Answer to Question #208317 in Algebra for rea

Question

Determine when matthew first ranked his intensity at 7.5. f(x)=5sin 3.14/2(n-2)+5

Answer 1

$f(x)=7.5$

$5sin[\frac{3.14}{2}(n-2)]+5=7.5$

Subtract 5 both sides:

$5sin[\frac{3.14}{2}(n-2)]+5-5=7.5-5$

$5sin[\frac{3.14}{2}(n-2)]=2.5$

Divide by 5 both sides

$sin[\frac{3.14}{2}(n-2)]=2.5÷5$

$sin[\frac{3.14}{2}(n-2)]=\frac{1}{2}$

$\frac{\pi}{2}(n-2)=\frac{π}{6}\\ wherebyπ=3.14$

$n-2=\frac{1}{3}$

Add 2 both sides

$n=\frac{1}{3}+2\\n=\frac{7}{3}$