A colour palette at a paint store has 6 shades of blue. Kelsie is choosing 2 shades of blue to paint her room. How many pairs of
1 answer:
Answer:
B.) 15
Step-by-step explanation:
The order in which the shades are chosen is not important. For example, choosing powder then sky is the same outcome as choosing sky then powder. So we use the combinations formula to solve this question.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
In this question:
2 shades from a set of 6. So
So the correct answer is:
B.) 15
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Differentiating the function
... g(x) = 5^(1+x)
we get
... g'(x) = ln(5)·5^(1+x)
Then the linear approximation near x=0 is
... y = g'(0)(x - 0) + g(0)
... y = 5·ln(5)·x + 5
With numbers filled in, this is
... y ≈ 8.047x + 5 . . . . . linear approximation to g(x)
Using this to find approximate values for 5^0.95 and 5^1.1, we can fill in x=-0.05 and x=0.1 to get
... 5^0.95 ≈ 8.047·(-0.05) +5 ≈ 4.598 . . . . approximation to 5^0.95
... 5^1.1 ≈ 8.047·0.1 +5 ≈ 5.805 . . . . approximation to 5^1.1
