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3 years ago

Mel drove 230 miles in 4 hours an pia drove 230 miles in 5 hours who drove faster?

1 answer:

5 0

Mel drove faster because they drove the same amount of miles (230) but Mel drove that in 4 hours and pia drove that in 5 hours so in conclusion Mel drove faster

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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

Can you help me with #7

Alex_Xolod [135]

2 miles-12 min.
3 miles- 18min
4 miles-24 min
5 miles-30 min

3 miles- 18
4 miles-24
5 miles-30
6 miles-36

Yes they are the same

7 0

3 years ago

Please help as soon as possible

GenaCL600 [577]

Answer:

The first is -4 and the second is 10

Step-by-step explanation:

7 0

2 years ago

In a statistics class there are 18 juniors and 10 seniors; 6 of the seniors are females and 12 of the juniors are males. If a st

Natasha_Volkova [10]

Answer:

P(a junior or a senior)=1

Step-by-step explanation:

The formula of the probability is given by:

$P(A)=\frac{n(A)}{N}$

Where P(A) is the probability of occurring an event A, n(A) is the number of favorable outcomes and N is the total number of outcomes.

In this case, N is the total number of the students of statistics class.

N=18+10=28

The probability of the union of two mutually exclusive events is given by:

$P(AUB)=P(A)+P(B)$

Therefore:

P(a junior or a senior) =P(a junior)+P(a senior)

Because a student is a junior or a senior, not both.

n(a junior)=18

n(a senior)=10

P(a junior)=18/28

P(a senior) = 10/28

P(a junior or a senior) = 18/28 + 10/28

Solving the sum of the fractions:

P(a junior or a senior) = 28/28 = 1

4 0

3 years ago

Alex

135inches2

Step-by-step explanation:

by multiplying both length and width you can get the sum

8 0

2 years ago