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3 years ago

Find the center and radius of the sphere whose equation is given by x2+y2+z2−2x−4y+8z+17=0x2+y2+z2−2x−4y+8z+17=0.

1 answer:

4 0

We know that
the equation of a sphere is
(x-h)²+(y-k)²+(z-l)²=r²
where (h,k,l) is the center and r is the radius

we have
x²+y²+z²−2x−4y+8z+17=0

Group terms that contain the same variable, and move the constant to the opposite side of the equation

(x²+2x)+(y²-4y)+(z²+8z)=-17
Complete the square. Remember to balance the equation by adding the same constants to each side
(x²+2x+1)+(y²-4y+4)+(z²+8z+16)=-17+1+4+16
(x²+2x+1)+(y²-4y+4)+(z²+8z+16)=4

Rewrite as perfect squares

(x+1)²+(y-2²)+(z+4)²=4

(x+1)²+(y-2²)+(z+4)²=2²

the center is the point (-1,2,-4) and the radius is 2 units

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To solve this problem, you will first want to convert 5 pounds into ounces. To do this, first determine how many ounces is in 1 pound.

There are 16 ounces in 1 pound, so to convert 5 pounds into ounces, you simply have to multiply 5 × 16. This will give you 80 ounces total.

Allie give 12 ounces away, so you must first subtract 12 ounces from your total (80 ounces). 80 - 12 gives us 68 ounces.

Allie then divides the trail mix up into 4 ounce portions. To figure out how many small bags she can make, you simply divide your new total (68 ounces) by 4.

68 ÷ 4 = 17

Allie made 17 small bags.

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3 years ago

Elementary Algebra Skill

mr_godi [17]

The answer is a = $\frac{4}{-3}$

Step-by-step explanation:

1. Convert the mixed fraction to an improper fraction

To find the numerator, multiply the denominator by the whole number and add the numerator to it.

The denominator remains the same.

So, 2 $\frac{2}{3}$ will be $\frac{8}{3}$

2. Now the equation is,

$\frac{3}{2}$ a - $\frac{4}{3}$ a = $\frac{10}{3}$ + $\frac{8}{3}$ a

3. Take LCM on both sides.

For the left side, multiply the first fraction by $\frac{3}{3}$ and multiply the second fraction by $\frac{2}{2}$

$\frac{3*3}{2*3}$ a - $\frac{4*3}{3*3}$ a = $\frac{10+8a}{3}$

4. Solve by making a the subject

$\frac{9a-8a}{6}$ = $\frac{10+8a}{3}$

$\frac{a}{6}$ = $\frac{10+8a}{3}$

$\frac{3a}{6}$ =10+8a

$\frac{a}{2}$ = 10 + 8a

a = 2(10 + 8a)

a = 20 + 16a

a-16a = 20

-15a = 20

a = $\frac{20}{-15}$

a = $\frac{4}{-3}$

Therefore, the answer is a = $\frac{4}{-3}$

Keyword: Equations

Learn more about equations at

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3 years ago

What is the slope of a trend line that passes through the points (1.3) and (10, 25)?

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Answer:

Step-by-step explanation:

-1/2

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3 years ago

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Megan recently invested $2,000 dollars in a fast-growing company. Her financial advisor expects that Megan's investment will gro

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Answer:

2090

Step-by-step explanation:

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2 years ago

Put the steps in correct order to prove that if x is irrational, then 1/x is irrational using contraposition.

SOVA2 [1]

Answer:

The correct order is:

Step-by-step explanation:

First, let's write 1/x in a convenient way for us:

a) Substitute 1/x = p/q, to obtain x = 1/(1/x) = 1/(p/q) = q/p.

Now we assume that 1/x is rational (we want to prove that this implies that x will be also rational and because we know that x is irrational assuming that 1/x is rational will lead to an incongruence), then:

c. If 1/x is rational, then 1/x = p/q for some integers p and q with q ≠ 0. Observe that p is not 0 either, because 1/x is not 0.

Now we know that we can write x as a quotient of two integers, we need to imply that, then the next one is:

d) Observe that x is the quotient of two integers with the denominator nonzero.

And that is the definition of rational, then we end with:

b) Hence x is rational.

Which is what we wanted to get.

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2 years ago