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11111nata11111 [884]

3 years ago

10

Find the 18th term of the arithmetic sequence whose common difference is d = 2 and whose first term is a, =5.

1 answer:

ikadub [295]3 years ago

7 0

Answer:

a=5

d=2

then t18=?

now we khow that

t18=a+(n-1)d

= 5+(18-1)2

= 5+17×2

=5+34

=39ans

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A photographer is 6 feet tall and cast a shadow that is 2 feet long. He is photographing a palm tree with a shadow that is 7 fee

Novay_Z [31]

Answer: The height of the tree is 21 feet.

Step-by-step explanation:

Here we can assume that the angle at which the sun impacts the photographer and the tree to be the same angle.

Then we can think in both cases as triangles rectangles, where the height is a cathetus, and the shadow is the other cathetus.

Then we will have a relationship like:

Tg(angle) = shadow/height

height = shadow/Tg(angle)

Now, because for both triangles we have the same angle, then Tg(angle) will be the same number for both cases, and we can just think of it as constant K

Tg(angle) = K

Then we have the equation:

Height = Shadow/K

We know that the photographer is 6ft tall, and his shadow is 2 ft long, we can replace those two things in the above equation and find the value of k:

6ft = 2ft/K

K = 2ft/6ft = (1/3)

Now we know that the shadow of the tree is 7ft long, then the height will be:

height = 7ft/(1/3) = 7ft*3 = 21ft

The tree is 21 ft tall.

6 0

3 years ago

Rewrite with only sin x and cos x.

Annette [7]

Option A

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

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

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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,

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

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7 0

3 years ago

Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.

Oksi-84 [34.3K]

3/3...............................

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3 years ago

If x=12 What is the value of the expression2(x)+3

GaryK [48]

Answer:

147

Step-by-step explanation:

2(X)= (X) x (X)

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7 0

3 years ago

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

dalvyx [7]

Matching each equation of the plecewise function represented in the graph will be:

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<h3>How to illustrate the information?</h3>

It should be noted that a domain simply means the set of inputs that are accepted by the function.

In this case, the equation of the piecewise function represented is given.

The graph is attached.

Learn more about equations on:

brainly.com/question/2972832

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2 years ago