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inn [45]
3 years ago
10

If a sphere is 120 feet in diameter what is the volume? Help please

Mathematics
1 answer:
natulia [17]3 years ago
3 0

Answer:

120

Step-by-step explanation:

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A hyena can run one over four mile in 22.5 seconds. Which of the following correctly shows this rate as miles per hour?
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Wouldnt you divide ? so itll be 5.62 
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F is the midpoint of GH. Point G is located at 32 and F is at 105. What is the location of point H?
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The location of point H is 68.
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Which solid has two triangular bases and three lateral faces, each in the shape of a rectangle?
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What is the written form for (8,8)
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81 900 000 000 000 is 8.19 × 10¹³

Step-by-step explanation:

Write the first number 8.

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Find a linear second-order differential equation f(x, y, y', y'') = 0 for which y = c1x + c2x3 is a two-parameter family of solu
Alisiya [41]
Let y=C_1x+C_2x^3=C_1y_1+C_2y_2. Then y_1 and y_2 are two fundamental, linearly independent solution that satisfy

f(x,y_1,{y_1}',{y_1}'')=0
f(x,y_2,{y_2}',{y_2}'')=0

Note that {y_1}'=1, so that x{y_1}'-y_1=0. Adding y'' doesn't change this, since {y_1}''=0.

So if we suppose

f(x,y,y',y'')=y''+xy'-y=0

then substituting y=y_2 would give

6x+x(3x^2)-x^3=6x+2x^3\neq0

To make sure everything cancels out, multiply the second degree term by -\dfrac{x^2}3, so that

f(x,y,y',y'')=-\dfrac{x^2}3y''+xy'-y

Then if y=y_1+y_2, we get

-\dfrac{x^2}3(0+6x)+x(1+3x^2)-(x+x^3)=-2x^3+x+3x^3-x-x^3=0

as desired. So one possible ODE would be

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(See "Euler-Cauchy equation" for more info)
6 0
3 years ago
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