Problem
There are nine cities which are served by two competing airlines. One or the other airline (but not both) has flight between every pair of cities. What is the minimum number of possible triangular flights (i.e., trips from A to B to C and back to A on the same airline)?
| A. 12 | C. 10 |
| B. 14 | D. 16 |
Problem
A circle of radius 1 inch is inscribed in an equilateral triangle. A smaller circle is inscribed at each vertex, tangent to the circle and two sides of the triangle. The process is continued with progressively smaller circles. What is the sum of the circumference of all the circles.
MATHalino's philosophy, I may say, is that our contents must be accessible to all. Whether you are logged in or not, you can still access all our contents without any constraint. We already done this last year to our Courses and Exams, and this year we extend it to downloads.
The product of the first $n$ terms of a Geometric Progression is given by the following:
Given the first term $a_1$ and last term $a_n$:
Given the first term $a_1$ and the common ratio $r$
Here are some tips and tricks in factoring the trinomial $ax^{2}+bx+c$ mentally. Once you master the techniques in this blog, you can simplify expressions and solve equations that require factoring with "lightning" speed, and impress your friends.
Problem
Evaluate $\displaystyle \int \dfrac{(6z - 1) \, dz}{\sqrt{(2z + 1)^3}}$
Problem
Evaluate $\displaystyle \int \dfrac{y \, dy}{\sqrt[4]{1 + 2y}}$
Problem
Evaluate $\displaystyle \int \dfrac{x^3 \, dx}{(x^2 + 1)^3}$
Problem
Evaluate $\displaystyle \int y^3\sqrt{2y^2 + 1} \,\, dy$
Problem
If the first derivative of the equation of a curve is a constant, the curve is:
| A. circle | C. hyperbola |
| B. straight line | D. parabola |
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