Answer:
Step-by-step explanation:
(f*g)(x) = (-5x² + 2x + 7) (x +1)
= x* (-5x² + 2x + 7) + 1*(-5x² + 2x + 7)
= x*(-5x²) + x*2x + x*7 - 5x² + 2x + 7
= -5x³ + 2x² + 7x - 5x² + 2x + 7
= - 5x³ + 2x² -5x² + 7x + 2x +7 {Combine like terms}
= -5x³ - 3x² + 9x + 7
4) (f*g)(x) = (x² + 2x + 4)(x - 2)
= x*(x² + 2x + 4) - 2*(x² + 2x + 4)
= x*x² + x*2x + x*4 - 2*x² - 2*2x -2* 4
= x³ + 2x² + 4x -2x² -4x - 8
= x³ - 8
[tex]2) Speed=\dfrac{distance}{time}\\\\\\= \dfrac{d(h)}{t(h)}\\\\= \dfrac{2\sqrt{h}}{3\sqrt{4h}}=\dfrac{2*\sqrt{h}}{3*2\sqrt{h}}\\\\\\=\dfrac{1}{3}[/tex]
[tex]1)d(h) = \sqrt{16h^{4}}=\sqrt{2*2*2*2*h*h*h*h}=2*2*h*h=4h^{2}\\\\\\t(h) = 3h^{4}-3h^{3}-5h^{2}= h^{2}(3h^{2}-3h - 5))\\\\Speed=\dfrac{4h^{2}}{h^{2}(3h^{2}-3h-5)}\\\\=\dfrac{4}{3h^{2}-3h-5}[/tex]
