Answer: 118.40, 300, $18,000
Step-by-step explanation:
a) p(x) = [tex]-\frac{1}{5} (8) + 120[/tex]
p(8) = [tex]-\frac{8}{5} + 120[/tex]
= -1.60 + 120
= 118.40
b) R(x) = x * p(x)
= [tex]x(-\frac{1}{5}x + 120)[/tex]
= [tex]-\frac{1}{5}x^{2} + 120x[/tex]
a=[tex]-\frac{1}{5}[/tex], b=120
x = [tex]\frac{-b}{2a}[/tex]
= [tex]\frac{-120}{-\frac{2}{5}}[/tex]
= [tex]\frac{-120(5)}{-2}[/tex]
= 300
c) R(x) = [tex]-\frac{1}{5}x^{2} + 120x[/tex]
R(300) = [tex]-\frac{1}{5}(300)^{2} + 120(300)[/tex]
= -18,000 + 36,000
= 18,000
***********************************************************************
sec θ = [tex]\sqrt{6}[/tex]
[tex]\frac{hypotenuse}{adjacent} = \frac{\sqrt{6}}{1}[/tex]
adjacent² + opposite² = hypotenuse²
1² + opposite² = (√6)²
1 + opposite² = 6
opposite² = 5
opposite = √5
csc θ = [tex]\frac{hypotenuse}{opposite} = \frac{\sqrt{6}}{\sqrt{5}} = \frac{\sqrt{30}}{5}[/tex]
cot θ = [tex]\frac{adjacent}{opposite} = \frac{1}{\sqrt{5}} = \frac{\sqrt{5}}{5}[/tex]
sin θ = [tex]\frac{opposite}{hypotenuse} = \frac{\sqrt{5}}{\sqrt{6}} = \frac{\sqrt{30}}{6}[/tex]
cos θ = [tex]\frac{adjacent}{hypotenuse} = \frac{1}{\sqrt{6}} = \frac{\sqrt{6}}{6}[/tex]
tan θ = [tex]\frac{opposite}{adjacent} = \frac{\sqrt{5}}{1} = \sqrt{5}[/tex]
**********************************************************************
Answer: 144°
Step-by-step explanation:
[tex]\frac{\pi}{180}=\frac{4\pi}{5(x)}[/tex]
π(5x) = 180(4π)
x = [tex]\frac{180(4\pi)}{5\pi}[/tex]
= 36(4)
= 144
