Tutor profile: Denton T.
Given L1 and L2 are parallel lines. L1 has points a and b; L2 has points c and d Draw a line L3 from a to d. Draw a line L4 from b to c so that they intersect at a point o that is the mid-point of line L3, forming 2 triangles. Prove that the triangles are congruent
Angle aob = Angle cod Vertical angles are equal Angle oab = Angle odc Interior angles of a line between parallel lines are equal line ao = line od
A campground owner has 1400 M of fencing. He wants to enclose a rectangular field bordering a river, with no fencing along the river. What is the length of the field that yields the maximum area?
Let the width of the field be X The length of the field is then 1400 - 2X Area of the field is therefore: X(1400 - 2X) = 1400X - 2X**2 To find the maximum area find the first derivative of the area and set that to 0, solve for X dA/dX = 1400 - 4X 1400 - 4X = 0 X = 350 M Length is 1400 - 2X = 700M Area = 700x350 = 245000 square meters
Find the sum of the smallest and largest of 3 consecutive odd integers whose sum is 47
To find the sum of the smallest and largest of 3 consecutive odd integers whose sum is 47: Let X represent the smallest odd integer; then X + 2 is the second of the 3 consecutive odd integers; X + 4 is the third of the 3 consecutive odd integers. The average is the sum divided by 3. [X + (X + 2) + ( X + 4)]/3 = [3X +6]/3 X + 2 + 47 X = 45 which is the smallest odd integer therefore 49 is the largest odd integer the sum of the smallest and largest odd integer is 45 + 49 = 94
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