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Find the two real roots of the equation x^4 -5=4x^2 Give the roots in an exact form.

Disguised quadratic. Let y=x^2So quadratic become y^2-4y-5=0so (y-5)(y+1)=0so y=5 and y=-1so x^2 = 5 or -1cannot be -1 as not real henso x^2=5x=+-sqrt(5)
RJ
Answered by Rishi J. • Maths tutor
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The straight line L1 passes through the points with coordinates (4, 6) and (12, 2) The straight line L2 passes through the origin and has gradient -3. The lines L1 and L2 intersect at point P. Find the coordinates of P.

Find equation of line 1 in terms of x. eg y=mx+c - Using gradient and points. Equation of line 2 is just y=-3xSo -3x=mx+c of line 1Find xSub into one equation to find the y point.Done
RJ
Answered by Rishi J. • Maths tutor
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A ball, dropped vertically, falls d metres in t seconds. d is directly proportional to the square of t. The ball drops 45 metres in the first 3 seconds. How many metres does the ball drop in the next 7 seconds?

d = kt 2 . 45 = k x 3 2 . 45 = k x 9 (/9). 5 = k.3+7 = 10 seconds total as we are investigating the NEXT 7 seconds. d = kt 2 . d = 5 x 10 2 . d = 5 x 100d = 500m in 10 seconds. As the ball drops 45m in the f...
EN
Answered by Emily N. • Maths tutor
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A curve is defined by the parametric equations x = 3^(-t) + 1, y = 2 x 2^(t). Show that dy\dx = -2 x 3^(2t).

Write 3^(t) as an expression involving x : We can rewrite x = 3^(-t) + 1 as x - 1 = 3^(-t) ; equivalently, 3^(t) = (x-1)^(-1). Substitute this expression into y, to write y in terms of x: y = 2 x 3^(t) = 2 x...
MK
Answered by Maleeha K. • Maths tutor
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expand and simplify (x+1)(x-1)

first begin by expanding the brackets using the CLAW method (shown using whiteboard diagram)multiply the first of each bracket together, we get x 2 multiply the first term of the first bracket and the second...
AT
Answered by Adam T. • Maths tutor
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