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tia_tia [17]
3 years ago
14

Derive the equation of the parabola with a focus at (6, 2) and a directrix of y = 1

Mathematics
1 answer:
geniusboy [140]3 years ago
5 0

Answer:

Step-by-step explanation:

eq. of directrix is y-1=0

let (x,y) be any point the parabola.

then\sqrt{ (x-6)^2+(y-2)^2}=\frac{y-1}{(-1)*2}

squaring

x²-12x+36+y²-4y+4=y²-2y+1

x²-12 x+40-1=4y-2y

2y=x²-12x+39=x²-12x+36+3

(x-6)²=2y-3

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Anyone please HELP cause I’m getting frustrated
pashok25 [27]

Answer:

U =35.5

Step-by-step explanation:

Since this is a right angle, we can use trig functions

tan theta = opp/ adj

tan U = 5/7

Take the inverse of each side

tan ^-1 tan U = tan ^-1 (5/7)

U = 35.53767779

Round to the nearest tenth

U =35.5

4 0
4 years ago
If a truck averages 12 miles to the gallon, how many pounds of carbon dioxide are emitted into the atmosphere when the truck tra
77julia77 [94]

Answer: 278.30 pounds (if the gasoline does not contain ethanol)

317.12 pounds (if the gasoline does contain ethanol)

Step-by-step explanation:

If the truck averages 12 miles per gallon, then in 170 miles it consumes:

170mi/12mi = 14.17 gallons.

We know that for one gallon consumed, the carbon dioxide emitted into the atmosphere is 19.64 pounds. (assuming it does not contain ethanol)

Then for 14.17 gallons consumed, we have a emission of:

14.17*19.64 pounds = 278.30 pounds

I the gasoline contains ethanlol, for a gallon the emiision is around  22.38 pounds.

In this case the total emission is:

14.17*22.38 pounds = 317.12 pounds

3 0
3 years ago
An ac unit uses 3500 watts or power. If it runs for 10 hours each day and the utility company charges $0.13 per kWh, how much do
Helga [31]

Cost = (3500 W)·(1 kw/1000 W)·(10 hrs/day)·(30 day/month)·($0.13/kw-hr)

Cost = (3500·1·10·30·0.13 / 1000)·(W·kW·hr·da·$ / W·da·month·kw·hr)

Cost = <em> 136.50  $/month</em>

5 0
3 years ago
Find the value of x. Then find the angle measures of the triangle.
Vesnalui [34]
3x + 40 + x = 180
-40. -40
——————————-
4x. 140
—. ——-
4. 4

x = 35
4 0
3 years ago
Read 2 more answers
26.55 rounded to the nearest whole number
Mazyrski [523]
The answer is......... 27
8 0
3 years ago
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