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Solve the simultaneous equations x^2 + y^2 = 9 and y = 3x + 3

y 2 = (3x + 3) 2 = 9x 2 + 18x + 9 x 2 + 9x 2 + 18x + 9 = 9 10x 2 + 18x = 0 (root a: x = 0) 5x + 9 = 0 (root b: x = -1.8) For x = 0, y = 3(0) + 3 (root a: y = 3) For x = -1.8, y = 3(-1.8) + 3 (root b: y = -2....
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Answered by Alistair R. • Maths tutor
4618 Views

How would you increase 400 by 7%

First, we'd want to find out what 1% of 400 is. If 400 is the total number, that would make 400 the whole 100%. In order to find out 1% we'd want to divide the number by 100 which is 4. Now that we know 1% i...
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Answered by Tharani T. • Maths tutor
15073 Views

Given that sin(x)^2 + cos(x)^2 = 1, show that sec(x)^2 - tan(x)^2 = 1 (2 marks). Hence solve for x: tan(x)^2 + cos(x) = 1, x ≠ (2n + 1)π and -2π < x =< 2π(3 marks)

sin(x) 2 + cos(x) 2 = 1 Dividing by cos(x) 2 gives: tan(x) 2 + 1 = sec(x) 2 Which rearranges as: sec(x) 2 - tan(x) 2 = 1 as required. tan(x) 2 + cos(x) 2 = 1 sec(x) 2 - 1 + cos(x) 2 = 1 sec(x) 2 + cos(x) 2 =...
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Answered by Alistair R. • Maths tutor
4440 Views

Find the exact length of side A in the triangle and give you answer in the simplest form. (It is a right angled triangle. Side C is (6+√(3)) and side B is (3 + 2√(3)).

a 2 + b 2 = c 2 (Pythagoras' Theorem) a 2 + (3 + 2√(3))(3 + 2√(3)) = (6 + √(3))(6 + √(3)) (Expanding brackets) a 2 + 9 + 6√(3) + 6√(3) + 12 = 36 + 6√(3) + 6√(3) + 3 (Multiplying and simplifying surds) a 2 + ...
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Answered by Rebecca A. • Maths tutor
4384 Views

Solve for 0 =< x =< 360 16/(cos(x+25)+1) = 10, give answers to 2 d.p.

Rearrange to get cos(x+25) = 0.6 Use inverse cosine to get (x+25) = -53.13... 53.13... 306.86... 413.13... Isolate x to get x = -78.13... 28.13... 281.86... 388.13... Apply the limits and round the answers t...
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Answered by Barnaby W. • Maths tutor
4642 Views