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3 years ago

6

Given this recursive rule : a^n=a^n-1 +6 where your a^1 =-13 . Find the next 4 terms in this sequence. Show your work to plzzzzz

z help idk this I’m terrible at math...thx

1 answer:

Anuta_ua [19.1K]3 years ago

7 0

Answer:

I think its c But i may be wrong

Step-by-step explanation:

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The volume of a sphere is decreasing at a constant rate of 116 cubic centimeters per second. At the instant when the volume of t

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Answer:

$\frac{dr}{dt} = -1.325 \ cm/s$

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

<u>Calculus</u>

Derivatives

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Taking Derivatives with respect to time

Step-by-step explanation:

<u>Step 1: Define</u>

Given:

<u /> $V = \frac{4}{3} \pi r^3$ <u />

<u /> $\frac{dV}{dt} = -116 \ cm^3/s$ <u />

<u /> $V = 77 \ cm^3$ <u />

<u />

<u>Step 2: Solve for </u><em><u>r</u></em>

Substitute: $77 = \frac{4}{3} \pi r^3$
Isolate <em>r</em> term: $\frac{77}{\frac{4}{3} \pi} = r^3$
Isolate <em>r</em>: $\sqrt[3]{\frac{77}{\frac{4}{3} \pi}} = r$
Evaluate: $2.63917 = r$
Rewrite: $r = 2.63917 \ cm$

<u>Step 3: Differentiate</u>

<em>Differentiate the Volume Formula with respect to time t.</em>

Define: $V = \frac{4}{3} \pi r^3$
Differentiate [Basic Power Rule]: $\frac{dV}{dt} = \frac{4}{3} \pi \cdot 3 \cdot r^{3-1} \cdot \frac{dr}{dt}$
Simplify: $\frac{dV}{dt} = 4 \pi r^2 \cdot \frac{dr}{dt}$

<u>Step 4: Find radius rate</u>

Substitute in variables: $-116 \ cm^3/sec = 4 \pi (2.63917 \ cm)^2 \cdot \frac{dr}{dt}$
Isolate dr/dt rate: $\frac{-116 \ cm^3/s}{4 \pi (2.63917 \ cm)^2} = \frac{dr}{dt}$
Evaluate: $-1.3253 \ cm/s = \frac{dr}{dt}$
Rewrite: $\frac{dr}{dt} = -1.3253 \ cm/s$
Round: $\frac{dr}{dt} = -1.325 \ cm/s$

Our radius is decreasing at a rate of -1.325 cm per second.

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