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The following is a (small) portion of a solution from a solutions manual keyed to a much renowned calculus text--author James Stewart. The whole problem is complex and not really relevant to report here. What I want to know is: How is this tangent equation being derived. I can't for the life of...

This is the solution to a problem that asked the student to find a function of the form ax^2 +bx+c given certain information relating to the slopes at certain values of x. Also a set of coordinates was given . Anyway, I worked out the problem and managed with the help of the solutions manual (I...

Here is the problem, actually it is an example from my text book: I worked this out as it is shown here and got the same result as the book. Then I began wondering what would happen if I used the sine function instead of the tangent for the equation and I got this result: Why didn't it come...

Here is the problem: Here is what I did with this: Now, how would I prove this correct or otherwise? Another way to ask this question is: How to find the lengths of a and b for this triangle when all you know is that a line from the 90 degree angle perpendicular to the hypotenuse is 12cm. I...

Here is the problem: Here is the attempt I made: Actually I see that the final expression on the right should be squarerooted, but enough of that. Now comes the solution given in the solutions manual. I have been puzzling over the this solution. Can't see how they go from the first step to the...

I need to find inverse function of: Here is as near as I could get to isolating x: I used the solve function on my calculator and the inverse I got I entered into a graphing window: Now what I want to know is how do you get the red function out of the blue one? I mean, how algebraically?

II started going through a textbook written by Dr Earl Swokowski titled "Precalculus" in March of 2019.. It is a book written or at at least revised and published (for the ninth time) in the early years of the present millennium. A dry book. Anyway, I have just finished the last exercise of the...

I was trying today to find the intersection of two circles by solving the system of their equations. I had already found the point, (2,2), but I wanted to see if I could get the same result by the systems of equation technique. Here is what I did: I did this again and again and couldn't get it...

Here is problem: The exercise referred to (62 in section 10.3) basically just describes a Cassegrain telescope configuration and asks how it works. Here is the only way I could come up to work this out: Sad, I know, but I couldn't find a way to translate the x into a or b or a combination...

How can I come from 1-cos(theta)/1-cos(theta)^2 to 1/1-cos(theta). I know these two are equivalent because they both generate the same graph...but try as I may I can't seem to massage number 1 into number 2. Any hints?

The instruction is to find an equation in x and y that has the same graph as the given polar equation. The given equation is: I rendered this in to the language of x and y thus: Also, because of the way my calculator wants polar equations to be input into the graphing facility rendered the...

Here are the instructions: I am trying to find an equation in x and y to replace this parametric system: Now, if only x=cos(t) instead of cos(2t) I would be in a good place. But as things stand this thing feels kinda mean and dreadful. Here is about as far as I get( I have gotten a little...

Here are the two problems I am going to ask about: Here are the solutions of these two problems from the solutions manual: and here is what I did with them: Now, my question is: Why doesn't my solution for 19 not work? It seems to me that we are choosing 4 cards from 13, no? So why in 19...

I came across this example in my precalculus book: I went through this carefully and then decided to see if I could apply it to a similar problem, namely instead of looking for 5 hearts, I asked what the probability would be for being dealt 4 hearts instead of 5. I figured that the probability...

Here is the exercise: ( I am being asked to find the smallest possible positive integer for which the following statement is true: I have already tested this and find that 6 is the magic number, 6 and higher which will make n true. Here is the best of many tries: Can anyone make anything out...

Here is what I'm being asked to prove for every positive integer n: First I tested with n=1: Then I tried this and that and that and this and the best I could come up with is represented by the following: I can't seem to get beyond this....has anyone got any ideas? I have tried things like...

Here is the exercise: (I am being asked to find the sum): Here is what I did and what the calculator said about it: I have worked this out in several ways. I have done the numerator and the denominator calculations separately and then divided them and still came up with the same answer. I...

Here is problem: Here is what I did with this: Obviously this is not working. But when change the - tan to +tan I do better: But this in not in the formula. What is wrong here?

Here is the problem: This is to be solved by employing a system of equations in a matrix form. Here is the best I could do for equations: This won't do, I know. How to proceed?

Here is where the problem is: My question is:Why is the point 1,1 not a solution to this system? 1,1 is not included in the shaded area but it satisfies both inequalities