Mathematics, 25.06.2021 20:00 smagallanes

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Answer from: kyrabrown33

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Distributive Property

Algebra I

Terms/CoefficientsFunctionsFunction Notation

Calculus

Limits

Limit Rule [Constant]: $\displaystyle \lim_{x \to c} b = b$

Definition of a Derivative: $\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}$

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 2x - 5

Step 2: Differentiate

[Limit] Substitute in x [Function f(x)]: $\displaystyle \lim_{\triangle x \to 0} \frac{[2(x + \triangle x) + 5] - f(x)}{\triangle x}$ [Limit] Substitute in function: $\displaystyle \lim_{\triangle x \to 0} \frac{[2(x + \triangle x) + 5] - (2x + 5)}{\triangle x}$ [Distributive Property] Distribute 2: $\displaystyle \lim_{\triangle x \to 0} \frac{[2x + 2\triangle x + 5] - (2x + 5)}{\triangle x}$ [Distributive Property] Distribute negative: $\displaystyle \lim_{\triangle x \to 0} \frac{2x + 2\triangle x + 5 - 2x - 5}{\triangle x}$ [Subtraction] Combine like terms: $\displaystyle \lim_{\triangle x \to 0} \frac{2\triangle x}{\triangle x}$ [Division] Simplify: $\displaystyle \lim_{\triangle x \to 0} 2$ Evaluate limit [Limit Rule - Constant]: $\displaystyle 2$

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

Unit: Derivatives

Book: College Calculus 10e

Answer from: Quest

56 ur welcome:

Answer from: Quest

answer: the answer is (b) amie should have multiplied

$54~\textup{m}^3~\textup{by}~\dfrac{4}{3}\pi.$

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

$v_s=\pi r^2h=\pi r^3,$

and the volume of the cylinder will be

$v_c=\dfrac{4}{3}\pi r^3=54~\textup{m}^3.$

therefore, we have

$v_c=\dfrac{4}{3}v_s=\dfrac{4}{3}\times 54=72~\textup{m}^3.$

thus, ammie should have multiplied the volume of the sphere $54~\textup{m}^3~\textup{by}~\dfrac{4}{3}\pi.$

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