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Artemon [7]
2 years ago
12

The Reunion Tower is one of the most recognizable landmarks in Dallas, Texas due to the giant sphere that sits atop the structur

e. The sphere, which houses observation decks accessible to visitors, has a diameter of 118 feet. Which value is closest to the volume of the dome? Use 3.14 for π.
A. 859,852ft^3
B. 1,679,406ft^3
C. 2,350,879ft^3
D. 2,510,782ft^3
Mathematics
1 answer:
ValentinkaMS [17]2 years ago
6 0
The volume of a sphere uses the following formula:

V = \frac{4}{3}\pi r^{3}

Because the question asks to use 3.14 in place of pi, the formula will now look like this:

V = (\frac{4}{3})(3.14)r^{3} = 4.18\overline{66} r^{3}

We are given a diameter of 118 feet. The radius is half of the diameter, so divide the diameter by 2 to find the radius:

118 \div 2 = 59
r = 59

Plug this value into the formula, and solve with a calculator:

4.18\overline{66} \times 59^3 = 4.18\overline{66} \times 205379 = 859853.413

Although our result is one cubic foot off, the answer is <span>A. 859,852ft^3.

(859,852 is the result if the constant in the given formula is 4.18666, but the result with infinitely repeating numbers is 859,853.)</span>
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Courtney has a total of 88 stamps worth $15.56. Some are $0.25 stamps and some are $0.02 stamps. How many of each foes she have?
olganol [36]

Let x = # of 25-cent stamps

y = # of 2-cent stamps

{   x+ y = 88

{ 0.25x + 0.02y = 15.56

60 25-cent stamps 28 2-cent stamps

5 0
2 years ago
A square has a side that measures 5.5 units. What is the area of a circle with a circumference that equals the perimeter of the
jonny [76]

Step-by-step explanation:

here first you have to find the perimeter of square

given that perimeter of circle is equal to perimeter of square,,,,, therefore with the perimeter of square you have to find the radius of the circle.....

now you have the radius of the circle so by applying the formula of area of circle the answer will be finded

Please follow

7 0
3 years ago
Type the correct answer in each box. (____)
trapecia [35]

Answer:

1. -16; 2. +64; 3. 16

Step-by-step explanation:

The formula for the volume of a cylinder is

V = πr²x

Data:

r = (x - 8)   mm

V = 1024π mm³

Calculations:

1. Find the cubic equation  

V = πr²h

1024π = π(x - 8)² × x

Divide each side by π

1024 = x(x - 8)²  

1024 = x(x² - 16x  + 64)

1024 =    x³ - 16x² + 64x

x³ - 16x² + 64x - 1024 = 0

2. Solve the cubic equation

The general formula for a third-degree polynomial is

f(x) = ax³ + bx² + cx + d

Your polynomial is  

f(x) = x³ - 16x² + 64x - 1024

a = 1; d = -1024

According to the <em>rational roots theorem</em>, the possible roots are

factors of d/factors of a

Factors of d = ±1, ±2, ±4, ±8, ±16, ± 32, ± 64, ±128, ±256, ±512, ±1024

Factors of a = ±1

Potential roots are x = ±1, ±2, ±4, ±8, ±16, ± 32, ± 64, ±128, ±256, ±512, ±1024

That's a lot of possibilities to check by trial and error. I will just use the one that works.

Try x = 16 by synthetic division.

16|1  -16   64  -1024

  <u>|     16     0   1024 </u>

   1     0   64        0

So,

(x³ - 16x² + 64x - 1024)/(x – 16) = x² + 64

and

(x - 16)(x² + 64) = 0

x - 16 = 0        x² + 64 =    0

     x = 16       x²         = -64

                       x          =  ±8i

There is only one real root: x = 16 mm

6 0
3 years ago
HELP ME WITH THISSS PLZZZ!!!! ahh thank youu lol
Naddik [55]
The answer is b I think
3 0
2 years ago
Find the volume of the cone​
irina1246 [14]

Answer:

The volume of the cone is 12936 cubic mm.

Step-by-step explanation:

Given

Circumference of base = 132 mm

Height of the cone = 28 mm

Solution

Formula  of circumference = 2\pi r = 132 mm

\therefore\ r= \frac{132}{2 \pi } = 21 mm

Now volume of cone = \frac{1}{3} \times\pi \times r^{2} \times h

on substituting the value of r and h  we get ;

\frac{1}{3}\times\frac{22}{7} \times21\times21\times28= 12936\ mm

thus volume of cone is 12936  cubic mm.

4 0
3 years ago
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