1Find the foci of thw ellipse given by the equation x236 y26

1)Find the foci of thw ellipse given by the equation x^2/36 +y^2/64=1

2) solve for x write your answer in interval notation x^2-x >_30

3) express log (x^4/ 3cuberoot y) in the terms of log x and log y.

1. x²/36 + y²/64=1

Here the larger denominator is under y²,so its a vertical ellipse

It is of the form

(x-h)²/b²+(y-k)²/a²=1

Here (h,k)=(0,0)

b²=36 a²=64

c²=a²-b²= 64-36=28

c=2sqrt7

focii= (h,k+-c) =(0,0+-2sqrt7)= (0,+-2sqrt7)

2. x²-x>=30

x²-x-30>=0

(x-6)(x+5)>=30

critical points are x=6,-5

And the solution is

(-inf,-5]U[6,inf)

3. log(x⁴/3 cube root y)

log (a/b)=log a - log b

therefore log(x⁴/3cuberoot y)= log x⁴- log 3 cube root y = 4 log x - log3 - 1/3 log y