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I wrote for Module A - 6.5 Module B - 5 Module C - 6

I need help with part ii) This is from last year's HSC paper by the way. So putting when displacement is 0, x = 0 5 + 6cos2t + 8sin2t = 0 6cos2t + 8sin2t = -5 Stuck here. Had a look at the solutions but I'm lost.

I don't really have a clue on this sort off stuff, but if you come first in all your subjects from a low ranking school and get internal marks like in the 70s, is it possible to get an ATAR 90+? Let the subjects be English Advanced, Chemistry, Biology, Physics, Maths (2U & 3U).

$Prove by mathematical induction that$ 5^{n}+2(11)^{n} $is a multiple of 3 for all positive integers.$ I am stuck of step 3. Here's what I've done so far. Step 1: Prove true for n = 1 5^{n}+2(11)^{n} = 5^{1}+2(11)^{1} = 5+22 = 27, $which is a multiple of 3.$ Step 2: Assume n...

How do you do these questions, 1) Noting that 2cos^{2}x\equiv%201+cos2x, prove that 8cos^{4}x\equiv%203+4cos2x+cos4x 2) Sketch on the same diagram, the curves y=cos%20x,%20y=cos^2x,%20for%20(0\leq%20x\leq%20\frac{\pi}{2}). Find the area enclosed between these curves and the volume...

How do you do this question with the substitution method? \int_{1}^{2}\frac{1}{\sqrt{4-x^{2}}}dx

When writing the story up, how are the concepts of belonging meant to be focused on in the plot? Plots would seem too cliche to start from someone not belonging, have all this stuff happening, then to someone belonging. Can you get high marks if you just focus on someone not belonging?

How do I make the coil and place it on the axle. What I've done is made a coil (wrapping it around a rectangular object) and just shoved the axle around the middle and connected it to the split ring commutator. Don't think I'm meant to do that anyway, and obviously it didn't spin, so any ideas?

Two point P (2ap, ap²) and Q (2aq, aq²) lie on the parabola x² = 4ay a) You are given that the tangents at P and Q intersect at an angle of 45 degrees. Show that p - q = 1 + pq b) By evaluating the expression x² - 4ay at T, or otherwise, find the locus of T when the tangents at P and Q...

Need help to Find the value of a and b if x = 1 is a double root of x⁴+ax³+bx²-5x+1=0

When the polynomial P(x) is divided by (x-1)(x+4), the quotient is Q(x) and the remainder is R(x). It is known that P(1) = -4. Find the value of R(1). I have no idea on how to solve this, so please help!

The cost of running a car at an average speed of V km/h is given by C=150 + (V²/80) cents per hour. Find the average speed to the nearest km/h, at which the cost of a 500km trip is a minimum.

Need help to find the equation of the directrix and the coordinates of the focus. (a) Sketch y= x²+2x-8, showing intercepts and the minimum point. (b) Find the coordinates of the focus and the equation of the directrix of the parabola. Part a done, giving (-1, -9) as the minimum which is...

The latus rectum of a parabola has endpoints (-2, 3) and (6, 3). Find two possible equations for the parabola. All I've done is found the equation of the latus rectum, which is y = 3. I'm not sure what to do next. Answers are: x²-4x-8y+12= 0 and x²-4x+8y-36= 0