Since 5 + 9 is 14 you can use ANY expression that has the same final value/ sum
Answer:
diagram shows a person and her twin at equal distances on opposite sides of a thin wall. Suppose a window is to be cut in the wall so each twin can see a complete view of the other. Show the size and location of the smallest window that can be cut in the wall to do the job.
Step-by-step explanation:
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:
A y= -3/4+6
Step-by-step explanation
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We can write and solve the differential equation that fits the statement given;
dy/dt = k(50-t)
∫dy = ∫ k(50-t)dt
= ∫ (50k - kt) dt
therefore;
y = 50kt - k/2(t²) + C
Alternatively, can be written as
y = - k/2 (50-t)² + C)
