Write 29/7 as a mixed number.

Mathematics

2 answers:

Crazy boy [7]4 years ago

5 0

Answer:

4 1/7

Step-by-step explanation

Basically the line is a division line so it would be 29 divided by 7. The answer would be 4 with one left over. I tried to make that make sence if it doesn't sorry.

Serhud [2]4 years ago

5 0

Answer:

4 1/7

Step-by-step explanation:

The first thing you want to do is see how many times 29 can go into seven. To do that, review your multiplication facts. We know that 7, 14, 21, 28, and 35 are all multiples of seven. Since 35 is too big, we take the smaller number, 28. 7 times 4 is 28, so we add 4 to the whole numbers and subtract 28 from 29, leaving us with 4 1/7

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What is the length of the curve with parametric equations x = t - cos(t), y = 1 - sin(t) from t = 0 to t = π? (5 points)

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Answer:

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General Formulas and Concepts:

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Differentiation

Derivatives
Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Parametric Differentiation

Integration

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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: $\displaystyle AL = \int\limits^{\pi}_0 {\sqrt{2[sin(x) + 1]} \, dx = 4\sqrt{2}$