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3 years ago

I need this before the 24th! 100 points!

Mathematics

1 answer:

Anestetic [448]3 years ago

6 0

Answer:

The interval is [4,7]

Step-by-step explanation:

The rate of change is given by

f(x2) - f(x1)

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

x2 -x1

We want the rate of change to be 56

f(x2) - f(x1)

------------------- = 56

x2 -x1

We also know that the x2 is 7 so f(x2) = 192

192 - f(x1)

------------------- = 56

7 -x1

192 - f(x1) = 56( 7 -x1)

192 - f(x1) = 392 -56x1

Now we need to pick points from the table and see where it is true

(6,96)

192 - 96 = 392 -56*6

96=56 False

( 5,28)

192 - 28 = 392 -56*5

164=112 False

(4,24)

192 - 24 = 392 -56*4

168=168 True

The interval is [4,7]

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3 years ago

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4 years ago

Use theorem 7. 4. 2 to evaluate the given laplace transform. do not evaluate the convolution integral before transforming. (writ

irga5000 [103]

With convolution theorem the equation is proved.

According to the statement

we have given that the equation and we have to evaluate with the convolution theorem.

Then for this purpose, we know that the

A convolution integral is an integral that expresses the amount of overlap of one function as it is shifted over another function.

And the given equation is solved with this given integral.

So, According to this theorem the equation becomes the

$\mathscr{L} \left( \int_{0}^{t} e^{-\tau} \cos \tau d \tau \right) = \frac{ \mathscr{L} (e^{-\tau} \cos \tau ) }{s} \\\mathscr{L} \left( \int_{0}^{t} e^{-\tau} \cos \tau d \tau \right) = \frac{\frac{s+1}{(s+1)^2+1}}{s} \\\mathscr{L} \left( \int_{0}^{t} e^{-\tau} \cos \tau d \tau \right) = \frac{1}{s}\left (\frac{s+1}{(s+1)^2+1} \right).$

Then after solving, it become and with theorem it says that the

$\mathscr{L} \left( \int_{0}^{t} f(\tau) d\tau \right) = \frac{\mathscr{L} ( f(\tau))}{s} .$

Hence by this way the given equation with convolution theorem is proved.

So, With convolution theorem the equation is proved.

Learn more about convolution theorem here

brainly.com/question/15409558

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2 years ago