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OLEGan [10]
1 year ago
11

Lynn has scores of 95, 91, and 88 on three tests. Write and solve an equation to find

Mathematics
1 answer:
Lynna [10]1 year ago
6 0

Answer:

86

Step-by-step explanation:

the equation that needs to be made is

(95+ 91+ 88+ x)/4 = 90

this means that the sum of 95, 91, 88, and x is 360.

95 plus 91 is 186. 186 plus 88 is 274

360-274 = 86

give brainliest please!
hope this helps :)

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Use the method of undetermined coefficients to find the general solution to the de y′′−3y′ 2y=ex e2x e−x
djverab [1.8K]

I'll assume the ODE is

y'' - 3y' + 2y = e^x + e^{2x} + e^{-x}

Solve the homogeneous ODE,

y'' - 3y' + 2y = 0

The characteristic equation

r^2 - 3r + 2 = (r - 1) (r - 2) = 0

has roots at r=1 and r=2. Then the characteristic solution is

y = C_1 e^x + C_2 e^{2x}

For nonhomogeneous ODE (1),

y'' - 3y' + 2y = e^x

consider the ansatz particular solution

y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x

Substituting this into (1) gives

a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1

For the nonhomogeneous ODE (2),

y'' - 3y' + 2y = e^{2x}

take the ansatz

y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}

Substitute (2) into the ODE to get

b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1

Lastly, for the nonhomogeneous ODE (3)

y'' - 3y' + 2y = e^{-x}

take the ansatz

y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}

and solve for c.

ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16

Then the general solution to the ODE is

\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}

6 0
1 year ago
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atroni [7]
The answer is 7.5.
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5 0
2 years ago
Which expression is a linear factor of x6 +x-66?
Naddik [55]

Answer:

Option D.

Step-by-step explanation:

The given expression is

x^6+x-66

It is a polynomial.

(x-c) is a linear factor of polynomial p(x) if p(c)=0.

Substitute x=-1 in the given expression.

(1)^6+(1)-66=-64\neq 0

It means (x+1) is not a linear factor of given expression.

Substitute x=-2 in the given expression.

(-2)^6+(-2)-66=-4\neq 0

It means (x+2) is not a linear factor of given expression.

Substitute x=-4 in the given expression.

(-4)^6+(-4)-66=4026\neq 0

It means (x+4) is not a linear factor of given expression.

None of the given options are a linear factor of given expression.

Therefore, the correct option is D.

7 0
3 years ago
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A person stands 10 feet away from the base of a 300-foot office building.
snow_tiger [21]

Answer:

The answer will be A.

Step-by-step explanation:

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3 years ago
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How do you calculate compound interest? Please help me understand this
photoshop1234 [79]

Answer:

Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one

Step-by-step explanation:

i just did it

8 0
3 years ago
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