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allochka39001 [22]
3 years ago
13

The measures of two supplementary angles are (2x + 10)° and (6x + 8)°.

Mathematics
1 answer:
bearhunter [10]3 years ago
5 0

Answer:

smaller angle is 50.5 degrees

Step-by-step explanation:

supplementary angles when added together = 180 degrees

(2x + 10) + 6x + 8 = 180

combine like terms

8x + 18 = 180

move the 18 over by subtraction

8x = 162

divide by 8 to get x by itself

x = 20.25

so plug in to find smaller angle

2(20.25) + 10 = 50.5

6(20.25) + 8 = 129.5

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3 years ago
What is the Laplace Transform of 7t^3 using the definition (and not the shortcut method)
Leokris [45]

Answer:

Step-by-step explanation:

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Now to solve the integral on the right hand side we shall use Integration by parts Taking 7t^{3} as first function thus we have

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Again repeating the same procedure we get

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\frac{3\times 2}{s^2}[\int_{0}^{\infty }te^{-st}dt]= \frac{3\times 2}{s^{2}}[t\int e^{-st} ]_{0}^{\infty}-\int_{0}^{\infty }[(t)\int e^{-st}dt]dt\\\\=\frac{3\times 2}{s^2}[0-\int_{0}^{\infty }\frac{1}{-s}e^{-st}dt]\\\\=\frac{3\times 2}{s^{3}}[\int_{0}^{\infty }e^{-st}dt]\\\\

Now solving this integral we have

\int_{0}^{\infty }e^{-st}dt=\frac{1}{-s}[\frac{1}{e^\infty }-\frac{1}{1}]\\\\\int_{0}^{\infty }e^{-st}dt=\frac{1}{s}

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L[7t^{3}]=\frac{7\times 3\times 2}{s^4}

where s is any complex parameter

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