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professor190 [17]
2 years ago
12

Question 2

Mathematics
1 answer:
Dominik [7]2 years ago
5 0

Answer:

24 miles

Step-by-step explanation:

Please find attached a diagram explaining the question

this would be solved using Pythagoras theorem

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c =  hypotenuse

15² + 19²

225 + 361

586

the square root of 586 = 24 miles

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1) We have that the equation is x^2=20y , hence y=x^2/20. The standard equation of such an equation is y=\frac{1}{4p} x^2. Hence, p=5 in this case. The focus is at (0,5) and the directrix is at y=-5 (a tip is that the directrix is always "opposite" the focus point of a parabola; if the directrix is at x=-7 for example, the focus is at (7,0)).
2) Similarly, we have that the equation is x=3y^2 \\  \frac{1}{4p} =3. Thus, p=1/12. In this case, the parabola opens along the x-axis and the focus is at (1/12, 0). Also, the directrix is at x=-1/12. Hence the correct answer is B.
3) We are given that the parabola has a p of 9. Also, the focus lies along the y-axis, hence the parabola is opening along the y-axis. Finally, the focus is on the positive half, so the parabola is opening upwards. The equation for this case is y=y=\frac{1}{4p} x^2= \frac{1}{36 } x^2.
4) Similarly as above. The directrix is superfluous, we only need the p-value. THe same comments about the parabola apply and if we substitute p=8 in the formula: y= \frac{1}{4p} x^2 we get y=\frac{1}{32} x^2.
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