Find all the powers of 3 in the range 3 through 1,000.

2 answers:

6 0

3^1=3
3^2=9

lets skip a couple and guess
3^10=59049 oops too high

3^6=729 good
3^7=2187 too high so

the answers are
3^1
3^2
3^3
3^4
3^5
3^6

5 0

3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243
3^6 = 729

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alexandr402 [8]

C; the first and last letters in each group is connected, after U and V being first and last it should be W and X being first and last.

3 0

2 years ago

zzz [600]

Answer:

B) 4√2

General Formulas and Concepts:

Calculus

Differentiation

Basic Power Rule:

Parametric Differentiation

Integration

Arc Length Formula [Parametric]: $\displaystyle AL = \int\limits^b_a {\sqrt{[x'(t)]^2 + [y(t)]^2}} \, dx$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \left \{ {{x = t - cos(t)} \atop {y = 1 - sin(t)}} \right.$

Interval [0, π]

Step 2: Find Arc Length

[Parametrics] Differentiate [Basic Power Rule, Trig Differentiation]: $\displaystyle \left \{ {{x' = 1 + sin(t)} \atop {y' = -cos(t)}} \right.$
Substitute in variables [Arc Length Formula - Parametric]: $\displaystyle AL = \int\limits^{\pi}_0 {\sqrt{[1 + sin(t)]^2 + [-cos(t)]^2}} \, dx$
[Integrand] Simplify: $\displaystyle AL = \int\limits^{\pi}_0 {\sqrt{2[sin(x) + 1]} \, dx$
[Integral] Evaluate: $\displaystyle AL = \int\limits^{\pi}_0 {\sqrt{2[sin(x) + 1]} \, dx = 4\sqrt{2}$