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3 years ago

You are downloading a song. The percent y(in decimal form) of megabytes remaining to download after x seconds is y=-0.1x+1.

2 answers:

5 0

The Y intercept is always when X equals 0. The X intercept is when Y equals 0.
An easy way to find x and y intercepts is to substitute these variables with 0.
To find the Y intercept, substitute 0 for X.
Y=-.1(0)+1=1 So you know that when Y equals 1 and X equals 0, you have you Y intercept.
Because we write coordinates as (X,Y), you can just plug in the numerals and have your coordinate for the Y intercept. So, x=0 y=1 (0,1)
To find the X intercept, substitute 0 for Y.
0=-.1x+1 -Add .1x to both sides
+.1x +.1x
.1x=1 -Divide both side to get x by itself.
.1x/.1=1/.1
x=10 So, we know that when y=0, x=10. This is our x intercept.
Coordinate form is (X,Y) so our x intercept is (10,0)

igomit [66]3 years ago

3 0

I would make the equation have both of your variables on the same side:

0.1x+y=1

Then I would use the cover-up method and say that

x-intercept= 10

y-intercept= 1

*Cover-Up Method: If you were finding the X-intercept, you would just ignore the y variable and divide your whole number by x.

In this case the whole number is 1. 1/0.1=10

Vice Versa with finding the Y-intercept

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Prove it. this question is from trigonometry

konstantin123 [22]

Answer:

See below for step-by-step proof.

Step-by-step explanation:

$\textsf{Given expression}:$

$\cos^6 \theta+\sin^6 \theta$

$\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:$

$\implies (\cos^2 \theta)^3+(\sin^2 \theta)^3$

$\textsf{Use the identity}\quad a^3+b^3=(a+b)^3-3ab(a+b):$

$\implies (\cos^2 \theta+\sin^2 \theta)^3-3 \cos^2 \theta\sin^2 \theta (\cos^2 \theta+\sin^2 \theta)$

$\textsf{Use the identity}\quad \sin^2 \theta + \cos^2 \theta=1:$

$\implies (1)^3-3 \cos^2 \theta\sin^2 \theta (1)$

$\implies 1-3 \cos^2 \theta\sin^2 \theta$

$\implies 1-3 (\cos \theta\sin \theta)^2$

$\textsf{Use the identity}\quad \sin 2 \theta=2 \sin \theta \cos \theta \implies \dfrac{1}{2}\sin 2 \theta= \sin \theta \cos \theta:$

$\implies 1-3 \left( \dfrac{1}{2}\sin 2 \theta\right)^2$

$\implies 1-\dfrac{3}{4} \sin^2 2 \theta$

$\textsf{Use the identity}\quad \sin^2 2\theta + \cos^2 2\theta=1 \implies \sin^2 2\theta=1-\cos^2 2\theta$

$\implies 1-\dfrac{3}{4} \left(1-\cos^2 2 \theta\right)$

$\implies 1-\dfrac{3}{4} +\dfrac{3}{4}\cos^2 2 \theta$

$\implies \dfrac{1}{4} +\dfrac{3}{4}\cos^2 2 \theta$

$\textsf{Factor out }\dfrac{1}{4}:$

$\implies \dfrac{1}{4}\left(1+3\cos^2 2 \theta\right)$

$\textsf{Use the identity}\quad \cos (4 \theta)=2 \cos^2 2\theta - 1 \implies \cos^2 2 \theta=\dfrac{1}{2}\cos 4 \theta+\dfrac{1}{2}:$

$\implies \dfrac{1}{4}\left(1+3\left(\dfrac{1}{2}\cos 4 \theta+\dfrac{1}{2}\right)\right)$

$\implies \dfrac{1}{4}\left(1+\dfrac{3}{2}\cos 4 \theta+\dfrac{3}{2}\right)$

$\implies \dfrac{1}{4}\left(\dfrac{5}{2}+\dfrac{3}{2}\cos 4 \theta\right)$

$\implies \dfrac{1}{4} \cdot \dfrac{1}{2}\left(5+3\cos 4 \theta\right)$

$\implies \dfrac{1}{8}\left(5+3\cos 4 \theta\right)$

6 0

2 years ago

Charmaine is on the swim team. Each day she swims 950m . How far does she swim in 5 days?

Roman55 [17]

950m * 5 days = 4750 m = 4.75 km

3 0

3 years ago

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Dahasolnce [82]

Answer:

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Step-by-step explanation:

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8 0

3 years ago

At a sale this week, a sofa is being sold for $584 . this is a 27% discount from the original price. what is the original price?

Effectus [21]

The original price should be 800$. Tell me if you need the calculations

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4 years ago

James earned $816 each year. He earned x dollars less per month than Matt, who earned $80 per month. Equation: 12(80 – x) = 816

Sphinxa [80]

Answer:

substitute 12 for x in the equation

multiply 68 by 12 months

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3 years ago

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