Graph the given function. f(x)=(x-1)^3+2
1 answer:
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Answer:
-675
Step-by-step explanation:
The sum can be broken into parts that you know. Here, one of those parts is the sum of numbers 1 to n. That sum is given by n(n+1)/2.
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Another way to do this is to realize the sequence of numbers is an arithmetic sequence with a first term of 65 and a last term of 67-2·75 = -83.
The sum of an arithmetic sequence is found by multiplying the number of terms by their average value. Their average value is the average of the first and last terms.
The average value of those 75 terms is (65 +(-83))/2 = -9, so their sum is ...
75(-9) = -675
For the red line, we have:
gradient (
) = 1/3
y-intercept = 3
Equation of straight line is given by
, where is the gradient and 
is where the line intercept the y-axis
So we have,
The shaded part is above the line, hence the first inequality is
The black line, we have
gradient,
= 3
y-intercept = -2
, rearranging gives
The shaded region is to the right of the line, hence the inequality is
Note: The first option should be the correct answer but the inequality sign for <span>y > 1/3x + 3 should be </span>
gradient (
y-intercept = 3
Equation of straight line is given by
So we have,
The shaded part is above the line, hence the first inequality is
The black line, we have
gradient,
y-intercept = -2
The shaded region is to the right of the line, hence the inequality is
Note: The first option should be the correct answer but the inequality sign for <span>y > 1/3x + 3 should be </span>