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Degger [83]
2 years ago
13

Which describes the combined variation in the formula h=v/ πr^2?

Mathematics
1 answer:
noname [10]2 years ago
3 0

Step-by-step explanation:

h varies directly with v and inversely with the square of r.

1/pi is the constant of variation.

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D^2(y)/(dx^2)-16*k*y=9.6e^(4x) + 30e^x
MA_775_DIABLO [31]
The solution depends on the value of k. To make things simple, assume k>0. The homogeneous part of the equation is

\dfrac{\mathrm d^2y}{\mathrm dx^2}-16ky=0

and has characteristic equation

r^2-16k=0\implies r=\pm4\sqrt k

which admits the characteristic solution y_c=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}.

For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be y_p=ae^{4x}+be^x. Then

\dfrac{\mathrm d^2y_p}{\mathrm dx^2}=16ae^{4x}+be^x

So you have

16ae^{4x}+be^x-16k(ae^{4x}+be^x)=9.6e^{4x}+30e^x
(16a-16ka)e^{4x}+(b-16kb)e^x=9.6e^{4x}+30e^x

This means

16a(1-k)=9.6\implies a=\dfrac3{5(1-k)}
b(1-16k)=30\implies b=\dfrac{30}{1-16k}

and so the general solution would be

y=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}+\dfrac3{5(1-k)}e^{4x}+\dfrac{30}{1-16k}e^x
8 0
2 years ago
Find the median of -12/4, 18/5, -25,1/5,10
sashaice [31]
Arrange from smallest to largest
-25, -12/4, 1/5, 18/5, 10
chose the middle number
1/5
4 0
2 years ago
What is the common point between lines y = -x + 7 and y = 3x + 10?
neonofarm [45]
Did you figure it out yet? lol
4 0
3 years ago
What is the similarity between numbers 85,17,19,4,and 2
8_murik_8 [283]
<span>They are each divisors of 6460.

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8 0
2 years ago
X2 -20x + y^2 - 10y+25=0<br> identify center of the circle and radius
nlexa [21]

Answer:

Center of the circle = (10, 5)

Radius = 10

Step-by-step explanation:

Look at the picture

5 0
2 years ago
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