15x+25y=1875
Let
y=95-x
15x+25 (95-x)=1875
Solve for x
15x+2375-25x=1875
15x-25x=1875-2375
-10x=-500
X=500/10
X=50 the number of $15 items
Y=95-50=45 the number of $25 items
Basically, the parabola has to have all points that are equidistant from the focus and the directrix, the directrix being a horizontal line, and the focus being a point given. To derive an equation from this you need to use the distance formula which I'm guessing you already know because you're already in precalc.
The gist of it is that we have a random point on the parabola (x,y), and the point (x,y) will be equidistant from both the focus and the directrix. If we use the distance formula, you get something like this:
The square root of y-(-1/2) coming from the directrix, and the righthand side of the equal sign being derived from the focus.
All you need to do is simplify now!
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Hope I helped!
Multiply 0.75 by 100
75 %
H(t) = Ho +Vot - gt^2/2
Vo = 19.6 m/s
Ho = 58.8 m
g = 9.8 m/s^2
H(t) = 58.8 + 19.6t -9.8t^2/2 = 58.8 + 19.6t - 4.9t^2
Maximun height is at the vertex of the parabole
To find the vertex, first find the roots.
58.8 + 19.6t - 4.9t^2 = 0
Divide by 4.9
12 + 4t - t^2 = 0
Change sign and reorder
t^2 - 4t -12 = 0
Factor
(t - 6)(t + 2) =0 ==> t = 6 and t = -2.
The vertex is in the mid point between both roots
Find H(t) for: t = [6 - 2]/2 =4/2 = 2
Find H(t) for t = 2
H(6) = 58.8 + 19.6(2) - 4.9(2)^2 = 78.4
Answer: the maximum height is 78.4 m
Answer:
They have a scale factor of 2
They are both the same shape
The big circle has a radius of 4 and the small circle has a radius of 2. You divide the bigger circle by the smaller circle. 4/2=2