Mathematics Question Thread

[Mate2425]

Thank you very much!!! 

[Aaron12038488]

help!
Bill thinks he can afford a
mortgage payment of $800
each month. How much can he
borrow
, to the nearest $100, over
25 years at 11.5% p.a.?   

[itssona]

heey, suppose I have the equations
cosx=1/root 2 and sinx=-1/root 2

and my domain is x is between 0 and pi/2

what answer fits both equations??

would I just say that sinx has no solutions in our domain?

[jamonwindeyer]

help!
Bill thinks he can afford a
mortgage payment of $800
each month. How much can he
borrow
, to the nearest $100, over
25 years at 11.5% p.a.?   

Hey! Form a series of the amount owed after each month, with \(P\) being the principal. Note that \(1+r=1+\frac{0.115}{12}\approx1.0096\). Your first few terms would be:



This would look the same as usual for this sort of question. Generalising:



Then just set \(n=25\times12=300\), and evaluate!

[jamonwindeyer]

heey, suppose I have the equations
cosx=1/root 2 and sinx=-1/root 2

and my domain is x is between 0 and pi/2

what answer fits both equations??

would I just say that sinx has no solutions in our domain?

You are looking for the quadrant where sine is negative and cosine is positive, that's the fourth quadrant! We can see the related angle is 45 degrees using the exact ratio triangles on our reference sheet, so that means the common solution is \(x=360-45=315\) degrees, using the angles of any magnitude 'system' (angles in the fourth quadrant are expressed as \(360-\theta\)

[RuiAce]

You are looking for the quadrant where sine is negative and cosine is positive, that's the fourth quadrant! We can see the related angle is 45 degrees using the exact ratio triangles on our reference sheet, so that means the common solution is \(x=360-45=315\) degrees, using the angles of any magnitude 'system' (angles in the fourth quadrant are expressed as \(360-\theta\)

Although it specified that x was between 0 and pi/2 instead of 0 and 2pi. So therefore there'd be no solutions?

(Of course, there's always the possibility that pi/2 was a typo.)

[jamonwindeyer]

Although it specified that x was between 0 and pi/2 instead of 0 and 2pi. So therefore there'd be no solutions?

(Of course, there's always the possibility that pi/2 was a typo.)

Oh I totally read it as \(2\pi\), so yeah, whichever sssona

[itssona]

Thanks Jamon and Rui

alsoo so if I was summing a geometric sequence - how many terms of -16+8-4+... must be taken to give a sum of -43/4

[Opengangs]

Thanks Jamon and Rui

alsoo so if I was summing a geometric sequence - how many terms of -16+8-4+... must be taken to give a sum of -43/4

Use the sum to n terms of a GP, and equate it to -43/4. Your goal now is to find the value of n.

[itssona]

Use the sum to n terms of a GP, and equate it to -43/4. Your goal now is to find the value of n.

oh thanks!!

[taliakaragiannis8]

Hi there, could  I have some help with this. Find the x-intercept of the tangent to the curve y = (4x - 3)/(2x+1) at the point where
x=1.

[RuiAce]

Hi there, could  I have some help with this. Find the x-intercept of the tangent to the curve y = (4x - 3)/(2x+1) at the point where
x=1.

[itssona]

for limiting sum, is it always a/1-r

[jamonwindeyer]

for limiting sum, is it always a/1-r

Yep! Provided the limiting sum actually exists, that is the formula you use to calculate it

[itssona]

Yep! Provided the limiting sum actually exists, that is the formula you use to calculate it

ooh awesomeee!