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2 years ago

Entrance to a state park costs $6 per vehicle, plus $2 per person in the vehicle the cost for a bus with 50 people?

Mathematics

1 answer:

ExtremeBDS [4]2 years ago

3 0

Answer:

$106

Step-by-step explanation:

So, this is what we know:

$6 per vehicle (1 bus) + $2 per person (50 people)

Here is the solution:

= $6 + $100

= $106

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B) 2 dogs.

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Step-by-step explanation:

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3 years ago

The weekly fee for staying at the Pleasant Lake Campground is $20 per vehicle and $10 per person. Last year, weekly fees were pa

natta225 [31]

For this case we have the following variables:
v: number of vehicles
p: number of people
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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]:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integrals

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

5 0

1 year ago

State the equation of the following graphs. Someone please help ASAP

Vaselesa [24]

Answer

y = 1(x +1) - 3

Explanation

A quadratic equation of the form y = ax^2 + bx + c

This written in complete the square form provides you with the vertex (either a maximum or minimum point depending on the equation).

This results in y = a(x + p) + q

Where - p is the x value and q is the y value of turning point.

For graph 22, x = -1 and y = -3

Therefore, the equation is of the form

y = a(x + 1) - 3 (*)

We still need the value a, this can be obtained by using the y-intercept we are given.

We are told x = 0 when y = -2

Substitute this in (*) equation:

-2 = a(0+1) - 3

-2 = a - 3

a = 1

Therefore final equation is

y = 1(x +1) - 3

This should provide you with the train of thought of how the second question should also be tackled.

If unsure about why the equation
y = a(x + p) + q gives the vertex ask in comments I will respond

4 0

2 years ago