Okay folks, below are the exercises you have to complete over the summer, in addition to your exam corrections. You can do these questions on separate sheets of paper or in your H.W. journals. You will submit this work to me in our first class in August. You can use the blog post to discuss questions with me or with each other. Some of the questions will challenge and stretch your understanding. For many of you this is a great opportunity to learn and catch up with the rest of the class. Please don't try and do it all at the last minute!
Page 171-175, Misc. Ex 7.:
# 4, 5, 6, 10, 15, 24, 26, 29, 30 & 31
Page 80 - 81, Misc. Ex.4:
# 1, 2, 3, 4, 5, 6, 9, 15, 16, 17, 18, 21 & 24
Page 95 - 97, Misc. Ex.5:
# 1, 2, 6, 7, 8, 10, 11, 14, 16, 17, 18, 20 & 24
Page 57 - 60, Misc. Ex. 3:
# 3, 5, 6, 10, 13, 14, 16, 19, 23, 24 & 28
[For question 28, you can use the software Graphmatica, which is
a graphing software that you can download from http://graphmatica.com/]
Page 34, Ex. 2.2:
# 13 - 16
[Again, for question 16 , you can use Graphmatica]
Page 240-241, Ex. 10.1:
# 1-11 (all questions)
[In these question when they say basic angle they mean the angle
the star makes with the horizon line, no matter what quadrant it is in.]
Page 247-248, Ex. 10.2:
# 1-11
Omg :S
ReplyDeletesir i dont understand question 11 in excercise 10.2
ReplyDeleteYou are already there :O
ReplyDeletedo we have to use some formula for this question 11 excercise 10.2?
ReplyDeleteNo, you don't need any formula for this Duaa. YOu just have to first imagine what sin 20 degrees looks like on the unit circle.. It'll be some length called k. Now see where 200 degrees is, as in what angle above or below the horizon line that makes. Most probably it will be either 20 degrees removed from the horizon (horizontal line). So now you'll just have to see on your diagram whether sine of 200 will be a positive k value or a negative k value.
ReplyDeleteLet me know if this makes sense to you.
the value of sin 200 is supposed to be negative as it is below the horizon line!(200-180)=sin 20
ReplyDeleteSir,I'm stuck on Q.11 of miscellaneous Ex 5, I dont get how to do it.
ReplyDeleteIt gives us two equations and then tells us that they have a common factor, how are we supposed to find the values of the unknown?
hira for question 11 you can make a common factor of suppose x-a=0 then you can pluggin the value of"a" in the equation and solve it. you will get two possible values of a which you are then supposed to manipulate in the equation and find the values of k.one possibility will be cube root of -7 which will be ignored so the other value of k=5/9 will be considered.
ReplyDeleteThank you duaa!
ReplyDeleteGreat explanation Duaa! However, can you explain to me why the cube root of -7 would be ignored?
ReplyDeletewait, giving answers is allowed??
ReplyDeleteAdeel, you do raise an interesting point with your question. To rephrase, we are asking, "to what extent is Duaa's explanation giving away too much?"
ReplyDeleteHere, in the case of this question, the work still needs to be done, regardless of whether you know the answer or not. I mean, let's face it, the text book gives you the "answers" anyway. But Duaa here has mainly suggested a strategy, which still needs to be applied by Hira in order to see how the answers are obtained. So here, the process is more relevant than the answers themselves.
I'm still waiting for a response on why the cube root of -7 is to be ignored...
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ReplyDeletesir actually while working i made this minor multiplication error while manipulating the value 1 in the equation so i did the mistake=
ReplyDeletek(1)^3=k^3
however the result was k so that is how i ended up getting cuberoot of negative 7 but the real values of k were -7 and 5/9 so both will be considered. i just got a little confused myself with the negative cuberoot but now i tend to understand it!
all odd number powers let the sign remain the saim, wether its positive or negative( powered or rooted)
ReplyDeleteIn Miscellaneous exercise 5, Question 6, They ask you to state the degree of the polynomial Q(X), Even if you know the degree you dont know the constant of that polynomial, will this problem the question?
ReplyDeleteTaha for this question the degree will remain same however the constants will need to be found as they ask for the values of a and b later in the question
ReplyDeleteThat's not my question,
ReplyDeleteDoes Q(X) have any constant?
The degree we know, But we dont know the constant of Q(X), Shall we take the constant value as 1?
Example, it can be, X^3 -1 or 3X^3 or anything with X^3 being there
Also im getting -2 for both A and B whilst the book says that A=-2 and B=1,
Also when it says divide Q(X) by X+2, should we expand the whole expression and then divide?
Okay Taha, you have asked a key questions here and you make a good point. So...
ReplyDeleteFirst of all, you will have to keep your capital letters and small letters different. You see, you're right that you only know the degree of Q(x) and not the constants, which include the coefficients. In this case you'll have to assume that it is some generalized cubic function. If you remember, the general case standard form for a quadratic is Ax^2 + Bx + C. So what do you think it will be for a cubic? (remember there will be more terms in this case)
{Note: I have used capital letters for constants on the RHS because the LHS already use a small "a" and "b" and one should not confuse the two.}
Answer what I have asked and then we'll move forward...
The standard form for cubic equations would be Ax^3+Bx^2+Cx+D right?
ReplyDeleteyea, that is the standard form but its not necessary that it should be like this.
ReplyDeleteSir, I don't get you.
ReplyDeleteI mean we know the question is an identity so whatever the coefficient on the L.H.S the same will be on the R.H.S and if you evaluate the expression on the right hand side whilst taking the degree of 3 and coefficient 1 for Q(X), it will give you X^5.
Sana is absolutely correct, the standard form generalized expression for the cubic is Ax^3+Bx^2+Cx+D. Now I don't know what Falah meant when she said it is not necessary that it should be like this, but I am guessing that she meant that some cubics don't have to have the x^2 term or the linear term etc. However, even if that is what she meant, the standard form is a generalized form and does not change because, for example, B could be zero and then you don't have a x^2 term or that C could be zero and then you don't have an x term etc. etc.
ReplyDeleteNow, given that Sana has astutely answered my question, I wish for all of you to move forward with the question and replace Q(x) with the standard form Ax^3+Bx^2+Cx+D. After this you'll have to expand stuff and then you'll get a better idea about the values of A, B, C, and D. It is in this attempt to figure them out that you will find the values of 'a' and of 'b'.
So again, don't skip any steps and do it all out, keeping in mind that nothing gets missed out. Remember, this question had a star in front of it meaning that it is slightly more challenging than the others. But truthfully it is not that challenging!!!:) One just has to be careful.
As for Taha's comment, you're right that in the Ax^3 expression, the value of A is 1. But that is an elementary discovery my friend. There is more to this that you have to consider. That value of 1 for that coefficient will also lead you to other terms in the expansion once you multiply the cubic standard form by (x^2 - 1). But you're right that you have to eventually keep comparing both sides as it is an identity.