Math Level 1 + Sat Physics

Test Preparation SAT Subject Test Preparation
1

<p>Hey guys, I came across a couple of problems that I really do not understand but perhaps you guys could help me.</p>

<li><p>For which of the following equations is the sum of the roots equal to the product of the roots?
There were two choices that it came down to
The right one is—x^2-4x+4 IDK WHY
I chose–x^2+4x+4 because that makes more logical sense and they actually do add up and multiply to 4? Help with that</p></li>
<li><p>If the positive integers starting with 1 are written consecutively what will be the 90th DIGIT
The choices are 0,1,5,8,9 with 5 being the right choice i have no idea how to do this.</p></li>
<li><p>What is the least integer value of k so that the equation x^2(3k+1)-6x+2=0 has no real roots?
Choices are 5,2,1,-1,-2 with 2 being the right choice</p></li>
</ol>

<p>SAT PHYSICS</p>

<li>If a constant net force F acts along the barrel of a toy cannon and a projectile of mass M leaves the barrel with speed V. With what speed will a projectile of mass 2M leave the barrel?
The answer is v/(square root)2
I have NOOO idea how to solve this</li>
</ol>

<p>As always, thanks</p>

2

<ol>
<li><p>for an equation:
ax^2 + bx + c = 0
Sum of roots = -b/a and Product = c/a
so x^2-4x+4 has -b/a = 4 AND c/a also = 4</p></li>
<li><p>1-9 = 9 digits
10-19 = 10x2 digits = 20 digits
Similarly, 20-29 = 20 digits
30-39 = 20 more
40-49 = 20 digits
Now upto here we have 89 digits
so the next number is 50, and the 90th digit is 5.</p></li>
<li><p>For no real roots, discriminant < 0
x^2(3k+1)-6x+2=0
36 - 4(2)(3k+1) <0
36 < 8(3k+1)
(9/2) - 1 < 3k
7/2 < 3k
7/6 < k
so k > 7/6 which is a little more than 1.
So 2 is the closest integer greater than 7/6.</p></li>
</ol>

<p>PHYSICS</p>

<ol>
<li>Force.distance = work
Let length of barrel = d
F.d = (1/2) MV^2
F.d is also = (1/2) 2M.x^2
SO:
(1/2) MV^2 = (1/2) 2M.x^2
M.V^2 = 2M.x^2
V^2/2 = x^2
x = v/sqrt(2) ------>your answer</li>
</ol>

3

<p>Thank you SO much you really are something else at math haha. =]</p>