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Alenkinab [10]
3 years ago
12

How many 1/4 are there in 9

Mathematics
1 answer:
miv72 [106K]3 years ago
3 0

Answer:

36

Step-by-step explanation:

9÷1/4

=9×4

=36

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y_1=e^x\cos x
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The particular solution is easiest to obtain via variation of parameters. We're looking for a solution of the form

y_p=u_1y_1+u_2y_2

where

u_1=-\displaystyle\frac13\int\frac{y_2e^x\sec x}{W(y_1,y_2)}\,\mathrm dx
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and W(y_1,y_2) is the Wronskian of the fundamental solutions. We have

W(e^x\cos x,e^x\sin x)=\begin{vmatrix}e^x\cos x&e^x\sin x\\e^x(\cos x-\sin x)&e^x(\cos x+\sin x)\end{vmatrix}=e^{2x}

and so

u_1=-\displaystyle\frac13\int\frac{e^{2x}\sin x\sec x}{e^{2x}}\,\mathrm dx=-\int\tan x\,\mathrm dx
u_1=\dfrac13\ln|\cos x|

u_2=\displaystyle\frac13\int\frac{e^{2x}\cos x\sec x}{e^{2x}}\,\mathrm dx=\int\mathrm dx
u_2=\dfrac13x

Therefore the particular solution is

y_p=\dfrac13e^x\cos x\ln|\cos x|+\dfrac13xe^x\sin x

so that the general solution to the ODE is

y=C_1e^x\cos x+C_2e^x\sin x+\dfrac13e^x\cos x\ln|\cos x|+\dfrac13xe^x\sin x
7 0
3 years ago
The volume of a​ cone-shaped hole is 50 pi ft cubed . If the hole is 6 ft​ deep, what is the radius of the​ hole?
True [87]

Answer:

r = 5

Step-by-step explanation:

The formula for volume of a cone is \pi r^2*\frac{h}{3}

h = 6

V = 50π

2\pi r^2=50\pi

r = 5

8 0
3 years ago
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