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:
Step-by-step explanation:
1) For each situation to grow or decay by a constant percent rate, it must be exponential. Therefore, the correct examples are
A. The number of cars sold doubles every year. It is a 200% growth every year.
D. Each time you start a car engine the remaining engine life decreases by 0.0075%. A case of decay
E. The number of people creating cat videos increases by 15% percent every year.
F. Computer technology increases by a factor of 3 every five years.
2) this is a case of exponential decay. The expression for exponential decay is
y = b(1 - r)^t
y = final value
b = initial value
r = decay rate
t = time
Given that
r = 10% = 10/100 = 0.1
b = 50 kilograms
y = W kilograms
The relationship is
W = 50(1 - 0.1)^t
W = 50(0.9)^t
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7 boxes - fish food; 1 box contained 6 pouches
Total amount of fish food is 7 × 6 = 42 pouches of fish food
2 packets - cat food; 1 packet contained 4 pouches
Total amount of cat food is 2 × 4 = 8 pouches
How many more pouches of fish food than cat food did Shelly buy?
42 pouches - 8 pouches = 34 pouches
Therefore there was 34 more pouches of fish food than cat food
So how many times does 92 go into 181? Well only once. So the mixed part of the fraction would be 1.
181/92 = 1 89/92
