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3 years ago

Please find X............

Mathematics

1 answer:

UNO [17]3 years ago

4 0

Answer:

$x=45.57^{\circ}$

Step-by-step explanation:

Given that,

Hypotenuse, H = 10

Base = 7

We need to find the value angle x. The relation between Hypotenuse, Base and the angle x is given by :

$\cos\theta=\dfrac{\text{Base}}{\text{Hypotenuse}}\\\\\cos\theta=\dfrac{7}{10}\\\\\theta=\cos^{-1}(\dfrac{7}{10})\\\\\theta=45.57^{\circ}$

So, the value of x is $45.57^{\circ}$ .

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Rewrite with only sin x and cos x.

Annette [7]

Option A

$\cos 3 x=\cos x-4 \cos x \sin ^{2} x$

<em><u>Solution:</u></em>

Given that we have to rewrite with only sin x and cos x

Given is cos 3x

$cos 3x = cos(x + 2x)$

We know that,

$\cos (a+b)=\cos a \cos b-\sin a \sin b$

Therefore,

$\cos (x+2 x)=\cos x \cos 2 x-\sin x \sin 2 x$ ---- eqn 1

We know that,

$\sin 2 x=2 \sin x \cos x$

$\cos 2 x=\cos ^{2} x-\sin ^{2} x$

Substituting these values in eqn 1

$\cos (x+2 x)=\cos x\left(\cos ^{2} x-\sin ^{2} x\right)-\sin x(2 \sin x \cos x)$ -------- eqn 2

We know that,

$\cos ^{2} x-\sin ^{2} x=1-2 \sin ^{2} x$

Applying this in above eqn 2, we get

$\cos (x+2 x)=\cos x\left(1-2 \sin ^{2} x\right)-\sin x(2 \sin x \cos x)$

$\begin{aligned}&\cos (x+2 x)=\cos x-2 \sin ^{2} x \cos x-2 \sin ^{2} x \cos x\\\\&\cos (x+2 x)=\cos x-4 \sin ^{2} x \cos x\end{aligned}$

$\cos (x+2 x)=\cos x-4 \cos x \sin ^{2} x$

Therefore,

$\cos 3 x=\cos x-4 \cos x \sin ^{2} x$

Option A is correct

7 0

3 years ago

Let p represent any number in the interval (- 18,22). Rewrite the possible values for p in inequality notation.

Nataliya [291]

Answer:

$-18 < p < 22$

Step-by-step explanation:

We are given the following information in the question.

The open interval: (- 18,22).

Let p belong to the given interval then p represents all the values belonging to the given interval.

Open Interval: An open interval is a interval that does not include the end points.

Thus, we can write:

$-18 < p < 22$

is the required inequality form required.

That is p can take values greater than -18 and smaller than 22.

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3 years ago

Tony leaves his house and rides his bike due north at 12 mph. At the same time, Jake leaves the same house and rides due west at

ElenaW [278]

Tony is 24 miles from the house.
Jake is 10 miles from the house.
They are 26 miles apart.

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3 years ago

Louis’s bill from dinner at a restaurant is $27.62 before tax. The local tax rate is 7.5%. Louis would like to leave a 20% tip o

shtirl [24]

As Louis is only leaving a 20% tip on the pretax bill, this means he's leaving 20% of $27.62
The best thing to do is to find 10% and double it.
27.62/10= 2.76 (as it rounds down)
2.76*2= 5.52
Therefore, you've got to add $5.52 to $27.62
$5.52+$27.62= $33.14
Hope this helps :)

4 0

2 years ago

What does the electronic fund transfer act do?

sammy [17]

Answer: The Electronic Funds Transfer Act is a federal law that protects consumers engaged in the transfer of funds through electronic methods. This includes the use of debit cards, automated teller machines and automatic withdrawals from a bank account.

Step-by-step explanation:

7 0

3 years ago