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natka813 [3]
3 years ago
5

Nimer was driving to a hotel. He looked at his Sat Nav at 13:30 and saw the following, Distance to destination = 65 miles Nimer

arrived at the hotel at 14:48 Work out the average speed of the car in mph, from 13:30 to 14:48
Mathematics
1 answer:
andre [41]3 years ago
7 0

Answer: 50 miles per hour

Step-by-step explanation:

The average speed of the car will be gotten by using the formula:

= Distance/Time

where,

Distance = 65 miles

Time = 14:48 - 13:30 = 1:18 hours = 1 hour 18 minutes = 1 18/60 = 1.3 hours

Speed = Distance / Time

= 65 miles / 1.3 hours

= 50 miles per hour

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Darya [45]

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Write the equation for a parabola with a focus at (6,-4) and a directrix at y= -7
shtirl [24]

Given:

The focus of the parabola is at (6,-4).

Directrix at y=-7.

To find:

The equation of the parabola.

Solution:

The general equation of a parabola is:

y=\dfrac{1}{4p}(x-h)^2+k                  ...(i)

Where, (h,k) is vertex, (h,k+p) is the focus and y=k-p is the directrix.

The focus of the parabola is at (6,-4).

(h,k+p)=(6,-4)

On comparing both sides, we get

h=6

k+p=-4                            ...(ii)

Directrix at y=-7. So,

k-p=-7                            ...(iii)

Adding (ii) and (iii), we get

2k=-11

k=\dfrac{-11}{2}

k=-5.5

Putting k=-5.5 in (ii), we get

-5.5+p=-4

p=-4+5.5

p=1.5

Putting h=6, k=-5.5,p=1.5 in (i), we get

y=\dfrac{1}{4(1.5)}(x-6)^2+(-5.5)

y=\dfrac{1}{6}(x-6)^2-5.5

Therefore, the equation of the parabola is y=\dfrac{1}{6}(x-6)^2-5.5.

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