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iren [92.7K]
3 years ago
5

25/35 Marks

Mathematics
1 answer:
Elenna [48]3 years ago
3 0

Answer:

\displaystyle (\frac{11}{2},5)

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right<u> </u>

<u>Algebra I</u>

  • Coordinates (x, y)
  • Midpoint Formula: \displaystyle (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})

Step-by-step explanation:

<u>Step 1: Define</u>

Point A(8, 2) → x₁ = 8, y₁ = 2

Point B(3, 8) → x₂ = 3, y₂ = 8

<u>Step 2: Find Midpoint</u>

Simply plug in your coordinates into the midpoint formula to find midpoint

  1. Substitute in points [Midpoint Formula]:                                                       \displaystyle (\frac{8+3}{2},\frac{2+8}{2})
  2. [Midpoint] [Fraction] Add:                                                                               \displaystyle (\frac{11}{2},\frac{10}{2})
  3. [Midpoint] Divide:                                                                                            \displaystyle (\frac{11}{2},5)
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Hello,

Here is the demonstration in the book Person Guide to Mathematic by Khattar Dinesh.

Let's assume
P=cos(a)*cos(2a)*cos(3a)*....*cos(998a)*cos(999a)
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As sin x *cos x=sin (2x) /2

P*Q=1/2*sin(2a)*1/2sin(4a)*1/2*sin(6a)*....
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 as sin(x)=-sin(2pi-x) and 2pi=1999a

sin(1000a)=-sin(2pi-1000a)=-sin(1999a-1000a)=-sin(999a)
sin(1002a)=-sin(2pi-1002a)=-sin(1999a-1002a)=-sin(997a)
...
sin(1996a)=-sin(2pi-1996a)=-sin(1999a-1996a)=-sin(3a)
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So  sin(2a)*sin(4a)*...
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= sin(a)*sin(2a)*sin(3a)*....*sin(998)*sin(999) since there are 500 sign "-".

Thus
P*Q=1/2^999*Q or Q!=0 then
P=1/(2^999)

       








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