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Katarina [22]
3 years ago
5

Which expression is equivalent to ? Assume

Mathematics
1 answer:
gladu [14]3 years ago
3 0

[(2x³y⁴)² × 2x]½

(2x³y⁴)½ ×(2x)½

2x³y⁴(2x)½

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Find the volume of the composite figure. Explain your thought, explain how your arrived at your answer. SHOW YOUR WORK FOR FULL
kobusy [5.1K]
We assume the composite figure is a cone of radius 10 inches and slant height 15 inches set atop a hemisphere of radius 10 inches.

The formula for the volume of a cone makes use of the height of the apex above the base, so we need to use the Pythagorean theorem to find that.
   h = √((15 in)² - (10 in)²) = √115 in

The volume of the conical part of the figure is then
   V = (1/3)Bh = (1/3)(π×(10 in)²×(√115 in) = (100π√115)/3 in³ ≈ 1122.994 in³


The volume of the hemispherical part of the figure is given by
   V = (2/3)π×r³ = (2/3)π×(10 in)³ = 2000π/3 in³ ≈ 2094.395 in³

Then the total volume of the figure is
   V = (volume of conical part) + (volume of hemispherical part)
   V = (100π√115)/3 in³ + 2000π/3 in³
   V = (100π/3)(20 + √115) in³
   V ≈ 3217.39 in³
4 0
2 years ago
35 out of 100 simplified
marshall27 [118]

Answer:

7/20

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
You are given g(x)=4x^2 + 2x and
Strike441 [17]

Answer:

324

Step-by-step explanation:

Given:

g(x)=4x^2+2x\\ \\f(x)=\int\limits^x_0 {g(t)} \, dt

Find:

f(6)

First, find f(x):

f(x)\\ \\=\int\limits^x_0 {g(t)} \, dt\\ \\=\int\limits^x_0 {(4t^2+2t)} \, dt\\ \\=\left(4\cdot \dfrac{t^3}{3}+2\cdot \dfrac{t^2}{2}\right)\big|\limits^x_0\\ \\=\left(\dfrac{4t^3}{3}+t^2\right)\big|\limits^x_0\\ \\= \left(\dfrac{4x^3}{3}+x^2\right)-\left(\dfrac{4\cdot 0^3}{3}+0^2\right)\\ \\=\dfrac{4x^3}{3}+x^2

Now,

f(6)\\ \\=\dfrac{4\cdot 6^3}{3}+6^2\\ \\=288+36\\ \\=324

4 0
3 years ago
At a collage bookstore Clara purchased a math textbook and a novel that cost a total of $54 not including tax if the price of th
diamong [38]

Answer:

m+n=54 and m=3n+8 is the system of equations that could be used to determine the price of each book.

Step-by-step explanation:

Given,

Total cost of maths book and novel = $54

Let,

Cost of maths book = m

Cost of novel = n

According to given statement;

m+n=54      Eqn 1

the price of the math textbook, m, is $8 more than 3 times the price of the novel

m = 3n+8     Eqn 2

m+n=54 and m=3n+8 is the system of equations that could be used to determine the price of each book.

Step-by-step explanation:

3 0
3 years ago
What is 10,000 x 1000,000
Hitman42 [59]

Answer:

10000000000

Step-by-step explanation:

10000000000

:) Hope this helps

4 0
2 years ago
Read 2 more answers
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