1. ## Practice Test

Hello. I am given various take-home tests throughout the semester in my Trigonometry class. I'm usually pretty good at remembering new material, but I'm having a lot of trouble remembering how to do the older problems from earlier in the year.

If someone could please refresh my memory and help me understand how to solve these questions, I would be very grateful. There are quite a few questions, so I apologize. The ones I am in need of assistance on are boxed. The last page is all questions that I don't really know where to start with. Thank you in advance!

2. Hi Thabaretta,

Try posting these one at a time. Don't believe I'd call this a take home test if you expect to get a lot of responses here.

Here's a couple to get you started.

(7) $\displaystyle \frac{\sqrt{7}+\sqrt{2}}{\sqrt{7}-\sqrt{2}}$

Multiply numerator and denominator by $\displaystyle \sqrt{7}+\sqrt{2}$

$\displaystyle \frac{(\sqrt{7}+\sqrt{2})^2}{7-2}=\frac{7+2\sqrt{14}+2}{5}=\frac{9+2\sqrt{14}}{5}$

(10) $\displaystyle \log_x4+\log_x9=2$

$\displaystyle \log_x(4)(9)=2$

$\displaystyle \log_x36=2$

$\displaystyle x^2=36$

$\displaystyle x=6$

3. Wow, thanks a bunch! You make it so easy to understand. Please let me know how to solve the rest of the problems if it's not too much trouble. You don't need to do all of the work for the longer problems, but rather throw me on the right track.

4. (11) Solve for x in simplest a + bi form.

$\displaystyle x^2+8x+25$

$\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\displaystyle x=\frac{-8 \pm \sqrt{8^2-4(1)(25)}}{2(1)}$

$\displaystyle x=\frac{-8 \pm \sqrt{-36}}{2}$

$\displaystyle x=\frac{-8 \pm 6i}{2}$

$\displaystyle x=-4 \pm 3i$

5. (12) Solve for C if V = 320

$\displaystyle V=20\sqrt{C+273}$

$\displaystyle 320=20\sqrt{C+273}$

Square both sides, and solve for C.

6. Originally Posted by ThaBeretta
Hello. I am given various take-home tests throughout the semester in my Trigonometry class. I'm usually pretty good at remembering new material, but I'm having a lot of trouble remembering how to do the older problems from earlier in the year.

If someone could please refresh my memory and help me understand how to solve these questions, I would be very grateful. There are quite a few questions, so I apologize. The ones I am in need of assistance on are boxed. The last page is all questions that I don't really know where to start with. Thank you in advance!

Question quoted for documenting purposes.

ThaBeretta - I am closing this thread until you PM me clearing some things up. If this is a take home test that is to be considered part of your grade, then this is blatant cheating and we do not condone this. Please PM me with your side of the story.

Thread re-opened after discussion with OP

7. Thank you, Jameson.

I believe I have the solution for #14. Please let me know if this is correct or needs work:

First, you subtract the sum of the two given angles from 180 to get the missing angle, which comes out to 45. Now you can do the Law of Sines (5280/Sin45)=(X/Sin75). Once solved, X = 6,246ft.

15)

Judging by the image, cart 4 is at approximately 135 degrees. It will need to travel 225 degrees to get to the base of ferris wheel (270 degrees). They are looking for the answer in radians, so (225)(π/180) = 1.25π

Would that be correct?

8. I think I figured out #17 as well if someone can check my work:

The diagonal across the trapezoid divides it into two triangles. You have two sides, an angle, and the unknown side (3 sides and 1 angle = Law of Cosines).

X^2 = 5.30^2 + 12.70^2 - 2(5.30)(12.70)(Cos68.4)

X^2 = 189.38 - 49.5569

X = sqrt(139.8231)

X = 11.8 ft.

16)

Common denominators for each fraction to make it one fraction divided by one fraction. Then you can do the numerator times the denominator (keep, change, flip rule). It ends up being:

(X+Y/XY) * (X²Y²/Y²-X²)

I believe the whole fraction on the left cancels with some of the terms on the right, leaving the fraction:

XY/Y-X

10. Originally Posted by ThaBeretta