GEOMETRY
This is the perimeter of a square that has an area of 625 feet2
What is 100 feet?
If x-2 = 64, this is the value of x1/3 + x0
What is 3/2?
These are the numbers that appear in row 6 of Pascal's triangle
What is 1,6,15,20,15,6,1?
This is the person who the number 2.718281828459045... was named after (First and last name if he/she has them)
Who is Leonhard Euler?
This is the area of a circle in which a 3 by 4 rectangle is inscribed (No decimals)
What is 25pi?. The length of a diagonal of a 6 by 8 rectangle is 10 (pythagorean theorem). The diagonal of the rectangle is the diameter of the circle inscribed, and A = pi*r^2
Let the function f be defined by f(x) = 3x-1 and let the function g be defined by g(x) = x^2. If m is a positive number such that f(7) = g(m) + g(2), this is the value of m
What is 3/(xlnx)?
This is the center point and the radius of the equation (y+1)2 + (X-5)2 = 125. (No decimals)
What is CP(5,-1) and radius (5√5)?
(x-h)2 +(y-k)2 = r2. CP is (h,k)
This is what RREF stands for
What is Reduced Row Echelon Form?
At a certain time of day, a 25-foot telephone pole casts a 10-foot shadow. At that same time, this is how high would a tree have to be in order to cast a 25-foot shadow
What is 62.5 feet? Proportional reasoning with similar triangles.
This is the standard form of the expression (8-i/3-2i)3
What is 2 +11i?
This is the simplified version of ∫(cosx-1)/(cotx) dx
What is -cosx -ln lsecxl + C?
OR
What is -cosx +ln lcosxl + C?
This is/ These are the solution(s) to 83x+2- 64(1/2)x^2 =0 is/are? (If there are more than one, you have to give all)
What are 2 and 1?
This is the person who came up with partial fractions and was a teacher to Euler (Both first and last name)
Who is John Bernoulli?
If the integer lengths of the three sides of a triangle are 4, x, and 9, this is the least possible perimeter of the triangle
What is 19? In a given triangle the sum of two sides has to be greater than the third. 4+x>9, x is 6, and 6+4+9 is 19.
This is the inverse equation of the equation of the graph obtained by shifting the graph of f(x)=x^2 horizontally to the left 4 units and vertically down 3 units
What is f-1(x) = √(x+3) -4 ?
Given x2 - y2 = 36, this is d2y/dx2 in terms of x and y in simplest form. (3 minutes)
What is -36/y3?
This is the sum of the odd integers from 1 to 199
What is 10,000? ((1+199)100)/2 is the equation. ((first term+last term)number of terms)/2
This is how many seconds are in a 9 week grading period (no calculator)
What are 5,443,200 seconds?
This is the number of sides of a polygon in which the sum of the degree measures of the interior angles is 4 times the sum of the degree measures of the exterior angles
What is 10 sides? Sum of the degree measures of exterior angles is 360. Total interior angles is S = (n-2)180. You need 4 x 360. Then solve for (n-2) = 8 or n=10.
This is the simplified form of
[ (1+(√3/3)) / (1-(√3/3)) ] +
[ (1- (-24/25)) / (7/25) ]
What is 9 + √3?
An offshore well is located in the ocean at point W, six miles from the closest shore point A, on a straight shoreline. The oil is to be piped to a shore point B that is eight miles from point A by piping it on a straight line under water from W to some shore point P between A and B, and then on to B via pipe along the shoreline. If the cost of laying pipe is $100,000 per mile under water and $75,000 per mile over land, this is how far from point A point P should be located to minimize the cost of laying the pipe. (4 minutes)
What is 18/√7 miles?
An arched footbridge over a 100-foot river is shaped like half an ellipse. The maximum height of the bridge over the river is 20 feet. This is the height of the bridge over a point in the river exactly 25 feet from the center of the river (No decimals)
What is 10√3 feet?
(x2/2500) + (y2/400)=1
Plug in x=25 and solve
These are the powers of infinity from smallest to largest
What are ln n, na, an, n!, nn?