2 years ago

Help me with this one question

Mathematics

1 answer:

Varvara68 [4.7K]2 years ago

6 0

Isn’t that just 90°?

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Find the angles between -pi and pi that satisfy:<br><br> (−√3) sin(v)+cos(v)=√3

MAXImum [283]

Observe that

$\sin\left(\dfrac\pi6-v\right)=\sin\dfrac\pi6\cos v-\cos\dfrac\pi6\sin v=\dfrac12\cos v-\dfrac{\sqrt3}2\sin v$

In the original equation, divide both sides by $\dfrac12$ :

$-\sqrt3\sin v+\cos v=\sqrt3\implies\dfrac12\cos v-\dfrac{\sqrt3}2\sin v=\dfrac{\sqrt3}2$

$\implies\sin\left(\dfrac\pi6-v\right)=\dfrac{\sqrt3}2$

Next,

$\sin x=\dfrac{\sqrt3}2\implies x=\dfrac\pi3+2n\pi,x=\dfrac{2\pi}3+2n\pi$

where $n$ is any integer. Then

$\sin\left(\dfrac\pi6-v\right)\implies v=-\dfrac\pi6-2n\pi,v=-\dfrac\pi2-2n\pi$

Fix $n=0$ to ensure $-\pi$ , so that

$v=-\dfrac\pi6,v=-\dfrac\pi2$

3 0

3 years ago

Factor -8x^3-2x^2-12x-3

inysia [295]

$-8x^3-2x^2-12x-3\\\\=-2x^2(4x+1)-3(4x+1)\\\\=(4x+1)(-2x^2-3)\\\\=\boxed{-(4x+1)(2x^2+3)}$

5 0

3 years ago

I need help with this

miv72 [106K]

Your answer would be 3

3 0

2 years ago

Pls help me with this question :)

natima [27]

I think it would be 4
:)

3 0

3 years ago

I need to know this answer

Free_Kalibri [48]

Answer:

r = 7

Step-by-step explanation:

Given

r + 15 = 4r - 6 ( subtract 4r from both sides )

- 3r + 15 = - 6 ( subtract 15 from both sides )

- 3r = - 21 ( divide both sides by - 3 )

r = 7

5 0

2 years ago

Read 2 more answers