Answer:
11.28m
Step-by-step explanation:
The computation of the height of the spire is shown below:
let us assume the height of the spire be x
Now
For triangle ABD
Tan 43 degrees = h ÷ x
x = h × cot 43 degrees
= 1.07236 h
For triangle ABC
tan 15 degrees = h ÷ (30 + x)
0.2679 = h ÷ 30 + 1.07236h
8.038 + 0.28728 h = h
h = 11.28m
Point slope: y - y1 = m(x - x1)
Plug in the points
Answer: y - 5 = 1/3(x + 2)
You need 3 points to graph a quadratic function.
It is advisable that one of these points be the vertex, because the line of symmetry passes through it
Next, you need to find two other points that lie on the curve, replacing an x-value into the function and calculating the y-value. It is easier if these two points are at the same distance from the line of symmetry.
For example, if the quadratic function is y = (x - 4)² + 3, the vertex is located at (4, 3). Replacing with x = 3 into the equation, we get:
y = (3 - 4)² + 3
y = 1 + 3
y = 4
Replacing with x = 5 into the equation, we get:
y = (5 - 4)² + 3
y = 1 + 3
y = 4
Now, we need to connect the points (3, 4), (4, 3), and (5, 4) with a U shape, as follows:
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Since x and y are directly related, the equation for their comparison will look like
kx = y
where k is your constant. They give you an instance in the problem where x = 27 and y = 81. Plug this into the above equation and solve for k.
kx = y
k (27) = 81
k = 3
Thus, the constant of variation is 3.