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3 years ago

6

The price of a gallon of milk was $2.65 the price Rose y dollars the price dropped $0.15Rose by $0.05 which expression represent

s the current price of milk

1 answer:

Ipatiy [6.2K]3 years ago

5 0

2.65 - 0.15 - 0.05

I hope you get it right

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A right triangle has sides 10 and 24. Use the Pythagorean Theorem to find the length of the hypotenuse.

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Evaluate the following definite integral

mihalych1998 [28]

Answer:

$\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = \frac{e}{3}$

General Formulas and Concepts:

<u>Symbols</u>

e (Euler's number) ≈ 2.71828

<u>Algebra I</u>

Exponential Rule [Multiplying]: $\displaystyle b^m \cdot b^n = b^{m + n}$

<u>Calculus</u>

Differentiation

Derivatives
Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integrals
Definite Integrals
Integration Constant C

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

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

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

U-Substitution

U-Solve

Integration by Parts: $\displaystyle \int {u} \, dv = uv - \int {v} \, du$

[IBP] LIPET: Logs, inverses, Polynomials, Exponentials, Trig

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

$\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx$

<u>Step 2: Integrate Pt. 1</u>

[Integrand] Rewrite [Exponential Rule - Multiplying]: $\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = \int\limits^1_0 {x^5e^{x^3}e} \, dx$
[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = e\int\limits^1_0 {x^5e^{x^3}} \, dx$

<u>Step 3: Integrate Pt. 2</u>

<em>Identify variables for u-solve.</em>

Set <em>u</em>: $\displaystyle u = x^3$
[<em>u</em>] Differentiate [Basic Power Rule]: $\displaystyle du = 3x^2 \ dx$
[<em>u</em>] Rewrite: $\displaystyle x = \sqrt[3]{u}$
[<em>du</em>] Rewrite: $\displaystyle dx = \frac{1}{3x^2} \ du$

<u>Step 4: Integrate Pt. 3</u>

[Integral] U-Solve: $\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = e\int\limits^1_0 {x^5e^{(\sqrt[3]{u})^3}\frac{1}{3x^2}} \, du$
[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = \frac{e}{3}\int\limits^1_0 {x^5e^{(\sqrt[3]{u})^3}\frac{1}{x^2}} \, du$
[Integral] Simplify: $\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = \frac{e}{3}\int\limits^1_0 {x^3e^u} \, du$
[Integrand] U-Solve: $\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = \frac{e}{3}\int\limits^1_0 {ue^u} \, du$

<u>Step 5: integrate Pt. 4</u>

<em>Identify variables for integration by parts using LIPET.</em>

Set <em>u</em>: $\displaystyle u = u$
[<em>u</em>] Differentiate [Basic Power Rule]: $\displaystyle du = du$
Set <em>dv</em>: $\displaystyle dv = e^u \ du$
[<em>dv</em>] Exponential Integration: $\displaystyle v = e^u$

<u>Step 6: Integrate Pt. 5</u>

[Integral] Integration by Parts: $\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = \frac{e}{3} \bigg[ ue^u \bigg| \limits^1_0 - \int\limits^1_0 {e^u} \, du \bigg]$
[Integral] Exponential Integration: $\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = \frac{e}{3} \bigg[ ue^u \bigg| \limits^1_0 - e^u \bigg| \limits^1_0 \bigg]$
Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = \frac{e}{3}[ e - e ]$
Simplify: $\displaystyle \int\limits^1_0 {x^5e^{x^3 + 1}} \, dx = \frac{e}{3}$

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

Unit: Integration

Book: College Calculus 10e

8 0

3 years ago

PLS HELP ME ASAP FOR 12 AND 14!! (MUST SHOW WORK!!) + LOTS OF POINTS!!

nignag [31]

R for ?
14) 96x1=24r
96=24r
r= 4

5 0

3 years ago

Read 2 more answers

could you possibly help me with this question? (its not part of a graded assignment, just a review from an online course of mine

Virty [35]

Let:

x = Pounds of walnuts in the mix.

Each pound of walnuts costs $0.80. thus x pounds of walnuts cost 0.8x dollars.

Each pound of cashews costs $1.25 and the mix will contain 8 pounds of cashews, so the cost is 8*$1.25 = $10

The total cost of the mix is, therefore: 0.8x + 10 dollars.

We are also given the pound of mix costs $1.00 and we have a total of 8 + x pounds, so the total cost of the mix is 1*(8 + x) dollars.

Equating both costs:

0.8x + 10 = 1*(8 + x)

Operating:

0.8x + 10 = 8 + x

Subtracting x and 10:

0.8x - x = 8 - 10

Simplifying:

-0.2x = -2

Dividing by -0.2:

x = -2/(-0.2)

x = 10

Answer: 10 pounds

8 0

1 year ago