2 years ago

Evaluate the equation: 1/24√26√2

Mathematics

1 answer:

Vanyuwa [196]2 years ago

6 0

Here is what I got
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Find a solution x = x(t) of the equation x′ + 2x = t2 + 4t + 7 in the form of a quadratic function of t, that is, of the form x(

Temka [501]

The particular quadratic solution to the ODE is found as follows:

$x=at^2+bt+c$
$x'=2at+b$

$(2at+b)+2(at^2+bt+c)=t^2+4t+7$
$2at^2+(2a+2b)t+(b+2c)=t^2+4t+7$

$\begin{cases}2a=1\\2(a+b)=4\\b+2c=7\end{cases}\implies a=\dfrac12,b=\dfrac32,c=\dfrac{11}4$

Note that there's also the fundamental solution to account for, which is obtained from the characteristic equation for the ODE:

$x'+2x=0\implies r+2=0\implies r=-2$

so that $x_c=Ce^{-2t}$ is a characteristic solution to the ODE, and the general solution would be

$x=Ce^{-2t}+\dfrac{t^2}2+\dfrac{3t}2+\dfrac{11}4$

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3 years ago

<img src="https://tex.z-dn.net/?f=7%20-%209w%20%3D%20%20-%2029%20" id="TexFormula1" title="7 - 9w = - 29 " alt="7 - 9w = - 29

Oksana_A [137]

7 - 9w = - 29

Subtract 7 from both sides

- 9w = - 36

Divide by - 9 on both sides

w = 4

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2 years ago

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WILL GIVE BRAINLIEST anitas and caseys bills do not vary from month to month. anita pays 80 more than casey does each month. ove

Mrac [35]

Answer:

1520/4=380 per month

Step-by-step explanation:

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2 years ago

Just need help with changing the y-intercepts of the asymptotes :) please help asap!!!

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2 years ago

Find the 100th term of the following arithmetic sequence <br> 5.5, 6, 6.5, 7, ...

AysviL [449]

Answer:

Step-by-step explanation:

The n-th term of an arithmetic sequence is given by the formula ...

an = a1 + d(n -1)

where a1 is the first term (5.5) and d is the common difference (0.5).

So, the n-th term is ...

an = 5.5 +0.5(n -1) = 5.0 +0.5n

For n = 100, the term is ...

a100 = 5.0 +0.5(100) = 55

The 100th term of the sequence is 55.

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3 years ago

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Evaluate the equation: 1/24√26√2