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
The slope of the line is 1/4
The tens digit is 8 more than the ones digit. There isn't any zeros.
The maximum digit is 9 because 10 would be 2 digits, 1 and 0.
So say the tens digits is 9.
9 _
The ones digit is 8 less so 9-8 = 1
9 1
There isn't any zeros which is correct.
The answer is 91.
First you have to divide 165 by 3, which is 55. and then 55 multiplied by 8 is 440. so in 8 hours, they could travel 440 miles.
Answer: a) Georgia, b) 120 words
Step-by-step explanation:
We can calculate how many words they each wrote by multiplying their time and the rate at which they write words.
Richard: 45*16 = 720 words total
Georgia: 70*12 = 840 words total.
Therefore, Georgia wrote 120 more words.
