# Tutor profile: Pranjal G.

## Questions

### Subject: Trigonometry

Find the maximum value of 5cosA + 12sinA + 12

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. Тhe greatest value is when sin(A + B) = 1 then value of the expression becomes 13.1 + 12 = 25

### Subject: Basic Chemistry

According to Henry’s Law, in gases, an increase in pressure increase______. a) Solubility b) saturation c) volume d) viscosity

a) Solubility

### Subject: Algebra

The sum of two consecutive odd numbers is 52. What are the two odd numbers?

First, an even number is a multiple of 2: 2, 4, 6, 8, and so on. It is conventional in algebra to represent an even number as 2n, where, by calling the variable 'n,' it is understood that n will take whole number values: n = 0, 1, 2, 3, 4, and so on. An odd number is 1 more (or 1 less) than an even number. And so we represent an odd number as 2n + 1. Let 2n + 1, then, be the first odd number. Then the next one will be 2 more -- it will be 2n + 3. The problem states that their sum is 52: 2n + 1 + 2n + 3 = 52. We will now solve that equation for n, and then replace the solution in 2n + 1 to find the first odd number. We have: 4n + 4 = 52 4n = 48 n = 12. Therefore the first odd number is 2· 12 + 1 = 25. And so the next one is 27. Their sum is 52.

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