X=length
y=width
Area (rectangle)=length x width
we suggest this system of equations:
y=x/5
xy=9/20
solve this system of equations by substitution method:
x(x/5)=9/20
x²/5=9/20
Least common multiple=20
4x²=9
x²=9/4
x=⁺₋√(9/4)
we have two solutions:
x₁=-3/2 it does not validate
x₂=3/2 ⇒y=x/5=(3/2)/5=3/10
The dimensions of the lake are:
lengh=3/2 miles
width=3/10 miles
to check:
Area=3/2 miles x 3/10 miles=9/20 miles².
width is 1/5 the length of the lake ⇒ 3/10 miles=(3/2) /5 miles
Mr.Fields would have 6,000 pounds
The vertex is at the point (0,0) and the focus at the point (0, 1/8). This is given to us. Both the vertex and focus are separated by a vertical distance in the positive direction.
This means that the parabola opens upward. The vertex form of the equation for a parabola that opens upward is:
y = a(x - h)^2 + k, where the point
(h, k) is the vertex of the parabola.
Plug the vertex given into the above equation.
y = a(x - 0)^2 + 0
y = ax^2 + 0
y = ax^2
What is a?
Note: a = 1/(4f), where f is the distance from the vertex to the focus or simply as given in the focus point above 1/8.
Let f = 1/8
a = 1/4(1/8)
a = 1/(1/2)
a = 2
The equation we want is
y = 2x^2.
f(x) = 2x^2
Choice A is the answer.
