## Doug C.'s Resources Hi Liz,    The correct answer is P and Q. See the following graph to get the idea.   https://www.desmos.com/calculator/a4owjrypmf   How to make the decision depends on the techniques you have available to you. Here is what I did on the graph above.   The... Hi Rachel,   The log of a quotient is the difference of the logs.   So log (1384/256) = log 1384 - log 256 = ?   Take a look here for confirmation:    https://www.desmos.com/calculator/ufy7s3u4bm Hi Brandon,   Here is a start for you. You might want to draw a rough sketch of the box (without a top).   Label the width of the bottom x. The length of the base is represented by 4x. For now the height of the box is h. We want to minimize surface area, but in terms of... Hi Janet,   We can introduce the fact that the definition of derivative asks us to find lim h->0 of that difference quotient. Let's focus on the simplest way to simplify the difference quotient that you have set up.       5         ... Hi Alexis,    I am assuming that DEF refers to a triangle. That means the sum of its angles is 180. Since the angles are in the ratio 2:4:4 there is a constant of proportionality that we can call k. So the angles could be represented by 2k, 4k, and 4k.    That... Hi Seth,   See the following graph to convince yourself that on the interval from [0, 2pi) this equation has 8 solutions.   https://www.desmos.com/calculator/4qqtxxk6wr   The question is how to you find those solutions algebraically?   Start by... 3/2  =  8/(2/3)Y     That is the proportion you can set up because corresponding sides of similar figures are in the same proportion.   Cross multiply to get 2Y = 16. So, Y=8.   Similarly to solve for X.   3/2 = [1/2(4x-2)]/(x+3)   3X... One way to locate point M is to use coordinate geometry. See this graph:   https://www.desmos.com/calculator/7puz1lavso   Using this graph you can see that the coordinates of the midpoint of diagonal AC are (5.5,4). Now write the equation of the line through B and that... Should not divide by sin x, but rather set equal to zero and solve by factoring.    So, 3 sinx - sinx tan x = 0. Factoring out sin x results in sinx (3 - tanx) = 0. Then by zero product property we have:   sinx = 0 OR tanx = 3.    x = arc sin 0 OR... Hi Lucy,   Please see the following graph to get the idea.    https://www.desmos.com/calculator/iv7cppipo6   Some texts call this volume by "slicing". You need to find a formula for the area of a typical cross-section. If you solve the equation... Hi Diamond,   See this picture to get the idea:    https://www.desmos.com/calculator/dhmbl3yt9h   The d1 in the diagram represents 1/2 of one of the diagonals. Use the cos 20 to find 1/2 of the other diagonal.  Those results can be doubled... Hi Jasmine,   Try replacing sin(a+b) with sina cosb + cosa sinb.   Replace tana with sina/cosa.   Replace tanb with sinb/cosb.   Now you have a complex fraction. There are a couple ways to go from there.    I like to multiply... Hi Bea,  Take a look at the following graph. I think it will give you the idea.   https://www.desmos.com/calculator/joydlmt3nv   Use Law of Sines on the green triangle to determine the hypotenuse of the red dotted triangle. Then use trig ratio "cosine"... Without a diagram it is difficult to surmise exactly what is going on, but perhaps the diagram looks something like this:   https://www.desmos.com/calculator/nkasdz0nbx   If that looks correct you might be able to sift through the equations and determine how the value of... Hi Michael,   Think of the reference angle and associated triangle for angle B. Its opposite side will be -1 with a hypotenuse of 3. Use Pythagorean theorem to get adjacent side: 2√2 (which will be negative in QIII). This means the cos B = -2√2/3.   There are several different... Assuming the given sequence continues on and is defined as shown in the question, it looks to me like what is intended is this:   a1=√5 a2=5+√5 a3=5+√(a2) ... an=5+√(an-1) for n=3,4,5... The idea is to find the height from the ground to the top of the statue and the distance from the ground to the base of the statue and then subtract to get the height of the statue. If we call the point on the ground directly below the statue point B, then the distance from B to C can be found by... Hi Gnarls,   Since tan = sin/cos and sec = 1/cos you can write:   (sinx/cosx) + (1/cosx) --------------------------           cosx   Think of this as a complex fraction which can be simplified by multiplying top and bottom... Hi Zakia,   My guess is that this question is expecting you to treat f(x) as some unknown parent function, and then describe the effect on the parent that the numbers 2 and -1 for F(x) have on the parent. Likewise for G(x) what effect do the 1 and -2 have on the parent.   For... Hi Linda,   Do you know your theorems on summation notation? You might have to review those in order to understand some of what is shown at the following: https://www.desmos.com/calculator/4op7pzywtj   The idea is to divide the indicated region into n rectangles of...