All Answers 352713 Answers

As Melody has said, the slope when x = pi/2 = 0.....and since the slope of the tangent line is 0, the line is just a horizontal one and will be given by [ y = the y coordinate of the point (pi/2, -4) ], i.e.,   y = -4

Thanks for your attempt, I also got the result -4... but I need an equation for it

Thanks Melody for your help.  A bit lost where to go next though with those details.  What formula would I use to calculate the time?

Cheers,

Lisa-sondra

I assume you want to graph    y = 2^{x+ 1} - 3 ..... ??

If so, here's the graph......

However 

y'=-6sin(2x)

When x= pi/2

Y'=-6 × 0 = 0

Incidentally y will equal -3-1 = -4

That point is not on the graph so this will be difficult.  

Do you have any questions lisasondra?

Yes but inverse functions usually have a restricted domain. Within the domain restrictions this will be true.

First change everything to ml and cm.

9425ml/min

P=3770cm

10mm=1cm

2pi×r=3770   so

r= 3770/(2pi)

V=pi× r^2 × 1  ml

(1minute / 9425ml) × V 

will give the time in minutes.

I am sorry about the presentation.  I am on my phone.

if x=3i, y=2i and z=m+i, the expression xy^2z equals....so we have...

(3i)(2i)²(m + i) =

(3i)(4i²)(m+i) =

(12i³)(m + i) =

12i³m + 12i⁴

Answer is 2015.

Using the length of the wooden beam (24) as the hypoteneuse, and noting that we're trying to find the side opposite the 71 degree angle, we can use the sine function....so we have

sin 71 = opp /  24   multiply both sides by 24

24 * sin 71  = opp = about 22.7  ft.  ..  and that's how high up the wall the beam reaches

Good attempt ororen1909  but you have only found the value of one years deposit.

I shall give you 3 points for you honest attempt :)

2548 [ (1 + .05)⁵ - 1] / .05

$${\frac{{\mathtt{2\,548}}{\mathtt{\,\times\,}}\left({\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.05}}\right)}^{{\mathtt{5}}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{{\mathtt{0.05}}}} = {\mathtt{14\,079.308\: \!425}}$$

Now if you want 25 years of 50 years you probably need to develope a formula or use one that someone else has already developed.

It it the future value of an annuity  problem.  

Use future value of an ordinary annuity with n=25 and 50 respectively 

I believe we have an annuity here...the "formula" for the accumulated amount after "n" years is given by

A = C [ (1 + i )ⁿ - 1 ] / i   where C is the cash flow per period, i is the interest rate per period, and n is the number of periods - (in this case, years)

I'll do the first one for you.....and you can "plug and play" to arrive at the other two answers

for the accumulated amount after 5 years, we have

A = 2548 [ (1 + .05)⁵ - 1] / .05  = $14, 079. 31

okay, Say you put the money in the bank at the END of each yeaar.

How much will you have at the END of 5 years.

Ok

the first deposit of $2548 will be earning 5% pa  interest for 4  years

This is how much it will grow to

$${\mathtt{2\,548}}{\mathtt{\,\times\,}}{\left({\mathtt{1.05}}\right)}^{{\mathtt{4}}} = {\mathtt{3\,097.109\: \!925}}$$

that is $3097.10

the second deposit of $2548 will be earning 5% pa  interest for 3  years

This is how much it will grow to

$${\mathtt{2\,548}}{\mathtt{\,\times\,}}{\left({\mathtt{1.05}}\right)}^{{\mathtt{3}}} = {\mathtt{2\,949.628\: \!5}}$$

that is $2949.63

the third deposit of $2548 will be earning 5% pa  interest for 2  years

This is how much it will grow to

$${\mathtt{2\,548}}{\mathtt{\,\times\,}}{\left({\mathtt{1.05}}\right)}^{{\mathtt{2}}} = {\mathtt{2\,809.17}}$$

that is $2809.17

the forth deposit of $2548 will be earning 5% pa  interest for 1  years

This is how much it will grow to

$${\mathtt{2\,548}}{\mathtt{\,\times\,}}\left({\mathtt{1.05}}\right) = {\mathtt{2\,675.4}}$$

that is $2675.40

the fith deposit of $2548 will be earning 5% pa  interest for 0  years (you only just now depositied it

So it will still be worth  $2548

NOW add all those together and you will see how much your deposits will grow to after 5 years.

$${\mathtt{3\,097.1}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2\,949.63}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2\,809.17}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2\,675.4}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2\,548}} = {\mathtt{14\,079.3}}$$

5%+100=105%=105/100=1.05

**without following years:

[saving - spending]*years*1.05^years=

[2548*(1.05) -2548]5*1.05^5=812.99

[2548*(1.05) -2548]25*1.05^25=

[2548*(1.05) -2548]50*1.05^50

WOW!!!....kitty<3  makes a "stealth" appearance on the forum!!

HAPPY NEW YEAR, kitty<3  ......!!!!!

(We sure do miss you around here)

9,884,000 would be your answer

Thanks Chris,

Those two interactive unit circles are really great.  I hope people put in effort and can work out what it is that they are supposed to be learning from them.

Of course we are here to help if people want us to help them understand.

Plus I expect the mathisfun blurb that goes with them is very good.  

Thanks Chris   

Very nice answer (and graphics), Melody......

 Hi Tetration, you have given the number of permutations NOT combinations. 

That is you have said:  Given 52 cards how many ways can they be ordered.

this is 52!     

or it is also    52P52  

The permutation calculation is available on any scietnific calculator.

In the web2 calc it can be entered as     nPr(52,52)

$${\left({\frac{{\mathtt{52}}{!}}{({\mathtt{52}}{\mathtt{\,-\,}}{\mathtt{52}}){!}}}\right)} = {\mathtt{80\,658\,175\,170\,943\,878\,571\,660\,636\,856\,403\,766\,975\,289\,505\,440\,883\,277\,824\,000\,000\,000\,000}}$$

NOW, in mathematics (probability) Combination has a very specific meaning

It means how many subsets of a specific size can be chosen from the original set.  

Order is NOT important.

So in order to answer this I need to know how many cards you will be chosing from the original 52.

If you are choosing all 52 the answer is just 1 because there is only one combination of 52 cards  that can be chosen from 52 cards.  That is, you must choose ALL of them.

However, say you wanted to choose 7 cards.

Then the number of possible combinations would be  52C7

$${\left({\frac{{\mathtt{52}}{!}}{{\mathtt{7}}{!}{\mathtt{\,\times\,}}({\mathtt{52}}{\mathtt{\,-\,}}{\mathtt{7}}){!}}}\right)} = {\mathtt{133\,784\,560}}$$