3 years ago

A number decreased by 25

Mathematics

1 answer:

Irina18 [472]3 years ago

6 0

It would be for example: f-25

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Sergeu [11.5K]

3 quarts, because 12 is how many cups you have, and there are 4 cups in a quart. 12/4 is 3, so 3 quarts.

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3 years ago

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Leno4ka [110]

Answer:b,they are not proportional

Step-by-step explanation:

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1 year ago

(3t + 7)−2(6.3t + 4) * 15.6t − 1 15.6t + 15 −9.6t + 15 −9.6t - 1

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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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3 years ago