<p>1) The height of a right circular cylinder is 5 and the
diameter of its base is 4. What is the distance from the
center of one base to a point on the circumference of
the other base? I put 3 but the answer is radical 29...</p>
<p>2)If j , k , and n are consecutive integers such that
0< j< k< n and the units (ones) digit of the product
jn is 9, what is the units digit of k ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
the answer is a</p>
<p>3)If x and y are positive integers, which of the
following is equivalent to (2x)^3y- (2x)^y ?
(A) (2x)^2y
(B) 2^y( x^3- x^y)
(C) (2x)^y<a href="D">(2x)^2y- 1</a> (2x)^y(4x^y-1)
(E) (2x)^y[(2x)^3-1]</p>
<p>thanks in advance!</p>
<p>the answer to 3 is c</p>
<p>1) The height of a right circular cylinder is 5 and the
diameter of its base is 4. What is the distance from the
center of one base to a point on the circumference of
the other base? I put 3 but the answer is radical 29…</p>
<p>-Since the diameter of either base is 4, the radius of either base is 2. Simply make a right triangle using this radius, the height, and the hypotenuse that completes the triangle, and use the Pythagorean theorem to solve for the hypotenuse length. (5^2) + (2^2) = 29 -> the square root of 29 is your answer.</p>
<p>2) Try 9, 10, and 11 for j, k, and n respectively. This set of integers should satisfy 0<j<k<n and jn = 9 in the units digit.</p>
<p>3) Both terms have a common factor of (2x)^y.
After you factor that out from each term, you should have</p>
<p>(2x)^y * [ (2x)^2y -1 ]</p>
<p>Note: (2x) ^ 3y = (2x) ^ y * (2x) ^ 2y</p>
<p>Question one;
In order to find the length of the diagonal, you must start at one end point of the diagonal, and move through the sides of the figure until you reach the other end point. Here, the end point of the diagonal is the center of the first base, right? The center is 2 cm away from the circle itself. That’s our first length. Then, you move upward to the other end point of the diagonal and what is this length? It’s called the height. So now we have both our measurements, 2, and 5. Now plug in the numbers in the following format: Square root of the sum of the square of 2 and the square of 5. The answer is root/radical 29.</p>
<p>Question two;
j, k, and n are consecutive integers greater than 0. Therefore, j=x, k=x+1, and n=x+2.
The unit digit (farthest to the right) of the product of j and n is 9. OK then. So x times x+2 = *9. Lets think of two consecutive integers that if multiplied together, give off a result that has a unit digit of 9. Easy. 9, and 11. If both are multiplied, then the result will be 99 which fits our equation.
j=9
k=10
n=11
What is the unit digit of 10? That is 0. The correct answer is A.</p>
<p>Question three;
Honestly, in these kinds of questions, I like to plug in random numbers into the original equation, get a result, then plug in the same numbers in the answers and see which one gives off the same result. I always prefer this trial and error method over arithmetic, which can go wrong at any point. However, you’re with replacing variables, you’re just doing a normal calculation on a calculator.
Let X be 2, and Y be 3. –> (4)^9 - (4)^3 = 262080.
And of course if I’m going to do trial and error, I always start with choice C and move upwards then downwards. Plug in X=2 and Y=3 in equation C. It’ll give the same answer. You have pinpointed the correct answer by then, which is choice C.
PS. knowthestuff’s method may be better to some people, but I like to stick to my trial and error method nonetheless. Do whatever you’re comfortable with.</p>