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3 years ago

8

Express the function graphed on the axes below as a piecewise function.

1 answer:

N76 [4]3 years ago

4 0

Answer:

f(x) =

if x ≤ -3, -2 + 1

if x > 1, 2x - 8

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Eliott is 63 inches tall, which is 9 inches taller than his cousin,Jackson. Write and solve an addition equation to find Jackson

olasank [31]

To find Jackson's height, you subtract 9 from 63 which gives you 54. 63-9=54

8 0

3 years ago

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

$u'=u^2-1$

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 $u$ :

$\dfrac12\ln\left|\dfrac{u-1}{u+1}\right|=t+C$

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

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

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

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

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

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

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

3 0

3 years ago

a calculator is listed for $110 and is on clearence for 35% off. sales tax is 7%. what is the cost of the calculator

goldfiish [28.3K]

Answer:

$76.51

Step-by-step explanation:

The price after discounting is (1.00 - .35)($110), or 0.65($110) = $71.50.

The price after 7% sales tax has been added in is

(1.00 + 0.07)($71.50) = $76.51.

6 0

3 years ago

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What is 4.48 written as a quotient of two integers

antiseptic1488 [7]

336 divided by 75 which equals 4.48

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3 years ago

Simplify Negative 3 over 2 ÷ 9 over 6 . (5 points) -4 -1 4 1

DiKsa [7]

Answer:

Step-by-step explanation:

$\frac{3}{2}$ ÷ $\frac{9}{6}$ = $\frac{3}{2}*\frac{6}{9}\\$

= $\frac{18}{18}$

= 1

Use KCF method,

Keep the first number.

Change the division to multiplication

Flip the second number

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2 years ago

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