Answer:
- hemisphere volume: 262 m³
- cylinder volume: 942 m³
- composite figure volume: 1204 m³
Step-by-step explanation:
A. The formula for the volume of a hemisphere is ...
V = (2/3)πr³
For a radius of 5 m, the volume is ...
V = (2/3)π(5 m)³ = 250π/3 m³ ≈ 261.799 m³
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B. The formula for the volume of a cylinder is ...
V = πr²h
For a radius of 5 m and a height of 12 m, the volume is ...
V = π(5 m)²(12 m) = 300π m³ ≈ 942.478 m³
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C. Then the total volume is ...
V = hemisphere volume + cylinder volume
V = 261.799 m³ +942.478 m³ = 1204.277 m³
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Rounded to the nearest integer, the volumes are ...
- hemisphere volume: 262 m³
- cylinder volume: 942 m³
- composite figure volume: 1204 m³
_____
As a rule, you only want to round the final answers. Here, the numbers are such that rounding the intermediate values still gives the correct final answer. That is not always the case.
F(x) =
2x² - 8x + 7=2(x²-4x) + 7
We are going to use formula a²-2ab+b² = (a-b)² to complete the square.
f(x)= 2(x² -2*2x+2²-2²)+7
f(x)=2(x² -2*2x+2²) -2*2² +7
f(x)=2(x-2)²- 1
Answer is D.
We can see that f(x) =
2x² - 8x + 7 and f(x)=
2(x-2)²- 1 are the same on the graph.
Speeds are s_c for car, s_m for motorcycle.
time is 2
distance of car is:
d_c = d_m + 20, d_m is distance of motorcycle.
speed is defined as:
s = d/t, distance over time.
hence:
d_c/2 = s_c = d_m/2 + 10
s_c = s_m + 10
from problem statement we know:
s_c = 2s_m - 30
so we have 2 simultaneous equations:
<span>s_c = s_m + 10
</span><span>s_c = 2s_m - 30
</span>
multiply second by -1 and sum them both:
<span> s_c = s_m + 10
</span>-s_c = -2s_m + 30
-------------------------
0 = -s_m + 40
s_m = 40
that is the speed of the motorcycle
s_c = <span>s_m + 10
</span> s_c = 40<span> + 10
</span>s_c = 50
that is the speed of car, both speeds in miles per hour
Answer:
3 of 9 is expected
since 7 of 21 (7+14) is 1/3 are coconut cupcake
7/21 = 1/3
1/3 x 9 = 3 coconut cupcakes
Answer:
200,000
Step-by-step explanation
10 x 2 is 10
So (8x100)x(2.5x100) is 200,000
8x100=800
2.5x100=250
800x250=200,000