HELP ME PLEASE!!!

Use differentials to estimate the amount of metal in a closed cylindrical can that is 26 cm high and 10 cm in diameter if the me

Afina-wow [57]

Answer:

The estimated amount of metal in the can is 87.96 cubic cm

Step-by-step explanation:

We can find the differential of volume from the volume of a cylinder equation given by

$V= \pi r^2 h$

Thus that way we will find the amount of metal that makes up the can.

Finding the differential.

A small change in volume is given by:

$dV =\cfrac{\partial V}{\partial h} dh + \cfrac{\partial V}{\partial r} dr$

So finding the partial derivatives we get

$dV =\pi r^2 dh + \pi 2r h dr$

$dV =\pi r^2 dh + 2\pi r h dr$

Evaluating the differential at the given information.

The height of the can is h = 26 cm, the diameter is 10 cm, which means the radius is half of it, that is r = 5 cm.

On the other hand the thickness of the side is 0.05 cm that represents dr = 0.05 cm, and the thickness on both top and bottom is 0.3 cm, thus dh = 0.3 cm +0.3 cm which give us 0.6 cm.

Replacing all those values on the differential we get

$dV =\pi 5^2 (0.6) + 2\pi (5) (26) (0.05)$

That give us

$V= 28 \pi \, cm^3$

Or in decimal value

$\boxed{dV= 87.96 \, cm^3}$

Thus the volume of metal in the can is 87.96 cubic cm.

6 0

3 years ago

I need answer Immediately pls!!!!!!

Illusion [34]

Given:

Total number of students = 27

Students who play basketball = 7

Student who play baseball = 18

Students who play neither sports = 7

To find:

The probability the student chosen at randomly from the class plays both basketball and base ball.

Solution:

Let the following events,

A : Student plays basketball

B : Student plays baseball

U : Union set or all students.

Then according to given information,

$n(U)=27$

$n(A)=7$

$n(B)=18$

$n(A'\cap B')=7$

We know that,

$n(A\cup B)=n(U)-n(A'\cap B')$

$n(A\cup B)=27-7$

$n(A\cup B)=20$

Now,

$n(A\cup B)=n(A)+n(B)-n(A\cap B)$

$20=7+18-n(A\cap B)$

$n(A\cap B)=7+18-20$

$n(A\cap B)=25-20$

$n(A\cap B)=5$

It means, the number of students who play both sports is 5.

The probability the student chosen at randomly from the class plays both basketball and base ball is

$\text{Probability}=\dfrac{\text{Number of students who play both sports}}{\text{Total number of students}}$

$\text{Probability}=\dfrac{5}{27}$

Therefore, the required probability is $\dfrac{5}{27}$ .

3 0

3 years ago

What is the slop of the line? slope = 1/3 slope = -3 slope = 3

Sladkaya [172]

Answer: slope = 3

Step-by-step explanation:

We can see from the point intersecting the y axis (y-intercept) to the point (1, 1) it goes up 3 and right 1 giving us the slope $\frac{3}{1}$ simplified to 3