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3 years ago

Determine whether each number is a solution of the inequality below. 3x+4<-7

Mathematics

1 answer:

ElenaW [278]3 years ago

7 0

Step-by-step explanation:

3x + 4 < -7

3x < -7 - 4

3x < -11

x < -11/3 ≈ -3,666

x = {3,2,1,0, etc}

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Find the balance if $500 is invested earning 4% compounded monthly, after 6 years.

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3 years ago

you are in line at an amusement park. You count 34 people in front of you. Each rollercoaster fits 11 people. How many rollercoa

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4 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

Solve the equation for y. Then find the value of y for each value of x.<br><br>3x-7y=13;x= -3, 0, 3

Sidana [21]

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$3\cdot \:0-7y=13\quad :\quad y=-\frac{13}{7}\quad \left(\mathrm{Decimal}:\quad y=-1.85714\dots \right)$

When x is 3

$3\cdot \:3-7y=13\quad :\quad y=-\frac{4}{7}\quad \left(\mathrm{Decimal}:\quad y=-0.57142\dots \right)$

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3 years ago

The bases of a circular cylinder are two *blank* circles.

PIT_PIT [208]

Hey there!

The answer that goes in your blank is:

Congruent is basically if a figures have the SAME shape and SIZE of the reflected area

So Thats why: CONGRUENT is your answer

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

4 0

3 years ago

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