3 years ago

If f(x) = 4x^2 + 6/ 2 and g(x)= 3/2x^2, find f(x)•g(x)

Mathematics

1 answer:

masya89 [10]3 years ago

5 0

Set up the composite function and evaluate
f(3x^2/2)=9x^4+3

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3 years ago

Evalute costheta if sintheta = (sqrt5)/3

torisob [31]

Answer:

$\large\boxed{\cos\theta=\pm\dfrac{2}{3}}$

Step-by-step explanation:

Use $\sin^2x+\cos^2x=1$ .

We have

$\sin\theta=\dfrac{\sqrt5}{3}$

Substitute:

$\left(\dfrac{\sqrt5}{3}\right)^2+\cos^2\theta=1\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\\dfrac{(\sqrt5)^2}{3^2}+\cos^2\theta=1\qquad\text{use}\ (\sqrt{a})^2=a\\\\\dfrac{5}{9}+\cos^2\theta=1\qquad\text{subtract}\ \dfrac{5}{9}\ \text{from both sides}\\\\\cos^2\theta=\dfrac{9}{9}-\dfrac{5}{9}\\\\\cos^2\theta=\dfrac{4}{9}\to \cos\theta=\pm\sqrt{\dfrac{4}{9}}\\\\\cos\theta=\pm\dfrac{\sqrt4}{\sqrt9}\\\\\cos\theta=\pm\dfrac{2}{3}$