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3 years ago

8

Tom is thinking of two numbers,a and b,where a is a positive and b is negative. write to inequalities that Tim can use to compar

e a and b
Explain

1 answer:

Advocard [28]3 years ago

8 0

Answer:a﹥0﹥b

Step-by-step explanation:

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$\dfrac{6}{9}=\dfrac{x+3}{3+9}\\
\dfrac{2}{3}=\dfrac{x+3}{12}\\
3(x+3)=24\\
x+3=8\\
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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

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

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

$u'=u^2-1$

which is separable as

$\dfrac{u'}{u^2-1}=1$

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

$\dfrac{u'}2\left(\frac1{u-1}-\frac1{u+1}\right)=1$

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

$\dfrac12(\ln|u-1|-\ln|u+1|)=t+C$

Solve for $u$ :

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

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

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

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

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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 $C$ :

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3 years ago

What is the value of t in the equation 3(2t + 5) = 5t + 25?

11Alexandr11 [23.1K]

<span>3(2t + 5) = 5t + 25
6t + 15 = 5t + 25
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3 years ago

Which ordered pair is a solution of the equation 2x − y = 9?

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You can try by plugging each ordered pair and seeing if the equation comes out true.

(5, 1)

2 * 5 - 1 = 9

That's correct so C is the correct answer.

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