Help possibly?

Pre-College Issues High School Life
1

<p>I was wondering if I could get some help with the some AP calculus problems which I have to do for summer work. If you know how to do any of these, even one, a reply would be greatly appreciated. </p>

<p>*Write an equation in slope-intercept form of the line with parametric equations x = 2t+1 and y = -3t-4</p>

<p>*Write the equation for the inverse of y = arccot x. Then graph the function and its inverse.</p>

<p>*Identify the equation of the line tangent to the graph of
(x^2/25) + (y^2/4) = 1 at (3, 1.6)<br>
A. 3x+10y-25=0 B. 15x-20y-13=0 C. 3x-10y+25=0 D. 20x-15y-36=0</p>

<p>*Write the polar equation 4r = 8/cos θ in rectangular form.
A. y = 2 B. x = 2 C. x = 1/2 D. y = 1/2</p>

<p>*Which equation represents a spiral of Archimedes?
A. r = 3 θ B. r = 3 + 3 sin θ C. r = 3 cos 2θ D. r = 3 + 2 cos θ</p>

<p>*Find the rectangular coordinates of the point whose polar coordinates are
(20, 140º). Round to the nearest hundredth.</p>

<p>*Find the quotient [cos (5π/12) + i sin (5π/12)] / [2{cos (π/12) + i sin (π/12)}]. Then write the result in rectangular form.</p>

<p>*Express 4[cos (π/6)+ i sin (π/6)] in rectangular form.</p>

<p>*Determine the eccentricity of the conic section represented by
9x^2 - 16x^2 = 144.</p>

<p>Thanks!!</p>

2

<p>what grade are you?</p>

3

<p>is this a summer assignment for AP calc? I remember doing this in precalc and i hated it with a passion!!!! I would just graph them all and make an estimate lol.</p>

4

<p>im going to be a senior and im gonna be takin ap calc... i took honors pre-calc last year and we didn't get to any of this stuff, so please help if you can.</p>

5

<p>WTH
looks pretty tough</p>

6

<p>W00T, I'm bored. </p>

<p>
[quote]
*Write an equation in slope-intercept form of the line with parametric equations x = 2t+1 and y = -3t-4

[/quote]
</p>

<p>Using the first equation, obtain t = (x-1)/2. Substitute into the second:</p>

<p>y = - 3((x-1)/2) - 4 = *-3x/2 - 5/2. *</p>

<p>
[quote]
*Write the equation for the inverse of y = arccot x. Then graph the function and its inverse.

[/quote]
</p>

<p>The inverse of arccotangent is cotangent. </p>

<p>
[quote]
*Identify the equation of the line tangent to the graph of
(x^2/25) + (y^2/4) = 1 at (3, 1.6)
A. 3x+10y-25=0 B. 15x-20y-13=0 C. 3x-10y+25=0 D. 20x-15y-36=0

[/quote]
</p>

<p>The answer is A. :D</p>

<p>
[quote]
*Write the polar equation 4r = 8/cos θ in rectangular form.
A. y = 2 B. x = 2 C. x = 1/2 D. y = 1/2

[/quote]
</p>

<p>Multiply both sides by cos(θ) to get </p>

<p>4rcos(θ) = 8.</p>

<p>Divide both sides by 4 and realize that rcos(θ) is just x: </p>

<p>rcos(θ) = 2
x = 2, or B. </p>

<p>
[quote]
*Which equation represents a spiral of Archimedes?
A. r = 3 θ B. r = 3 + 3 sin θ C. r = 3 cos 2θ D. r = 3 + 2 cos θ

[/quote]
</p>

<p>The answer is A.</p>

<p>
[quote]
*Find the rectangular coordinates of the point whose polar coordinates are
(20, 140º). Round to the nearest hundredth.

[/quote]
</p>

<p>This point is in the second quadrant. Think of the part in the second quadrant with an angle of 50 degrees left of the y-axis. It is a triangle. We know θ, and we have the hypotenuse. Sin 50, should, therefore be equal to the horizontal distance from the y-axis [let's call it x] divided by 20. X = 20sin50, or approximately 15.32. This is negative, since it is in the second quadrant. Now we can use the Pythagorean Theorem, to get approximately 12.86 for our third side. Therefore, the coordinate should be <a href="-15.32,%2012.86">B</a>**. I think. :p </p>

<p>
[quote]
*Find the quotient [cos (5π/12) + i sin (5π/12)] / [2{cos (π/12) + i sin (π/12)}]. Then write the result in rectangular form.

[/quote]
</p>

<p>The answer is 1/4 + i√3/4. I don't quite understand the last bit. </p>

<p>I'll do the last two later. :p</p>