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1. B Methods of integration: direct and indirect substitution

@Stephen Tashi , I read about it here: http://math.feld.cvut.cz/mt/txtd/3/txe3da3b.htm.
2. B Methods of integration: direct and indirect substitution

I have seen two approaches to the method of integration by substitution (in two different books). On searching the internet i came to know that Approach I is known as the method of integration by direct substitution whereas Approach II is known as the method of integration by indirect...
3. Resonance pi bond problem

@jim mcnamara, Nope this is not homework. I was just trying to figure out the steps to draw resonance structures of any compound, that is, the rules for "delocalising" the electrons.
4. Resonance pi bond problem

@DrDu, but the electrons are delocalised (due to which they can move). Aren't they? If these rules are wrong then how does one draw the resonance structures of a compound?
5. Resonance pi bond problem

@mjc123 why does this happen?
6. Resonance pi bond problem

@mjc123 , could you please explain this line in your post: "whose pi electrons can move somewhere else to allow the new pi bond to be formed"
7. Resonance pi bond problem

In my chemistry study material a set of rules to draw resonance structures are given. They are: (1) Only electrons move. The nuclei of the atoms never move. (2) The only electrons that can move are pi electrons (electrons in pi bonds) and lone-pair electrons. (3) The total number of electrons...
8. Bullet trajectory: Aiming a gun

The direction of \vec{U}?
9. Bullet trajectory: Aiming a gun

@haruspex, Why?
10. Bullet trajectory: Aiming a gun

@haruspex, here it is:
11. Bullet trajectory: Aiming a gun

@haruspex, Here is the diagram i drew while solving this problem,
12. Bullet trajectory: Aiming a gun

1. Homework Statement : A person aims a gun at a bird from a point at a horizontal distance of 100m. If the gun can impart a speed of 500m/s to the bullet , then above what height of the bird he should aim his gun to hit it ? 2. Homework Equations : H_{max}=\frac{u^2\sin^2\theta}{2g}...
13. Find the angle between this vector and the coordinate axes

I am getting cos(θ)=3/[sqrt{5(5+5t^2−8t)}]. I am not posting my attempt because it is very lengthy and on top of that i do not know how to type them properly.
14. Find the angle between this vector and the coordinate axes

I cannot understand how to proceed. Could you please help.
15. Find the angle between this vector and the coordinate axes

Not working. I am getting some weird expression.
16. Find the angle between this vector and the coordinate axes

I cannot read the equation. Could you please edit it?.
17. Find the angle between this vector and the coordinate axes

A.B=ABcos(x) A.B=AxBx+Ay+By Therefore, ABcos(x)=AxBx+Ay+By =>cos(x)=(AxBx+Ay+By )/AB
18. Find the angle between this vector and the coordinate axes

Yes. Infact i had applied that formula along with this one.
19. Find the angle between this vector and the coordinate axes

1. Homework Statement : r vector = 3t i + (4t-5t2)j. Find the angle made by the vector with respect to the x-axis and the y-axis. 2. Homework Equations : A.B=AxBx+AyBy 3. The Attempt at a Solution : I tried to take the dot product of the unit vector along x-axis and r. I did the same for...
20. Doubts regarding basic chemistry concepts

Here is the numerical part with proper editing. Let A and C combine in the ratio \frac{a}{c1} and let B and C combine in the ratio \frac{b}{c2}=\frac{b*c1}{c1*c2}.(by mass). Then according to the law of reciprocal proportions, \frac{a*c2}{b*c1}=k \frac{a}{b} where k is whole number. If we...
21. Doubts regarding basic chemistry concepts

Doubts regarding the law of reciprocal proportions: What i have understood by reading the definition is that the ratio of the masses in which two elements A and B combine with a fixed mass of a third element C, will be a whole number multiple of the ratio of the masses in which A and B combine...
22. Finding the resultant of three vectors

Then how do i express R vector in terms of i and j. BTW what is wrong with my approach?
23. Finding the resultant of three vectors

How do i express F1, F2 and F3 in terms of i and j?
24. Finding the resultant of three vectors

@Spinnor, I mean R1, R2 and R3 in terms in terms of i and j.
25. Finding the resultant of three vectors

@jedishrfu, How did you get R1, R2 and R3 in terms of i and j and what is R3?
26. Finding the resultant of three vectors

1. Homework Statement : Determine the resultant of three vectors of magnitude 1, 2 and 3 whose directions are those of sides of an equilateral triangle taken in order. 2. Homework Equations : R2 = A2 + B2 + 2 A B cos θ tan α = B sin θ/(A+B cos θ) 3. The Attempt at a Solution ...
27. Fundamental problem regarding mole concept

@Buffu , so number of moles has the unit moles. Right?
28. Fundamental problem regarding mole concept

Background: Amount of substance is a fundamental physical quantity which has mole (mol) as it's SI unit. Therefore all expressions for amount of substance should have the unit mole on simplification. Therefore, if A = Amount of substance (normally in moles), m = Mass of the substance in a...
29. B What are some strategies to prove trigonometric results

I am facing a lot of problem in proving trigonometric results (advanced ones). There are a lot of formulas (compound angle related ones, transformation of sum into product ones and vice versa, multiple angle and sub-multiple angle ones). I am unable to figure out how to proceed forward in...
30. Find α+β+αβ

4.2 and 2.1 are 8 and 2 respectively which are integers. Aren't they?