Here are two functions:
\(f(x) = 3x^2-2x+4 \)
\(g(x) = x^2 - kx - 6\)
If \(f(10)-g(10)=10\) what is the value of k?
+45 we first solve for \(f(10)\):
\(\begin{align*} f(10) &= 3(10)^2 - 2(10) + 4 \\ &= 300 - 20 + 4 \\ &= 284 \end{align*}\)
then, we solve for \(g(10)\) in terms of \(k\):
\(\begin{align*} g(10) &= 10^2 - 10k - 6 \\ &= 100 - 10k - 6 \\ &= 94 - 10k \end{align*}\)
plugging in these two values into \(f(10) - g(10) = 10\), we get
\(\begin{align*} 284 - (94 - 10k) &= 10 \\ 284 - 94 + 10k &= 10 \\ 190 + 10k &= 10 \\ 10k &= -180 \\ k &= \boxed{-18}. \end{align*} \)
