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An investor brought an antique table for $6000. He paid 5% as a deposit and borrowed the remaining from the bank for two years at 18% p.a. simple interest,payable monthly. How much interest does he have to pay each month.

As Alan has calculated, the investor will have to borrow $5,700 from the bank. In loans of this type, he/she can't be paying monthly interest forever!!!!. Therefore, the payment must include principal PLUS interest, so that the loan of $5,700 is paid off in TWO YEARS. Based on that, the monthly payment will be=$284.57. So, in two years, there will be $284.57 X 24 payments=$6,829.68 principal + interest. $6,829.68 - $5,700=$1,129.68 will the total interest paid on the loan in two years. As a monthly average, it will be:$1,129.68/24=$47.08 per rmonth.

The formula you use to calculate this is:PMT=PV. R.{[1 + R]^N/ [1 + R]^N - 1}=PMT NEEDED TO PAY OFF A LOAN OF $1, Where R=Interest rate per period, N=number of periods, PMT=periodic payment. PV=Present value.

Hi Eloise and Solveit,  

Thanks for all those answers Solveit. :)

I have only just seen your post.  Do you understand now Eloise?  If not then say so!

And, it is great to see you one the forum again too Eloise :)

You are most welcome Solveit :)

Thank you Melody ! :)

Hi Solveit and Guest.   :)

Solveit asked me to look at this question too :)  

Thanks Solveit, it is a good question  :)

A person of height 2 meters is walking away from an 8 meter tall street light at a speed of .5 meters per second. At what rate is the person's shadow increasing in length??

\(\frac{dx}{dt}=0.5 \qquad find \quad \frac{dy}{dt}\)

\(tan\theta = \frac{8}{x+y}=\frac{2}{y}\\ 8y=2x+2y\\ 6y=2x\\ y=\frac{x}{3}\\ \frac{dy}{dx}=\frac{1}{3} \)

\(\frac{dy}{dt}=\frac{dy}{dx}\times \frac{dx}{dt}\\ \frac{dy}{dt}=\frac{1}{3}\times0.5\\ \frac{dy}{dt}=\frac{1}{6} \\ \mbox{So the shadow increases at at the rate of } \;\frac{1}{6 }\;\;m/s\)

On second thoughts, the men and women changing seat colours just leads to rotations that are equivalent as far as the placement of individuals are concerned, so I think 576 is probably the better solution!

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The men and women must alternate in position.  Imagine there are 4 red seats and 4 blue ones in alternating positions.  

If the men sit in the red seats there are 4! = 24 ways of arranging them.  For each of these there are 4! ways of seating the women in the blue chairs, so there are 24^2 =  576 ways of doing this.  

There are the same number of ways if the men sit in the blue seats and the women are in the red seats, so there are 2*576 = 1152 ways in total.

The above assumes that a rotation of a given arrangement is different from the arrangement of which it is a rotation.

Do you mean \(\frac{x^2+x\times y}{x^2} \rightarrow 1+\frac{y}{x}\) ?

285 ml = 285 cm³

Assuming the bottle is cylindrical we have A*19 = 285 where A is the base area.  So A = 285/19 = 15 cm².

Capacity of bottle = A*h  where h = 19 + 4 cm = 23 cm  so Capacity of bottle = 15*23 cm³ = 345 cm³ = 345ml

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5% of $6000 is  (5/100)*6000 = $300  so he borrowed $5700 

18% p.a. of $5700 is (18/100)*5700 = $1026   

If he pays this back each month he pays $1026/12 = $85.50 each month.

(25/45)*100 ≈ 55.6%

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24000=12000(1+ 4/100)^t    divide both sides by 12000

24000/12000 = (1 + .04)^t

2 = (1.04)^t     take the log of both sides

log (2)  = log (1.04)^t   and we can write

log (2)  = t * log(1.04)    divide both sides by log (1.04)

log(2) / log (1.04)  = t   = about 17.673

Here's (1)

Area of a rhombus =  (1/2) d₁*d₂ ....where d₁, d₂ are the diagonals......so  let d₁  = 6   and we have

48 =(1/2) 6 *d₂   

48 = 3 * d₂    divide both sides by 3

16 = d₂

And since the diagonals bisect each other at right angles, they form two legs of a right triangle.....so...the length of the base = √[8^2 + 3^2]  = √[64 + 9]  = √73

And the area can also be expressed as  a*b  where a is the altitude and b is the base....so we have

48 = a * b

48 = a * √73   

altitude  = 48 / √73  = about 5.618  cm

Solution to #10

\(\text {Calculate the compression load in terms of the cross-sectional area.}\\ \displaystyle {3^2*\pi = 28.27 {in}^2} \Rightarrow \dfrac{150 {~kilopounds}}{28.27 {in}^2} = 5.305 {~ksi}\\\ \text {Calculate the longitudinal compression }\\ \dfrac {5.305}{8000}*12 in = 0.0079575{in}\\ \)

\(\text {Calculate the expansion in the radial direction.}\\ \dfrac{5.305}{8000}(0.35)*6{in} = 0.00139256 {in} \)

\(\text {Final length } (12 - 0.00796) = 11.99204in\\ \text {Final diameter } ( 6.0 + 6.00139) = 6.00139in\)

Source:

Formulae Esoterica

Processus algorythmic

Twelfth edition

Morgan le Fay

S={(-1, 4), (6, -8), (4, 0), (5, 5)}

Domain =   { -1, 6, 4, 5} .......this is just the set of x values in the relation

Range = { 4, -8, 0, 5}   ........this is just the set of y values in the relation

172 divided by 2? Simple. 86

Thank you Chris 

x+7²/2+7x+x=671832.47472846

x+49/2+7x+x=671832.47472846

x+24.5+7x+x=671832.47472846

24.5+8x+x=671832.47472846

24.5+9x=671832.47472846

9x=671827.97472846

x=74645.3305253845303177

\(\sqrt{5}=2.2360679774997897\)

1. 2/5^3 = 2/125

2.(-1/4)^2 = 1/16

Now...we can take the slope that geno found and writie an equation of the tangent line at  x = 6

So....when x = 6, y = 8cot(6)  = -27.4908

So...the equation becomes

y - ( -27.4908) = -102.4682(x - 6)

y + 27.4908 = -102.4682x + 614.8092

y = -102.4682x + 614.8092 - 27.4908

y = -102.4682x + 587.3184

The only factors of 7 are 7 and 1.

There are several pairs of factors of 54, the pair that works is 3 and 18.

7x² + 3x - 54  =  (7x - 18)(x + 3)

Let's use this identity:  sin²x + cos²x  =  1     --->     sin²x  =  1 - cos²x

cosx - sin²x - 1     --->     cosx - (sin²x) - 1     --->     cosx - (1 - cos²x) - 1     --->     cosx - 1 + cos²x - 1

     --->     cos²x + cosx - 2     --->     (coxx + 2)(cosx - 1)

This will probably be easier if all the times are converted to minutes.

4 hours  =  4 x 60  =  240 minutes.

Delano  =  3/4 hour  =  3/4 x 60  =  45 minutes.

Alex  =  2/3 hour  =  2/3 x 60  =  40 minutes.

Jordan  =  3/5 hour  =  3/5 x 60  =  36 minutes.

Now lets take the 240 minutes and divide that be each of the times.

Delano:  240 / 45  =  5, remainder 15   --->  means that he made 5 signs and had 15 minutes left over.

Alex:  240 / 40  =  6, remainder 0   --->  means that he made 6 signs and had no minutes left over.

Jordan:  240 / 36  =  6, remainder 24   --->   means that he made 6 signs and had 24 minutes left over