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a) dy/dx =2x-5. Sub in x=2 into dy/dx to find gradient. Then use the y-y1=m(x-x1) to find tangent. The normal is the same but the gradient is the negative inverse of the tangent. Since the gradient is different then you have to use the new gradient in y-y1=m(x-x1) to find equation of normal b)...

Im pretty sure when it says that x=2 is a zero, it means that its an intercept, such that when x=2, y=0.

Ah mb, didn't read that the parabola was a tangent to the x-axis

How can you be sure that the gradient at the x-axis is always 0? Like if it cuts the x axis twice, then wouldn't it have a non-zero gradient?

likelihood of a non-hsc graduate being mod?

Posted this thread some time ago, but anyways St Mary's is good, but it favours self-learning. They do give you a lot of resources and you can just study of it and if you need help you, the teachers are always there to help you. It wasn't really that much of a change since I was a bit ahead in...

Yeh tan inverse is from pi/2 to -pi/2 cos inverse is from 0 to pi sin inverse is from pi/2 to -pi/2

The range of sin inverse is from pi/2 to -pi/2 so that would be in the first and 4rth quadrant. cos inverse range is from 0 to pi so 1st or 2nd quadrant, but since the cos is positive should be in 1st quadrant. Is this what you were asking?

why not all

Once you used difference of two squares, use sum to product formula, then multiply them so that you can use double-angleformula to get rid of the theta/2

hopefully it's not too blurry,

AHAHA unluggy

Cause they are repeating. If you had MMM theres only one way since they are considered the same. If that makes sense

Combinations is similar to permutations, just that the order matters. Permuation is when the order doesnt matter, and combination is when the order does matter. Combinations are in the form nCr, which is \frac{n!}{r!(n-r)!}. The 4C4 means that from 4 choose 4, and 4C3 means from 4 choose 3 and...

Case 1: One M's - choose the other 4 letters from AOTH: 4C4 = 1 Case 2: Two M's - choose the other 3 letters from AOTH: 4C3 = 4 Case 3: Three M's - choose the other 2 letters from AOTH: 4C2 = 6 Total = 4+6+1 = 11

So out of 5 letters to choose out of 7 total letters : _ _ _ _ _. Number of ways to do that is 7P5, which should = to 2520. However hte word MAMMOTH has the letter M repeating 3 times, so you would divide by 3!. Thus the answer should be (I think) 2520/3!. Check with the answers cos im not 100% sure

I mean... Whats everyone watching rn? Tower of god is sick rn for me

Lmao its g dw

For questions like this, its best to actually graph if it since it becomes easier once you visually know whats going on. To do part b, you need to find the equation of the tangents P and Q. So just sub the x and y values into y -y1 = m(x-x1) and you would get the equations. Then since the...

Yeah nah, I coulnd't seem to find the answer to that. Might have to ask your teacher or jazz, sorry!