Reference no: EM131015933
QUESTION 1) A conic has equation
ax2 + by2 = c, where a = 3, b = -21 and c = 7.
To two decimal places what is the gradient of the asymptote that has a positive gradient?
QUESTION 2) A conic with equation
ax2 + by2 = c, has two focus points, where a = 3, b = 24 and c = 57.
One of those focus points has a positive x-coordinate. To two decimal places, what is the value of that positive x-coordinate?
QUESTION 3) What is the value of the Fibonacci number Fn, where n = 30?
QUESTION 4) Suppose a second-order difference equation is of the form Yn+2 + byn+1 + cyn = dn, where b = 6, c = 41 and d = 41.
In radians and to two decimal places, what is the value of θ in the complementary function?
QUESTION 5) A conic M, in standard or reflected standard form, is rotated through an angle r about the origin to obtain the conic N with equation
ax2 + bxy + cy2 = d, where a = 21, b = 2, c = 34 and d = 46.
To two decimal places, what is the absolute value of the angle r in degrees? As usual, do not give any units in your answer. Do not include a minus sign in your answer.
QUESTION 6) To two decimal places, what is the value of the eccentricity of the conic with equation
ax2 + by2 = c, where a = 6, b = -17 and c = 75?
QUESTION 7) A sequence Ln is such that L1 = 0.2, L2 = 0.1 and Ln = 2Ln-1 - 1.5Ln-2(n ≥ 3).
Use Mathcad to determine the value of L43, giving your answer to 2 decimal places.
QUESTION 8) To two decimal places, what is the value of the eccentricity of the conic with equation
ax2 + by2 = c, where a = 5, b = 28 and c = 34?
QUESTION 9) If you rationalise the denominator in the expression
1/a√b - c, where a = 21, b = 151 and c = 20, and you do not simplify your answer (i.e. do not divide top and bottom by some number), then what is the absolute value of the new denominator? There should not be a negative sign in your answer.
QUESTION 10) Suppose a second-order difference equation is of the form
Yn+2-byn=dn2, where b = 49 and d = 2.
To two decimal places, what is the value of the positive root in the auxiliary equation?
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