The length of a rectangle is 2 inches more than the width. The perimeter is 24 inches. Find the length and width

A system contains n atoms, each of which can only have zero or one quanta of energy. How many ways can you arrange r quanta of e

My name is Ann [436]

Answer:

$\mathbf{a)} 2\\ \\ \mathbf{b)} 184 \; 756 \\ \\\mathbf{c)} \dfrac{(2\times 10^{23})!}{(10^{23}!)(10^{23})!}$

Step-by-step explanation:

If the system contains $n$ atoms, we can arrange $r$ quanta of energy in

$\binom{n}{r} = \dfrac{n!}{r!(n-r)!}$

ways.

$\mathbf{a)}$

In this case,

$n = 2, r=1$ .

Therefore,

$\binom{n}{r} = \binom{2}{1} = \dfrac{2!}{1!(2-1)!} = \frac{2 \cdot 1}{1 \cdot 1} = 2$

which means that we can arrange 1 quanta of energy in 2 ways.

$\mathbf{b)}$

In this case,

$n = 20, r=10$ .

Therefore,

$\binom{n}{r} = \binom{20}{10} = \dfrac{20!}{10!(20-10)!} = \frac{10! \cdot 11 \cdot 12 \cdot \ldots \cdot 20}{10!10!} = \frac{11 \cdot 12 \cdot \ldots \cdot 20}{10 \cdot 9 \cdot \ldots \cdot 1} = 184 \; 756$

which means that we can arrange 10 quanta of energy in 184 756 ways.

$\mathbf{c)}$

In this case,

$n = 2 \times 10^{23}, r = 10^{23}$ .

Therefore, we obtain that the number of ways is

$\binom{n}{r} = \binom{2\times 10^{23}}{10^{23}} = \dfrac{(2\times 10^{23})!}{(10^{23})!(2\times 10^{23} - 10^{23})!} = \dfrac{(2\times 10^{23})!}{(10^{23}!)(10^{23})!}$

3 0

3 years ago

Find the area of the shaded region

Setler79 [48]

Answer:

I would help you and say the answer but..

Step-by-step explanation:

I dont know what it is :c

7 0

2 years ago

Solve the system of equations by the addition method. 1 - 3x = -5y - 8 6x 3y = -5

Advocard [28]

$-3x = -5y -8~~~....(i) \\\\6x -3y = -5 ~~......(ii)\\\\\text{Multiply equation (i) by 2 and do (i) + (ii):}\\\\2 \cdot (-3x) + 6x -3y = 2(-5y-8) + (-5)\\\\\implies -6x +6x -3y = -10y -16 -5 \\\\\implies -3y = -10y -21\\\\\implies -3y +10y =-21\\\\\implies 7y = -21 \\\\\implies y = -\dfrac{21} 7 = -3\\\\\text{Substitute}~y =-3~ \text{in equation (ii):} \\\\6x - 3(-3) = -5\\\\\implies 6x +9 = -5\\\\\implies 6x = -5 -9 = -14\\\\\implies x = -\dfrac{14}6 = - \dfrac{7}3\\$

$\text{Hence}~ (x,y) = \left(-\dfrac 73, -3 \right)$

3 0

2 years ago

Choose the correct simplification of the expression (3x2y3z4)(2x5y2z3).

puteri [66]

Here is the answer to the given question above.
In order to correctly simplify the given expression above, we will be multiplying both expressions.
(3x^2 y^3 z^4)(2x^5 y^2 z^3)
Now, multiply the who numbers normally. But when an exponent is multiplied by another exponent, the exponents are added together.
Therefore we get, 6x^7y^5z^7.
Therefore, the correct answer would be option A.
Hope this answer helps.

5 0

3 years ago

Read 2 more answers

ANYONE i need help more than ever this is my ls day of school

Alchen [17]

It would be C. Division.

4 0

3 years ago