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Natalija [7]
3 years ago
5

Eva opened a bank account. She deposited $68.40 into her account every month for 20 months. She used $42.40 every month to pay f

or craft classes. After 20 months, she used 1 over 2 of the total money left in her account to go to a crafting summer camp. What is the total amount of money Eva spent to go to the summer camp?
Mathematics
2 answers:
ioda3 years ago
8 0
I think it would be $1,368....hope its right...
Anna11 [10]3 years ago
5 0
260$ its 68.40 - 42.40 x 20 divided b 2
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Help differentiate this
Arte-miy333 [17]

Answer:

\displaystyle y' = 20x^3 + 6x^2 + 70x + 9

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Distributive Property

<u>Algebra I</u>

  • Terms/Coefficients
  • Expand by FOIL
  • Functions
  • Function Notation

<u>Calculus</u>

Derivatives

Derivative Notation

Derivative Property [Multiplied Constant]:                                                              \displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)

Derivative Property [Addition/Subtraction]:                                                            \displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹  

Derivative Rule [Product Rule]:                                                                                \displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

<em />\displaystyle y = (x^3 + 7x - 1)(5x + 2)<em />

<em />

<u>Step 2: Differentiate</u>

  1. Product Rule:                                                                                                    \displaystyle y' = \frac{d}{dx}[(x^3 + 7x - 1)](5x + 2) + (x^3 + 7x - 1)\frac{d}{dx}[(5x + 2)]
  2. Basic Power Rule [Derivative Property - Addition/Subtraction]:                   \displaystyle y' = (3x^{3 - 1}+ 7x^{1 - 1} - 0)(5x + 2) + (x^3 + 7x - 1)(5x^{1 - 1} + 0)
  3. Simplify:                                                                                                             \displaystyle y' = (3x^2+ 7)(5x + 2) + 5(x^3 + 7x - 1)
  4. Expand:                                                                                                             \displaystyle y' = 15x^3 + 6x^2 + 35x + 14 + 5(x^3 + 7x - 1)
  5. [Distributive Property] Distribute 5:                                                                 \displaystyle y' = 15x^3 + 6x^2 + 35x + 14 + 5x^3 + 35x - 5
  6. Combine like terms:                                                                                         \displaystyle y' = 20x^3 + 6x^2 + 70x + 9

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

Unit: Derivatives

Book: College Calculus 10e

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Answer:

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