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2 years ago

Choose the correct elements in the set for the following:

Mathematics

1 answer:

Ber [7]2 years ago

8 0

Answer:

Step-by-step explanation:

Y => - 3 that is {−3, −2, −1, 0, . . .}

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AlexFokin [52]

The Correct Answer Is
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2 years ago

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:

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

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

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

3 years ago

Find p(4) p(x) = 3x - 9<br>

never [62]

Answer:

p(4)=3

Step-by-step explanation:

p(4)=3(4)-9=12-9=3

3 0

2 years ago

Help plzz <br> 2decimal places<br> 165 x 0.38²

allsm [11]

Answer:

23.83

Step-by-step explanation:

3 0

2 years ago

Solve the proportion 15/6 = 10/p

V125BC [204]

Answer:

p = 4

Step-by-step explanation:

The usually recommended procedure for solving a proportion is to "cross multiply", then divide by the coefficient of the variable. (Solve the remaining one-step equation.)

<h3>Cross multiply</h3>

This means multiply both sides of the equation by the product of the denominators:

(15/6)(6p) = (10/p)(6p) . . . . "cross multiply"

15p = 60 . . . . . . simplify

<h3>Second step</h3>

Now, divide by the coefficient of the variable.

15p/15 = 60/15

p = 4

The solution is p = 4.

<em>Additional comment</em>

If the variable is in the <em>numerator</em> of the proportion, using cross multiplication, you will find that you end up multiplying and dividing by the other denominator. To solve it in that case, you only need to multiply by the denominator under the variable.

For example, to solve ...

2/5 = p/10

you only need to multiply by 10. You don't need to multiply by 50, then divide by 5.

Any proportion can be written 4 ways:

$\dfrac{a}{b}=\dfrac{c}{d}\ \Leftrightarrow\ \dfrac{a}{c}=\dfrac{b}{d}\ \Leftrightarrow\ \dfrac{b}{a}=\dfrac{d}{c}\ \Leftrightarrow\ \dfrac{c}{a}=\dfrac{d}{b}$

This suggests another strategy: invert the whole proportion, then solve it as one with p in the numerator:

6/15 = p/10 ⇒ p = 10(6/15) = 4

4 0

1 year ago

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