Inequality
What is the integer greater than 25/24 but less than 3444/1722?
Trick question, no integer!
what is the difference between a filled dot and a hollow dot in inequalities?
a filled dot includes the number it is on, while a hollow dot doesn't.
If you cut an equilateral triangle to two right triangles, prove the longest side of the right triangle is twice as big as the shortest side.
This is because let's say the equilateral triangle has side length 2. If we cut it in half, one of the side lengths is gonna get chopped up to one, but the other side remains 2. the height also is not longest side, because if we draw a circle with radius height, the 2-length proves to be longer.
What fraction of a circle with radius 5 gets taken up by a square if the square is as large as possible but cannot go outside the circle? Assume pi = 22/7
50/
there is a triangle with side lengths a,b,c and angle C, which is opposite to side length c, where a^2 + b^2 - 2ab*cos(C) = c^2, where cos is a function operating on angles.
Assuming C is less than 180 degrees and greater than 0 degrees,if the angle is bigger than a right angle, cos(C) is negative. If the anger is smaller than a right angle, cos(C) is positive. If it IS a right angle, cos(C) is 0. Why? Explain using the given formula and an arbitrary triangle.
This is because the greater the angle, the wider C is extended, and the right angle, where the function cos(C) is 0,is pythagorean theorem, proven by square with side length (a+b)^2 and four right triangles with lengths a and b. if C was small, c would be very small too.
Why do we say the surface area of a sphere with radius x is 4 circles with same radius x when you cant directly put 4 circles on there?
Because this is the combined area
Example, 2 1x6 rectangles still have the same area as a 4x3 rectangle.
the teacher puts the expression x < y < z where y = -x and z = x^2. What is the domain of possible real values for x?
x is less than -1 and greater than negative infinity.