May 29, 2020, 12:43:17 pm

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#### fun_jirachi

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« Reply #4305 on: August 09, 2019, 05:30:44 pm »
+1
You should try following a similar process to what Rui previously outlined:
- Asymptotes, limiting value as x approaches positive and negative infinity
In this case, the horizontal asymptote is at x=4, and as x approaches positive infinity y approaches 4 from below.
- Dilation/Shift to the right/left, orientation
The dilation is likewise pretty hard to see, but basically, note that from the two negative signs (or by subbing in numbers) that the exponential will tend towards negative infinity as y approaches negative infinity.

Hope this helps
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#### Coolmate

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« Reply #4306 on: August 10, 2019, 01:19:34 pm »
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You should try following a similar process to what Rui previously outlined:
- Asymptotes, limiting value as x approaches positive and negative infinity
In this case, the horizontal asymptote is at x=4, and as x approaches positive infinity y approaches 4 from below.
- Dilation/Shift to the right/left, orientation
The dilation is likewise pretty hard to see, but basically, note that from the two negative signs (or by subbing in numbers) that the exponential will tend towards negative infinity as y approaches negative infinity.

Hope this helps

Hi fun_jirachi!

This was extremely helpful and I understood the question perfectly, thankyou for your help!

Coolmate
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#### LoneWolf

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« Reply #4307 on: August 13, 2019, 11:44:50 am »
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Hi Guys,
Bit confused over logs atm (in year 11)
the question says:
"Find which two integers each expression lies between"
Log2(50) and the answers say 5 & 6 can someone explain this please!
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#### LoneWolf

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« Reply #4308 on: August 13, 2019, 11:49:54 am »
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Pls dont worry... have since got it! : |
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#### Coolmate

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« Reply #4309 on: August 23, 2019, 10:16:22 pm »
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Hello Everyone!

Would someone please be able to help me with these questions based on Logarithms, b,e, and h?(Attached) I have no idea about how to go about answering them --> and also explain a bit about natural logs compared against normal logs?

Cheers,

Coolmate
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#### RuiAce

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« Reply #4310 on: August 23, 2019, 10:31:40 pm »
+2
Hello Everyone!

Would someone please be able to help me with these questions based on Logarithms, b,e, and h?(Attached) I have no idea about how to go about answering them --> and also explain a bit about natural logs compared against normal logs?

Cheers,

Coolmate
Your calculator should have a button that can compute all of those for you. And then you just round it.

The "natural" logarithm is just a special name we give to the base $e$ logarithm, where $e$ is this fancy number (Euler's number) that behaves like $\pi$ with its weird decimals and $e\approx 2.718281828459045$.

Saying $y = \ln x$ is the exact same thing as saying $y = \log_e x$.

#### Coolmate

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« Reply #4311 on: August 23, 2019, 11:00:02 pm »
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Your calculator should have a button that can compute all of those for you. And then you just round it.

The "natural" logarithm is just a special name we give to the base $e$ logarithm, where $e$ is this fancy number (Euler's number) that behaves like $\pi$ with its weird decimals and $e\approx 2.718281828459045$.

Saying $y = \ln x$ is the exact same thing as saying $y = \log_e x$.

Hey Rui!

Thankyou! I just checked with the calculator and it does have the button!

Also, just clarifying; so ln is essentially just exactly written as loge?

Cheers,

Coolmate
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#### RuiAce

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« Reply #4312 on: August 23, 2019, 11:01:08 pm »
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Hey Rui!

Thankyou! I just checked with the calculator and it does have the button!

Also, just clarifying; so ln is essentially just exactly written as loge?

Cheers,

Coolmate
Awesome

And yep

#### Coolmate

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« Reply #4313 on: August 23, 2019, 11:04:35 pm »
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Thanks Rui for helping me! That's awesome

Cheers,

Coolmate
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#### mirakhiralla

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« Reply #4314 on: August 29, 2019, 10:47:30 pm »
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Hey sorry I need help in ii
In the Jackpot Lottery, the probability of the Jackpot prize being won in any draw is approximately 1 in 50.

i) What is the probability that the jackpot prize will be won in each of the three consecutive draws?

ii) How many consecutive draws must be made for it to be 99% certain that a Jackpot prize will have been won?

#### DrDusk

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« Reply #4315 on: August 29, 2019, 11:36:48 pm »
+1
Hey sorry I need help in ii
In the Jackpot Lottery, the probability of the Jackpot prize being won in any draw is approximately 1 in 50.

i) What is the probability that the jackpot prize will be won in each of the three consecutive draws?

ii) How many consecutive draws must be made for it to be 99% certain that a Jackpot prize will have been won?

$\text{Since there is a 1/50 change of winning, we can say there is a 49/50 chance of losing}$
$\text{So what we want to do is do 49/50 * 49/50 'n' number of times/draws such that the probability of losing is 0.01}$
$\therefore \bigg(\frac{49}{50}\bigg)^n = 0.01$
$\therefore nln\bigg(\frac{49}{50}\bigg) = ln(0.01)$
$\therefore n = 228\hspace{2mm}\text{draws}$
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#### RuiAce

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« Reply #4316 on: August 30, 2019, 10:14:21 am »
+1
Hey sorry I need help in ii
In the Jackpot Lottery, the probability of the Jackpot prize being won in any draw is approximately 1 in 50.

i) What is the probability that the jackpot prize will be won in each of the three consecutive draws?

ii) How many consecutive draws must be made for it to be 99% certain that a Jackpot prize will have been won?
Basically see above for the answer. Just want to provide a small remark for extra intuition.

The question is probably doable directly, but it would probably be messy. Because you only require the probability that it is won at least one out of the first $n$ draws, you get different results depending on if it's won exactly once, twice, three times, all the way up to $n$ times.

And in 2U maths, of course we learn that the complement is a natural way to navigate around the "at least" issue wherever possible. The complement is when you don't win it at all, which you know can only happen one possible way. (Namely, it is never won.)

So this probability will be $\left( \frac{49}{50} \right)^n$, and hence what we require is $1 - \left( \frac{49}{50} \right)^n = 0.99$. Which of course, becomes what was computed above.
-snip-
You can use \times for $\times$ and you should use \ln for $\ln$ for better LaTeX in the future

#### Kombmail

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« Reply #4317 on: September 09, 2019, 06:17:46 pm »
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does anyone know how Ln(1)= Ln(d)
becomes d=e?
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#### RuiAce

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« Reply #4318 on: September 09, 2019, 06:19:45 pm »
+1
does anyone know how Ln(1)= Ln(d)
becomes d=e?
Except it doesn’t, so somewhere in there is a mistake.

$\ln d=1$ becomes $d=e$.
« Last Edit: September 09, 2019, 06:24:23 pm by RuiAce »

#### Coolmate

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« Reply #4319 on: September 11, 2019, 09:58:09 pm »
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Hi Everyone!

I am in Year 11 revising Calculus for my prelims and was wondering if someone would be able to step through how to do the Product Rule with these questions below (attached). I am confused with 'a', 'h', and 'i'.