Answer:
q = -8, k = 2.
r = -6.
Step-by-step explanation:
f(x) = (x - p)^2 + q
This is the vertex form of a quadratic where the vertex is at the point (p, q).
Now the x intercepts are at -6 and 2 and the curve is symmetrical about the line x = p.
The value of p is the midpoint of -6 and 2 which is (-6+2) / 2 = -2.
So we have:
f(x) = 1/2(x - -2)^2 + q
f(x) = 1/2(x + 2)^2 + q
Now the graph passes through the point (2, 0) , where it intersects the x axis, therefore, substituting x = 2 and f(x) = 0:
0 = 1/2(2 + 2)^2 + q
0 = 1/2*16 + q
0 = 8 + q
q = -8.
Now convert this to standard form to find k:
f(x) = 1/2(x + 2)^2 - 8
f(x) = 1/2(x^2 + 4x + 4) - 8
f(x) = 1/2x^2 + 2x + 2 - 8
f(x) = 1/2x^2 + 2x - 6
So k = 2.
The r is the y coordinate when x = 0.
so r = 1/2(0+2)^2 - 8
= -6.
Answer:
25.
Step-by-step explanation:
5 ft 7 in = 5.583 ft.
We have 2 similar triangles here.
If h is the height of the tree, then:
h / 5.583 = 18/4
h = 18*5.583/4
h = 25.12 ft
I'm guessing the equation should read something like
or possibly with minus signs in place of +.
Multiply both sides by 
to get
Now substitute
to transform the equation to
which simplifies to
The ODE is now separable.
Integrate both sides. On the left, substitute
Solve for 
.
Put this back in terms of 
.
Put this back in terms of 
.
Solve for .
