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A circle has the equation x^2 + y^2 = 25. There is a point P on this circle with coordinates (4,3). A line is drawn tangental to the circle at point P. This line crosses the x axis at point Q. Find the co-ordinates of Q.

(7,0)

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Sketch, on a pair of axes, the curve with equation y = 6 - |3x+4| , indicating the coordinates where the curve crosses the axes, then solve the equation x = 6 - |3x+4|

One helpful method for solving questions like these is to sketch the curve in stages. First begin with the straight line y=3x+4 (taking 3x+4 from within the modulus lines) crossing the x axis at -4/3 and ...

Answered by Wesley S. • Maths tutor

4395 Views

Find the exact value of sin(75°). Give your answer in its simplest form.

sin(A+B) ≡ sin(A)cos(B) + sin(B)cos(A)

⇒ sin(75°) = sin(30+45)° = sin(30°)cos(45°) + sin(45°)cos(30°)

= ½ × 1/√2 + 1/√2 ×(√3)/2 = 1/(2√2) + (√3)/(2√2)

= (1+√3)/(2√2)

Answered by Leigh M. • Maths tutor

103971 Views

4x+9y=59.5 and x+y=8. Find the values of x and y.

Firstly, take the second equation and make either x or y the subject, which means to make it either x equals or y equals. To make x the subject, we take y away from both sides giving x=8-y. Then, substitu...

Answered by Bethany K. • Maths tutor

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