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Alborosie
3 years ago
8

Suppose that y varies directly with x

Mathematics
1 answer:
Olin [163]3 years ago
8 0

Answer:

y=6

Step-by-step explanation:

x=20

y=10

x=15 > 20x=15

x=15/20

x=3/5

y=10(3/5)

=6

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Why should people conserve energy? (Please don’t get the answer form the internet)
Taya2010 [7]
People should conserve energy because it produces a higher quality of life. Reduced emissions result in cleaner air quality. It also helps create a healthier planet and helps sustain resources we have.
7 0
2 years ago
Solve for x.<br><br> 3/4x + y = e<br><br> Show work.
12345 [234]
To solve for x you need to get it by itself
start by subtracting y
3/4x=e-y
then divide by 3/4 or multiply by 4/3
so, x=(4(e-y))/3
distribute
x=(4e-4y)/3 or x=4/3e-4/3y
5 0
3 years ago
(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
What is the mean deviation of the following numbers 2 4 6 8 10 12​
olga nikolaevna [1]

Step-by-step explanation:

mean is always equal to additon of total no.s by total no.s

2 + 4 + 6 + 8 + 10 + 12

=42

total no.s = 6 no.s

42/6

=7

therefore 7 is the answer which is the mean deviation of the following no.s .

3 0
3 years ago
I need help please somebody
jekas [21]

Answer:

Step-by-step explanation:

6 minutes

3 0
3 years ago
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