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2 years ago

If a tree 28 meters tall casts a shadow 32 meters long, what is the angle of elevation of the sun to the nearest degree?

1 answer:

4 0

Since we need an angle measure we have to use an inverse trig ratio, sin^-1, cos^-1, or tan^-1.
Setting up the right triangle we have the opposite and adjacent so we use tan.
tan angle = 28/32
tan^-1 (28/32) = 41 degrees

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The curves y = √x and y=(2-x) and the Cartesian axes form two distinct regions in the first quadrant. Find the volumes of rotati

makkiz [27]

Answer:

Step-by-step explanation:

If you graph there would be two different regions. The first one would be

$y = \sqrt{x} \,\,\,\,, 0\leq x \leq 1 \\$

And the second one would be

$y = 2-x \,\,\,\,\,, 1 \leq x \leq 2$ .

If you rotate the first region around the "y" axis you get that

$A_1 = 2\pi \int\limits_{0}^{1} x\sqrt{x} dx = \frac{4\pi}{5} = 2.51$

And if you rotate the second region around the "y" axis you get that

$A_2 = 2\pi \int\limits_{1}^{2} x(2-x) dx = \frac{4\pi}{3} = 4.188$

And the sum would be 2.51+4.188 = 6.698

If you revolve just the outer curve you get

If you rotate the first region around the x axis you get that

$A_1 =\pi \int\limits_{0}^{1} ( \sqrt{x})^2 dx = \frac{\pi}{2} = 1.5708$

And if you rotate the second region around the x axis you get that

$A_2 = \pi \int\limits_{1}^{2} (2-x)^2 dx = \frac{\pi}{3} = 1.0472$

And the sum would be 1.5708+1.0472 = 2.618

7 0

3 years ago

Which expression shows a way to find 50% of 632

Ilya [14]

Answer:

Well 50% of 632 is 316 but i need to see the expressions to be sure

Step-by-step explanation:

3 0

2 years ago

Suppose KLMN ~ PQRS. Find the value of x.

arlik [135]

Complete question is attached.

Answer:

B) 8

Step-by-step explanation:

In this question, KLMN ~ PQRS. This means they are similar shapes.

From the image, we could denote that:

KL ~ PQ

LM ~ QR

Given that:

KL = 12

PQ = 30

QR = 20

LM = x

To find x, let's use tge expression:

$\frac{KL}{PQ} = \frac{LM}{QR}$

$= \frac{12}{30} = \frac{x}{20}$

Cross multiplying, we have:

12 * 20 = 30x

240 = 30x

To find x, let's divide both sides by 30.

$\frac{240}{30} = \frac{30x}{30}$

8 = x

x = 8

The correct option is option B.

3 0

3 years ago

A group of friends wants to go to the amusement park. They have $87.25 to spend on parking and admission. Parking is $6.25, and

Snezhnost [94]

Answer:

p = 3

Step-by-step explanation:

27p + 6.25 = 87.25

- 6.25 -6.25 = 27p + 0 = 81 = 27p = 81

81/27 = 3

p = 3

4 0

2 years ago

Solve by completing the square 4x^2-30=12+10x

natali 33 [55]

16x - 30 = 12 + 10

6x = 42

x = 7

5 0

3 years ago