answersseeker
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Hey guys just wanted to ask you for some help with maths.

Q11.: Find the equation of a line passing through (-4,0) which makes an angle of 120 degrees with the positive direction of the x-axis.

Q14.: In triangle ABC,AB has equation 4x-y=5, BC has equation 4x-3y=-9 and AC has equation 4x+y=35. Determine the equation of the altitude from A.

So far for Q14 I got the perpendicular gradient of BC to be -3/4 and if I am correct I think that I need to find point A next, but I am not sure how to do that. Can anyone help me please?
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Ecasx
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(Original post by answersseeker)
Hey guys just wanted to ask you for some help with maths.

Q11.: Find the equation of a line passing through (-4,0) which makes an angle of 120 degrees with the positive direction of the x-axis.

Q14.: In triangle ABC,AB has equation 4x-y=5, BC has equation 4x-3y=-9 and AC has equation 4x+y=35. Determine the equation of the altitude from A.

So far for Q14 I got the perpendicular gradient of BC to be -3/4 and if I am correct I think that I need to find point A next, but I am not sure how to do that. Can anyone help me please?
11. What do you need to know to find the equation of a line? Two things: the gradient and a point it passes through.

You know a point, so you only need to find the gradient. Remember: m = tan(x), where x is the angle that the line makes with the x-axis (in the positive direction).


14. You have triangle ABC where the points of the vertices themselves aren't given to you, but the equations of each side are. How can you find the coordinates of each vertice given the equations of its sides? Well the vertices will just be the points of intersection of the lines! For example, A will be the point of intersection of AB and AC, etc. Find the points, and proceed as normal.
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answersseeker
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Thank you so much for your help now I know what to do.
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Q.20 Stephen has no sense and when offered a store-card at an exorbitant rate of interest per month he stupidly accepts but does not pay it off every month. His mother finds the card and destroys it, but not before he has run up the considerable debt of £400. She gets the store to agree to him repaying a fixed amount each month and the following two months he owns £370 and £339.25.
a) Use a recurrence relation to determine the rate of interest per month and the fixed amount repaid each month.
b) How much will he still owe after a further six months if he continues to repay the same fixed amount?

Q.Solve these equations for 0 x < 2π.
a) 2sin²x - 1=0 b) 2sin²x - sinx=0 c) 2sin²x - sinx -1=0

Q. Function f(x)= 1/x-4 and g(x)= 4x+1/x.
Determine f(g(x)) and g(f(x)).

Please help. I can't ask my teacher because we have holidays and this homework is due straight after.... I really don't know how to do these..
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Hasufel
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q"). If you take the general term of a relation being:

u_{n+1} = (1+% ) u_{n} +a where % = interest to be determined, and a = fixed amout paid back, u_0 =400 - you can substitute the above amount in successive equations, and solve them "simultaneously" (a further 6 months takes you to u_8)

Q

a). re-arrange to have trig term on one side, number term on other.

b) take out a factor of "sin x", then, as the product of 2 terms is zero, one or the other or both of them is zero, so equate each in turn to zero and solve.

c) treat this like a quadratic (try "seeing" the "sin(x)" as "p", and it becomes 2p^{2}-p-1 which can then easily be factorized and solved as previously.

let me know if you need any clarification
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answersseeker
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Q. Function f(x)= 1/x-4 and g(x)= 4x+1/x.
Determine f(g(x)) and g(f(x)).
All I got was:
f(4x+1/x) and for g(f(x))= g(1/x-4)
= 1/(4x+1/x)-4 = 4(1/x-4)+1/(1/x-4)
=x/4x+1-4
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Hasufel
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notice that, since triangle PQS is isosceles, if we get the side QS for the smaller triangle QSR, which we can by using the sine rule:

\displaystyle \frac{QS}{\sin \frac{\pi}{2}}=\frac{3}{\sin \frac{\pi}{6}}

we can then use pythag to get QR since

QR^{2}=QS^{2}-RS^{2}

THEN, since the triange PQS is isosceles, PQ=QS, so we can again use pythag for the lengths we get for RS=3, and (PQ+QR)

i.e. PS^2=RS^2+(PQ+QR)^2

for your functions, can you put parentheses around the appropriate parts to clarify?
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Thank you for your help. As for the function it's fine I somehow managed to do it.
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