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Mamont248 [21]
3 years ago
12

What value of the expression ¡^0x¡^1x¡^2x¡^3x¡^4?

Mathematics
1 answer:
siniylev [52]3 years ago
7 0

Step-by-step explanation:

Seems that given expression is of complex numbers.

If it is so then let us simplify it.

{i}^{0}  \times  {i}^{1}  \times  {i}^{2}  \times  {i}^{3}  \times  {i}^{4}   \\  \\  =  {i}^{0 + 1 + 2 + 3 + 4}\\  \\  =  {i}^{10} \\  \\  = ( {i}^{2} )^{5}  \\  \\   = ( - 1 )^{5}  \\  \\   =  - 1 \\  \\   \pink{ \boxed{\therefore \:  {i}^{0}  \times  {i}^{1}  \times  {i}^{2}  \times  {i}^{3}  \times  {i}^{4}   =  - 1}}

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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
In your own words explain how you would solve this two step equation for the variable x. 9x-7=-7
NeX [460]

Answer:

Add 7 to both sides

Step-by-step explanation:

The equation has to be just x = y

There cannot be another number on the same side as the variable

Now that we did that, the equation is 9x = 0

x = 0

Well, that was easy lol

6 0
3 years ago
Read 2 more answers
1/4(4y+16)-6=-1/5(10y-35)
Marizza181 [45]
Y=3
Simplify
Distribute
Combine like terms
Add 2y to both sides
Add 2 to both sides
Divide by 3 , both sides.
If u want me to write the numbers and all just reply
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What does 7 represent

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A proportional relationship has a constant rate of change.<br> True or False
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Step-by-step explanation:

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