TMSCA State Questions

[Celsion]

09E-28. NASA sent the Phoenix Probe to Mars in 2007/08. It traveled 423 million mi on the trip from Earth to Mars. If the mean orbital radii of the Earth and Mars are 1.496x10^8 km and 2.279x10^8 km, respectively, what is the percent difference in the average closest approach of the planet's and the distance Phoenix traveled.

Answer: 7.69x10^2 (3SD)

09E-36. The volume of water in the world's oceans is 317 million cubic miles which is 97.24% of the total water on the earth. What fraction of the earth's volume is water?

Answer: 1.25x10^-1

09E-37. The Colossus of Rhodes, one of the seven wonders of the ancient world, stood 100 ft. It was clad with bronze plate averaging 0.5 in thickness. The surface area of a man 6ft tall is 1.9 m^2. Based on this, estimate the weight of bronze used in the Colossus. The density of bronze is 8.75 g/cm^3.

Answer: 1.29x10^5

09E-38. Lenny starts with a full, 2-cup container of 30% salt solution. He divides the solution in half. To one half, he adds water to double the volume and refills the original container, discarding the leftover mixture. How many times must this procedure be done to dilute the original 30% solution down to just less than 5%?

Answer: 7 integer

09E-46. A stone mason stacks rectangular cut stones to build a wall of fixed height and length. The stones are available in different sizes but have the same shape. The cost of a stone is proportional to its volume. If the wall materials cost is $2000 when an 8-in stone is used, what is the cost of the wall when 10-in stones are used?

Answer: $2500.00

09E-56. What is the minimum value of x for the ellipse [unparseable or potentially dangerous latex formula]?

Answer: -8.11

09E-57. A backpacker is 2 miles away from a straight road and 10 miles away from a town. The road goes directly to the town. If the backpacker hikes at 3 mph off-road and 4 mph on the road, at what angle should she hike toward the road (directly towards the road is zero degrees) to get to the town as quickly as possible?

Answer: 4.86x10^1

Thanks in advance. :)

[stupidityismygam]

[Celsion]

I'll just add on more questions here.

08F-26. Josh completes a job in 4 hr, but Jane can do it in 3.3 hr. What is the percent difference in the total time to complete the job if Josh does it alone, and if Jane joins Josh after 2 hr?

Answer: -2.74x10^1

08F-37. Marie starts a project at a rate to finish in 5 hr. After 2 hr, her rate decelerates such that she finishes 6.3 hr after starting. What was the deceleration rate, a negative number?

Answer: -2.81x10^-2

08F-57. A right triangle with hypotenuse equal to 3 inches is rotated about a leg to produce a cone. What is the maximum volume of the cone?

Answer: 1.09x10^1

I'm awful when it comes to stated problems. These are probably really simple and I'm overlooking the answer. Always miss the easy ones...

[B3ndythumbs]

[Celsion]

Questions from this year's study list:

06A-37. A thin-walled circular cylinder is filled 85% with water, closed up and then tipped over on a table so it would roll if pushed. What is the height of the water level over the tabletop divided by the cylinder diameter?

Answer: .793

07G-38. A screen transmits 35% of incident light and reflects the rest. What fraction of incident light passes through two screens stacked together?

Answer: 21.2

08A-36. A towel weights 3.5 lbs soaking wet but only 1.1 lbs when 80% of the water is wrung out. What does it weight after it dries?

Answer: .500

Thanks in advance.

[stupidityismygam]

37) I don't have a way without nasty solver of the calculator. This would be an excellent problem to skip.

38) For light to go through the 2nd screen, it obviously first has to go through the first screen, which occurs with probability of [unparseable or potentially dangerous latex formula] Then, the light can be transmitted by the 2nd screen or reflected by the 2nd screen. If it is reflected by the 2nd screen it must be reflected by the 1st screen and then you have the same possibilities again...essentially an infinite geometric sequence...

[unparseable or potentially dangerous latex formula]

36) Let [unparseable or potentially dangerous latex formula] be the weight of the towel and [unparseable or potentially dangerous latex formula] be the weight of the water. Then, [unparseable or potentially dangerous latex formula]

So, [unparseable or potentially dangerous latex formula].

[AuSmith]

[Celsion]

Hm...problems 05G-60, 06I-60, and 08E-60 on the study list geo problems.

Help on these problems would be great. Thanks in advance. :D

[AuSmith]

05G-60
Use the law of sines to get another angle, [unparseable or potentially dangerous latex formula].

05G-60.jpg (14.31 KiB) Viewed 2820 times

[unparseable or potentially dangerous latex formula]

We get [unparseable or potentially dangerous latex formula].

Find the area of the parallelogram using the formula [unparseable or potentially dangerous latex formula],

[unparseable or potentially dangerous latex formula]

Use Bretschneider's Formula [unparseable or potentially dangerous latex formula],

[unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula]

06I-60
This looks ambiguous to me. I am taking the front, back (left,right) triangles to be equilateral (isosceles). If the [unparseable or potentially dangerous latex formula] angle is a base angle, the back equilateral triangle is the same size as the front. This should be too easy. Therefore, assume the [unparseable or potentially dangerous latex formula] angle is the vertex. Still, you can easily find the base of that triangle, which is the side of the back equilateral triangle.... but it's the wrong answer. Anybody?

[unparseable or potentially dangerous latex formula]

08E-60
The area of a sector is [unparseable or potentially dangerous latex formula] (fixing [unparseable or potentially dangerous latex formula], area is proportional to [unparseable or potentially dangerous latex formula], and for [unparseable or potentially dangerous latex formula], we have [unparseable or potentially dangerous latex formula]). We know [unparseable or potentially dangerous latex formula] due to the isosceles triangle.

Then, [unparseable or potentially dangerous latex formula]. Find the base angle of the isosceles triangle.

[unparseable or potentially dangerous latex formula]. Find the base of the triangle.

[unparseable or potentially dangerous latex formula]. Subtract off the side of the equilateral triangle, or the length of the radius.

[unparseable or potentially dangerous latex formula]

[B3ndythumbs]

[AuSmith]

[B3ndythumbs]

Do u ever see this formula used in any other problem?