All categories

2 years ago

Solve for x. please explain in detail

Mathematics

1 answer:

Sholpan [36]2 years ago

6 0

Use the cosine formula

Cos(angle) = adjacent/ hypotenuse

cos(30) = x/8

Cos(30) can be written as sqrt(3)/2

Now you have :

sqrt(3)/2 = x/8

Multiply both sides by 8:

X = sqrt(3)/2 x 8

Simplify:

X = 4sqrt(3)

You might be interested in

Is the number<img src="https://tex.z-dn.net/?f=%5Csqrt%7B2%2C500%7D" id="TexFormula1" title="\sqrt{2,500}" alt="\sqrt{2,500}" al

Virty [35]

Yes because the square root of 2,500 is 50 and 50 is a rational number.

8 0

3 years ago

What is the distance between these two points on a number line?

olga nikolaevna [1]

The answer is D.207

The distance cannot be a negative number, so options C or D can be correct. However, choice C cannot be correct since the first point is negative.


The distance is:
114 - (-93) = 114 + 93 = 207

3 0

3 years ago

I’m doing quadratic functions. I don’t understand the question.

Anettt [7]

The answer should be Letter H

4 0

3 years ago

Mom baked a Dutch apple pie in a 9-inch pie pan. She cut the pie into 6 equal pies so that

Hatshy [7]

The area and arc length of each piece can be found using the

relationship between a circle and a sector of the circle.

Responses (b, c, and d are approximated):

a. 120°

b. 10.6 square inch

c. 28.3 in.

d. Area: 15.8 in.², Central angle: 89.1°

<h3>How can the pie pieces dimensions be evaluated?</h3>

Given:

Diameter of the pan, d = 9-inch

Number pie pieces cut from the apple pie = 6

The pie pieces are sectors of a circular pie.

a. The central angle of one pie pieces = $\dfrac{360^{\circ}}{6}$ = 60°

Therefore;

The central angle of two pie pieces = 2 × 60° = 120°

b. Area of circular pie = π·r²

Where;

$r = \mathbf{\dfrac{d}{2}}$

Therefore;

$r = \dfrac{9}{2} = \mathbf{ 4.5}$

$The \ area \ covered \ by \ each \ pie \ piece = \dfrac{\pi \times 4.5^2}{6} \approx \mathbf{10.6}$

The area covered by each pie piece is approximately 10.6 square inch

c. The circumference of a circle = 2·π·r

The circumference of the original pie = 2 × π × 4.5 in. ≈ 28.3 in.

d. Let the arc length of the pie piece = 7 inches

$\mathbf{Area} \ of \ the \ \mathbf{pie \ piece}= \dfrac{7}{2 \cdot \pi \cdot 4.5} \times \pi \times 4.5^2 = \dfrac{7}{2 } \times 4.5 = 15.75 \approx 15.8$