Simplify these radicals

9) 7sqrt(2)

11) 8sqrt(2)

13) 3sqrt(7)

Step-by-step explanation:

9) factor the radicand 98 into 7*7*2, 7^2*2, and then factor out the 7 squared to the outside of the radical to get 7 square roots of 2

11) factor the radicand 128 into 8*8*2, 8^2*2, and then factor out the 8 squared to the outside of the radical to get 8 square roots of 2

13) factor the radicand 63 into 3*3*7, 3^2*2, then factor out the 3 squared outside of the radical to get 3 square roots of 7

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204