Answer:
(a) 0.107 million per year
(b) 0.114 million per year
Step-by-step explanation:
(a) The average rate of change between 2000 and 2014 is determined by dividing the difference in the populations in the two years by the number of years. In the year 2000, 
and in 2014, 
. Mathematically,
(b) The instantaneous rate of change is determined by finding the differential derivative at that year.
The result of differentiating functions of the firm 
(where 
is a constant) is 
. Let's use in this in finding the derivative of 
.
In the year 2014, .
Answer:
x= 1, x= 4, and x= -3
Step-by-step explanation:
Use the possible combinations of factors of the constant term of the polynomial to find a first root. Try 1, -1, 2, -2, 3, -3, etc.
Notice in particular that x = 1 is a root (makes f(1) = 0):
So we know that x=1 is a root, and therefore, the binomial (x-1) must divide the original polynomial exactly.
As we perform the division, we find that the remainder of it is zero (perfect division) and the quotient is: 
This is now a quadratic expression for which we can find its factor form:
From the factors we just found, we conclude that x intercepts (zeroes) of the original polynomial are those x-values for which each of the factors: (x-1), (x-4) and (x+3) give zero. That is, the values x= 1, x= 4, and x= -3. (these are the roots of the polynomial.
Mark these values on the number line as requested.
The first answer is correct as the dot is on -34.5 and the bar is shaded to its left, therefore, x is less than -34.5
Hope this helped :)
Answer:
Step-by-step explanation:
We can immediately elimate two answers since x cannot be larger than the hypotenuse, which is 9. You can cosine = adjaent/hypotenuse, which gives the equation cos(54) = x/9, which simplifies to x = 9*cos(54). When you plug this into a calculator, you should get 5.29. Keep in mind that 54 is measured in degrees and not radians because.
1st day: 1 1/2 hours
2nd day: half of first day = 1/2 * 1 1/2 hours
3rd day: 2 1/2 times as long as first day: 2 1/2 * 1 1/2 hours
1 1/2 + 1/2 * 1 1/2 + 2 1/2 * 1 1/2 =
= 3/2 + 1/2 * 3/2 + 5/2 * 3/2
= 3/2 + 3/4 + 15/4
= 6/4 + 3/4 + 15/4
= 24/4
= 6
Answer: She studied for 6 hours over the 3-day period.
