Tutor profile: Devin F.
Subject: SAT II Mathematics Level 2
A right circular cylinder has a radius of 1 and a height of 2. If a and b are two points on its surface, what is the maximum possible shipwright line distance between a and b?
Step 1: Determine what the farthest two points on the cylinder would be. If we were to draw out a right circular cylinder and look at it, we would be able to see that the farthest two points could be away from each other would be if we had on point on top and to the left and another on the bottom and as far right as possible. We can explain these points mathematically by using a= (0,h) and b=(2r,0) where h is the height and r is the radius. We can then determine that a=(0,2) and b=(2(1),0) or b=(2,0). Step 2: Use the distance formula to determine the distance between these two points. By applying the distance formula: d=√((x1-x2)^2+(y1-y2)^2)) we can find our solution. d=√((0-2)^2+(2-0)^2) d=√((-2^2)+(2^2)) d=√(4+4) d=√(8) d=(√4)(√2) d=2√2 Thus we have our solution being 2√2 being the farthest possible distance between the two points.
Subject: SAT II Mathematics Level 1
Chris and Derek both sold raffle tickets for an event. Chris sold his tickets for $2 and Derek sold his tickets for $5. Together the sold 50 tickets and made $130 dollars. How many tickets did Derek sell?
Step 1: Create an equation for the overall amount of tickets sold. Since we don't know how many tickets Chris and Derek sold, we will assign this values the variables of x and y respectively. This will give us the equation of: 2x+5y=130. Step 2: Replace x with as function y. Because we cannot solve the above equation with two separate variables, we need to replace x as a function of y. To do this we need a separate equation to find y in terms of x. Since we know that together Chris and Derek sold 50 tickets, we can write the equation x+y=50. Then we can subtract y to isolate x which will leave us with x=50-y. Now we have x in terms of y. We can then substitute this '50-y" back into our original equation for x. This will give us: 2(50-y)+5y=130. Step 3: Solve for y. After this we can solve for y to find our solution. See below. 2(50-y)+5y=130 100-2y+5y=130 100+3y=130 3y=30 y=10. After solving for y, we can see that Derek sold 10 tickets.
What is x in the equation below: 3x+5(4x+2)= 79
To solve this equation, first you need to isolate "x". Step 1: Using "Order of Operations" multiply whats in the parenthesis by 5. Now you have the following. 3x+20x+10=79. Step 2: Add together common terms. Add numbers with an "x" together. Now we have the following: 23x+10=79. Step 3: Continue to isolate x by moving the 10 to the other side of the equation. We can do this by subtracting 10 from both sides as shown: 23x+10-10=79-10. This will give us the following: 23x=69. Step 4: Continue to isolate "x" by dividing by 23 from both sides as shown: (23x/23)=(69/23). This will give us our final answer of x=3
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