Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtract Property of Equality
<u>Geometry</u>
Volume of a Cone:
Diameter: d = 2r
<u>Calculus</u>
Derivatives
Derivative Notation
Differentiating with respect to time
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Step-by-step explanation:
<u>Step 1: Define</u>
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<u>Step 2: Rewrite Volume Formula</u>
<em>We need to rewrite the cone volume formula in terms of height h only.</em>
Base <em>b</em> = diameter <em>d</em> of the circular base
- Define: b = d
- Substitute: b = 2r
We are given that the base of the cone is the same as the height.
- Define: b = 2r
- Substitute: h = 2r
Now solve for height.
- Divide 2 on both sides: h/2 = r
- Rewrite expression: r = h/2
Now find new volume formula.
- Define [VC]:
- Substitute:
- Exponents:
- Multiply:
We now have the same volume formula in terms of height <em>h</em> only.
<u>Step 3: Differentiate</u>
- Basic Power Rule:
- Simplify:
<u>Step 4: Solve for height rate</u>
- Substitute:
- Isolate <em>h </em>rate:
- Exponents:
- Multiply:
- Divide:
- Rewrite:
Here this tells us that the rate at which the height is moving at a rate of 0.101859 feet per minute.
Answer:
The real question is, why are they trick-or-treating in March?
Step-by-step explanation:
The answer is 4.
Answer:
6
Step-by-step explanation:
the answer is 6 because you can just count the sides.
Answer:
b. 0.09
Step-by-step explanation:
0.09 is the only one smaller than 0.59
0.59>0.09
Assuming these are dimensions of a rectangle, and you are interested in the perimeter and area, you can use the appropriate formulas.
P = 2(L +W)
P = 2(7 cm +7 cm) = 28 cm
A = L*W
A = (7 cm)*(7 cm) = 49 cm²