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3 years ago

99 POINTS AND IF CORRECT, WILL GIVE BRAINLYIST

Mathematics

2 answers:

Arisa [49]3 years ago

8 0

The functions are both increasing

the function for plan II has a greater unit rate

The function for plan I has a greater y intercept

Vlada [557]3 years ago

8 0

Answer: The functions are both increasing.

The function for plan II has a greater unit rate.

The function for plan I has a greater y-intercept.

Step-by-step explanation:

According to the given question we have two functions.

Function 1. $y=12,000+400x$

Function 2. $y=11,000+420x$

Both are written in intercept form of linear equation $y=mx+c$ , where m is the slope of line or rate of change of y w.r.t. x.

Slope of function 1. = 400

i.e. Unit rate = $400 per month

Slope of function 2. = 420

i.e. Unit rate = $420 per month

⇒The function for plan II has a greater unit rate.

As both has positive slopes.

∴ Both functions are increasing functions.

For y intercept , put x=0 in the functions.

The y-intercept of function 1 = $12000

The y-intercept of function 2= $11000

⇒The function for plan I has a greater y-intercept.

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2 years ago

Help evaluating the indefinite integral

Dafna11 [192]

Answer:

$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }$

General Formulas and Concepts:
Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]:
$\displaystyle (cu)' = cu'$

Derivative Property [Addition/Subtraction]:
$\displaystyle (u + v)' = u' + v'$
Derivative Rule [Basic Power Rule]:

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Integration Rule [Reverse Power Rule]:
$\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Property [Multiplied Constant]:
$\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Integration Methods: U-Substitution and U-Solve

Step-by-step explanation:

Step 1: Define

Identify given.

$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx$

Step 2: Integrate Pt. 1

Identify variables for u-substitution/u-solve.

Set u:
$\displaystyle u = 4 - x^2$
[u] Differentiate [Derivative Rules and Properties]:
$\displaystyle du = -2x \ dx$
[du] Rewrite [U-Solve]:
$\displaystyle dx = \frac{-1}{2x} \ du$

Step 3: Integrate Pt. 2

[Integral] Apply U-Solve:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-x}{2x\sqrt{u}}} \, du$
[Integrand] Simplify:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-1}{2\sqrt{u}}} \, du$
[Integral] Rewrite [Integration Property - Multiplied Constant]:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \frac{-1}{2} \int {\frac{1}{\sqrt{u}}} \, du$
[Integral] Apply Integration Rule [Reverse Power Rule]:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = -\sqrt{u} + C$
[u] Back-substitute:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }$

∴ we have used u-solve (u-substitution) to find the indefinite integral.

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Learn more about integration: brainly.com/question/27746495

Learn more about Calculus: brainly.com/question/27746485

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

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2 years ago

Maria bought a blouse on sale for 30% off. The sale price was $28.76. What was the original price? Write an equation to model th

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Step-by-step explanation:

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