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3 years ago

8

Given fx) = 10– 2x, find (7). оооо 7 56

1 answer:

damaskus [11]3 years ago

8 0

Answer:

Substitute the value of 7 into the variable x. Then solve the equation.

f(7) = 10 - 2(7)

f(7) = 10 - 14

<h2><em><u>f(7) = -4 is the answer.</u></em></h2>

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2 points) Sometimes a change of variable can be used to convert a differential equation y′=f(t,y) into a separable equation. One

Stells [14]

$y'=(t+y)^2-1$

Substitute $u=t+y$ , so that $u'=y'$ , and

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which is separable as

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Integrate both sides with respect to $t$ . For the integral on the left, first split into partial fractions:

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$\displaystyle\int\frac{u'}2\left(\frac1{u-1}-\frac1{u+1}\right)\,\mathrm dt=\int\mathrm dt$

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$\ln\left|1-\dfrac2{u+1}\right|=2t+C$

$1-\dfrac2{u+1}=e^{2t+C}=Ce^{2t}$

$\dfrac2{u+1}=1-Ce^{2t}$

$\dfrac{u+1}2=\dfrac1{1-Ce^{2t}}$

$u=\dfrac2{1-Ce^{2t}}-1$

Replace $u$ and solve for $y$ :

$t+y=\dfrac2{1-Ce^{2t}}-1$

$y=\dfrac2{1-Ce^{2t}}-1-t$

Now use the given initial condition to solve for $C$ :

$y(3)=4\implies4=\dfrac2{1-Ce^6}-1-3\implies C=\dfrac3{4e^6}$

so that the particular solution is

$y=\dfrac2{1-\frac34e^{2t-6}}-1-t=\boxed{\dfrac8{4-3e^{2t-6}}-1-t}$

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2 years ago

(35 ÷ 5) - 5<br><br> show work!! help

saveliy_v [14]

Answer:

Step-by-step explanation:

(35/5) - 5

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