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A function p is defined as p(x)=(x-a)(x-15)(x-20)+15 where a is a constant. Given that p(7)=15, what is the value of a?
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A function $p$ is defined as $p(x)=(x-a)(x-15)(x-20)+15$ where $a$ is a constant. Given that $p(7)=15$ , what is the value of $a$ ? $\newline$ $\square$

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Find derivatives using implicit differentiation

Full solution

Q. A function

p

is defined as

p(x)=(x-a)(x-15)(x-20)+15

where

a

is a constant. Given that

p(7)=15

, what is the value of

a

?

\newline

\square

Plug in $x=7$ : Plug $x=7$ into the function to find $a$ . $p(7)=(7-a)(7-15)(7-20)+15$
Simplify the equation: Simplify the equation. $p(7)=(7-a)(-8)(-13)+15$
Set equation equal to $\newline$ $15$ : Since $\newline$ $p(7)=15$ , set the equation equal to $\newline$ $15$ and solve for $\newline$ $a$ . $\newline$ $\newline$ $15=(7-a)(-8)(-13)+15$
Isolate the variable term: Subtract $15$ from both sides to isolate the variable term. $\newline$ $0=(7-a)(-8)(-13)$
Set $(7-a)$ equal to $0$ : If the product of numbers is $0$ , one of the numbers must be $0$ . So, set $(7-a)$ equal to $0$ . $\newline$ $7-a=0$
Solve for a: Solve for $a$ . $a=7$

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