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They are all prime numbers so the smallet multiple of them all is

2*3*5*7*19 = 3990

then every multiple of that will also be divisable by all the little ones.

19.      12² + b²  = 20²

20.     5²  +  10²   =   25   + 100  = 125 = c²           ( 'c' then = sqrt (125)  )

The amount of tax he has to pay is :

   the amount of his bill   x   .05 = .........................

(amount) X .05   =  15.00

amount =  15.00 / (.05) = $...........................

 Slope = m  =  rise / run    or    (y1-y2) / (x1-x2)    =    ( -1 -  -2) / ( -3-9 ) =  1/(-12) = - 1/12      = m

a is directly proportional to m and n^2, and inversely proportional to y^3.  

  means   a = k mn^2 / y^3

     or    a y^3 / (mn^2) = k    a constant

             9 (4^3) / (2(8^2)) = k

                k = 4.5

       then    a  (3)^3 / ( 6(7^2)) = k = 4.5      solve for 'a'

3990 , 7980 , Total =  2 such numbers.

(1, 2, 3, 5, 6, 8, 10, 12, 15, 18, 20, 24, 27, 30, 40, 45, 48, 50, 54, 60, 72, 75, 80, 90, 108, 120, 125, 135, 150, 180, 200, 216, 240, 250, 270, 300, 360, 375, 432, 450, 500, 540, 600, 675, 720, 750, 1000, 1080, 1125, 1200, 1350, 1500, 1800, 2000, 2160, 2250, 2700, 3000, 3375, 4500, 5400, 6000, 6750, 9000, 10800, 13500, 18000, 27000, 54000)>>Total No. 69>>Total Sum==187,981

A unit fractionis a fraction of the form 1/n for some nonzero integer n. Compute the number of ways we can write 1/16 as the sum of two distinct positive unit fractions. (The order of the fractions in the sum does not matter, so 1/2+1/3 would be considered the same sum as 1/3+1/2)  

Well, there are

1/32 + 1/32 

1/64 + 3/64 

1/128 + 7/128 

We could keep doubling the denominator indefinitely, so I conclude there is no end to it.  

Not to mention 

1/48 + 2/48  

1/96 + 5/96 

1/192 + 11/192 

And we could keep doubling that denominator as well.  

_.

It looks like the bottom of the b is cut off.  In the original, is there a number under that b similar to the way there's a number alongside the a? 

The prime factorization of k is :
k=pn11⋅pn22⋅...⋅pnmm
That factorization must contain 2, 3 and 5 as prime numbers :
⇒k=2n1⋅3n2⋅5n3
n1 must be odd, multiple of 5, and multiple of 3⇒15
n2 must be 2 modulo 3, even, and multiple of 5⇒20
n3 must be 4 modulo 5, even, and multiple of 3⇒24
So, 15+20+24=59 is the number asked.

😎😎😎

thanks

What???

\(\frac{1}{m} + \frac{1}{n} = \frac{2^2}{(mn^2)}\) whereby m and n are positive integers and \(m \neq 0\) and \(n \neq 0\).

So when m and n are positive then \(n(m + n) = 4\).

Distribute \(n^2 + nm = 4\).

There is only one solution: m = 3 and n = 1.

so it's x.05

(The amount of the bill)  x  .05 = amount of tax to be paid

i need help plzz

If m + 1/m = 8, what is the value of m^3 + 1/m^3?

Hello Guest!

\(m+\frac{1}{m}=8\\ m^2-8m+1=0\\ \color{blue}m\in \{4-\sqrt{15},4+\sqrt{15}\}\)

If  \(m\in \{4-\sqrt{15},4+\sqrt{15}\}\),  then  \(m^3+\dfrac{1}{m^3}=488\)

  !

If \(x^2 - x - 1 = 0\), what is the value of \(x^3 - 2x^2 \)?

Hello Guest!

\(x^2-x-1=0\\ \color{blue}x\in\{-0.618034,1.68034\}\)

\(If\ x\in\{-0.618034,1.68034\}, then\ \color{blue}x^3-2x^2=-1\)

  !

1357 , 1375 , 1537 , 1573 , 1735 , 1753 , 3157 , 3175 , 3517 , 3571 , 3715 , 3751 , 5137 , 5173 , 5317 , 5371 , 5713 , 5731 , 7135 , 7153 , 7315 , 7351 , 7513 , 7531 , Total =  24 such integers.

paralellogram rule

2 (30)² + 2(20)²  = 40² + d²

d = sqrt 1000 = 10 sqrt (10)

h(t) = -16t^2 +32t +48       Max will occur at   t = - b/2a =  -  32/(2 *(-16)) = 1

   use this value of 't' in the equation to calculate the max height attained.....

90 % * 15% = 13.5 %       then add 10%