what is the actual length of the living space if the length of the scale drawing is 16.8 centimeters ?
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Information : The given hyperbola is a horizontal hylerbola with its centre (3 , -5) and one of its focus at (9 , -5) and vertex at (7 , -5) and as we can see that the focus and vertex have same y - coordinates, it must have its Transverse axis on line y = - 5.
Now,
it's vertex is given, I.e (7 , -5)
so, length of semi transverse axis will be equal to distance of vertex from centre, i.e
- a = 7 - 3 = 4 units
Now, it's focus can be represented as ;
so,
- ae + 3 = 9
and we know, a = 4
Now, let's find the measure of semi - conjugate axis (b)
So, it's time to write the equation of hyperbola, as we already have the values of a and b ~
[ plug in the values, and h = x - coordinate of centre, and k = y - coordinate of centre ]
25mph.
using the equation distance = speed x time, you can make 2 equations. let x be the original speed of the train, and t be the original time it takes. the first equation is the original trip, the 2nd is your new speed and shortened time.
this is because you are adding 5mph, and taking off 1 hour of time, to still cover the 150 miles. you can solve the first equation for t, and substitute into the second, and then solve for x.
and using the quadratic formula you can find x=25.
using the equation distance = speed x time, you can make 2 equations. let x be the original speed of the train, and t be the original time it takes. the first equation is the original trip, the 2nd is your new speed and shortened time.
this is because you are adding 5mph, and taking off 1 hour of time, to still cover the 150 miles. you can solve the first equation for t, and substitute into the second, and then solve for x.
and using the quadratic formula you can find x=25.