Use cos(t) and sin(t), with positive coefficients, to parametrize the intersection of the surfaces x^2+y^2=81 and z=5x^4.

Step-by-step explanation:

We are given that two surfaces

and

We have to find the parametrize the intersection of the given surfaces using cost and sin t with positive coefficient.

We know that intersection curve S(t) is given by

S(t)=(x(t),y(t),z(t)),

Compare with the equation of circle

Where (h,k) is center of circle and r is the radius of the circle.

The center and radius of given circle is (0,0) and 9.

because cost  takes along x - axis and sin t takes along y- axis.

When we substitute these values then we get

()

Hence,

Substitute the value of x in second equation of surface

Hence, the intersection curve s(t) is given by

1,150 give brainliest

step-by-step explanation

2r= 2300

r =1150

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)