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1 year ago

What is the period of the function f(x) = -4 cos(5x-9) - 7? Give an exact value. units

Mathematics

2 answers:

ehidna [41]1 year ago

5 0

Answer:

2pi/5

Step-by-step explanation:

The only thing in this equation that affect the period is the '5' in front of the 'x'

cos period is usually 2pi

this is compressed by 5

period = 2pi/ 5

N76 [4]1 year ago

4 0

General equation

y=Acos(Bx+C)+D

Our Equation

y=-4cos(5x-9)-7

On comparing

A=-4
B=5
C=-9
D=-7

Now

Period

2π/B
2π/5

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2 years ago

Write the equation of the line that is the perpendicular bisector of the segment with endpoints (4, 1) and (2, -5)

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Answer: $\bold{y=-\dfrac{1}{3}x-1}$

<u>Step-by-step explanation:</u>

(4, 1) & (2, -5)

First, find the slope (m) and then the perpendicular (opposite reciprocal) slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\\m=\dfrac{-5-1}{2-4} = \dfrac{-6}{-2}=3\quad \rightarrow \quad m_{\perp}=-\dfrac{1}{3}\\$

Next, find the midpoint of (4, 1) and (2, -5):

$Midpoint=\bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)\\\\\\.\qquad \qquad=\bigg(\dfrac{4+2}{2},\dfrac{1-5}{2}\bigg)\\\\\\.\qquad \qquad=\bigg(\dfrac{6}{2},\dfrac{-4}{2}\bigg)\\\\\\.\qquad \qquad=(3, -2)$

Lastly, input the perpendicular slope and the midpoint into the Point-Slope formula to find the equation of the line:

$y - y_1 = m_{\perp}(x - x_1)\\\\y - (-2) = -\dfrac{1}{3}(x - 3)\\\\y + 2=-\dfrac{1}{3}x +1\\\\y =-\dfrac{1}{3}x - 1\\$

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