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MArishka [77]
3 years ago
15

AP Calculus Help Please!

Mathematics
1 answer:
ivanzaharov [21]3 years ago
4 0
4. By the fundamental theorem of calculus,

\displaystyle\frac{\mathrm dg(x)}{\mathrm dx}=\frac{\mathrm d}{\mathrm dx}\int_{-2}^xf(t)\,\mathrm dt=f(x)

g(x) is increasing on those intervals where g'(x)=\dfrac{\mathrm dg(x)}{\mathrm dx}>0. So you have

g'(x)=f(x)=\begin{cases}3&\text{for }-3\le x

which is clearly positive for x\in[-3,0), and in the second interval you have

-x+3>0\implies x

Together, this means g'(x)>0 for all x\in[-3,3).

5. When 0\le x\le6, f(x) reduces to -x+3, so you have

g(x)=\displaystyle\int_{-2}^xf(t)\,\mathrm dt=\int_{-2}^03\,\mathrm dt+\int_0^x(-t+3)\,\mathrm dt
g(x)=6+\left(3t-\dfrac12t^2\right)\bigg|_{t=0}^{t=x}
g(x)=6+3x-\dfrac12x^2
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What's 5.96 as a fraction
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3.6 minutes.

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Goal
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The development of the personal budget that convinces parents that one can maintain an independent living is detailed as follows using the 50: 30: 20 rule:

50% for necessities (housing, food, transportation, utilities) $740

30% for luxuries, savings, vacations, entertainment, etc. $461

20% for Emergency Funds and Retirement $335

<h3>What is a personal budget?</h3>

A personal budget is the household budget for a single person for a period.

The personal budget shows an estimate of the person's revenue and expenses over the period.

<h3>Data and Calculations:</h3>

Hourly rate of earnings = $12

Working hours per week = 40 hours

Working hours per month = 160 hours (40 x 4 weeks)

Total monthly earnings = $1,920 ($12 x 160)

Assumed tax rate = 20%

After-tax take-home pay = $1,536 ($1,920 x 1 - 20%)

<h3>Monthly Necessities:</h3>

Rent of apartment = $300

Heating = $40

Water cost = $20

Sewage bill = $10

Food = $300

Transportation = $50

Other costs = $20

Total cost for necessities = $740

Thus, the development of the personal budget shows that one can maintain an independent living from the parents as a single person.

Learn more about personal budgets at brainly.com/question/1943261

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