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3 years ago

72 is between which 2 integers

Mathematics

1 answer:

hoa [83]3 years ago

5 0

Answer:

71 and 73?

Step-by-step explanation:

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Please help me with the below question.

Snezhnost [94]

6a. By the convolution theorem,

$L\{t^3\star e^{5t}\} = L\{t^3\} \times L\{e^{5t}\} = \dfrac6{s^4} \times \dfrac1{s-5} = \boxed{\dfrac5{s^4(s-5)}}$

6b. Similarly,

$L\{e^{3t}\star \cos(t)\} = L\{e^{3t}\} \times L\{\cos(t)\} = \dfrac1{s-3} \times \dfrac s{1+s^2} = \boxed{\dfrac s{(s-3)(s^2+1)}}$

7. Take the Laplace transform of both sides, noting that the integral is the convolution of $e^t$ and $f(t)$ .

$\displaystyle f(t) = 3 - 4 \int_0^t e^\tau f(t - \tau) \, d\tau$

$\implies \displaystyle F(s) = \dfrac3s - 4 F(s) G(s)$

where $g(t) = e^t$ . Then $G(s) = \frac1{s-1}$ , and

$F(s) = \dfrac3s - \dfrac4{s-1} F(s) \implies F(s) = \dfrac{\frac3s}{\frac{s+3}{s-1}} = 3\dfrac{s-1}{s(s+3)}$

We have the partial fraction decomposition,

$\dfrac{s-1}{s(s+3)} = \dfrac13 \left(-\dfrac1s + \dfrac4{s+3}\right)$

Then we can easily compute the inverse transform to solve for f(t) :

$F(s) = -\dfrac1s + \dfrac4{s+3}$

$\implies \boxed{f(t) = -1 + 4e^{-3t}}$

6 0

1 year ago

Becky adds 3/4 gallon of gasoline into her snow thrower's empty fuel tank. She uses 1/4 gallon for the snowstorm on Friday, and

Kaylis [27]

Amount of fuel in the tank before the story begins . . . . . zero.

Total amount poured in . . . . . 3/4 gallon.

Total amount burned:
   on Friday . . . . . 1/4 gallon
   on Sunday . . . . 1/4 gallon
   Total used . . 1/2 gallon .

Amount remaining in the tank on Monday:

   (3/4 gallon in) - (1/2 gallon burned) = 1/4 gallon left.
      ==> NOT empty

The tank would have been empty on Monday IF Becky
had poured in only 1/2 gallon, instead of 3/4 of a gallon
before the first flakes began to fly.

8 0

3 years ago

Rohit wants to find the best model for a bivariate data set. He used a calculator to create a linear model, a quadratic model, a

san4es73 [151]

The answer is quadratic, I took the test.

8 0

3 years ago

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56°<br> х<br> 20<br> Solve for x. Round to the nearest<br> tenth.

otez555 [7]

Answer:

vgkf çµr nm 5hr 6tqy7gu8hibyg7tf6r5d4es3

Step-by-step explanation:

4 0

2 years ago

NEED URGENT HELP!! WILL GIVE BRAINLIEST

Flauer [41]

1. You need to multiply the denominator by something that will make the content of the radical be a square—so that when you take the square root, you get something rational. Easiest and best is to multiply by √6. Of course, you must multiply the numerator by the same thing. Then simplify.

$\displaystyle\frac{2}{\sqrt{6}}=\frac{2}{\sqrt{6}}\cdot\frac{\sqrt{6}}{\sqrt{6}}\\\\=\frac{2\sqrt{6}}{\sqrt{6}\cdot\sqrt{6}}=\frac{2\sqrt{6}}{6}\\\\=\bf{\frac{\sqrt{6}}{3}}$

2. Identify the squares under the radical and remove them.

$5\sqrt{12xm^3}=5\sqrt{(4m^2)(3xm)}=5\sqrt{(2m)^2}\sqrt{3xm}\\\\=5\cdot 2m\sqrt{3xm}=\bf{10m\sqrt{3xm}}$

7 0

3 years ago

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