## Doug C.'s Resources Hi Anne Marie,   So, the formula for finding the midpoint of a segment given the coordinates of its endpoints is:   ((x1+ x2)/2, (y1 +  y2)/2   {Average of the x coordinates, average of the y coordinates}.   For this problem we know the... TRIGONOMETRY (answer)

Hi Nick,    Start like this:   (4x)2 + x2 = 252   You should reach 17x2 = 625. See if you can solve that for x (divide both sides by 17, then take square root of both sides). Hi MGK,    I see this question was posted yesterday. If you still need some help please see:   https://www.desmos.com/calculator/oof6qlevx3   You will want to use the washer method (outer radius squared) - (inner radius squared), etc. The graph and integral... 20 = 49(.5)20/h   Doris I assume you got this far based on the fact you did not know how to solve for h.   20/49 = (.5)20/h   Take the natural log of both sides (any base works but ln is customary).   ln (20/49) = ln (.5)20/h   ln... Hi Zicheng,   Try this and see if it helps get you going in the right direction.   Picture looking at the barrel from one of its ends. The cross section will be a circle with radius 16 in. Draw a horizontal line parallel to the ground that is 8 inches above where the barrel... n ∑     24k(k-1)/n7 = 24/n7 ∑ k(k-1) = 24/n7 ∑ (k2 - k) = 24/n7 (∑ k2 - ∑ k)  -- realizing the 24/n7 is a constant k=1   Omitted the from k =1 to n in all except the first ∑.   Now the key is understanding the formulas for ∑... I have a feeling the intent of this problem was to include he circumference of the semi-circle as part of the perimeter.   The following graph depicts the window:   https://www.desmos.com/calculator/jdfm5acoyf   Drag the slider for the radius of the semi-circle... Hi Ethan,   Try something like this.   Let x= # 2-pt field goals and y = # 3-point field goals   Then set up 2 equations with two unknowns based on the given information.   X + Y = 17   (There were 17 total field goals) 2x + 3Y... Hi Kim,   Take a look at this graph to get the idea: https://www.desmos.com/calculator/lkvil0oqhm   The vertical red strip represents a "typical" rectangle with a height that can be represented by 2 - f(x).    So, ∫02 (2 - f(x))dx where... Hi Caleb,   I will try to get you started on this by giving you a strategy. You will need formulas for volume of a sphere and cylinder and lateral surface area for a cylinder and surface area of a sphere.   The Total volume of the fuel tank can be represented by V = 4/3πr3... Hi John,   I have seen like 3 different solutions to this problem. The one I recall is to extend side ST to point X so that UT = TX. Then consider triangle RUX. Segment VT (passing through M) now passes through the midpoints of RU and UX and so MT is a midsegment of that triangle... Hi Michelle,   Check out the following graph. It will show you that A(x) = x(25-x2).   https://www.desmos.com/calculator/wvym4ekler   Next step will be to determine the value of x that generates the maximum area (would be my guess). Hi Alondra,   I'll try and get you started. See this graph for a picture of triangle ABC:    https://www.desmos.com/calculator/3xvoqw0ovq   After heading from point A 6 miles east, going northwest means North then 45 degrees towards the west. That is represented... Try this (where OF stands for Original Fraction):   OF = A/(x-3) + (Bx+C)/(x2-2) + (Dx+E)/(x2-2)2   Now multiply every term on both sides of the equation by the LCD: (x-3)(x2-2)2   Simplify the right side of the equation and collect coefficients... Hi Alex,   Take a look at the following page: https://www.desmos.com/calculator/de42wunlpa   Highlight the graph of y2 = x2 (x-2). You will see it is identical to the combination of the two functions containing the square root symbols. Not sure exactly how the answer... There are a couple ways to set up a coordinate system to model this problem. Here is how I did it. Letting (0,0) be the point on which the tank touches the ground, the center of the sphere would be located at (0,4). A cross section of the sphere through its diameter would be a circle with equation... Here is an alternative for solving this problem. After drawing segment BD, triangle BCD is isosceles with legs 10 and vertex angle (C) 132. You can find the base angles of that triangle, which will allow you to determine the measure of <ABD. You can use straightforward trig ratios to find the... Hi Josh,   Several ways to think about this. How about converting the fractional parts of the mixed numbers to 16ths?     --------------(-2 12/16)--------------(-2 6/16)---------- (-1) ------- (0)   The above picture emphasizes the location of the... Hi Pat,   In order to find the points of intersection of the line with the parabola, substitute x=7-y for x into the equation of the parabola. You will find that the points of intersection are located at (7,0) and (0,7).   Sketch a graph then realize that the height of...