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2 years ago

9

Find the scale factor.

1 answer:

charle [14.2K]2 years ago

6 0

Answer:

2/9

Step-by-step explanation:

Scale factor = 10/45 = 2/9

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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,

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

or

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

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

please help. use the table below to answer the questions. i just took a picture of the answer and stuff.

Sergeu [11.5K]

Answer:

1) 400

2) 62

3) i want to say 4.5%

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Evaluate the expression. 7.2 + 6.3(5.4 – 6)

REY [17]

$\text{Hey there!}$

$\text{Evaluate the expression: 7.2 + 6.3(5.4 - 6)}$

$\mathsf{7.2+6.3(5.4-6)}\\\\\mathsf{5.4 -6=-0.6}\\\\\mathsf{7.2+6.3(-0.6)}\\\\\mathsf{6.3(-0.6)=-3.78}\\\\\mathsf{7.2 - 3.78= \underline{3.42}}\\\\\boxed{\boxed{\mathsf{Answer:3.42}}}\checkmark$

$\text{Good luck on your assignment and enjoy your day!}$

~ $\frak{LoveYourselfFirst:)}$

7 0

2 years ago

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Evaluate 7 + (-3x^2) for x = 0. 4

Goshia [24]

Step-by-step explanation:

By substituting x = 0.4 in equation 7 + (-3x^2)

= 7 - 3 (0.4)^2

First solving o.4^2 as per the rule of BODMAS

= 7- 3 (0.16)

Now multiplying -3 with 0.16

= 7 - 0.48

= 6.52 THIS IS THE ANSWER

6 0

2 years ago

Classify ∠2 and ∠6. Compare angle measures, and give the postulate or theorem that justifies it.

LenaWriter [7]

Answer:

Explanation

Step-by-step explanation:

Angles 2 and 6 are corresponding angles in a transversal meaning they have the same measure.

4 0

2 years ago