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.
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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 |
Problem
A triangular shaped channel is to be designed to carry 700 L/s on a slope of 0.0001. Determine what vertex angle and depth of water over the vertex will be necessary to give a section with minimum perimeter, assuming the channel is made of timber, n = 0.012. Use Manning’s formula.
| A. θ = 45°, h = 1.425 m | C. θ = 45°, h = 2.125 m |
| B. θ = 90°, h = 2.215 m | D. θ = 90°, h = 1.215 m |
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