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2 years ago

Simplify the complex fraction. 2 1/2 / 5/8

Mathematics

2 answers:

lbvjy [14]2 years ago

5 0

First do 2 1/2 / 5/8
5/2/ 5/8=2/5 * 5/8=1/4
now you can do anything with 1/4 so
your answer is 1/4

Masja [62]2 years ago

3 0

They stay the same because 2 can’t go into 21 evenly not 5 can go into 8 evenly

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What is the value of y in the equation 5x+2y=20, when x=0.3

Rasek [7]

5x+2y=20

Substitute 0.3 for x

5(0.3)+2y=20

Multiply 5 by 0.3

1.5+2y=20

Subtract 1.5 from both sides

2y=18.5

Divide 2 on both sides

Final Answer: y= 9.25

8 0

2 years ago

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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svet-max [94.6K]

Answer:

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