Mammals and Math - The Solutions
October 13, 2008
First we need to determine how far Nelly traveled at the 45 degree path in those 5 minutes.
Distance = (rate)(time) = (15mph)(5/60) = 1.25 miles.
Since Nelly is diving at an angle of 45 degrees, by drawing a straight line from her position 5 minutes into the dive and the surface of the water we can form a 45-45-90 triangle. 1.25 miles will be the length of the hypotenuse.
Now, using the Pythagorean Theorem, we can solve for x.
x2 + x2 = 1.252 à 2x2 = 1.252à x2 = 1.252/2 àx = 1.25/√2 = (5√2)/8 miles
**This is a great example of when memorizing the side relationship in 45-45-90 triangles is useful. Recall that both legs of a 45-45-90 triangle are x and the hypotenuse is x√2. Thus 1.25 = x√2, and x = (5√2)/8.**
First let’s set up the relevant equations.
m/f = 3/4
(m + 3) = f
Now we have two equations and two variables, so we can use substitution to solve.
Let’s rearrange the first equation so that it is set equal to f.
m/f = 3/4 à 3f = 4màf = 4m/3
Now substitute it into the second equation and solve.
m + 3 = 4m/3 à 3m + 9 = 4màm = 9
If there were 9 males in the family, that means there were 12 females. (f = 4(9)/3 = 12)
Thus, there were 9 + 12 = 21 monkeys in the family before the babies were born.
First we need to determine the actual amount that his weight increased.
2.6 – 1.82 = 0.78 poundsNow we can determine what percent increase this is from the first exam.(0.78/1.82)(100) = 43%, to the nearest whole number.