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2 years ago

14

A line includes the points (9,0) and (-9,2). What is its equation in slope-intercept form?

1 answer:

horsena [70]2 years ago

4 0

Y=mx+b

First use the two point slope formula to find m

(y2-y1)/(x2-x1)
(2-0)/(-9-9)
2/-18
1/-9=m

Next use the point slope formula to find the answer

y-y1=m(x-x1)

y-0=1/-9(x-9)

Now use Distributive Property
y-0=1/-9(x)+1/-9(-9)
y-0=1/-9x+1

Your answer would be
y=-1/9x+1

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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

2 years ago

Find the area of the figure below by first finding the areas of the rectangle and triangle

Dmitrij [34]

Answer:

The total area is 45

Step-by-step explanation:

It's basically the same steps at the last problem

3 0

3 years ago

Can someone please help me this?<br> Math 8

Viefleur [7K]

Answer:

$5x + ( - 8)x + 9 + ( - 4) \\ 5x - 8x + 9 - 4 \\ - 3x + 5$

this is the solution

5 0

2 years ago

HELPPPPPPPPPPP!!!!!!!!!!!!!!!!!!!!

zimovet [89]

Answer:

1: 155

2: 222

3: 44

4: 132

5: 163

6: i dont know

7: 202

8:?

9: ?

hope this helped!

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

Please halp meh—- at what X-coordination are the two functions equal?

ycow [4]

Answer:

The x- coordinates are equal at -3.

Step-by-step explanation:

7 0

2 years ago