2 MATH Questions!

Test Preparation SAT Preparation
1

<p>1) 2 , -4 , 8,.............
the first term of the sequence above is 2 , and every term after the first term is -2 times the preceding term. How many of the first 50 terms of this sequence are less than 100?</p>

<p>A) 22
B) 25
C) 28
D) 30
E) 37</p>

<p>Answer is C
..............................................................................................................................................................................</p>

<p>2) A cube with volume 8 cubic centimeters is inscribed in a sphere so that each vertex of the cube touches the sphere. What is the length of the diameter, in centimeters, of the sphere?</p>

<p>A) 2
B) √6 (approximately 2.45)
C) 2.5
D)2√3 (approximately 3.46)
E) 4</p>

<p>Answer is D</p>

2

<p>Hi, for 1, this is how i did it.
continue and you get 2,-4,8,-16,32,-64. That’s 6 numbers less than 10, and the first 6 of the 50 terms. there’s 44 left, and half of those will be negative = less than 100. so 44/2 = 22. 22+ the first 6 = 28. C</p>

<p>For 2:
volume = 8 so 1 side is 2cm since v= s^3
using 3d geometry the 2nd side is 2 radical2, use pythagorean to find the diamater of the sphere and you get 2 radical 3</p>

3

<p>of the first 50, 25 are negative so you only need to figure out the positive ones and there are only 3 (2, 8, 32) are positive and less than 100. 25+3 = 28</p>

<p>For the second problem it is easier if you can sketch it, but it isn’t bad - you just have to use the pythagorean theorem twice. You have a cube of side length = 2. If you want to find the length of the diagonal across the cube (which is the same as the diameter of the sphere) you need to use the pythagorean theorem - but first you must find the other two sides (the height, which is two) and the diagonal of one of the faces of the cube (which is simply a square) - the diagonal is side length 2 * square root of 2 (by the pythagorean theorem with two shorter sides length 2). So to calculate the diagonal across the cube you have a right triangle with sides 2 and 2<em>square root of 2 and need to figure out the hypotenuse - so by the pythagorean theorem the long side would be 2</em>square root of 3.</p>

4

<p>Thank you :)</p>

5

<p>Check this </p>

<p><a href=“A diagonal in a cube”>http://mathcentral.uregina.ca/QQ/database/QQ.09.04/brett1.html&lt;/a&gt;&lt;/p&gt;

<p>Fwiw, it is not a bad idea to know the formula for the diagonal of a cube. </p>