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Mathematics: Post your doubts here!
Though the focus is on (ii), it is based on part (i) which takes much more work. I will put my work through part (i) as well. You can use it to check your answer. -
Mathematics: Post your doubts here!
Ouch forgot to tell you this is from the answer to part (ii), sorry about that. The solution to that DE is r = 25 / (5 - 2t). If you are interested in how this function is obtained, here's my work for part (ii). -
Physics: Post your doubts here!
You are right. There is force on the particle only when its motion is cutting or crossing the magnetic field lines. For this one, can you provide part (b) of the question? -
Physics: Post your doubts here!
1. Suppose one uses the same heater to: - heat a cup of water to boil - heat a full pot of water to boil Are they going to take the same time? The answer is no. Different time required means different thermal energy into the two portions of water. However, their starting and ending... -
Physics: Post your doubts here!
Forget about that statement for a moment. F_c = F + F_g is always the case, when the forces here are seen as vectors. When the stone is at the bottom, centripetal force is upward, and gravity is downward. So F_c > 0, F_g = -3.0 N So, plug in the value, we can see that F_c = F + (-3) -->... -
Physics: Post your doubts here!
I think I explained that a bit vaguely at first. Let's start it again from the beginning. First, two things hold true at any moment: 1. F_c = F + F_g 2. F_g always acts downward Now, since we know that a force has directions, that may affect its sign (positive / negative), let's suppose that... -
Physics: Post your doubts here!
Not always. The weight always acts downward. And since: 1. the centripetal force (F_c) is constantly changing direction as the object changes position 2. F_c = F + F_g ( F is the force exerted by the glue) So... The required magnitude of F is also changing. And the largest F required... -
Physics: Post your doubts here!
When talking about circular motion, the centripetal force should always be the net force on the object. This is why we need to take into account every single force on the stone, including its weight. Why necessarily net force? Because Newton's Second Law demands that the F in F = ma be the net... -
Mathematics: Post your doubts here!
This is the same as reply #17847, posted by areeba240 several days ago. I have posted my explanation to it here, on #17851. If you want to solve it in another way (different from the method provided), you can use the principle where two points are enough to determine a line. This method is... -
Mathematics: Post your doubts here!
If you did part (b) (i) correctly, you should arrive at the following result: Here, x = Re z and y = Im z. The shaded area should be a circle centred at (2, -2), with radius R = 2, but partially cut off by the lines x = 1 and y = - π/4. Now it is easy to find the largest value of Re z... -
Mathematics: Post your doubts here!
It only means the outlet rate. Inlet rate always stays constant at 400, in both (i) and (ii). -
Thought blocker I'm a senior in chemical engineering, going to graduate in one term.
Thought blocker I'm a senior in chemical engineering, going to graduate in one term.- DragonCub
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Thought blocker You mean grade? I got an A
Thought blocker You mean grade? I got an A- DragonCub
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Thought blocker Thanks! And yeah, I have taken further math, but I think I've forgotten most of...
Thought blocker Thanks! And yeah, I have taken further math, but I think I've forgotten most of it...- DragonCub
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Mathematics: Post your doubts here!
I suppose you know how to do part (i), since it doesn't require differential equations at all. I'll jump straight to part (ii). ------------------------------------------------------------------------------ One thing worth noticing is that, when we use substitution to shift the integral from... -
Mathematics: Post your doubts here!
You know the principle where a point and a direction are enough to determine a line. The method provided uses this principle. The first step is to find a point that is on both the planes, which sufficiently means the point is also on the line of intersection. To do this, solve the simultaneous... -
Mathematics: Post your doubts here!
You don't find the initial value. You arbitrarily pick one, but within a reasonable domain. In this case, it is clear that 0 ≤ x ≤ π/2. So randomly pick an initial value within this region, and you will be good to find the final value of x. -
Mathematics: Post your doubts here!
You should get a single value of θ when you used the calculator, and the value is positive. Now recall that cosine is an even function, which means cos -θ = cos θ. So, the negative value is -1 * (whatever value you got for θ).