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netineya [11]
4 years ago
12

Help with Math!! z - 5 ------ = -1 7 z = ?

Mathematics
1 answer:
strojnjashka [21]4 years ago
7 0
Z = -2.

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Set up, but do not evaluate, the integral that represents the length of the curve given by
netineya [11]

Answer:

L = ∫₀²ᵖⁱ √((1 − sin t)² + (1 − cos t)²) dt

Step-by-step explanation:

Arc length of a parametric curve is:

L = ∫ₐᵇ √((dx/dt)² + (dy/dt)²) dt

x = t + cos t, dx/dt = 1 − sin t

y = t − sin t, dy/dt = 1 − cos t

L = ∫₀²ᵖⁱ √((1 − sin t)² + (1 − cos t)²) dt

Or, if you wish to simplify:

L = ∫₀²ᵖⁱ √(1 − 2 sin t + sin²t + 1 − 2 cos t + cos²t) dt

L = ∫₀²ᵖⁱ √(3 − 2 sin t − 2 cos t) dt

7 0
4 years ago
Look at the picture.
Zanzabum

Answer:

(4, 8) where =(x, y)

Step-by-step explanation:

x + 4(-x + 12) = 36

x -4x + 48 = 36

-3x = -12

x = 4

4 + 4y = 36

4y = 32

y = 8

4 0
3 years ago
The harmonic motion of a particle is given by f(t) = 2 cos(3t) + 3 sin(2t), 0 ≤ t ≤ 8. (a) When is the position function decreas
iren [92.7K]

For the last part, you have to find where f'(t) attains its maximum over 0\le t\le8. We have

f'(t)=-6\sin3t+6\cos2t

so that

f''(t)=-18\cos3t-12\sin2t

with critical points at t such that

-18\cos3t-12\sin2t=0

3\cos3t+2\sin2t=0

3(\cos^3t-3\cos t\sin^2t)+4\sin t\cos t=0

\cos t(3\cos^2t-9\sin^2t+4\sin t)=0

\cos t(12\sin^2t-4\sin t-3)=0

So either

\cos t=0\implies t=\dfrac{(2n+1)\pi}2

or

12\sin^2t-4\sin t-3=0\implies\sin t=\dfrac{1\pm\sqrt{10}}6\implies t=\sin^{-1}\dfrac{1\pm\sqrt{10}}6+2n\pi

where n is any integer. We get 8 solutions over the given interval with n=0,1,2 from the first set of solutions, n=0,1 from the set of solutions where \sin t=\dfrac{1+\sqrt{10}}6, and n=1 from the set of solutions where \sin t=\dfrac{1-\sqrt{10}}6. They are approximately

\dfrac\pi2\approx2

\dfrac{3\pi}2\approx5

\dfrac{5\pi}2\approx8

\sin^{-1}\dfrac{1+\sqrt{10}}6\approx1

2\pi+\sin^{-1}\dfrac{1+\sqrt{10}}6\approx7

2\pi+\sin^{-1}\dfrac{1-\sqrt{10}}6\approx6

4 0
3 years ago
Answer 8 and 9 for 10+ points
castortr0y [4]

Answer:

question 8 : it is equal to 0

Question 9 : 4+5\sqrt{2}

Step-by-step explanation:

= \sqrt{7} -\sqrt{28}\\2\sqrt{7} - \sqrt{4x7}\\2\sqrt{7} - 2\sqrt{7}\\0\\\sqrt{2} (5+\sqrt{8})\\5\sqrt{2} + \sqrt{2*8}\\5\sqrt{2} + 4\\4 + 5\sqrt{2}

4 0
3 years ago
The ratio of red to green tiles in a pattern is 2:3<br> What fraction of the tiles are green
baherus [9]

Answer:

3 /5

Step-by-step explanation:

Given that:

Ratio of red to green to tiles = 2:3

Red = 2

Green = 3

Total sum of each part (red + green) = (2 + 3) = 5

Fraction of green tiles :

Green / total sum

3 / 5

8 0
3 years ago
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