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Use the calc on the home page :)

Find the angle of least positive measure that is coterrminal with -3061  (degrees I will assume)

3060/60 = 51

so this is the same as -1 degree

-1 is equavalent to  359 degrees

This is coterminal with +1 degree

As Melody says, this is a very interesting and college-level advanced question in financial investments. As melody has shown, there a direct solution to it, but not many people have the skill in manipulating logs as Melody has done to arrive at the accurate solution.

One look at it, it immediately tells me what it is: It is the FV of two separate TVM formulae added together as one equation: Namely, It is the FV of $1,500 per year deposited at 7% annual rate + the FV of a fixed amount of $10,000 both for N number of years, which give a combined FV of $40,396.20.

I entered those 2 formulas into my computer and combined them. Then I entered all the known variables into the computer, and by using iteration and interpolation it came out, almost immediately with an N = 10.

And to check the result, I calculated them separately as follows:

1) $1,500 doposited @ 7% for 10 years gives a FV of =$20,724.67

2) $10,000 deposited @ 7% for 10 years gives a FV of=$19,671.51

3) Adding the two FV together:$20,724.67 + $19,671.51 =40,396.18 rounded to $40,396.2, which is spot on. CONGRATULATIONS TO MELODY!.

P.S. You should heed her advice of becoming a member, if you wish to have relatively complicated questions, such as this, answered by competent people.

If a ball is thrown vertically upward with a velocity of 128ft/s, then its height after t seconds is s=128t-16t^2.

a) what is the velocity of the ball when it is 240 ft above the ground on its way up? (consider pos direction)

b) what is the velocity of the ball when it is 240ft above the ground on its way down?

- I calculated maximum height reached by the ball which is 256 feet.   :)  You didn't need to do this.

To start with it is symmetrical so whatever the velocity is going up it will be the same only minus going down.

To avoid confusion I am going to replace the s which is a height with the letter y.

\(y=128t - 16t^2\\ \dot y=128-32t\\ \text {you are being asked to find } \dot y \text{ when y=240 }\\ \text{But to do this you need to find t when y=240 first}\\ 240=128t-16t^2\\ 16t^2-128t+240=0\\ t^2-8t+15=0\\ (t-3)(t-5)=0\\ t=3\;\;or\;\;t=5\\ when\;\;t=3\\ \dot y=128-32*3\\ \dot y=128-96\\ \dot y=32\;feet/sec\\ \text{The velocity on the way up is } 32f/sec\\ \text{The velocity on the way down is } -32f/sec\\ \)

2  x  sqrt(3)

why?   because sqrt(12)  = sqrt( 4   x  3)  = sqrt (4)   x sqrt(3)  =2 x sqrt (3)

Hi guest,

This is a good question, if you appreciate your answer and you will use this site again, how about becoming a members.  Members often get priority when we are answering question - especially polite members that are trying hard to learn from our answers. :)    

Becoming a member is easy - you just need an email address but you won't get nuisance emails sent to you, it is just used for validation purposes :)

-1500*[(1-(1+.07)^-N)/(.07)]+40396.2*(1+.07)^-N-10000=0

\(-1500*\frac{1-(1+.07)^{-N}}{0.07}+40396.2*(1+.07)^{-N}-10000=0\\ -1500*\frac{1-(1.07)^{-N}}{0.07}+\frac{40396.2}{(1.07)^{N}}-10000=0\\ \frac{-150000[1-(1.07)^{-N}]}{7}+\frac{40396.2}{(1.07)^{N}}-10000=0\\ \frac{-150000[1-(1.07)^{-N}]}{1}+\frac{7*40396.2}{(1.07)^{N}}-70000=0\\ -220000+150000(1.07)^{-N}+\frac{7*40396.2}{(1.07)^{N}}=0\\ -220000(1.07)^{N}+150000(1.07)^{-N}(1.07)^{N}+7*40396.2=0\\ -220000(1.07)^{N}+150000+282773.4=0\\ -220000(1.07)^{N}+432773.4=0\\ 220000(1.07)^{N}=432773.4\\ (1.07)^{N}=\frac{432773.4}{220000}\\ (1.07)^{N}\approx 1.967151818\\ log(1.07)^{N}\approx log(1.967151818)\\ Nlog(1.07)\approx log(1.967151818)\\ N\approx \frac{ log(1.967151818}{log(1.07)}\\ \)

log(1.967151818)/log(1.07) = 10.0000034615204508

N = 10      approximately.

check:

-1500*((1-(1+.07)^-10.0000034615204508)/(.07))+40396.2*(1+.07)^(-10.0000034615204508)-10000 = 0.0000029048699091459732438786634643045252961939322074922

Well, that is pretty close to zero :)))

I don't get what you are talking about.

Are you saying that you want to know how to express calculations by the existing chars on the keyboard?

a rational number means it can be expressed by a fraction a a irational number means the opposite.

-7/9 is a fraction so it is a rational number.

Err....  could it be 210  ???

2- -1=  2 + 1 = 3

You need to understand what rational and irrational mean.

A rational number means a number that can be written as a RATIO of two whole numbers.For example 0.9 is rational because you can write it as the ratio 9/10 .Or another one, 0.25 is rational because it's a quarter which you can write as the ratio 1/4.      Numbers like pi or root3  are irrational,because you can't express them as a ratio of two whole numbers.

So your question is  -       is -7/9 rational or irrational? Well,it's already a ratio of two whole numbers,so it's rational.

New birthday post for Rosala   2016  (and 2014)

2016

Mmm maybe you are right ElecticPavlov.  I never was great at English.

BUT

If I was talking about shoe that belonged to Dennis I would call it Dennis's shoe.  Maybe that is wrong - I don't know.

Anyway, in this question the singular word is product. The plural word is products.

The apostrophy indicates ownership so the data on safety and effectiveness belongs to more than one of the companies products.  It may only refer to one type of product at a time, like a specific machine but the company makes more than one of these machines so it is still plural.

That is my 2 cents worth but I am a mathematician - not a grammar expert :))

Find the nth derivative of each function by calculating the first few derivatives ....

\(\begin{align}a)\quad f(x)&=x^n\\ f'^{(1)}(x)&=nx^{n-1}\\ f'^{(2)}(x)&=n(n-1)x^{n-2}\\ ...\\ f'^{(n)}(x)&=n(n-1)......1x^{n-n}\\ f'^{(n)}(x)&=n!\\ \end{align}\)

\(\begin{array} \\ b)\\\; f(x)&=&x^{-1}\\ f'^{(1)}(x)&=&-1x^{-2}\\ f'^{(2)}(x)&=&(-1*-2)x^{-3}\\ f'^{(3)}(x)&=&(-1*-2*-3)x^{-4}\\ ...\\ f'^{(n)}(x)&=&(-1*-2*-3*.....*-n)x^{-(n+1)}\\ f'^{(n)}(x)&=&(-1)^n n!\;x^{-(n+1)}\\ f'^{(n)}(x)&=&\frac{(-1)^n n!\;}{x^{(n+1)}}\\ \end{array}\)

 You had best be very careful to check through my working and my logic but this answer seems ok to me.

s= t^3-1.5t^2-16t  given as position function.

velocity is ds/dt  = 3t^2-3t-16.  we want velocity to be 2 m/s

so solve for  3t^2-3t-16=2

3t^2-3t =18    so t^2-t=6   then t^2-t-6=0  which factorises to

(t+2)(t-3)=0 giving a choice of solutions of t= -2 or t=3. we reject t=-2 as you can't have a negative answer here,so t=3,that is velocity is 2 m/s  after 3seconds. 

For acceleration,differentiate again ,ie we want to differentiate 3t^2-3t-16 this time  because acceleration is the derivative of velocity.  So now we  get d/dt of 3t^2-3t-16 =6t-3  which we want to be zero.

6t-3=0  so the acceleration is zero after 0.5 seconds.

WHAT ARE YOU TALKING ABOUT?

What's the difference between (-x)^y and -x^y?

THEY ARE NOT THE SAME :)

\((-x)^y = (-1)^y\times x^y\\~\\ -x^y=-1\times x^y\\~\\ \text{these two expressions will be the same only if }(-1)^y=-1\\ \text{when will this be true?}\\~\\ \text{Well, it will be true if y is odd, it will be false if y is even}\\ \text{so they are definitely not the same thing.}\)

This has no "real roots" but three "complex roots".

Solve for x:
x^3 = 10 x

Subtract 10 x from both sides:
x^3-10 x = 0

Factor x from the left hand side:
x (x^2-10) = 0

Split into two equations:
x = 0 or x^2-10 = 0

Add 10 to both sides:
x = 0 or x^2 = 10

Take the square root of both sides:
Answer: |x = 0    or    x = sqrt(10)    or    x = -sqrt(10)

There is NO difference.

what is 25P25 =25!/(25-25)! =1.55 x 10^25

-2.78 as a fraction= - 2 39/50

-278/100

41/99 =  41 divided by 99......just use the calculator on this website...you can do it!