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2 years ago

Please explain how to do this well I really need help

Mathematics

1 answer:

astraxan [27]2 years ago

6 0

Simply the radical expression

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If tan 0=1/3<br> find cot 0.

Karolina [17]

Answer: cot 0 = 3

Cotangent is the reciprocal of tangent, so it would be 3/1, which simplified to 3.

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2 years ago

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) :

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

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

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1 year ago

Find the unit rate of 135 miles in 5 hours

aliina [53]

To do this you have to divide 135 miles by 5 hours. You will get the answer of 27 miles per hour.

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2 years ago

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Write all names that apply to 7/8

pogonyaev

Seven eighth, 7 over 8, 7/8, 0.875,

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(x + 2) is raised to the fifth power. The third term of the expansion is:

morpeh [17]

Answer:

Step-by-step explanation:

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2 years ago