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PSYCHO15rus [73]
3 years ago
15

Expand the expression (z-k)^6 using the binomial theorem

Mathematics
1 answer:
VARVARA [1.3K]3 years ago
8 0
Here is your answer z^6 - 6z^5k + 15z^4k^2 - 20z^3k^3 + 15z^2k^4 - 6zk^5 + k^6
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Please help me I don’t understand how to do it. If you can please use a data table to explain how to do it.
Ksivusya [100]

Answer:

The 70% mixture makes up 0.7 liters of the solution whereas the 60% mixture makes up 2.8 liters of the solution.

Step-by-step explanation:

Let us have x liters of the .7 mixture and y liters of the .6 mixture.

We want total liters to be 3.5 which means we need x+y=3.5 . I don't like the decimal in the equation so I'm going to multiply both sides by 10: 10x+10y=35

We also need the .7x+.6y=.62(3.5) . I hate the decimal business going on in this question so I'm going to multiply by 1000 which gives 700x+600y=62(35) .

So we have the system

700x+600y=62(35)

10x+10y=35

I'm going to setup this up for linear combination/elimination.

Multiply bottom equation by 60.

700x+600y=62(35)

600x+600y=60(35)

Subtract equations (bottom from top):

(700-600)x+(600-600)y=35(62-60)

Simplify:

100x+0y=35(2)

100x=70

Divide both sides by 100:

x=70/100

x=7/10

Going back to x+y=3.5 along with x=7/10 or .7 liters to find y.

y=3.5-x with x=.7

y=3.5-0.7

y=2.8

The 70% mixture makes up 0.7 liters of the solution whereas the 60% mixture makes up 2.8 liters of the solution.

Pic added.

Another way to do problem:

.7x+.6(3.5-x)=.62(3.5)

Multiply and distribute:

.7x+2.1-.6x=2.17

Combine like terms on left:

.1x+2.1=2.17

Subtract 2.1 on both sides:

.1x=.07

Multiply both sides by 10:

x=0.7 liters

Now the other acid solution is 3.5-0.7 which is 2.8 litera.

4 0
3 years ago
Evaluate The following expression . in e^e
erik [133]

\bf \textit{Logarithm Cancellation Rules} \\\\ \stackrel{\stackrel{\textit{let's use this one}}{\downarrow }}{log_a a^x = x}\qquad \qquad a^{log_a x}=x \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ln(e^e)\implies log_e(e^e)\implies e

3 0
3 years ago
- 3 ( n + 5 ) = 12<br> What is N?
lana66690 [7]
The answer will be n=-9

5 0
2 years ago
2. Find the area and circumference of the circle to the right.<br>16.6 m<br>​
adoni [48]

Answer:

AREA:

A=216.42m^2

CIRCUMFERENCE:

C=52.15m

Step-by-step explanation:

The formula that is used to calculate the area of a circle is:

A=\pi r^2

Where "r" is the radius of the circle.

The formula for calculate the circumference of a circle is:

C=2\pi r

Where "r" is the radius of the circle.

Then, you need to find the radius. This is:

r=\frac{16.6m}{2}=8.3m

Substituting the radius, you get that the area and the circumference are:

AREA:

A=\pi (8.3m)^2=216.42m^2

CIRCUMFERENCE:

 C=2\pi (8.3m)=52.15m

7 0
3 years ago
Read 2 more answers
The sum of 4 consecutive integers is 354.<br> What is the second number in this sequence?
Ulleksa [173]

354 / 4 = 88.5

 so2 numbers below that and 2 numbers above that:

87 + 88 + 89 +90 =


2nd number is 88

8 0
3 years ago
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