$ .

(h) True or False: $\sum_{k = 1}^{n} {(e^{x})}^{2} = \frac{e^{x} (e^{x} + 1) (2 e^{x} + 1)}{6}$ .

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Find the equation of a sphere with center (4, -2, -3) and radius 3.

Short Answer

Step by step solution

Given information

Finding the equation

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Most popular questions from this chapter

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