It takes Chris 4 hours to mow the lawn. It takes Larry only 2 hours to mow the lawn. How long would it take them to mow the lawn working together?

The volume of [tex]E[/tex] is

[tex]\displaystyle V(E)=\iiint_E\mathrm dV[/tex]

To compute the integral, convert to cylindrical coordinates:

[tex]x=r\cos\theta[/tex]

[tex]y=r\sin\theta[/tex]

[tex]z=z[/tex]

[tex]\implies\mathrm dV=r\,\mathrm dr\,\mathrm d\theta\,\mathrm dz[/tex]

[tex]\displaystyle V(E)=\int_0^{2\pi}\int_0^3\int_0^{9-r^2}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta=\frac{81\pi}2[/tex]

Now integrate [tex]f[/tex] over [tex]E[/tex]. In cylindrical coordinates, we get

[tex]\displaystyle\iiint_E3x^2z+3y^2z\,\mathrm dV=3\int_0^{2\pi}\int_0^3\int_0^{9-r^2}r^3z\,\mathrm dz\,\mathrm dr\,\mathrm d\theta=\frac{6561\pi}8[/tex]

Then the average value of [tex]f[/tex] over [tex]E[/tex] is [tex]\dfrac{\frac{6561\pi}8}{\frac{81\pi}2}=\dfrac{81}4[/tex].

The average value of a function over a certain region can be found by integrating the function over the volume and then dividing by the volume. For the given function and region, one would integrate over the range of values that satisfy the inequality z = 9 - [tex]x^2 - y^2[/tex] >= 0.

The average value of the function f(x, y, z) = [tex]3x^2z + 3y^2z[/tex] over the region enclosed by the paraboloid z = 9 −[tex]x^2 - y^2[/tex] and the plane z = 0 can be calculated by integrating the function over the volume and then dividing by the volume. This is somewhat analogous to how one would calculate an average in a discrete distribution.

The volume V(E) of the region E enclosed by the paraboloid and the plane can be found by integrating the equation of the paraboloid over the range of x and y values that satisfy the inequality z = 9 - [tex]x^2 - y^2[/tex] ≥ 0. After finding V(E), you then integrate the function f(x, y, z) over the same range of x, y, and z values to find the total of f over the volume. The average value is then the total divided by V(E).

https://brainly.com/question/32589988

#SPJ3

Answer: There is probability of 0.367 that there will be no breakdown on his car in the trip.

Step-by-step explanation:

Since we have given that

Mean (λ) = 0.5 breakdown per week

Number of weeks the owner of the car is planning to have a trip on his car for = 2 weeks

So, mean for 2 weeks would be

[tex]0.5\times 2=1.0[/tex]

We need to find the probability that there will be no breakdown on his car in the trip.

Probability that there will be no breakdown on his car in the trip is given by

P(X=0) is given by

[tex]\dfrac{e^{-\lambda}\lambda^k}{k!}\\\\=\dfrac{e^{-1}1^0}{0!}\\\\=0.367[/tex]

Hence, there is probability of 0.367 that there will be no breakdown on his car in the trip.

Answer: The net is made of 6 squares, but one face is open. I would add the area of 5 squares to get the surface area in square feet. Then, I would multiply the area by 4 to find the number of tiles needed to cover the surface area.

Step-by-step explanation:

How to use a net to find the number of tiles needed to cover the entire outer surface of the bird bath is: Multiply the surface area by 4.

Surface area can be defined as the number  of space that  cover the outer surface of a dimensional shape.

Since 4  cover one square foot of area in order to determine the number of tiles to cover the outer surface let the net be 6 squares and the surface area be 5 squares because we have one open face.

Multiply the surface area by the 4 tiles which will give us the number of tiles needed.

Therefore Multiply the surface area by 4.

Learn more about surface area here:https://brainly.com/question/16519513

#SPJ2