Author Topic: Standard Math Q+A Thread (Read 182514 times) Tweet Share

morning_sunshine · « **Reply #450 on:** October 21, 2017, 05:39:50 pm »

Quote from: RuiAce on October 21, 2017, 04:42:59 pm

$\text{Firstly, }\$3340\text{ amounted to }\$4022.\\ \text{That means that the interest charged was }\boxed{\$4022 - \$3340}$
$\text{From here, we can plug into }\boxed{I=Prn}\\ I = 4022-3340, \, P = 3340\text{ and }n=11\text{. Hence,}\\ 4022-3340 = 3340\times r \times 11$
$\text{Rearranging:}\\ \boxed{r = \frac{4022-3340}{3340\times 11}}$
So A.

(I'm leaving that other question for the time being because I'm not quite sure how to do it either, having not done general. Someone else might get to it before I get back to it.)

Thank you so much Rui! Appreciate this so so much! You have no idea how grateful I am for your help!
The answers for this question say it's C ?
Which is why I was confused also

What do you think I should do?
Stick with the answer being A?

morning_sunshine · « **Reply #451 on:** October 21, 2017, 05:43:38 pm »

One more question I have for you

Sorry for alll the questions
but here it is

Alice was driving her car at 40 km/h through a school zone.
A school student ran onto the road 15 metres in front of her.
If her reaction time is 0.50 seconds and her braking distance was 7.9 metres, was Alice able to stop her car without hitting the child?
Show calculations to support.

RuiAce · « **Reply #452 on:** October 21, 2017, 05:49:00 pm »

Quote from: morning_sunshine on October 21, 2017, 05:39:50 pm

Thank you so much Rui! Appreciate this so so much! You have no idea how grateful I am for your help!
The answers for this question say it's C ?
Which is why I was confused also

What do you think I should do?
Stick with the answer being A?

Oops, that's my fault.

I completely forgot that $n$ was measured in years, not months. Because that's the case, $ n = \frac{11}{12}$, not just 11. That's my fault - fixing it now

emilybrooks99 · « **Reply #453 on:** October 21, 2017, 07:08:45 pm »

can someone explain how to answer this please!
thanks

morning_sunshine · « **Reply #454 on:** October 21, 2017, 07:09:57 pm »

I feel so bad for asking so many questions

But I am stuck on how they found the sixty in the angle of ABC

There's no form of alternate angles that would lead me to believe the 60 is formed from that so I really would love some clarification

Thanks in advance

Regards

RuiAce · « **Reply #455 on:** October 21, 2017, 07:11:11 pm »

Quote from: emilybrooks99 on October 21, 2017, 07:08:45 pm

can someone explain how to answer this please!
thanks
(Image removed from quote.)

$\text{Add the labels:}\\ \begin{align*}x+18y&= 1510\tag{1}\\ x+36y&=2770\tag{2}\end{align*}$
$\text{The equations are set out so that the elimination method}\\ \text{is very convenient.}\\ \text{Performing }(2) - (1)\text{ gives:}\\ 18y = 1260$
$\text{So }\boxed{y = 70}\\ \text{Subbing this back into (1) then gives us}\\ x + 1270 = 1510 \implies \boxed{x = 240}$

RuiAce · « **Reply #456 on:** October 21, 2017, 07:19:56 pm »

Quote from: morning_sunshine on October 21, 2017, 05:43:38 pm

One more question I have for you
Sorry for alll the questions
but here it is

Alice was driving her car at 40 km/h through a school zone.
A school student ran onto the road 15 metres in front of her.
If her reaction time is 0.50 seconds and her braking distance was 7.9 metres, was Alice able to stop her car without hitting the child?
Show calculations to support.

$\text{We firstly convert}\\ 40\text{ km/hr} = \frac{40\text{ km}}{1\text{ hr}}$
$\text{Since 1 km is 1000 m and 1 hr is 3600 s}\\ \frac{40 \text{ km}}{1\text{ hr}} = \frac{40000\text{ m}}{3600\text{ s}} = \boxed{\frac{100}9 \text{m/s}}.$
Or you could've just divided by 3.6 straight away for the conversion.
$\text{So this is speed Alice drives at.}\\ \text{Using }\boxed{D=ST}\text{ we have}\\ D = \frac{100}{9} \times 0.50 = \frac{50}{9}\text{ m}.$
I hope I did this right but again I cannot guarantee that I did.
$\text{Since stopping distance = reaction-time distance + braking distance}\\ \text{we have stopping distance} = \frac{50}{9}+7.9\approx 13.456$
Therefore yes she was able to stop her car and save the lucky little soul

RuiAce · « **Reply #457 on:** October 21, 2017, 07:26:33 pm »

Quote from: morning_sunshine on October 21, 2017, 07:09:57 pm

I feel so bad for asking so many questions

But I am stuck on how they found the sixty in the angle of ABC

There's no form of alternate angles that would lead me to believe the 60 is formed from that so I really would love some clarification

Thanks in advance

Regards

morning_sunshine · « **Reply #458 on:** October 21, 2017, 08:49:37 pm »

Quote from: RuiAce on October 21, 2017, 07:26:33 pm

(Image removed from quote.)

Following this question
they ask how far the ship is from its starting point?

I used the cosine rule and didnt get the correct answer ?

What else can i do?

Potatohater · « **Reply #459 on:** October 21, 2017, 10:01:49 pm »

Quote from: morning_sunshine on October 21, 2017, 08:49:37 pm

Following this question
they ask how far the ship is from its starting point?

I used the cosine rule and didnt get the correct answer ?

What else can i do?

Have you tried the sine rule?

RuiAce · « **Reply #460 on:** October 21, 2017, 10:04:53 pm »

Quote from: morning_sunshine on October 21, 2017, 08:49:37 pm

Following this question
they ask how far the ship is from its starting point?

I used the cosine rule and didnt get the correct answer ?

What else can i do?

$\text{The cosine rule should've given}\\ d^2 = 85^2 + 120^2 - 2\times 85\times 120\times\cos 110^\circ$
This should've given $d=169.12$. What was their answer?

pvee123 · « **Reply #461 on:** October 21, 2017, 10:07:06 pm »

Lel this is a stupid question, but is compound interest, annuity, and future value the same thing or?

RuiAce · « **Reply #462 on:** October 21, 2017, 10:11:00 pm »

Quote from: pvee123 on October 21, 2017, 10:07:06 pm

Lel this is a stupid question, but is compound interest, annuity, and future value the same thing or?

$\text{Compound interest is just the act of}\\ \text{applying interest over and over to }\textbf{one cash flow}.$
$\text{An annuity is a }\textbf{whole stream of cash flows}.$
So if we had a hypothetical scenario with 6% p.a. interest rate and 1000 principal, then after 5 years this would've been compounded up to $ 1000(1.06)^5$.

In the case of an annuity, you would be given 1000 every year, not just the first year. Its value will accumulate to $ 1000(1.06)^5 + 1000(1.05)^4 + \dots + 1000(1.05)^1 $, because you gained an extra $1000 at the start of EVERY year.
________________________________
$\text{The future value is time value of your money}\\ \textbf{at a certain point in time}.$
The FV of the above cash flow in five years will be exactly $1000(1.06)^5$. But its FV in three years would've only been $1000(1.06)^3$. Its present value is just 1000

The computation of a FV is done through the means of compound interest. Compound interest is just the name for a method; future value is the name for the result of the method.

pvee123 · « **Reply #463 on:** October 21, 2017, 10:21:18 pm »

Thank you so much, you're amazing!

morning_sunshine · « **Reply #464 on:** October 22, 2017, 09:47:35 am »

Quote from: RuiAce on October 21, 2017, 10:04:53 pm

$\text{The cosine rule should've given}\\ d^2 = 85^2 + 120^2 - 2\times 85\times 120\times\cos 110^\circ$
This should've given $d=169.12$. What was their answer?

That was the answer they gave but when I put it in my calculator it comes up with 28602.21092

Why is that?

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