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kodGreya [7K]
2 years ago
5

Please help — Which ratio represents cos(c)?

Mathematics
1 answer:
lions [1.4K]2 years ago
5 0
48/50

option A is correct
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3y''-6y'+6y=e*x sexcx
Simora [160]
From the homogeneous part of the ODE, we can get two fundamental solutions. The characteristic equation is

3r^2-6r+6=0\iff r^2-2r+2=0

which has roots at r=1\pm i. This admits the two fundamental solutions

y_1=e^x\cos x
y_2=e^x\sin x

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
u_2=\displaystyle\frac13\int\frac{y_1e^x\sec x}{W(y_1,y_2)}\,\mathrm dx

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
a certain shade of blue is made by mixing 1.5 quarts of blue paint with 5 quarts of white paint. If you need a total of 16.25 ga
Law Incorporation [45]

we know the blue and white paints are on a 1.5 : 5 ratio, thus, if we have a total of 16.25 gallons of paint to be split along that ratio, we can simply divide 16.25 by (1.5+5) and distribute accordingly.

\bf \cfrac{blue}{white}\qquad \stackrel{ratio}{1.5:5}\qquad \cfrac{1.5}{5}~\hspace{5em}\cfrac{1.5\cdot \frac{16.25}{1.5+5}}{5\cdot \frac{16.25}{1.5+5}}\implies \cfrac{1.5\cdot \frac{16.25}{6.5}}{5\cdot \frac{16.25}{6.5}} \\\\\\ \cfrac{1.5\cdot 2.5}{5\cdot 2.5}\implies \cfrac{3.75}{12.5}\qquad \qquad \boxed{\stackrel{blue}{3.75}~:~\stackrel{white}{12.5}}

5 0
3 years ago
Can someone explain to me in words how to do this problem 3x+122=22x-11
inn [45]

When you have this type of problem, you need to combine the like-terms and isolate the variable.

3x + 122 = 22x - 11

Add 11 to both sides to get rid of it

3x + 122 + 11 = 22x - 11 + 11     (-11 + 11=0)

3x + 133 = 22x

Then you would bring the 3x to the other side, so subtract 3x from both sides

3x + 133 = 22x

-3x             -3x

133 = 22x - 3x

133 = 19x

Then divide both sides by 19 to isolate x

133/19 = 19x/19

133/19 = 7, so x = 7

Hope this helps!!

8 0
2 years ago
1 2 3 4 5 6 7 8 9 10
kirza4 [7]
Yes so i do need to doing the times and multipics then get a fraction then u will get tot eh answer
6 0
3 years ago
Hannah earned $1536 in 8 years on an investment at a 4% annual simple interest rate. How much was Hannah’s investment? $4800 $30
Nonamiya [84]

Simple interest calculates interest on initial amount only. The investment by Hannah was : Option A: $4800

<h3>How to calculate simple interest amount if rate of interest is R% annually?</h3>

Suppose that the initial amount of investment is P

And the rate of simple interest is R% annually,

And the time of investment is T years.

Then, the amount of simple interest is calculated as:

I = \dfrac{P \times R \times T}{100}

For the given case, let the initial investment Hannah made was of $P

Then, the time of investment is T = 8 years, R% = 4%, and given that Hannah earned interest I = $1536

Putting values in the above formula, we get;

I = \dfrac{P \times R \times T}{100}\\\\1536 = \dfrac{P \times 8 \times 4}{100}\\\\P = \dfrac{153600}{32} = 4800

Thus,

The investment by Hannah was : Option A: $4800

Learn more about simple interest here:

brainly.com/question/5319581

5 0
2 years ago
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