The complete question in the attached figure

we have that
f(x) = x²<span> + 1
g(x) = x – 4

step 1
find </span>(f o g)(x)
(f o g)(x)= (x - 4)² + 1(f o g)(x) = x² - 8x + 16 + 1
(f o g)(x) = x² - 8x + 17

step 2
find (f o g)(10)
(f o g)(10) = 10² - 8*(10) + 17
(f o g)(10 = 100 - 80 + 17
(f o g)(10)= 37

the answer is 37

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3 years ago

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What is the radius of a circle given by the equation x2 + y2 – 2x + 8y – 47= 0? radius = units

il63 [147K]

ANSWER

The radius is 8

EXPLANATION

We were given,

${x}^{2} + {y}^{2} - 2x + 8y - 47 = 0$

We rewrite the above equation to obtain,

${x}^{2} - 2x \: \: \: \: + {y}^{2} + 8y \: \: \: \: = 47$

We now add half the square of the coefficient of
$x \: and \: y$
to both sides of the equation to get,

${x}^{2} - 2x + ( - 1) ^{2} + {y}^{2} + 8y + {(4)}^{2} = 47 + ( - 1) ^{2} + {4}^{2}$

We now got two perfect squares on the left hand side of the equation,

$(x - 1)^{2} + {(y + 4)}^{2} = 47 + 1 + 16$

$(x - 1)^{2} + {(y + 4)}^{2} =64$

$(x - 1)^{2} + {(y + 4)}^{2} = {8}^{2}$

By comparing to the general formula of the circle,

${(x - a)}^{2} + {(y - b)}^{2} = {r}^{2}$

We can see that the radius is 8.

4 0

3 years ago

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