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3 years ago

What is the solution to the system of equations graphed below?

Mathematics

1 answer:

Annette [7]3 years ago

3 0

Yea I also don’t see a graph sorry

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What is the length of the rectangle if the perimeter is 102 cm?

elixir [45]

The perimeter of a rectangle is 102 cm. If the length is 15 cm less than twice the width

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3 years ago

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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) :

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

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

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2 years ago

Algebra 1 help please

Karo-lina-s [1.5K]

Short leg = 18 Long leg= 24 Hypotenuse= 30 My calculations were simple trial and error. I started with a trial of 10 for the short leg to begin with, averaging and estimating the appropriate proportions based off 6 additional increments. Sorry I don't have an algebraic method for you. Hope this has helped somewhat :)

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3 years ago

Which of the following is the solution to the inequality below ? -6/5(4-x)<_-4(X+1/2)

LuckyWell [14K]

Answer:

The answer is the option D

$x\leq 7/13$

Step-by-step explanation:

we have

$-\frac{6}{5}(4-x)\leq -4(x+\frac{1}{2})$

Multiply by $-5$ both sides

$6(4-x)\geq 20(x+0.5)\\24-6x\geq20x+10\\24-10\geq 20x+6x\\14\geq 26x$

Rewrite

$26x\leq 14\\x\leq 14/26\\ x\leq 7/13$

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3 years ago

-4c - 11 = 4c +21 Please help! I have literally no idea

MissTica

-4c - 11 = 4c +21 add 4c to both sides

 -4c - 11 + 4c = 4c + 21 + 4c simplify

- 11 = 8c + 21 subtract 21 from both sides

- 11 - 21 = 8c + 21 - 21 simplify

- 32 = 8c divide both sides by 8

c = - 4

That's it

I hope you got the idea

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3 years ago

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