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Dahasolnce [82]
3 years ago
7

What are the focus and directrix of the parabola with the equation y = 1/2 x2

Mathematics
2 answers:
choli [55]3 years ago
6 0

Answer:

Step-by-step explanation:

Please write this as y = (1/2)x^2 for greater clarity.  (1/2) is the coefficient of x^2 here.  

The applicable form for the equation of this quadratic is 4py = x^2.  

Your y = (1/2)x^2  becomes 2y = x^2.  Therefore, 4p = 2, or p = (1/2).

Thus, the focus is (0, 1/2) (just above the vertex, (0, 0) ), and the equation of the directrix is y = -1/2.

VMariaS [17]3 years ago
4 0

Answer:

1/9

Step-by-step explanation:

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Number of weekend minutes used: x
Number of weekday minutes used: y

This month Nick was billed for 643 minutes:
(1) x+y=643

The charge for these minutes was $35.44
Telephone company charges $0.04 per minute for weekend calls (x)
and $0.08 per minute for calls made on weekdays (y)
(2) 0.04x+0.08y=35.44

We have a system of 2 equations and 2 unkowns:
(1) x+y=643
(2) 0.04x+0.08y=35.44

Using the method of substitution
Isolating x from the first equation:
(1) x+y-y=643-y
(3) x=643-y

Replacing x by 643-y in the second equation
(2) 0.04x+0.08y=35.44
0.04(643-y)+0.08y=35.44
25.72-0.04y+0.08y=35.44
0.04y+25.72=35.44

Solving for y:
0.04y+25.72-25.72=35.44-25.72
0.04y=9.72

Dividing both sides of the equation by 0.04:
0.04y/0.04=9.72/0.04
y=243

Replacing y by 243 in the equation (3)
(3) x=643-y
x=643-243
x=400


Answers:
The number of weekends minutes used was 400
The number of weekdays minutes used was 243
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