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2 years ago

HELPP

1 answer:

8 0

Answer
A small class has five boys and six girls. A group of four students are to be selected at random to interview a new school director. a) Find the probability that the group contains at least one boy. b) Find the probability that the majority of the group is girls. c) Given that the group contains at least one boy, what is the chance that the boys are in the majority?

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Consider the following differential equation to be solved by undetermined coefficients. y(4) − 2y''' + y'' = ex + 1 Write the gi

kompoz [17]

Answer:

The general solution is

$y= (C_{1}+C_{1}x) e^0x+(C_{3}+C_{4}x) e^x +\frac{1}{2} (e^x(x^2-2x+2)-e^x(2(x-1)+e^x(2))$

+ $\frac{x^2}{2}$

Step-by-step explanation:

Step :1:-

Given differential equation y(4) − 2y''' + y'' = e^x + 1

The differential operator form of the given differential equation

$(D^4 -2D^3+D^2)y = e^x+1$

comparing f(D)y = e^ x+1

The auxiliary equation (A.E) f(m) = 0

$m^4 -2m^3+m^2 = 0$

$m^2(m^2 -2m+1) = 0$

$(m^2 -2m+1) this is the expansion of (a-b)^2$

$m^2 =0 and (m-1)^2 =0$

The roots are m=0,0 and m =1,1

complementary function is $y_{c} = (C_{1}+C_{1}x) e^0x+(C_{3}+C_{4}x) e^x$

<u>Step 2</u>:-

The particular equation is $\frac{1}{f(D)} Q$

P.I = $\frac{1}{D^2(D-1)^2} e^x+1$

P.I = $\frac{1}{D^2(D-1)^2} e^x+\frac{1}{D^2(D-1)^2}e^{0x}$

P.I = $I_{1} +I_{2}$

$\frac{1}{D^2} (\frac{x^2}{2!} )e^x + \frac{1}{D^{2} } e^{0x}$

$\frac{1}{D} means integration$

$\frac{1}{D^2} (\frac{x^2}{2!} )e^x = \frac{1}{2D} \int\limits {x^2e^x} \, dx$

applying in integration u v formula

$\int\limits {uv} \, dx = u\int\limits {v} \, dx - \int\limits ({u^{l}\int\limits{v} \, dx } )\, dx$

$I_{1}$ = $\frac{1}{D^2(D-1)^2} e^x$

$\frac{1}{2D} (e^x(x^2)-e^x(2x)+e^x(2))$

$\frac{1}{2} (e^x(x^2-2x+2)-e^x(2(x-1)+e^x(2))$

$I_{2}$ $= \frac{1}{D^2(D-1)^2}e^{0x}$

$\frac{1}{D} \int\limits {1} \, dx= \frac{1}{D} x$

again integration $\frac{1}{D} x = \frac{x^2}{2!}$

The general solution is $y = y_{C} +y_{P}$

$y= (C_{1}+C_{1}x) e^0x+(C_{3}+C_{4}x) e^x +\frac{1}{2} (e^x(x^2-2x+2)-e^x(2(x-1)+e^x(2))$

+ $\frac{x^2}{2!}$

3 0

3 years ago

Find an equation of the line through (2,7) and parallel to y=3x-6 Y=

Sliva [168]

As we know the formula to calculate the line of equation is y - y1 = m (x - x1)

Where m is the slope. y1 is the first y co ordinate. x1 is the first x co ordinate.

Now we do know that the slope of parallel line is the same as the slope of the original line.

So parallel line slope is 3 so slope for our line is 3. Hence equation is y - 7 = 3 (x - 2) which becomes y = 3x + 1.

6 0

3 years ago

Which of the following equations represents the axis of symmetry for the parabola shown? (5 points)

IceJOKER [234]

Which of the following equations represents the axis of symmetry for the parabola shown? (5 points)y = 10x
x = 10
x = y + 10
y = x + 10
The following equations that best represents the axis of symmetry for the parabola shown is x = 10.

6 0

2 years ago

The measure of the supplement of an angle is 20° more than three times the measure of the original angle. find the measures of t

viva [34]

If the original angle is x degrees then its supplement is 180 - x degrees.

we have the equation:-

180 - x = 3x + 20

160 = 4x

x = 40

The original angle is 40 degrees and its supplement is 140 degrees

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3 years ago

when a measurement in inches is converted to centimeters, will the number of centimeters be greater or less than the number of i

Margarita [4]

Greater because a centimeter is smaller than an inch.

4 0

3 years ago