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3 years ago

a sandbox must be filled with sand. the sandbox has a depth of 2ft and a diameter of 14 ft. how much sand to fill the sandbox

1 answer:

4 0

The formula for volume of a sphere is πr²h. The diameter is 14 ft, and the radius is 1/2of the diameter, so the radius is 7. The depth is the height, which is h. Now, substitute the known values into the expression:

π*7²*2

49π*2

98π is the exact amount of sand needed to fill the sandbox, and the approximate value is 307.87608.

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Find sin(a)&cos(B), tan(a)&cot(B), and sec(a)&csc(B).

Reil [10]

Answer:

Part A) $sin(\alpha)=\frac{4}{7},\ cos(\beta)=\frac{4}{7}$

Part B) $tan(\alpha)=\frac{4}{\sqrt{33}},\ tan(\beta)=\frac{4}{\sqrt{33}}$

Part C) $sec(\alpha)=\frac{7}{\sqrt{33}},\ csc(\beta)=\frac{7}{\sqrt{33}}$

Step-by-step explanation:

Part A) Find $sin(\alpha)\ and\ cos(\beta)$

we know that

If two angles are complementary, then the value of sine of one angle is equal to the cosine of the other angle

In this problem

$\alpha+\beta=90^o$ ---> by complementary angles

$sin(\alpha)=cos(\beta)$

Find the value of $sin(\alpha)$ in the right triangle of the figure

$sin(\alpha)=\frac{8}{14}$ ---> opposite side divided by the hypotenuse

simplify

$sin(\alpha)=\frac{4}{7}$

therefore

$sin(\alpha)=\frac{4}{7}$

$cos(\beta)=\frac{4}{7}$

Part B) Find $tan(\alpha)\ and\ cot(\beta)$

we know that

If two angles are complementary, then the value of tangent of one angle is equal to the cotangent of the other angle

In this problem

$\alpha+\beta=90^o$ ---> by complementary angles

$tan(\alpha)=cot(\beta)$

<em>Find the value of the length side adjacent to the angle alpha</em>

Applying the Pythagorean Theorem

Let

x ----> length side adjacent to angle alpha

$14^2=x^2+8^2\\x^2=14^2-8^2\\x^2=132$

$x=\sqrt{132}\ units$

simplify

$x=2\sqrt{33}\ units$

Find the value of $tan(\alpha)$ in the right triangle of the figure

$tan(\alpha)=\frac{8}{2\sqrt{33}}$ ---> opposite side divided by the adjacent side angle alpha

simplify

$tan(\alpha)=\frac{4}{\sqrt{33}}$

therefore

$tan(\alpha)=\frac{4}{\sqrt{33}}$

$tan(\beta)=\frac{4}{\sqrt{33}}$

Part C) Find $sec(\alpha)\ and\ csc(\beta)$

we know that

If two angles are complementary, then the value of secant of one angle is equal to the cosecant of the other angle

In this problem

$\alpha+\beta=90^o$ ---> by complementary angles

$sec(\alpha)=csc(\beta)$

Find the value of $sec(\alpha)$ in the right triangle of the figure

$sec(\alpha)=\frac{1}{cos(\alpha)}$

Find the value of $cos(\alpha)$

$cos(\alpha)=\frac{2\sqrt{33}}{14}$ ---> adjacent side divided by the hypotenuse

simplify

$cos(\alpha)=\frac{\sqrt{33}}{7}$

therefore

$sec(\alpha)=\frac{7}{\sqrt{33}}$

$csc(\beta)=\frac{7}{\sqrt{33}}$

6 0

4 years ago

8x plus 8y equals 8. 8x plus 2y equals 28. Find x and y

alukav5142 [94]

Answer:

x,y = 13/3, -10/3

Step-by-step explanation:

8x+8y=8

8x+2y=28 Subtract eq1 by eq 2

6y=-20

y=-20/6 y = -10/3

8x - 80/3=8

8x=34 2/3

x=4 1/3

x=13/3

Hope this helps plz hit the crown :D

6 0

3 years ago

Read 2 more answers

Find the number, if 3 1/3 of it is 10

Ugo [173]

Answer:

Step-by-step explanation:

You want a number that if it is multiplied by 3 1/3 the result will be 10. Let the number be x

3 1/3 * x = 10 Change to a mixed number

10/3 * x = 10 Multiply by 3/10

(10/3)*x * 3/10 = 10 * 3/10 Combine

x = 10*3 / 10 Simplify

x = 30/10 = 3

6 0

4 years ago

Find the slope of the line below. Enter your answer as a fraction or decimal. Use a slash mark (/) as the fraction bar if necess

Llana [10]

Answer:

1/4

Step-by-step explanation:

We can use the slope formula to find the slope

m = (y2-y1)/(x2-x1)

= (2-0)/(4 - -4)

= (2-0)/( 4+4)

= ( 2/8)

= 1/4

3 0

3 years ago

Read 2 more answers

Help fast please....

SIZIF [17.4K]

Answer:

a triangular prism

Step-by-step explanation:

they are all 180)

7 0

3 years ago

Read 2 more answers