Exam in 7 hours need help!

[Saif905]

I can't seem to solve this page of the revision for the exam. Really need help
that's image of the paper if someone would help with the working out I would be grateful.
https://postimg.org/image/4cx5xdmjz/

11 (a) If the lines 8x + py - 2 = 0 and qx - 9y + 3 = 0 are parallel, show that pq + 72 = 0.

. ..(b) If the lines in part (a) are perpendicular, show that 9p - 8q = 0.

. ..(c) If the lines in part (a) intersect on the y-axis, find the values of p and q.

12 (a) Expand out and simplify the following:

. . . . .[FONT=MathJax_Size3][[/FONT][FONT=MathJax_Math]t[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Math]b[/FONT][FONT=MathJax_Main]/(2[/FONT][FONT=MathJax_Math]a [/FONT][FONT=MathJax_Size3]) ][/FONT]^{[FONT=MathJax_Main]2[/FONT]}

Hence, show the following:

. . . . .[FONT=MathJax_Math]a[/FONT][FONT=MathJax_Size3]([/FONT][FONT=MathJax_Math]t[/FONT][FONT=MathJax_Main] +[/FONT][FONT=MathJax_Math] b[/FONT][FONT=MathJax_Main]/[2[/FONT][FONT=MathJax_Math]a][/FONT][FONT=MathJax_Size3])[/FONT]^{[FONT=MathJax_Main]2 [/FONT]}[FONT=MathJax_Main]−[/FONT][FONT=MathJax_Math] b[/FONT]^{[FONT=MathJax_Main]2[/FONT]}[FONT=MathJax_Main]4[/FONT][FONT=MathJax_Math]a[/FONT][FONT=MathJax_Main] + [/FONT][FONT=MathJax_Math]c [/FONT][FONT=MathJax_Main]= [/FONT][FONT=MathJax_Math]a[/FONT][FONT=MathJax_Math]t[/FONT]^{[FONT=MathJax_Main]2[/FONT]}[FONT=MathJax_Main]+[/FONT][FONT=MathJax_Math]b[/FONT][FONT=MathJax_Math]t[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Math]c[/FONT]

. ..(b) Use the result of part (a) to find the values of p, q, and r such that 8x² - 12x - 15 = p (x + q)² + r.

. ..(c) Find the value of x for which 8x² - 12x - 15 has its minimum.

. ..(d) By using the Quadratic Formula or otherwise, find the values of x for which the parabola y = 8x² - 12x - 15 and the line y = 17x - 3 meet.

 

[stapel]

The full page of text is as follows:

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11 (a) If the lines 8x + py - 2 = 0 and qx - 9y + 3 = 0 are parallel, show that pq + 72 = 0.

. ..(b) If the lines in part (a) are perpendicular, show that 9p - 8q = 0.

. ..(c) If the lines in part (a) intersect on the y-axis, find the values of p and q.

12 (a) Expand out and simplify the following:

. . . . .\(\displaystyle \left(t\, +\, \dfrac{b}{2a}\right)^2\)

Hence, show the following:

. . . . .\(\displaystyle a\left(t\, +\, \dfrac{b}{2a}\right)^2\, -\, \dfrac{b^2}{4a}\, +\, c\, =\, at^2\, +\, bt\, +\, c\)

. ..(b) Use the result of part (a) to find the values of p, q, and r such that 8x² - 12x - 15 = p (x + q)² + r.

. ..(c) Find the value of x for which 8x² - 12x - 15 has its minimum.

. ..(d) By using the Quadratic Formula or otherwise, find the values of x for which the parabola y = 8x² - 12x - 15 and the line y = 17x - 3 meet.

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No work is shown on the document at the remote location, either. :shock:

 

[stapel]

I can't seem to solve this page of the revision for the exam.

11 (a) If the lines 8x + py - 2 = 0 and qx - 9y + 3 = 0 are parallel, show that pq + 72 = 0.

What must be true of the slopes, for two lines which are parallel? (here) After you solved each equation for "y=" (here), what did you get as being the slopes of each of the lines; what expressions did you get? What did you do with this information?

. ..(b) If the lines in part (a) are perpendicular, show that 9p - 8q = 0.

What must be true of the slopes, for two lines which are perpendicular? (here) After you solved each equation for "y=" (here), what did you get as being the slopes of each of the lines; what expressions did you get? What did you do with this information?

. ..(c) If the lines in part (a) intersect on the y-axis, find the values of p and q.

If they intersect on the y-axis, what must be true of their y-values when x = 0? (here) What did you do with this information?

12 (a) Expand out and simplify the following:

. . . . .\(\displaystyle \left(t\, +\, \dfrac{b}{2a}\right)^2\)

So you multiplied out the square
(here), and... then what? Where are you stuck?

Hence, show the following:

. . . . .\(\displaystyle a\left(t\, +\, \dfrac{b}{2a}\right)^2\, -\, \dfrac{b^2}{4a}\, +\, c\, =\, at^2\, +\, bt\, +\, c\)

So you took the result from part (a), multiplied each side by "p", and... then what? Where are you stuck?

. ..(b) Use the result of part (a) to find the values of p, q, and r such that 8x² - 12x - 15 = p (x + q)² + r.

So you plugged the given values in for the given variables in the given formula, simplified, and... then what?

. ..(c) Find the value of x for which 8x² - 12x - 15 has its minimum.

What formula have they given you for finding the vertex of parabolas? (Hint: It's the "Hence" from part (a) above.) What did you get, when you extracted the specified information from part (b) above?

. ..(d) By using the Quadratic Formula or otherwise, find the values of x for which the parabola y = 8x² - 12x - 15 and the line y = 17x - 3 meet.

You set the two "y=" expressions equal to each other, moved everything over to the side with the quadratic, simplified, and... then what? Where are you stuck in applying the given formula to the given equation? (here)

When you reply, please show all of your thoughts and efforts so far. Thank you!