Ramp Learning

1. The mechanics at Lincoln Automotive are reborning a 6 in deep cylinder to fit a new piston. The machine they are using increa

Firdavs [7]

Answer:

$0.0239\frac{in^{3}}{min}$

Step-by-step explanation:

In order to solve this problem, we must start by drawing a diagram of the cylinder. (See attached picture)

This diagram will help us visualize the problem better.

So we start by determining what data we already know:

Height=6in

Diameter=3.8in

Radius = 1.9 in (because the radius is half the length of the diameter)

The problem also states that the radius will increase on thousandth of an inch every 3 minutes. We can find the velocity at which the radius is increasing with this data:

$r'=\frac{1/1000in}{3min}$

which yields:

$r'=\frac{1}{3000}\frac{in}{min}$

with this information we can start solving the problem.

First, the problem wants us to know how fast the volume is increasing, so in order to find that we need to start with the volume formula for a cylinder, which is:

$V=\pi r^{2}h$

where V is the volumen, r is the radius, h is the height and π is a mathematical constant equal approximately to 3.1416.

Now, the height of the cylinder will not change at any time during the reborning, so we can directly substitute the provided height, so we get:

$V=\pi r^{2}(6)$

or

$V=6 \pi r^{2}$

We can now take the derivative to this formula so we get:

$\frac{dV}{dt}=2(6)\pi r \frac{dr}{dt}$

Which simplifies to:

$\frac{dV}{dt}=12\pi r \frac{dr}{dt}$

We can now substitute the data provided by the problem to get:

$\frac{dV}{dt}=12\pi (1.9) (\frac{1}{3000})$

which yields:

$\frac{dV}{dt}=0.0239\frac{in^{3}}{min}$

3 0

4 years ago

I got disconnected from my tutor, can't reconnect. need an explanation

kherson [118]

The absolute value function |x| always returns a non-negative number. It takes any number x and returns x if it's already non-negative, or -x if it is negative in order to make it positive.

$|x|=\begin{cases}x&\text{for }x\ge0\\-x&\text{for }x$

For the equation

-3 + 4 |2x - 5| = 14

rearrange terms to get

|2x - 5| = 17/4

Now,

• if 2x - 5 ≥ 0, then |2x - 5| = 2x - 5. Then

2x - 5 = 17/4

• and if instead 2x - 5 < 0, then |2x - 5| = -(2x - 5), so that

-(2x - 5) = 17/4, or

2x - 5 = -17/4

In the first case,

2x - 5 = 17/4

2x = 17/4 + 5 = 37/4

x = 37/8

In the second case,

2x - 5 = -17/4

2x = -17/4 + 5 = 3/4

x = 3/8

5 0

3 years ago

A magazine provided results from a poll of 1000 adults who were asked to identify their favorite pie. Among the 1000 respondents

rjkz [21]

Answer:

Step-by-step explanation:

76/29 $9/77$

4 0

3 years ago

3/8 c−2= 3/2 c−12 helpp

ivann1987 [24]

I think C is 80/9
But i dont know if thats what you are looking for

5 0

3 years ago

Danny is thinking of buying a gym membership. He has two gums available to choose from. Gym A has a $35 initial fee and costs $4

Ivanshal [37]

For this, all you have to do is create equations where all you have to do is change the x value. The equation for gym A would be 35 + 42x, where x is the number of months he has the membership, and the first number is the initial fee. The equation for gym B would be 65 + 36x, following the same rules. Now all you have to do is set both of these equations equal to each other:
65+36x=35+42x
Solving this equation results in x=5, which means that he has to have the memberships for 5 months for them to be equal. Now just plug that in to one side of the equation to get the amount he has to spend:
65+36(5) = $245

6 0

3 years ago