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irga5000 [103]
3 years ago
5

Use the function f(x) = 2x2 − 3x − 5 to answer the questions.

Mathematics
1 answer:
Dovator [93]3 years ago
5 0

Answer:

see below

Step-by-step explanation:

A:  2x² - 3x - 5

    (2x - 5)(x + 1)

B:  Set the factored equation equal to zero and solve for x.

(2x - 5)(x + 1) = 0

2x - 5 = 0

2x = 5

x = 5/2

x + 1 = 0

x = -1

The x-intercepts are 5/2 and -1

C)  To find the end behavior, you need to look at the term in the unfactored equation with the highest exponential number.  For this equation, that is 2x².  Since the exponent is positive,  both ends of the graph will point in the same direction.  Because the leading coefficent is positive, the graph will point upwards.  The end behavior of the graph is that as the x-values approach both ∞ and -∞, the function approaches ∞.

D)  Since we know that the x-intercepts are 5/2 and -1, you can plot these points.  You also know that the graph will be in an upward U shape.  Plug in  a couple x-values and plot them to make the graphing of the equation more accurate.

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$450

<h3>Step-by-step explanation:</h3>

Each year, the amount of interest earned is ...

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A sample of final exam scores is normally distributed with a mean equal to 23 and a variance equal to 16. Part (a) What percenta
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Answer:

Let X = score of final exam.

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(a)

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3 years ago
Solve differential equation:<br><br> y'''+4y''-16y'-64y=0 y(0)=0, y'(0)=26, y''(0)=-16
Ipatiy [6.2K]

Answer:  The required solution of the given differential equation is

y(x)=3e^{4x}-3e^{-4x}+2xe^{-4x}.

Step-by-step explanation:  We are given to solve the following differential equation :

y^{\prime\prime\prime}+4y^{\prime\prime}-16y^\prime-64y=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\\y(0)=0,~y^\prime(0)=26,~y^{\prim\prime}(0)=-16.

Let, y=e^{mx} be an auxiliary solution of equation (i).

Then, y^\prime=me^{mx},~~y^{\prime\prime}=m^2e^{mx},~~y^{\prime\prime\prime}=m^3e^{mx}.

Substituting these values in equation (i), we get

m^3e^{mx}+4m^2e^{mx}-16me^{mx}-64e^{mx}=0\\\\\Rightarrow (m^3+4m^2-16m-64)e^{mx}=0\\\\\Rightarrow m^3+4m^2-16m-64=0,~~~~~~~~~[\textup{since }e^{mx}\neq 0]\\\\\Rightarrow m^2(m-4)+8m(m-4)+16(m-4)=0\\\\\Rightarrow (m-4)(m^2+8m+16)=0\\\\\Rightarrow (m-4)(m+4)^2=0\\\\\Rightarrow m-4=0,~~(m+4)^2=0\\\\\Rightarrow m=4,~m=-4,~-4.

So, the general solution is given by

y(x)=Ae^{4x}+Be^{-4x}+Cxe^{-4x}.

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y^\prime=4Ae^{4x}-4Be^{-4x}-4Cxe^{-4x}+Ce^{-4x},\\\\y^{\prime\prime}=16Ae^{4x}+16Be^{4x}+16Cxe^{-4x}-4Ce^{-4x}-4Ce^{-4x}\\\\\Rightarrow y^{\prime\prime}=16Ae^{4x}+16Be^{4x}+16Cxe^{-4x}-8Ce^{-4x}.

With the conditions given, we get

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y^\prime(0)=4A-4B+C\\\\\Rightarrow 4A-4B+C=26\\\\\Rightarrow 4(A+A)+C=26~~~~~~~~~~~~~~~~[\textup{using equation (i)}]\\\\\Rightarrow C=26-8A~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)

and

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C=26-8A\\\\\Rightarrow 2=26-8A\\\\\Rightarrow 8A=24\\\\\Rightarrow A=3.

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B=-3.

Therefore, the required solution of the given differential equation is

y(x)=3e^{4x}-3e^{-4x}+2xe^{-4x}.

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