What is the equation for a parabola with a focus of (0,-4) and a directrix of y=4 if the vertex is at the origin?..1)..y=1/16x2.
1 answer:
Answer:
y = - x²
Step-by-step explanation:
Since the vertex is at the origin and the focus at (0, - 4) then the parabola opens vertically down with equation
x² = 4py ( p is the distance from the vertex to the focus )
Here p = - 4 ( focus is below the vertex ), thus
x² = 4(- 4)y = - 16y ( divide both sides by - 16 )
y = - x²
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Answer:
- (a) C(d) = 270 + 0.20d
- (b) C(1800) = 630
- (c) see attached (lower right graph). The slope represents the cost (in dollars) per mile.
- (d) It represents the fixed cost (amount she pays even if she does not drive)
- (e) the cost increases as the number of miles driven increases
Step-by-step explanation:
(a) You are given two points, (d, C) = (360, 342) and (780, 426). The two-point form of the equation for a line can be helpful.
... y = (y2 -y1)/(x2 -x1)(x -x1) +y1
Using the given points and variables, ...
... C = (426 -342)/(780 -360)(d -360) +342
... C = (84/420)(d -360) +342
... C = 0.20d +270 . . . . the equation for cost as a function of miles driven
(b) Fill in the value for d and do the arithmetic.
... C = 0.20·1800 +270 = 360 +270 = 630
(c) The slope of the curve is (change in dollars)/(change in miles) = $/mile, the cost of each mile driven. (It is $0.20 per mile.)
(d) The C-intercept is C(0) = cost for 0 miles driven. (It is $270.)
(e) Both your own experience and the problem statement tell you that the cost of vehicle operation varies with miles driven. If nothing else, you need to pay more for gas the farther you drive.
(In real life, you don't expect the model to be exactly linear, becasue you get a large jump in cost when you reach certain maintenance interval miles: 15,000, 30,000, and so on.)
We must find the radius so we can plug this into the formula for surface area.
Circumference =
We are going to plug this in as our radius for the most accurate answer.
The surface area of a sphere is
Surface Area =
≈ 451.93 units
Circumference =
We are going to plug this in as our radius for the most accurate answer.
The surface area of a sphere is
Surface Area =