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TMSCA Test D March 2,2013
#7,8,18,39,56-59 please help

I will answer these when I get my test back...

Ok thanks

#8

Note that since the sphere is inscribed is tangent to two faces, its diameter is the length of the edge of the square, so it's radius is e/2.

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[unparseable or potentially dangerous latex formula]

#18

Population density equals people divided by area

[unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula]

Using your percent difference formula, and noting that your answer must have two significant digits,

[unparseable or potentially dangerous latex formula]

#39

Given the circumradius of a triangle, denoted by R, and triangle sides a, b, and c, the area can be calculated as

[unparseable or potentially dangerous latex formula]

and rearranging this for R we get

[unparseable or potentially dangerous latex formula]

Here we have an isosceles triangle with congruent sides of length a, and a side of length b.
Given an isosceles we can calculate the area given the two congruent sides and the angle in between those sides

[unparseable or potentially dangerous latex formula]

Plugging this back into the equation we have for the circumradius, we get

[unparseable or potentially dangerous latex formula]

which is your golden formula for these problems. Here since you're finding the diameter you just multiply the radius by 2 and plug and chug.

[unparseable or potentially dangerous latex formula]

#56
I'm assuming that you haven't been exposed to integral calculus yet. The area between the functions [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula], where f is greater than than g on the interval between their two intersections, a and b, is given by the integral

[unparseable or potentially dangerous latex formula]

Since you already have the two functions, all you need is the two intersection points.
My calculator tells me that they are [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula]. Your integral, whose button you could find on your calculator, is

[unparseable or potentially dangerous latex formula]

#58
I would calculate the determinant of matrix U first, because it is just a constant that can be kept outside of the matrix along with the 7. Calculating it really fast you see it's 222, so you can factor out [unparseable or potentially dangerous latex formula] from the matrix S.

I would just use my calculator to multiply the matrices T and U, getting

[unparseable or potentially dangerous latex formula]

You're looking for [unparseable or potentially dangerous latex formula]. The first subscript denotes which row of the matrix you're dealing with while the second denotes the column you're using. Here we have first row and second collumn which is [unparseable or potentially dangerous latex formula].

Multiply your constant by that to get your entry for S

[unparseable or potentially dangerous latex formula]

#59

This is another calculus problem, but you can apply the same principles as #56. Here [unparseable or potentially dangerous latex formula], so you're integral is

[unparseable or potentially dangerous latex formula]

You're given an coordinate in [unparseable or potentially dangerous latex formula], so you can just plug that into the equation to find A.

[unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula]

I'm not sure if you could still solve this on your calculator, so I'll solve the rest by hand, or typing...

[unparseable or potentially dangerous latex formula]

The natural log of 1 is 0, so we are left with

[unparseable or potentially dangerous latex formula]

Use your calc to solve for b,
[unparseable or potentially dangerous latex formula]

#8
To find the greatest number which will yield an integer great than 1, divide the number by the next greatest integer, 2.

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From there just work your way down to see which one satisfies the equation

[unparseable or potentially dangerous latex formula]

Through trial and error you'll find [unparseable or potentially dangerous latex formula]

Do any of you guys know how to do 66-70 in that test I am seriously clueless there

Here are the study guides for ya




Here's a that started working on some of the problems there, and if you need help with any of them I'll be open to help you out.