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aev [14]
3 years ago
13

help please Compute the volume of a sphere with a radius of 6 inches. a. 864π in3 b.72π in3 c. 216π in3 d. 288π in3

Mathematics
1 answer:
Neporo4naja [7]3 years ago
7 0

Answer:

d. 288π in3

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

The radius is 6

V = 4/3 pi 6^3

V = 288 pi in^3

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A door of a lecture hall is in a parabolic shape. The door is 56 inches across at the bottom of the door and parallel to the flo
Arada [10]

Answer:

The parabolic shape of the door is represented by y - 32 = -\frac{2}{49}\cdot x^{2}. (See attachment included below). Head must 15.652 inches away from the edge of the door.

Step-by-step explanation:

A parabola is represented by the following mathematical expression:

y - k = C \cdot (x-h)^{2}

Where:

h - Horizontal component of the vertix, measured in inches.

k - Vertical component of the vertix, measured in inches.

C - Parabola constant, dimensionless. (Where vertix is an absolute maximum when C < 0 or an absolute minimum when C > 0)

For the design of the door, the parabola must have an absolute maximum and x-intercepts must exist. The following information is required after considering symmetry:

V (x,y) = (0, 32) (Vertix)

A (x, y) = (-28, 0) (x-Intercept)

B (x,y) = (28. 0) (x-Intercept)

The following equation are constructed from the definition of a parabola:

0-32 = C \cdot (28 - 0)^{2}

-32 = 784\cdot C

C = -\frac{2}{49}

The parabolic shape of the door is represented by y - 32 = -\frac{2}{49}\cdot x^{2}. Now, the representation of the equation is included below as attachment.

At x = 0 inches and y = 22 inches, the distance from the edge of the door that head must observed to avoid being hit is:

y -32 = -\frac{2}{49} \cdot x^{2}

x^{2} = -\frac{49}{2}\cdot (y-32)

x = \sqrt{-\frac{49}{2}\cdot (y-32) }

If y = 22 inches, then x is:

x = \sqrt{-\frac{49}{2}\cdot (22-32)}

x = \pm 7\sqrt{5}\,in

x \approx \pm 15.652\,in

Head must 15.652 inches away from the edge of the door.

8 0
3 years ago
The temperature in Bloomington on Sunday was 32.6°C. On Monday, the temperature changed by -8.25°C. What was the temperature on
Afina-wow [57]
Subtract 8.25 from 32.6 (32.6-8.25) = 24.35
8 0
3 years ago
Maria and Liam work in a banquet hall. Maria earns a 20% commission on her food sales. Liam earns a weekly salary of $625 plus a
Ksju [112]

Let us say that S is the total food sales therefore we can create the following equation:

0.20 S = 625 + 0.10 S

Solving for S:

0.10 S = 625

S = 6250

 

<span>Therefore the food sales should amount to $6,250</span>

4 0
2 years ago
By 2020, California is expected to have 2 million more senior citizens than Florida, and the sum of the number of senior citizen
Vsevolod [243]

Answer:

ok i need ore detial

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
What is the width of a rectangle with an area fo 5\8in2 and a length of 10 inches?
Travka [436]
Hi, do you mean an area of 58 inches squared? If you do, then your answer is: 5.8... the width would be 5.8. 

Hoped I helped, 
Dawn
7 0
3 years ago
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