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3 years ago

A is a graph that is unbroken

Mathematics

1 answer:

vichka [17]3 years ago

4 0

Answer:A function whose graph is an unbroken line or curve with no gaps or breaks. Direct Variation

Step-by-step explanation:

A function whose graph is an unbroken line or curve with no gaps or breaks. Direct Variation. A linear relationship between two variables, x and y, that can be written in the form y=kx, where k is a nonzero constant. Discontinuous Function. A function whose graph has one or more jump, breaks, of holes.

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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

The cost our summer school trip is $17 per students plus a $175 fee for the bus. 1) Write a linear equation for the total cost o

scZoUnD [109]

Answer:

Step-by-step explanation:

1) 17x + 175 = y

2) 17(28) + 175 = y

476 + 175 = y

651 = y

Cost for bus and 28 students is $651

3) 889 - 175 = 714

714/ 17 = 42

42 students attempted the trip

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3 years ago

A toxic radioactive substance with the density of 4 mg/cm² is detected in the been detected in the ventilating ducts that was us

Kruka [31]

The formula for half-life is:

$A = P(0.5)^{t/h}$

A is the amount remaining, P is the initial amount, t is the time that has passed, and h is the half-life of the substance. Plug in the values that you know and solve:

$4 = P(0.5)^{35/20} \\ \\ 4 = P(0.5)^{1.75} \\ \\ P = \frac{4}{0.5^{1.75}} \\ \\ P \approx 13.4543426441$

Rounded to the nearest whole number, the density of the substance was about 13<span>mg / cm².</span>

8 0

3 years ago

Vicky and sarah have a total of 53 magnets on the inside of their lockers. Vicky has 4 fewer than twice as many as sarah. How ma

Alexeev081 [22]

Answer: 102

Step-by-step explanation: 53x2=106 and 106-4 is 102

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3 years ago

What is a benefit of a drawing program over a compass and straightedge?

viva [34]

<span> using a drawing program is easier and faster</span>

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2 years ago

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