Verify this trigonometrical identity?
Question Show that cos^4(x)-sin^4(x)=cos(2x) Answer We use the identities below. (you should know them by heart) sin^2(x) +…
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Complete the following pattern and what do you think this pattern really is? 6, 24, 60, 120, 210, …?
Answer 6 = 1 x 2 x 3 24 = 2 x 3 x 4 60 = 3…
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What is the discriminant of the equation x^ 2 + 4x – n^2= 0 ? And how many solutions does it have?
Answer Discriminant for ax^2 + bx + c is b^2 – 4ac. Thus, in our case, Discriminant =…
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Time question
Question Martina leaves home at 9 am, bicycling at a rate of 24 mi/h. Two hours later, John…
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Can someone PROVE hero’s (or Heron’s) formula?
Answer We use the formula area = (1/2)bc.sin(A) The formula above can be “proven” easily by definition that…
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Is the sine and cosine of a 60 degree angle A in a right triangle always the same?
Answer No. Here are the “sames’”. Sin(60 deg) = Cos(30 deg) = 0.866 Sin(30 deg) = Cos(60 deg)…
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Math Pattern
Question if 1=5 2= 25 3=125 4=625 then 5= what? Answer Think as follows. 1 is 5^1 =…
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What is a Permutation Algorithm?
Answer Permutation algorithm is the process of choosing r things out of n possible things, where r <=…
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What is the geometric mean between 5 and 10?
Answer To find the geometric mean of two numbers x and y, it’s just (formula): (xy)^(1/2). That…
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Subspace question? (Linear Algebra)
Question Show that the solution vectors of a consistent non-homogenous system of m linear equations in n unknowns…