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kvv77 [185]
3 years ago
10

Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AB = 8

Mathematics
1 answer:
Delicious77 [7]3 years ago
4 0

Answer:

x = 32

Step-by-step explanation:

∠BCA = ∠DBA (90 - ∠DBC)

∠A = ∠A

ΔABD similar to ΔACB

AC/AB = AB/AD

x / 8 = 8 / 2

x = 32

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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
Choose the equation below that represents the line passing through the point (1, −4) with a slope of one half.
AVprozaik [17]

Answer:

the equation would be y=1/2x-9/2

Step-by-step explanation:

next time try to put the answers like the question did because that's always helpful

6 0
3 years ago
I need help on numbers 3 and 4
nignag [31]
3. 45/3= 15, so she runs 1 mile in 15 minutes.

4. 45/9= 5, so each square foot can contain 5 plants.

Hope this helped!!
3 0
3 years ago
Read 2 more answers
5
Dmitry [639]

Answer:

im pretty sure its ACD

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
What’s 9n-3 simplified
Katarina [22]

Answer:

9n-3

Step-by-step explanation:

since 9n has a variable, u can't add or subtract 9n with 3

but if you were multiplying: 9n(3) then it would be 27n

:)

7 0
3 years ago
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