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200 he has  + 200(20) more = 4200 apples..... I hope Alex likes apples!

First figure out the downslope and 'normal' forces of the 50kg mass

Downslope = 50 sin27 = 22.69

Normal      = 50 cos27 = 44.55 kg

Since you are pushing the box UP the hill the force of friction is acting against you ...down the hill

  coeff of fric = .4     .4 x normal force = friction force = .4 (44.55kg) =  17.82 kg

to push the box uphill you must overcome the friction force and the downslope force

Pushing force = 17.82 + 22.69 kg = 40.51 kg force

The first equation can be re-arranged to  y =3x+9     sub this into the second equation for 'y'

-3x -2 (3X+9) =0

-9X-18=0

X= -2

Now sub this value of x into one of the equations to find y

y=3x+9    y= 3(-2)+9 = 3

x,y  =  -2,3

FV=PV (1+i)^n     FV=future value  PV = present value

FV= 900 (1.02)^6 = $ 1013.55

Mmm I don't know.  Anybody get any sensible ideas?

=  (1 x 3 x 4)  / ( 2 x 5 x 9)   = 12/90 = 2/15

cos^2(x)=.79 (=0.79) for x=0.48

edit: (0.48 rad x 180 deg) / Pi rad= 27.501974166279514 deg

That is incorrect.

\(-1\le cos^2(X)\le1\\~\\ cos^2(X)=.79\\ cos(X)=\pm\sqrt{0.79}\)

acos(sqrt(0.79)) = 27.274728680412

\(X\approx 180n\pm 27.3^\circ \qquad n\in Z\)

Well.....if you combine the  11/16 and the 5/16  you will have 16/16   or a full case......and you still have the 7/16 left over...

Here is the website I used: 

https://www.mathsisfun.com/numbers/sigma-calculator.html

In reality, I THINK we may still not have QUITE the correct answer...I think the first year the payment is 2400 then the NEXT year it goes up 4 percent etc etc

so it would be

\( \sum_{0}^{39}\)2400(1.04)^n  = 228061.24       But that is not what I was asked.......

Find a Common denominator, then add the numerators. To find CD, multiply both denominators by each other, then the respective numerators by the same number. Then just simplify

sorry, i wrote it wrong
Change \( {x+1}^{2} \) For:

\({(x+1)}^{2}\)

The statement :"This graph is tangent at both its x intercepts x=-5 and x=2"  DOES NOT MAKE SENSE.

Anyway, it does have x intercepts of -5 an 2    

(it is tangent bit that makes no sense - maybe this was translated into English and the translation is wrong? )

Anyway if I ignore the tangent bit, this could be a concave up parabola. It could be other things too.

y=a(x+5)(x-2)             'a' can be any constant.

y interept, x=0

y=a*5*-2 = -10a

(0,-10a)

13.1129706779203926

For 13.1129706779203926 x 13.1129706779203926 = 13.1129706779203926^2 = 171.95

1. 

What the statement says:

 \(({n+1}^{2})-{n}^{2} = 2n+1\)

 
Demonstration:

\(({n+1}^{2})-{n}^{2} = ({n}^{2}+2n+1)-{n}^{2}- ={n}^{2}+2n+1 -{n}^{2}- =2n+1\)

Example:

\({6}^{2}-{5}^{2}= 36-25=11\)
 

The sum of these two integers
\(6+5= 11\)
I hope it was helpful

= -0
=(-1)*0         (remember "-" is actually (-1))

=0 /               (for property, any number that is multiplied by 0 is 0)

it´s not possible that cos^2(X)>1...

Hold on, did you use Wolfram online for the calcs, lol?

Yes, I think that is the correct answer based on the sum series type word problem I posed. How did you calculate that? I am studying costs of house ownership based on inflation rates and would like an online calculator that could do that for me. Thanks by the way!

\(\sum_{1}^{40}\)2400(1.04)^n = 237183.69  sound about right?

Are you trying to calculate the value of a series of payments of 2400  over 40 periods with simple interest of 4% per period? ?

No, sorry, not making sense. Here, I will give you the word problem that I am trying to find a mathematical solution to. Over a 40 year period a person pays property tax on their dwelling. In year 1 they pay $2400. They get a 4 percent increase in the tax rate every year, hence year 2 they will pay $2400 x 1.04 =  $2496.  Now, after 40 years of paying property taxes, I am trying to see what the total of payments are. There is no way they paid $2 million for property taxes over the years. See what I am trying to get at?

Not sure what that is in relation to, but that would be:

2400 x \(\sum_{1}^{40}\) n   *1.04 = 2400 (1.04)(820) = 2046720

No, it is the sum of 2400 increased 4 percent per a period over the total of 40 periods:

(2400 x 1.04)  +  (2400 x 1.04 x 1.04) + (2400 x 1.04 x 1.04 x 1.04)   etc.    for a total of 40 periods.