Find an equation for the plane y=4x in cylindrical coordinates. (Type theta for θ in your answer.)

Step-by-step explanation:

Given the equation of a plane in rectangular coordinates to be y = 4x.

The cylindrical coordinates of the axis is as given below;

x = rcosθ

y = rsinθ

z = z

Since there is no z coordinate in the equation of the plane given, we will only substitute x = rcosθ and y = rsinθ into the equation y = 4x and simply the result as shown;

y = 4x

rsinθ = 4( rcosθ)

rsinθ = 4rcosθ

sinθ = 4cosθ

sinθ - 4cosθ = 0

Hence the equation for the plane in cylindrical coordinate is expressed as sinθ - 4cosθ = 0

step-by-step explanation:

a cube has 6 sides

the probability of getting 5 on the first cube is 1/6 since only one side of the cube has 5 on it.

there are 3 sides of the cube with even number on it [2,4,6]

therefore the probability of getting even number is 3/6

for both events to happen together, the probability would be

1/6 x 3/6 = 12/36

which simplifies to 1/12

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: