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Alright thanks!

Are we allowed to stop at (1), or do we have to do (2). "Q" is pretty much letting it to be the stuff in the brackets right? (ie. 5M + 4(11)^k)

$Prove by mathematical induction that$ 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...

Cool, thanks!

Could you help me on the bit with finding the volume, that's the one I'm stuck on as shown in title.

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...

Cheers :)

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?

Alright my motor is twitching A tiny little bit. Why's that the case? I have 50 loops and using a power pack with 4x AA Batteries

Jacaranda Biology, Biology in Focus. Check your school library, there should be other books as well. (not just for Biology obviously)

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?

Okay, thank you! What do I need to do in this question to prove this: The tangent at the parabola x² has point P(2ap,ap²). S is the focus of the parabola, and T is the point of the intersection of the tangent and the y axis. Show that angle SPT is equal to the acute angle between the tangent...

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...

Thanks guys :) However is the multiple root theorem part of the 4 Unit course, since I've never heard of it before? If so, is there a different method to solve this?

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

Cheers for that! :)

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.

Thanks that helps! By the way, how would I approach this question: Find the equation of the parabola with vertex (-2, 3) that also passes through (2, 1) and is concave downwards.