Atheeq A.

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Trigonometry

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Question:

Find the minimum value of 5cosA + 12sinA + 12?

Atheeq A.

Answer:

5cosA +12sinA + 12 = 13(5/13 cosA +12/13sinA) + 12 Now, for any values of B we can get sinB =5/13 and we can replace cosB = 12/13. We see that our assumption is right because we satisfy the condition sin^2B + cos^2B=1 so we get 13(sinBcosA +cosBsinA) + 12 =13(sin(A+B))+12. Therefore we know that minimum value of sinx=-1 and greatest is 1 so the least value of the expression becomes when sin(A+B) =-1 then the value of the whole term becomes 13.(-1) + 12 = -13 +12 = -1

Mechanical Engineering

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Question:

what is the difference between projectile motion and a rocket motion?

Atheeq A.

Answer:

A projectile has no motor/rocket on it, so all of its momentum is given to it as it is launched. An example of a projectile would be pen that you throw across a room. A rocket or missile does have a motor/rocket on it so it can accelerate itself while moving and so resist other forces such as gravity.

Algebra

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Question:

if 4b^2+(1/b^2)=2 then find 8b^3+(1/b^3)

Atheeq A.

Answer:

so given 4b^2+(1/b^2)=2 -------> 1 Now writing 4b^2 = (2b)^2 so now it becomes (2b)^2+(1/b^2)=2 so expanding (2b+(1/b))^2= 4b^2+(1/b^2)+2*2b*(1/b) ( Now subtiting 1 in the equation) = 2+4=6 now weget 2b+(1/b)= 6^1/2 now cubing on both sides using (a + b)3 = a3 + b3 + 3ab(a+b) (2b+(1/b))^3=8b^3+(1/b^3)+3*2b*(1/b)* (2b+(1/b)) 6^3/2 =8b^3+(1/b^3)+6* 6^1/2 6^3/2 -6* 6^1/2=8b^3+(1/b^3) 8b^3+(1/b^3)=6^3/2 - 6^3/2 ( using am * an = a(m+n)) 8b^3+(1/b^3)=0

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