wonderbread091

Let's start by solving for p and q using the given equations:

Given:

x = va(sinu + cosv)

y = va(cosu - sinv)

z = 1 + sin(u - v)

To find p and q, we need to eliminate u and v from the equations. Here's how we can do it:

1. Square both sides of the first equation:

x^2 = v^2a^2(sinu + cosv)^2

2. Square both sides of the second equation:

y^2 = v^2a^2(cosu - sinv)^2

3. Add the squared equations together:

x^2 + y^2 = v^2a^2(sinu + cosv)^2 + v^2a^2(cosu - sinv)^2

4. Expand and simplify the equation:

x^2 + y^2 = v^2a^2(sin^2u + 2sinucosv + cos^2v) + v^2a^2(cos^2u - 2sinvcosu + sin^2v)

5. Combine like terms:

x^2 + y^2 = v^2a^2(sin^2u + cos^2u + sin^2v + cos^2v) + 2v^2a^2(sinucosv - sinvcosu)

6. Simplify further using trigonometric identities:

x^2 + y^2 = v^2a^2 + 2v^2a^2(sin(u + v))

7. Now, let's look at the equation for z:

z = 1 + sin(u - v)

8. Square both sides of the equation:

z^2 = (1 + sin(u - v))^2

9. Expand and simplify the equation:

z^2 = 1 + 2sin(u - v) + sin^2(u - v)

10. Substitute the value of z from the original equation:

z^2 = 1 + 2sin(u - v) + sin^2(u - v)

11. Simplify further:

z^2 = 1 + 2sin(u - v) + (1 - cos^2(u - v))

12. Simplify even more:

z^2 = 2 - cos^2(u - v) + 2sin(u - v)

13. Rearrange the equation:

cos^2(u - v) = 2 - z^2 - 2sin(u - v)

14. Substitute the value of sin(u - v) from the equation derived in step 6:

cos^2(u - v) = 2 - z^2 - 2v^2a^2

15. Take the square root of both sides:

cos(u - v) = ±√(2 - z^2 - 2v^2a^2)

16. Now, let's find sin(u - v) using the equation derived in step 6:

sin(u - v) = (x^2 + y^2 - v^2a^2) / (2va^2)

17. Substitute the values of cos(u - v) and sin(u - v) into the equation for x:

x = va(sinu + cosv)

18. Substitute the values of sin(u - v) and cos(u - v) into the equation for y:

y = va(cosu - sinv)

19. Simplify the equations further and solve for p and q:

p = arcsin((x - y) / (2va))

q = arccos((x + y) / (2va))

These are the values of p and q based on the given equations. Please note that there may be other solutions or constraints depending on the specific values of x, y, z, v, and a.

Two boxes (24 kg and 62 kg) are being pushed across a horizontal frictionless surface. The 47-N pushing force is horizontal and is applied to the 24-kg box, which in turn pushes against the 62-kg box. Find the magnitude of the force that the 24-kg box applies to the 62-kg box.

A 140.0 kg box is pushed by a horizontal force F at constantspeed up a frictionless ramp which makes an angle of 29.0 deg withthe horizontal. Find the magnitude of the applied force F.

A lab cart is moving on a straight horizontal frictionless track. The above graph of velocity versus time for the cart is given above. During some intervals a force is applied to the cart. Assume the cart has a mass of 0.5 kg. Rank the magnitude of the applied force for each of the following intervals.

Find the derivative of the polynomial;  

A star maintains its internal thermal pressure this is possible due to which of the following energy sources.

A) Balance of gravity and outward pressure

B) presence of helium and fission reaction

C) formation of black hole and supernova

D) chemical reactions and contraction due to gravity

E) chemical reaction and brightness

HELPPPP!!

Create a multimedia presentation about the pros and cons of using fission as an energy source. 

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