Answer:
r = 9.8475 in
Step-by-step explanation:
We assume that the ball is spherical.
The volume of a spherical ball is:
We know that:
Then
Below is the graph of the cubic function
The depth of the box is 2 inches. How much cardboard is needed to create the box? NEED BY TOMORROW MORNING!!!!
1 answer:
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According to the <em>compound interest</em> model, we find the following results: I) x ≈ 11.5 yr, C' = $ 101317.36, II) r ≈ 7.4 %, x ≈ 9.8 yr, III) C = $ 7626.38, x ≈ 8.6 yr, IV) r ≈ 6.5 %, C = $ 12801.61
<h3>How to determined all the variables associated with compound interest</h3>
<em>Compound</em> interest describes the <em>capital</em> gain in term of <em>deposited</em> capital and the consideration that such capital is increased continuously in time. The compound interest model is shown below:
C' = C · (1 + r/100)ˣ (1)
Where:
- C - Initial capital
- C' - Current capital
- r - Interest rate, in percentage.
- t - Time, in years
The <em>doubling</em> time (x) is the period needed for a capital to be doubled. It is described by the following expression based on (1):
x = (㏒ 2)/[㏒ (1 + r/100)] (2)
Now we proceed to calculate each missing variable:
Case I - Doubling time
x = (㏒ 2)/[㏒ (1 + 6.2/100)]
x ≈ 11.5
Case I - Current capital
C' = 75000 · (1 + 6.2/100)⁵
C' = 101317.36
Case II - Interest rate
r ≈ 7.4
Case II - Doubling time
x = (㏒ 2)/[㏒ (1 + 7.3/100)]
x ≈ 9.8
Case III - Initial capital
C = 11414.71/(1 + 8.4/100)⁵
C = 7626.38
Case III - Doubling time
x = (㏒ 2)/[㏒ (1 + 8.4/100)]
x ≈ 8.6
Case IV - Interest rate
r ≈ 6.5
Case IV - Initial capital
C = 17539.32/(1 + 6.5/100)⁵
C = 12801.61
To learn more on compound interest: brainly.com/question/14295570
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Answer:
g'(0) = 0
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
- Left to Right
<u>Algebra I</u>
- Function Notation
<u>Pre-Calculus</u>
- Unit Circle
<u>Calculus</u>
- Derivatives
- Derivative Notation
- The derivative of a constant is equal to 0
- Derivative Property:
- Trig Derivative:
Step-by-step explanation:
<u>Step 1: Define</u>
g(x) = 8 - 10cos(x)
x = 0
<u>Step 2: Differentiate</u>
- Differentiate [Trig]: g'(x) = 0 - 10[-sin(x)]
- Simplify Derivative: g'(x) = 10sin(x)
<u>Step 3: Evaluate</u>
- Substitute in <em>x</em>: g'(0) = 10sin(0)
- Evaluate Trig: g'(0) = 10(0)
- Multiply: g'(0) = 0