Cheers! The volume of the roof layer is equal to the volume of the cylinder formed by the outer edge minus the volume of the cylinder formed with the inner edge. The outer cylinder is (1/2) *lr2 = (1/2)*250*62 The inner cylinder is (1/2) *lr2 = (1/2)*250*42 Subtracting the two we get 7850m3
If b = 1/3, and if m and n are positive integers, which of the following has the greatest value?
bm - nbm + n(bm)*(b2*n)bm*n The answer cannot be determined.
The trick is that 1/3 raised to the smallest number will have the greatest value. If m and n are positive integers, then m - n must be the smallest exponent. Therefore, bm - n will have the greatest value.
Let z||w be defined for all z,w as z+w+12
What is the value of 12||12?
The expression 12||12 is defined as the sum of the two numbers, plus 12. That gives 36. The math on this one is pretty straightforward, but it can be a little confusing to have so many twelves running around...
Unlike her ---- sister, Maria would boldly join the conversation at any gathering.
brash obstinate apathetic timid humorless
The sentence tells you that Maria and her sister are not alike. Bold and timid are antonyms or OPPOSITES. Well done!
Science and justice are two great ---- institutions that fostered Western society's ---- wealth and freedom.
academic . . current European . . detrimental oppressive . . continual secular . . unprecedented financial . . impressive
This is the best answer. The most important reason this one is right is that unprecedented is the word that best captures the author's approving attitude towards science and justice. (We know the author approves of these institutions because he calls them great.)
How many points are there on the line that are 1/2 as far from v as they are from u?
There is one point between u and v, and one point to the right of v. The point between u and v is 1/3 of the distance from v to u. The point to the right of v is a point beyond v a distance equal to the distance between u and v. That last part sounds complicated, but it just means that you have to travel a certain distance from the point to v, and then the same distance again to u. The final result is that it is twice as far to u as it is to v. All points to the left of u are closer to u than v.