C) Write 2400 000 in standard form.
2 answers:
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<h3>Answer: 33.75 feet</h3>
In fraction form, this value is equal to 135/4
33.75 ft is equivalent to 33 ft, 9 inches.
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Explanation:
Refer to the diagram below.
The key point to start with is point H, which is the vertex of the parabola.
Recall that vertex form is
y = a(x-h)^2 + k
What we'll do is plug in the vertex (h,k) = (60,30) which is the location of point H. We'll also plug in (0,45) which is the y intercept, aka the location of point C.
So,
y = a(x-h)^2 + k
y = a(x-60)^2 + 30 .... plug in vertex
45 = a(0-60)^2 + 30 .... plug in y intercept coordinates
45 = a(-60)^2 + 30
45 = a(3600) + 30
45 = 3600a + 30
45-30 = 3600a
3600a = 15
a = 15/3600
a = 1/240
This then means:
y = a(x-h)^2 + k
y = (1/240)(x-60)^2 + 30
This is the equation of our parabola. Plug in x = 30 to determine the height of point K
y = (1/240)(x-60)^2 + 30
y = (1/240)(30-60)^2 + 30
y = (1/240)(-30)^2 + 30
y = (1/240)(900) + 30
y = 15/4 + 30
y = 15/4 + 120/4
y = 135/4
y = 33.75
Therefore, the height of the power line, when it is 30 feet away from one of the poles, is 33.75 feet. This is the y coordinate of point K.
Side note: 33.75 ft = 33 ft + 0.75 ft = 33 ft + 12*0.75 in = 33 ft + 9 inches
well, the recursive rule of aₙ = aₙ₊₁ + 7, where a₁ = 15, is simply saying that
we start of at 15, and the next term is obtained by simply adding 7, and so on.
well, that's the recursive rule.
so then let's use that common difference and first term for the explicit rule.