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2 years ago

Identify next three numbers in this sequence: 2, 6, 3, 9, 6, 18, 15…

Mathematics

2 answers:

Colt1911 [192]2 years ago

5 0

Jam is djndkenzie sjwnxjezi 29 djdjdj 38383

Pani-rosa [81]2 years ago

4 0

45,42,126 it’s times 3 -3 so every time yu times yu minus that number by 3

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the surface area of a square pyramid is 84 square inches. the side length of the base is 6 inches. what is the value of x?

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The formula is(V=B•h)(84•6)

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3 years ago

How to solve the math equation

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3 years ago

Sandeep has twice as much as sonia. together they have rs 150. how much does sonia have

Inga [223]

let sonia has the (x)

Sandeep would have twice as much as Sonia so (2x)

together they'd have 150.

so, x+2x=150

solve for X

3x=150

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So x=50 is what Sonia has,

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5 0

3 years ago

Consider the differential equation:

Wewaii [24]

(a) Take the Laplace transform of both sides:

$2y''(t)+ty'(t)-2y(t)=14$

$\implies 2(s^2Y(s)-sy(0)-y'(0))-(Y(s)+sY'(s))-2Y(s)=\dfrac{14}s$

where the transform of $ty'(t)$ comes from

$L[ty'(t)]=-(L[y'(t)])'=-(sY(s)-y(0))'=-Y(s)-sY'(s)$

This yields the linear ODE,

$-sY'(s)+(2s^2-3)Y(s)=\dfrac{14}s$

Divides both sides by $-s$ :

$Y'(s)+\dfrac{3-2s^2}sY(s)=-\dfrac{14}{s^2}$

Find the integrating factor:

$\displaystyle\int\frac{3-2s^2}s\,\mathrm ds=3\ln|s|-s^2+C$

Multiply both sides of the ODE by $e^{3\ln|s|-s^2}=s^3e^{-s^2}$ :

$s^3e^{-s^2}Y'(s)+(3s^2-2s^4)e^{-s^2}Y(s)=-14se^{-s^2}$

The left side condenses into the derivative of a product:

$\left(s^3e^{-s^2}Y(s)\right)'=-14se^{-s^2}$

Integrate both sides and solve for $Y(s)$ :

$s^3e^{-s^2}Y(s)=7e^{-s^2}+C$

$Y(s)=\dfrac{7+Ce^{s^2}}{s^3}$

(b) Taking the inverse transform of both sides gives

$y(t)=\dfrac{7t^2}2+C\,L^{-1}\left[\dfrac{e^{s^2}}{s^3}\right]$

I don't know whether the remaining inverse transform can be resolved, but using the principle of superposition, we know that $\frac{7t^2}2$ is one solution to the original ODE.

$y(t)=\dfrac{7t^2}2\implies y'(t)=7t\implies y''(t)=7$

Substitute these into the ODE to see everything checks out:

$2\cdot7+t\cdot7t-2\cdot\dfrac{7t^2}2=14$

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3 years ago