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3 years ago

95 compsite or prime

Mathematics

1 answer:

Furkat [3]3 years ago

6 0

Answer:composite

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

3 years ago

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Find the lenght of ab

DerKrebs [107]

Answer:

20.6 cm (im pretty sure lol)

Step-by-step explanation:

sine rule:

(ab = x)

13.5/sin41 = x/sin90

13.5sin90/sin41 = x

x = 20.57741667

ab = 20.6cm

7 0

3 years ago

Write the equation of the line in slope-intercept form that has a slope of 3 and y-intercept of

lisov135 [29]

Answer:

y=3x-2

Step-by-step explanation:

y=mx+b where m=slope and b=y-intercept

y=3x-2

7 0

3 years ago

After transforming f(x) = 2x² + 4x + 3 into vertex form, the vertex is easily identifiable. Which ordered pair is the vertex?

vagabundo [1.1K]

Answer:

The correct answer to your question is A because your asking for the vertex of the equation.

Step-by-step explanation:

Vertex Algebraic Equations

6 0

4 years ago

Points J and K lie in plane H. Plane H contains two points. Point J is to the lower left and point K is to the uppercase right.

xxMikexx [17]

Answer:

Step-by-step explanation:

There's a theorem that says "through 2 points it only cross one and only one line". Having this as our start point, we can guarantee that there's only one line that can be drawn through those points

4 0

4 years ago

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