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So x is the current amount of lemonade as a fraction which may be less than one. You are taking 1/3 of current amount of lemonade not the full jug.

So what you have is a separable differential equation.

cos(theta)(16cos^4 theta -1) = 0 cos^4 theta = 1/16 => cos(theta) =1/2 Since 1/16 = 2^-4 and (2^-4)^1/4 = 2^-1

So you just need to complete the square. The process is the same for a circle it may help to look into that. So (x+1/2)^2 = x^2 + x +?

Just use the textbook. It will have all the concepts you need

So you would end up with geometric series = num_minutes_in_a_year, where n= num_times_finger_snapped. There is no way to solve this numerically so you will need to use inspection

Yes just plus 1

Just consider the worst case. In this case it would 8 balls of the same color or each color. Of course you will only have 6 balls for red.

So if 3-2i is root then 3+2i is root because of some theorem . Then use long division

You will go anticlockwise from the numerator to the denominator when you have positive angle. When you have an negative angle you will go clockwise from the numerator from the denominator. In this particular case I don't think it will matter. As if you go anticlockwise from the numerator to the...

So finding the locus is based on the exterior angles of a triangle (Read some MM2 textbook). If memory serves well straight line joining the dots is the 180 degrees. So you have arg([z-i]/[z-1]) = 180

So the first step will be figure out the meaning of the technical terms, e.g. displacement, velocity. It looks like might bit hard to determine appropriate distance scale. So maybe you could try 1cm = 1m in the image or something.

Can you give the question a go. Maybe as a start you could multiply the fraction by (1-z) and then show that it is imaginary.

If you feel like you don't know your definitions, axioms or theorems or how apply them then use the textbook

This might help https://www.intmath.com/plane-analytic-geometry/perpendicular-distance-point-line.php Perhaps you can search for the proof?

We know that: sin x = cos(pi/2 - x) #Note: This is one of the complementary angle there are 5 other identities(Use wikipedia if need be). The co in cosine means complementary. Similarly co has the same meaning with cot...

Than you

No just be careful. It is not a good sign.

Have you read any articles?

19 a) 0^infinity = 0. infinity^0 ln(y) = ln(x)/x lim x-> infinity (ln(x)/x) = lim x-> infinity 1/x = 0 (L'Hopital rule) => ln(y) = 0 => y = 1 as x->infinty ans 1