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3 years ago

12

5. What is the distance between two points

1 answer:

Kobotan [32]3 years ago

4 0

Answer:

6

Step-by-step explanation:

distance required=8-2=6

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Before beginning a vigorous aerobic exercise routine all adults should

Roman55 [17]

You should probably warm up with a stretching routine and a light job, because all your muscles (including your heart) cannot remain healthy and will be overworked if you dive into a vigorous aerobic routine without a proper warm up.

5 0

3 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:

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

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

3 years ago

What is the solution of y= -5x + 1 and y= 3x - 2

Nezavi [6.7K]

Answer:

x=3/8, y=-7/8. (3/8, -7/8).

Step-by-step explanation:

y=-5x+1

y=3x-2

----------

-5x+1=3x-2

-5x-3x+1=-2

-8x+1=-2

-8x=-2-1

-8x=-3

8x=3

x=3/8

y=3(3/8)-2=9/8-2=9/8-16/8=-7/8

8 0

3 years ago

Elementary Algebra Skill

mr_godi [17]

The answer is a = $\frac{4}{-3}$

Step-by-step explanation:

<em>1. Convert the mixed fraction to an improper fraction</em>

To find the numerator, multiply the denominator by the whole number and add the numerator to it.

The denominator remains the same.

So, 2 $\frac{2}{3}$ will be $\frac{8}{3}$

<em>2. Now the equation is,</em>

$\frac{3}{2}$ a - $\frac{4}{3}$ a = $\frac{10}{3}$ + $\frac{8}{3}$ a

<em>3. Take LCM on both sides. </em>

For the left side, multiply the first fraction by $\frac{3}{3}$ and multiply the second fraction by $\frac{2}{2}$

$\frac{3*3}{2*3}$ a - $\frac{4*3}{3*3}$ a = $\frac{10+8a}{3}$

<em>4. Solve by making a the subject</em>

$\frac{9a-8a}{6}$ = $\frac{10+8a}{3}$

$\frac{a}{6}$ = $\frac{10+8a}{3}$

$\frac{3a}{6}$ =10+8a

$\frac{a}{2}$ = 10 + 8a

a = 2(10 + 8a)

a = 20 + 16a

a-16a = 20

-15a = 20

a = $\frac{20}{-15}$

a = $\frac{4}{-3}$

Therefore, the answer is a = $\frac{4}{-3}$

Keyword: Equations

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4 0

3 years ago

The diameter of a circle is 12 mm. what is its radius?

MrMuchimi

Answer:

6mm

Step-by-step explanation:

radius = 1/2 of diameter

5 0

3 years ago

Read 2 more answers