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Danish N.
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Physics (Newtonian Mechanics)
TutorMe
Question:

Did Einstein completely prove Newton wrong? If so, why we apply Newtonian mechanics even today? Because Newton said that time is absolute and Einstein suggested it relative?

Danish N.
Answer:

In physics, it is often true that theories with vastly, "qualitatively" different assumptions and pictures to imagine what is going on yield virtually indistinguishable predictions, and Newton's vs Einstein's physics is the simplest example of that. According to Newton, for example, time was absolute. According to Einstein, time depends on the observer but time t′t′ according to one observer is expressed as a function of time tt of another observer as: t′=t−v⃗ ⋅x⃗ /c21−v2/c2−−−−−−−−√∼t−v⃗ ⋅x⃗ c2 This approximation is good at low enough velocities, v<<c. You may see that the "times" only differ by a small number that depends on 1/c21/c2 which is 10−17 in SI units (squaread seconds over squared meters). They're different in principle but the difference is so small for achievable speeds that it is (almost) unmeasurable in practice. Similar comments apply to many other phenomena and deviations. Newton would say that they're "strictly zero"; Einstein says that they are "nonzero" but their size is tiny, comparable to 1/c21/c2 times a "finite" expression.

Java Programming
TutorMe
Question:

What is the ThreadLocal class? How and why would you use it?

Danish N.
Answer:

A single ThreadLocal instance can store different values for each thread independently. Each thread that accesses the get() or set() method of a ThreadLocal instance is accessing its own, independently initialized copy of the variable. ThreadLocal instances are typically private static fields in classes that wish to associate state with a thread (e.g., a user ID or transaction ID). The example below, from the ThreadLocal Javadoc, generates unique identifiers local to each thread. A thread’s id is assigned the first time it invokes ThreadId.get() and remains unchanged on subsequent calls. I have explained this with an example of code below public class ThreadId { // Next thread ID to be assigned private static final AtomicInteger nextId = new AtomicInteger(0); // Thread local variable containing each thread's ID private static final ThreadLocal<Integer> threadId = new ThreadLocal<Integer>() { @Override protected Integer initialValue() { return nextId.getAndIncrement(); } }; // Returns the current thread's unique ID, assigning it if necessary public static int get() { return threadId.get(); } } Each thread holds an implicit reference to its copy of a thread-local variable as long as the thread is alive and the ThreadLocal instance is accessible; after a thread goes away, all of its copies of thread-local instances are subject to garbage collection (unless other references to these copies exist).

Calculus
TutorMe
Question:

What is the parametrized equation of the curve formed after intersecting a plane(2x+y+2z=1),with the surface formed after rotating the 2 dimensional curve(y=x^2)about the y-axis?

Danish N.
Answer:

So the first task is to find the equation of the surface formed after the rotation of the 2-d curve about the y-axis.. So it can be clearly seen that the surface formed is a parabloid(because a parabola is being rotated about it's axis) with the equation -> y=x^2+z^2. Now we want the intersection of the plane (2x+y+2z=1) with the parabloid(y=x^2+z^2). eliminate y by plugging it into the first equation: we get: x^2+z^2+2x+2z=1 now forming the squares (x+1)^2+(z+1)^2=3 this is the equation of a circle in the x-z plane with centre(-1,-1) and radius square root(3). hence x=-1+ squareroot(3)*cos(t), z=-1+ squareroot(3)*sin(t).. and y=1-2x-2z.

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