Identify the three similar triangles in the figure. Be sure to name the vertices in the correct order.

Galina-37 [17]

Solve the second equation for y so that you can substitute it in for y in the first equation..

y = 5x - 4

Substitute:

3x + (5x - 4) = 1

3 0

3 years ago

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(5) Find the Laplace transform of the following time functions: (a) f(t) = 20.5 + 10t + t 2 + δ(t), where δ(t) is the unit impul

Aloiza [94]

Answer

(a) $F(s) = \frac{20.5}{s} - \frac{10}{s^2} - \frac{2}{s^3}$

(b) $F(s) = \frac{-1}{s + 1} - \frac{4}{s + 4} - \frac{4}{9(s + 1)^2}$

Step-by-step explanation:

(a) $f(t) = 20.5 + 10t + t^2 +$ δ(t)

where δ(t) = unit impulse function

The Laplace transform of function f(t) is given as:

$F(s) = \int\limits^a_0 f(s)e^{-st} \, dt$

where a = ∞

=> $F(s) = \int\limits^a_0 {(20.5 + 10t + t^2 + d(t))e^{-st} \, dt$

where d(t) = δ(t)

=> $F(s) = \int\limits^a_0 {(20.5e^{-st} + 10te^{-st} + t^2e^{-st} + d(t)e^{-st}) \, dt$

Integrating, we have:

=> $F(s) = (20.5\frac{e^{-st}}{s} - 10\frac{(t + 1)e^{-st}}{s^2} - \frac{(st(st + 2) + 2)e^{-st}}{s^3} )\left \{ {{a} \atop {0}} \right.$

Inputting the boundary conditions t = a = ∞, t = 0:

$F(s) = \frac{20.5}{s} - \frac{10}{s^2} - \frac{2}{s^3}$

(b) $f(t) = e^{-t} + 4e^{-4t} + te^{-3t}$

The Laplace transform of function f(t) is given as:

$F(s) = \int\limits^a_0 (e^{-t} + 4e^{-4t} + te^{-3t} )e^{-st} \, dt$

$F(s) = \int\limits^a_0 (e^{-t}e^{-st} + 4e^{-4t}e^{-st} + te^{-3t}e^{-st} ) \, dt$

$F(s) = \int\limits^a_0 (e^{-t(1 + s)} + 4e^{-t(4 + s)} + te^{-t(3 + s)} ) \, dt$

Integrating, we have:

$F(s) = [\frac{-e^{-(s + 1)t}} {s + 1} - \frac{4e^{-(s + 4)}}{s + 4} - \frac{(3(s + 1)t + 1)e^{-3(s + 1)t})}{9(s + 1)^2}] \left \{ {{a} \atop {0}} \right.$

Inputting the boundary condition, t = a = ∞, t = 0:

$F(s) = \frac{-1}{s + 1} - \frac{4}{s + 4} - \frac{4}{9(s + 1)^2}$

3 0

3 years ago

0.09 is 10 Times as much as

Mumz [18]

0.09/10=0.009
we check it: 0.009*10=0.09, so it's right

8 0

3 years ago

Write a quadratic equation ax²+ bx + C = 0, whose coefficients are a =-9, b = 0, c = -2

aksik [14]

Let's write -9 where we see A:

Let's write 0 where we see B:

(Since B = 0, when it is multiplied by x, it becomes 0 again)

Let's write -2 where we see C:

Now we can move on to solving our equation:)

Let's put the known and the unknown on different sides:

(-2 goes to the opposite side positively)

(it goes as a division because it is in the case of multiplying -9 across)

 

I could not find the rest of it, but I did not want to delete it for trying very hard. Sorry. It felt like we should take the square root, but I couldn't find it, maybe this can help you a little bit.

Please do not report:(

I hope I got it right, I'm trying to improve my English a little :)

<h3>Greetings from Turkey:)</h3>

<h3>#XBadeX</h3>

8 0

3 years ago

Kenny types 280 words. How long did he type for? A.4 B. 5 C.6 D. 7

zlopas [31]

Are you sure you didn’t miss anything while writing the question?

Cause we have nothing to go off. Everybody types differently so there is no way for us to say how long he typed for, unless we were given aprox how many words he wrote in a minute or something

5 0

3 years ago

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