Study Guide Questions

[redhawk2015]

4 questions off the study list (which I finally worked through)

11D-38 (Stated): Mike and Mary stand unmoving 24 ft apart. Ned stands 18 ft from Mike and 8 ft from Mary. What is the shortest distance Ned can move to create a right triangle? ANSWER: 4.93 ft

11I-38 (Stated): Marin runs a mile in 5 min 30 sec. She and Mary, who runs a mile in 7 min 26 sec, start at the south end of a 1/4 mi circular track. Marin takes off running on the track and, at the same time, Mary takes off in a straight line across the track, meeting up with Marin before she finishes one lap. Considering due east to be 0 degrees, at what positive angle does Mary need to run? ANSWER: 1.30 radians = 74.5 degrees

05C-60 (Geometry): Circular Arc, Right Triangles. ANSWER: 0.608 rad

11G-50 (Geometry): Truncated Rectangular Solid. ANSWER: 190

[rcoker7]

11D-38: Let C be the distance between Mike and Mary, A the distance between Ned and Mike, and B the distance between Ned and Mary. The answer should be C/2 - 1/2 * sqrt(2(A^2 + B^2) - C^2)

[Fredfredburger]

11I-38
This isn't my solution, but it works.


You have two rates here, Marin is taking the arc path s and Mary is taking the straight path d. It's easier to put the numbers in seconds, so we'll put that in the formulas along with the time t.

Their respective rates are
[unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula]

Observing your triangle you see that you could use trig to come with the the ratio
[unparseable or potentially dangerous latex formula]

From your arc length formula you know that [unparseable or potentially dangerous latex formula] and substituting that into the preceding formula you get
[unparseable or potentially dangerous latex formula]

Plugging back in your rate equations into this you get.
[unparseable or potentially dangerous latex formula]

Use your solver and you get theta equals 2.6076.
Now, since it's a isosceles triangle it's relatively simple to find the angle at which she runs from there. I use [unparseable or potentially dangerous latex formula] [unparseable or potentially dangerous latex formula]

The easiest form for this is
[unparseable or potentially dangerous latex formula]
And then just finding the other angle with theta

[Fredfredburger]

5C60
My solution to this is in this .

The general solution is [unparseable or potentially dangerous latex formula]

[Fredfredburger]

11C-50

The chunck you're cutting off is a pyramid with volume [unparseable or potentially dangerous latex formula] where B is your Base area and H is your height.
Your base is a triangle with dimension 419-x and w, where w is your width. We will denote H by h, and our volume now is
[unparseable or potentially dangerous latex formula]

The volume of the original solid was 419wh, so plugging these into the ratio you're given you get.
[unparseable or potentially dangerous latex formula]

Use your calculator solver to find the answer.