Tutor profile: Brian D.
Subject: Basic Math
A student goes to the store to buy pencils with $10. Pencils are $0.30 each. how many pencils can the student buy?
The student can buy 33 pencils ( and will have $0.10 left over) There are many ways to solve this, but the key points are to recognize that you should divide $10 by $0.30, to get a answer of 33 1/3. Then recognize that you can't buy a third of a pencil
A truck weighing 40,000 kg is speeding toward a cliff at 108 km/hr. when its brakes fail. If superman reaches the truck 300 meters away from the edge, and is able to apply a constant force of 120,000 Newtons, will he be able to stop the truck before it plummets over the edge?
Yes. First we start with Newton's second law: F = m*a (Force equals mass times acceleration) where F = -120,000 N (1 Newton = 1 kg*m/s^2) The force is negative, because it is in the opposite direction of the travel of the truck m = 40,000 kg solve for a: a = F/m a = -120,000 kg*m/s^2 / 40,000 kg a = -3 m/s^2 so the acceleration ( or deceleration in this case) is -3 m/s^2 the speed of the truck is given by: S = Si + a*t (speed equals the initial speed plus the acceleration times the time elapsed) We want to find the time where the speed reaches zero: 0 = Si + a*t and solve for t t = -Si / a where Si = 108 km/hr = 108,000 m / 3600 s = 30 m/s (just unit conversion) and a = -3 m/s^2 therefore: t = - (30 m/s) / (-3 m/s^2) t = 10 s superman is able to stop the truck in 10 seconds. If the truck had not slowed down at all, it would have traveled the remaining 300m in these 10 seconds (distance = speed * time .... d = 30 m/s * 10 s = 300 m) but since it was slowing the entire time, it will travel less than the remaining distance in those 10 seconds, stopping short of the edge. (calculating the exact stopping distance is possible, but beyond the scope of this problem)
What is the slope and intercept of a line that passes through the points (2,4) and (8,12)?
The slope is found by finding the change in the 'y' coordinate (in this case 12-4=8) divided by the change in the 'x' (in this case 8-2=6). This results in a slope of 8/6. However, this can be further reduced by finding the greatest common factor. The factors of 8 are 8,4,2,1. The factors of 6 are 6,3,2,1. The greatest common factor is 2, so we will divide the top (8) and bottom (6) by 2. Therefore: Slope = 4/3 To find the intercept we take the equation for a line given by: ax + b = y , where a is the slope, b is the y-axis intercept, and x and y are the coordinates. So far the equation for our line is: (4/3)*x + b = y. (a = 4/3) if we substitute one of our coordinate sets--lets pick the first one, (2,4) where x=2 and y=4-- we now have: (4/3)*2 + b = 4 which evaluates to: 8/3 + b = 4 solving for b: b = 4 - 8/3 substituting the equivalent fraction of 12/3 for 4: b= 12/3 - 8/3 evaluating: b = 4/3 Therefore, the slope is 4/3 and the y intercept is also 4/3
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