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The easiest way I do it is as follows: say you have the decimal .124. I just count the number of digits in it and multiply it by 1 + number of zeros / by the same number thus: .124 X 1000/1000=124/1000=31/250(I divided both sides by 4). That is all there is to it.

Here's the last one

Plus sir cphil if I have a funnel 20cm wide and 25 cm long connected to a cylinder 12 cm high and 10 cm base with how much is its liquid capacity?

Assuming the funnel is a cone, the volume is (1/3)pi r^2 * h =  (1/3)pi (10^2) (25) cm^3  = pi*(1/3)(2500)cm^3

And assuming that the 10cm base of the cylinder is the diameter [r = 5 cm], we have

Volume = pi(r^2)(h)  = pi(5^2)(12)  cm^3  = pi (300) cm^3

Adding both of these gives  :   pi [ (1/3)*2500 + 300]  = [3400/3]pi cm^3

I vote for guest 6

Guest 5 forgot to multiply by 500

Nope...

500 ( 1.0018^10) = 509.99 at the end of ten years ....    9.99 in interest

CPHIL is NOT right..... she is only getting 0.18% interest annually. (.0018)

thEYe add the interest to her account at the end of the year and THAT new amount gets interest the following year

500 (1.0018^10) = 1.018 DOLLARS IN INTEREST IN 10 YEARS  !!!

Correction:

Assuming she is getting a pathetic 0.18 %  annual interest

Her interest over the years is  500 (1. 0018)^10 = $ 1.1081

500 + 1.1081 = 501.11     at the end of ten years

is she reallly getting 0.18%       or 1.8 %     or   18% ?????

NO!!!!!!!, Guest #2. CPhill is right. She will have $500 + 9 =$509.00 at the end of ten years.

Here's the third one:

3.The reservoir is in the form of the frustum of an inverted square pyramid with upper base edge 24m, lower base edge 18m and altitude 3m. how many hours will it require for an inlet pipe to fill the reservoir if water flows in at the rate of 200 liters per min. 

The area of the upper base (A1) is  [24m]^2 = [2400cm]^2 

The area of the lower base  (A2) = [18m]^2   = [1800cm[^2

The total volume is :

(1/3)(altitude) [ A1 + A2 + sqrt( A1 * A2) ]

(1/3)(3)( 2400^2  + 1800^2  + sqrt [ 2400^2  * 1800^2] ) = 13,320,000 cm^3

And 200 liters = 200,000cm^3

So....it takes...... [13,200,000 / 200/000] =  66 min = 1.1 hr to fill the tank

Assuming this is a RIGHT triangle and these are the TWO legs and NOT the hypoteneuse then the angle is 90 degrees

Her interest over the years is  500 (1.18)^10 = 26.17

500 + 26.17 = 526.17

159b + 3.3c=1000    Solve equation for c

3.3c=1000-159b

c=(1000-159b)/3.3

Substitute this value of c into the second equation:

2.3b + 0.3 (1000-159b)/3.3 =18    Sove THIS equation for b

2.3b + (300 - 47.7b)/3.3 =18

2.3b + 90.909  - 14.45b = 18

-12.15b = --72.909

b= 72.909/12.15 = 6.000

c=(1000-159b)/3.3 = (1000-159(6.000))/3.3 = 13.94

I think you want to know the amount of interest earned after 10 years......this  is just :

I = Prt    =   500(.0018)(10)  =   $9   

Then....the total amount in her account at the end of ten years =   beginning amount plus earned interest =  $500 +  9  = $509

Here is one formula that  you can use,

F X (1 - R^n) / (1 - R),

F=First term

R=ratio of change

n=number of terms

Here's the second one :  [it's a little difficult]

2.Find the volume of the frustum of a regular hexagonal pyramid if an edge of the lower base is 12 cm, a laterral edge is 10 cm and whose altitude is 4cm.

We need to find the length of the edge  of the upper base 

This is given by:   12 - 2sqrt(10^2 - 4^2)   =   [12 - 2sqrt(84)]

The area of the lower base - ( A1) =   [3*sqrt(3)/2] [12^2]  =  about  216sqrt(3) cm^2  = about 374.12 cm^2

The area of the upper base - (A2) = [3*sqrt(3)/2] [12- 2sqrt(84)]^2 =   about 104.11cm^2

And the volume is given by :   (1/3) h [ A1 + A2 + sqrt(A1 * A2)]   .....so we have

V = (1/3) (4) [ 374.12 + 104.11 +  sqrt(374.12 * 104.11) ]  =   about 900.72 cm^3

y+6=5/7x-5/7

Your equation has MANY solutions, such as, y=4, x=15 or, y=9, x=22......etc.

I doubt that Excell will allow you to display a 100-digit number in one cell, because they will rouded off and display it in "scientific notation".

You didn't get it quite right:

1-He is charged interest at a rate 1.35% per month. Since his bill is two months in arears, he will have to pay them: $130.5 X .0135=$1.76 for one month X 2=$3.52 for two months. So, in total he will owe them $130.5 + $3.52=$134.02

2-If he doesn't pay it for the whole year, then he gets charged 14.4% interest. If this is compounded annually, then he will owe them:$130.50 X 1.144=$149.29. And that's all. If the interest rate is compounded say, monthly, then he will owe them:$150.58.

Hallo guest!

Hallo guest!

Here's the first one.......

We need to  calculate the slant height (h)  of the sides

This is given by :

sqrt [ [( 12 - 6)/2]^2  + 4^2]   =  sqrt [3^2 + 4^2]   = sqrt[9 + 16] =  sqrt(25) = 5cm

The lateral area is formed by 4 trapezoids each having this area :

(1/2)h(b1 + b2]   =  (1/2)(5)(12 + 6]  = 5* 18/ 2 = 90/ 2 = 45 cm^2

So....4 times this =  180 cm^2

what is 3-(x+7)=3(2x+1)

Your answer is x= -1

Wouldn't you have to specify which one is the Opposite and the Adjacent sides, because you get different answers:  tan(14/17)=.8235=39.472 degrees. The other way around, or tan(17/14)=1.21428=50.528.

sqrt(90x^4y^2),

3 sqrt(10) sqrt(x^4 y^2) which is your answer.

thanks so much!