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3 years ago

Find the slope and the y-intercept of the line with equation 9x + 10y = 91.

Mathematics

1 answer:

skelet666 [1.2K]3 years ago

6 0

y=mx+b

M is also slope. b= y-intercept

9x + 10y = 91

move 9x to the other side

sign changes from +9x to- 9x

9x-9x+10y=-9x+91

10y=-9x+91

Divide both sides by 10 to get y by itself

10y/10=-9/10x+91/10

y=-9/10x+91/10

y-intercept (x=0)

9x + 10y = 91

9(0)+10y=91

0+10y=91

10y=91

Divide both sides by 10

10y/10=91/10

y=91/10

Answer:

slope (m)=-9/10

y-intercept :(0, 91/10)

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If θ is a first quadrant angle in standard position with P(u,v) = (3,4) evaluate cos 2 θ

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We have to evaluate cos(2θ), knowing that θ is in the first quadrant and in standard position P(u,v) = (3,4).

We can picture this as:

We can write the relation:

$\tan \theta=\frac{4}{3}$

We now look at the identities to find cos(2θ):

$\cos (2\theta)=\frac{1-\tan^2(2\theta)}{1+\tan^2(2\theta)}$

There are many identities for cos(2θ), but this is expressed in the information we already know, so we can solve as:

$\begin{gathered} \cos (2\theta)=\frac{1-\tan^2(2\theta)}{1+\tan^2(2\theta)} \\ \cos (2\theta)=\frac{1-(\frac{4}{3})^2}{1+(\frac{4}{3})^2} \\ \cos (2\theta)=\frac{1-\frac{16}{9}}{1+\frac{16}{9}} \\ \cos (2\theta)=\frac{\frac{9-16}{9}}{\frac{9+16}{9}} \\ \cos (2\theta)=\frac{-7}{25} \end{gathered}$

Answer: cos(2θ) = -7/25