Show that the cylinder x 2 + y 2 = 4 and the sphere x 2...

Show that the cylinder x 2 + y 2 = 4 and the sphere x 2 + y 2 + z 2 − 8y − 6z + 21 = 0 are tangent at the point (0, 2, 3). That is, show that the cylinder and sphere intersect at that point, and that they share the same tangent plane at that point.

Expert Solution

milcah answered 2 years ago

Q. Show that the ellipse x^2/4+ y^2/9= 1 in R2 is connected, and show that the function...

Q. Show that the ellipse x^2/4+ y^2/9= 1 in R2 is connected, and show that the function f(x, y) = 3 x^3− 5y^3 − 4 has a zero on the above ellipse.

For the differential equation (2 -x^4)y" + (2x -4)y' + (2x^2)y=0. Compute the recursion formula for...

For the differential equation (2 -x^4)y" + (2*x -4)y' + (2*x^2)y=0. Compute the recursion formula for the coefficients of the power series solution centered at x(0)=0 and use it to compute the first three nonzero terms of the solution with y(0)= 12 , y'(0) =0

by using double integral find the volume of the region that bounded between two cylinder x^2+y^2=4...

by using double integral find the volume of the region that bounded between two cylinder x^2+y^2=4 and x^2+z^2=4

Solve this differential equation y''+(-4-2-2)y'+(4+4+4+4)y=x y(0)=3-2 y'(0)=2-3 Answer it as y(x)=... and motivate all the steps...

Solve this differential equation y''+(-4-2-2)y'+(4+4+4+4)y=x y(0)=3-2 y'(0)=2-3 Answer it as y(x)=... and motivate all the steps of the calculation

Hyperbolas 4(y - 1)^2 - (x + 4)^2 - 36 =0 find the x- and y-...

Hyperbolas 4(y - 1)^2 - (x + 4)^2 - 36 =0 find the x- and y- intercepts. label on graph state the domain and range

Evaluate ∫ C ( 2 x − y ) d x + ( 4 y −...

Evaluate ∫ C ( 2 x − y ) d x + ( 4 y − x ) d y where C consists of the line segment from( 0 , 1 ) to ( 1 , 0 ), followed by the line segment from ( 1 , 0 ) to( 3 , 0 ), followed by the line segment from ( 3 , 0 ) to ( 2 , 2 ). Submit answer as a number rounded to two decimal...

Consider the ODE y"+ 4 y'+ 4 y = 5 e^(− 2 x ). ( a)...

Consider the ODE y"+ 4 y'+ 4 y = 5 e^(− 2 x ). ( a) Verify that y 1 ( x) = e − 2 x and y 2 ( x) = xe − 2 x satisfy the corresponding homogeneous equation. (b) Use the Superposition Principle, with appropriate coefficients, to state the general solution y h ( x ) of the corresponding homogeneous equation. (c) Verify that y p ( x) = 52 x 2 e − 2 x...

Use spherical coordinates to find the volume of solid within the sphere x^2 + y^2 +...

Use spherical coordinates to find the volume of solid within the sphere x^2 + y^2 + z^2 = 16 and above the cone 3z^2 = x^2 + y^2 and lying in the 1st octant.

Let E be the solid region below the sphere x^2 + y^2 + z^2 = 16,...

Let E be the solid region below the sphere x^2 + y^2 + z^2 = 16, above the cone z = Sqrt[x^2 + y^2], and by the planes x = 0, y = 0, and z = 0 in the first octant. Compute the Triple Integral [(x+y+z)Cos(x^2+y^2+z^2)]dV on the region E. Please set up the integral.

x y fxy(x,y) -1 -2 1/8 -0.5 -1 1/4 0.5 1 1/2 1 2 1/8 Show...

x y fxy(x,y) -1 -2 1/8 -0.5 -1 1/4 0.5 1 1/2 1 2 1/8 Show that the function above satisfies the probabilities of a joint probability mass function. Find E(X), E(Y), V(X), V(Y) Find marginal probability distribution of X Find the covariance and correlation.

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