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3 years ago

Solve the given third-order differential equation by variation of parameters. y''' − 5y'' − y' + 5y = e4x

Mathematics

1 answer:

sineoko [7]3 years ago

3 0

Consider, please, the attached solution.

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Find the value of x using angle properties & the measure of

Jobisdone [24]

Answer:

15.

$x = 20$

16.

$\angle BFH$ = $100\textdegree$

$\angle CBD$ = $100\textdegree$ (if needed)

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17.

$x = 7$

18.

$\angle BFH$ = $68\textdegree$

Step-by-step explanation:

15. The two following angles, which is $\angle CBD$ and $\angle BFH$ , are Corresponding Angles. Write an expression by using the following measurements from $\angle CBD$ and $\angle BFH$ . Then, solve the expression for the value of $x$ :

$\angle CBD$ = $5x$

$\angle BFH$ = $3x + 40$

$5x = 3x + 40$

Solve for $x$ :

$5x = 3x + 40$

$5x - 3x = 3x - 3x + 40$

$2x = 40$

$\frac{2x}{2} = \frac{40}{2}$

$x = 20$

16. After you have the value $x$ use it to find the actual measurements of both $\angle CBD$ and $\angle BFH$ , by applying $x$ to the following expressions from both $\angle CBD$ and $\angle BFH$ and solve them:

-The value of $x$ :

$x = 20$

-Solve for $\angle CBD$ :

$\angle CBD$ = $5x$

$5(20)$

$100$

-The actual measurement of $\angle CBD$ :

$\angle CBD$ = $100\textdegree$

-Solve for $\angle BFH$ :

$\angle BFH = 3x + 40$

$3(20) + 40$

$60 + 40$

$100$

-The actual measurement of $\angle BFH$ : (if needed)

$\angle BFH$ = $100\textdegree$

----------------------------------------------------------------------------

17. The two following angles, which is $\angle BFE$ and $\angle DBF$ are Alternate Interior Angles .Write an expression by using the following measurements from $\angle BFE$ and $\angle DBF$ . Then, solve the expression for the value of $x$ :

$\angle BFE$ = $16x$

$\angle DBF$ = $4x + 84$

$16x = 4x + 84$

-Solve for $x$ :

$16x = 4x + 84$

$16x - 4x = 4x - 4x + 84$

$12x = 84$

$\frac{12x}{12} = \frac{84}{12}$

$x = 7$

18. After you have the value $x$ use it to find the actual measurement of $\angle DBF$ , by applying $x$ to the expression from $\angle DBF$ and solve it and find the actual measurement of an angle that is not labeled, which is $\angle BFH$ :

-The value of $x$ :

$x = 7$

Solve for $\angle DBF$ :

$\angle DBF$ = $4x + 84$

$4(7) + 84$

$28 + 84$

$112$

-The actual measurement of $\angle DBF$ :

$\angle DBF$ = $112\textdegree$

-Since both $\angle DBF$ and $\angle BFH$ are supplementary (two angles that equals to $180\textdegree$ ), and you want to find the actual measurement of $\angle BFH$ , Use the measurement of $\angle DBF$ and subtract it from $180\textdegree$ :

$\angle DBF - 180\textdegree$

$112\textdegree - 180\textdegree = 68\textdegree$

-The actual measurement of $\angle BFH$ :

$\angle BFH$ = $68\textdegree$

8 0

3 years ago

Find three consecutive odd integers such that the sum of the smaller two is three times larger increased by seven

sukhopar [10]

Answer:

three consecutive odd integers: 2n-1 2n+1 2n+3

that the sum of the smaller two is three

times larger increased by seven: 2n-1 + 2n+1 = 3(2n+3) +7

4n = 6n+ 9 +7

4n = 6n+ 16

4n -6n = 16

-2n = 16

n = 16/(-2)

n=-8

a) 2n -1 = 2(-8) -1 = -17

b) 2n+1 = 2(-8)+1 = -15

c) 2n+1 = 2(-8)+3 = -13

Ans. -17 ; -15 ; -13

4 0

3 years ago

Solve the following and explain your steps. Leave your answer in base-exponent form. (3^-2*4^-5*5^0)^-3*(4^-4/3^3)*3^3 please st

Naily [24]

Answer:

$\boxed{2^{\frac{802}{27}} \cdot 3^9}$

Step-by-step explanation:

I will try to give as many details as possible.

First of all, I just would like to say:

$\text{Use } \LaTeX !$

Texting in Latex is much more clear and depending on the question, just writing down without it may be confusing or ambiguous. Be together with Latex! （＊＾Ｕ＾）人（≧Ｖ≦＊）/

$(3^{-2} \cdot 4^{-5} \cdot 5^0)^{-3} \cdot (4^{-\frac{4}{3^3} })\cdot 3^3$