Maths Homework help...

Question 1 10 pts

f(x) = ax2 + bx + c, where a = 2, b = -32 and c = -18.  There are two fixed points at x1 and x2, where x1 > x2.  To two decimal places what is the value of x1?

 

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Question 2 10 pts

To 2 decimal places, what is the coefficient of x8 in the expansion of (ax3+bx)8 where a = 3.2 and b = 1.8?

 

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Question 3 10 pts

f(x) = ax3 + (b - ad)x2 + (c - bd)x - cd, where a = 33, b = 3, c = 21 and d = 9. 

What value of x satisfies the equation f(x) = 0?

 

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Question 4 10 pts

What is the area of the triangle with vertices at (a, b), (c, d) and (m, n)

if a = 4, b = -5, c = -12, d = 3, m = 17, and n = 6?

As usual, your answer should be a number only (with no units).

 

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Question 5 10 pts

f(x) = ax2 + bx + c, where a = -35, b = 9 and c = 19.  What is the gradient of the point, with x coordinate 12, on the graph of y = f(x)?

 

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Question 6 10 pts

The composite transformation qa o rb can be expressed as the single transformation qc, where a = 0.4, b = 4.7 and 0≤c<π. To 2 decimal places, what is the value of c?

 

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Question 7 10 pts

The composite of three translations given by

ta,b o tc,d o th,k

is equivalent to the single translation tm,n.

What is the value of m if a = -22, b = 11, c = 14, d = -5, h = -20 and k = -8 ?

 

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Question 8 10 pts

The composite transformation qa o qb can be expressed as the single transformation rc, where a = 0.7, b = 1.6 and 0≤c<2π. To 2 decimal places, what is the value of c?

 

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Question 9 10 pts

f(x) = x2 + bx + c, where b = -8 and c = 59.  What is the coefficient of x2 in the function f(f(x))?

 

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Question 10 10 pts

f and g are linear transformations.  The matrices for f and g are respectively  and  where a = -8, b = 3, c = 9, d = -9, m = 7, n = -7, p = -6 and q = 11.

What is the lower-left entry in the matrix that represents the composite transformation g o f?