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2 years ago

Can someone help me? y=2.5x

Mathematics

1 answer:

Alina [70]2 years ago

4 0

Answer:

x = y / 2.5

Step-by-step explanation:

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Save me the headache

maxonik [38]

$(9\sin2x+9\cos2x)^2=81$

Taking the square root of both sides gives two possible cases,

$9\sin2x+9\cos2x=9\implies\sin2x+\cos2x=1$

$9\sin2x+9\cos2x=-9\implies\sin2x+\cos2x=-1$

Recall that

$\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta$

If $\alpha=2x$ and $\beta=\dfrac\pi4$ , we have

$\sin\left(2x+\dfrac\pi4\right)=\dfrac{\sin2x+\cos2x}{\sqrt2}$

so in the equations above, we can write

$\sin2x+\cos2x=\sqrt2\sin\left(2x+\dfrac\pi4\right)=\pm1$

Then in the first case,

$\sqrt2\sin\left(2x+\dfrac\pi4\right)=1\implies\sin\left(2x+\dfrac\pi4\right)=\dfrac1{\sqrt2}$

$\implies2x+\dfrac\pi4=\dfrac\pi4+2n\pi\text{ or }\dfrac{3\pi}4+2n\pi$

(where $n$ is any integer)

$\implies2x=2n\pi\text{ or }\dfrac\pi2+2n\pi$

$\implies x=n\pi\text{ or }\dfrac\pi4+n\pi$

and in the second,

$\sqrt2\sin\left(2x+\dfrac\pi4\right)=-1\implies\sin\left(2x+\dfrac\pi4\right)=-\dfrac1{\sqrt2}$

$\implies2x+\dfrac\pi4=-\dfrac\pi4+2n\pi\text{ or }-\dfrac{3\pi}4+2n\pi$

$\implies2x=-\dfrac\pi2+2n\pi\text{ or }-\pi+2n\pi$

$\implies x=-\dfrac\pi4+n\pi\text{ or }-\dfrac\pi2+n\pi$

Then the solutions that fall in the interval $[0,2\pi)$ are

$x=0,\dfrac\pi4,\dfrac\pi2,\dfrac{3\pi}4,\pi,\dfrac{5\pi}4,\dfrac{3\pi}2,\dfrac{7\pi}4$

5 0

2 years ago

Read 2 more answers

☆+☆+☆=18 ♡+♡+☆=14 ♤+♤+♡=2 ♡+♤+☆☆= Genius only look closely at the details

Dmitriy789 [7]

Answer:

Step-by-step explanation:

3 stars = 18

1 star = 6

14-6=8/2 = 4

1 heart = 4

1 spade = -1

4 + -1= 3

3 + (2 stars)

3 + 12 = 15

5 0

3 years ago

In 16years, Ben will be 3 times as old as he is right now.

dedylja [7]

Answer:

Don't quote me on this but I believe the answer is that he is 8 years old right now if that's what you're looking for

Step-by-step explanation:

8 + 16 = 24

8 × 3 = 24

That's what I thought

5 0

3 years ago

What value is true of x makes this equation true 0.7x-5=0.2x+1

Sever21 [200]

Answer:

x=12

Step-by-step explanation:

First you make sure x is on both sides of the equation. So you do 0.7x-5-0.2x=0.2x+1-0.2x. Which just simplifies to 0.5x-5=1. You make sure x is the only thing on that side of the equation so you do 0.5x-5+5=1+5 which simplifies to 0.5x=6. Multiply the equation times 2 to just have x. x=12. The value that makes true of x is 12.

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2 years ago

James has just sold his motorbike for £1,890. He bought the motorbike for £2,700. What fraction of the original cost did he sell

valentina_108 [34]

1890/2700=7/10
7/10 is the answer

3 0

2 years ago

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