Answer:
65625/4(x^5)(y²)
Step-by-step explanation:
Using binomial expansion
Formula: (n k) (a^k)(b ^(n-k))
Where (n k) represents n combination of k (nCk)
From the question k = 5 (i.e. 5th term)
n = 7 (power of expression)
a = 5x
b = -y/2
....................
Solving nCk
n = 7
k = 5
nCk = 7C5
= 7!/(5!2!) ------ Expand Expression
=7 * 6 * 5! /(5! * 2*1)
= 7*6/2
= 21 ------
.........................
Solving (a^k) (b^(n-k))
a = 5x
b = -y/2
k = 5
n = 7
Substituting these values in the expression
(5x)^5 * (-y/2)^(7-5)
= (3125x^5) * (-y/2)²
= 3125x^5 * y²/4
= (3125x^5)(y²)/4
------------------------------------
Multiplying the two expression above
21 * (3125x^5)(y²)/4
= 65625/4(x^5)(y²)
Answer:The distributive property of equality
Step-by-step explanation:the 8 was distributed into the -6
Essentially, the rule goes as so: odd + odd = even, even + even = even.
Although that may not be the answer you're looking for, it is a math rule that is never debunked and essentially the premises for why you get an even sum practically always depending on the numbers.
Hope this helps!
At the start, the tank contains
(0.02 g/L) * (1000 L) = 20 g
of chlorine. Let <em>c</em> (<em>t</em> ) denote the amount of chlorine (in grams) in the tank at time <em>t </em>.
Pure water is pumped into the tank, so no chlorine is flowing into it, but is flowing out at a rate of
(<em>c</em> (<em>t</em> )/(1000 + (10 - 25)<em>t</em> ) g/L) * (25 L/s) = 5<em>c</em> (<em>t</em> ) /(200 - 3<em>t</em> ) g/s
In case it's unclear why this is the case:
The amount of liquid in the tank at the start is 1000 L. If water is pumped in at a rate of 10 L/s, then after <em>t</em> s there will be (1000 + 10<em>t</em> ) L of liquid in the tank. But we're also removing 25 L from the tank per second, so there is a net "gain" of 10 - 25 = -15 L of liquid each second. So the volume of liquid in the tank at time <em>t</em> is (1000 - 15<em>t </em>) L. Then the concentration of chlorine per unit volume is <em>c</em> (<em>t</em> ) divided by this volume.
So the amount of chlorine in the tank changes according to
which is a linear equation. Move the non-derivative term to the left, then multiply both sides by the integrating factor 1/(200 - 5<em>t</em> )^(5/3), then integrate both sides to solve for <em>c</em> (<em>t</em> ):
There are 20 g of chlorine at the start, so <em>c</em> (0) = 20. Use this to solve for <em>C</em> :
Answer:
2.2
Step-by-step explanation:
A kilogram is 2.2lbs so if you weigh yourself and it says you weigh 60k then you multiply 60 times 2.2 you get 132lbs.