Step-by-step explanation:
A left Riemann sum approximates a definite integral as:
Given ∫₂⁸ cos(x²) dx:
a = 2, b = 8, and f(x) = cos(x²)
Therefore, Δx = 6/n and x = 2 + (6/n) (k − 1).
Plugging into the sum:
∑₁ⁿ cos((2 + (6/n) (k − 1))²) (6/n)
Therefore, the answer is C. Notice that answer D would be a right Riemann sum rather than a left (uses k instead of k−1).
Anyway
so the recursive rule tells the relationship between the previous term and the term we want to find
given
an=2n+11
it is clear that the first term is 13
2nd term is 15
3rd term is 17
each term increases by 2
so
a term is equal to the previous term plus 2
an=a(n-1)+2
the first one is the answer
125 = 5 * 5 * 5 = 5^3
Its a perfect cube.
Steps in constructing a circumscribed circle on a triangle using a just a compass and a straight edge.
1) construct a perpendicular bisector of one side of ΔRST.
2) construct another perpendicular bisector of another side of ΔRST
3) the point where the two bisectors intersect will be the center of the circle.
4) place the compass on the center point, adjust its length to ensure that any corner of the triangle will be reached and draw the circumscribed circle.
