Ummm D i think i could be wrong
Answer:
Standard form:
(1/9)(y - 1)^2 - (1/4)(x - 3)^2 = 1
Step-by-step explanation:
4y^2 -9x^2 +54x-8y-113=0
-9(x^2 - 6x) + 4(y^2 - 2y) - 113 = 0
Completing the square:-
-9 [(x - 3)^2 - 9] + 4 [ y - 1)^2 - 1] = 113
-9(x - 3)^2 + 81 + 4(y - 1)^2 - 4 = 113
-9(x - 3)^2 + 4(y - 1)^2 = 113 - 77
-9(x - 3)^2 + 4(y - 1)^2 = 36.
Divide through by 36:-
(1/9)(y - 1)^2 - (1/4)(x - 3)^2 = 1.
On the first part, all you need to write down first is the 8/27 with the square root symbol on it. Once done, you need to divide them evenly into two parts to create something that will multiply the two later on: namely square root of 4 over 9 multiplied by square root of two over three. Now, you need to make sure that the square root of four over nine is expanded further: meaning, you need to turn it into 2 over three and square root of three over square root of three, and multiplied by the other number. Combine the two fractions that have square roots via multiplication, and that will result to 2 over 3 times 6 (with square root) over three. Finally, simplify the two further in order to create (two times square root of six) over three.
Answer:
6,000 meters
Step-by-step explanation:
Length of one lap d = 400 m
Lee's speed = u = 7.2 km/h. Shelby's speed v = 9 km/h
After time t, Shelby will run x meters to cover exactly 3 more laps than Lee.
So x = vt
and
x - 3d = ut
Note t = x/v, then
x - 3d = x*u/v
x (1 - u/v) = 3d
x = 3d/(1 - u/v) = 3*400/(1 - 7.2/9) = 6,000 meters