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I think my answer above might be a little confusing, so I'll re-state it. 

Odd number * odd number = Odd. 

Since n is a multiple of 9, the prime factorization of n (other than 0) has at least two 3s. 

Since m is a multiple of 3, the prime factorization of m (other than 0) has at least one 3. 

We cannot consider the possibility that m and n are even because they are not always even. 

The largest integer that mn is always divisible by is \(3\cdot3\cdot3 = \boxed{27}\), which is proven by prime factorization. 

Hope this helps more, 

 - PM

Since \(m = 6 (mod 9)\)  \(n = 0 (mod 9)\) and , we know that \(m\) is a multiple of 3 and \(n\) is a multiple of 9. \(m\) can also sometimes be a multiple of 6. (For example, m = 24, 24 (mod 9) = 6). To make sure that the largest integer that \(mn\) is necessarily divisible by is always true, we must assume that m is a multiple of 6. The largest integer that \(mn\) is necessarily divisible by is \(3\cdot3\cdot3 = \boxed{27}\).

Hope this helps,

- PM

a/19 has a remainder of 4. b/19 has a remainder of 2. c/19 has a remainder of 18. 

2a/19 then must have a remainder of 8. (4 + 4 = 8) 

The remainder of \(2a + b - c\) when divided by 19 is just \(8 + 2 - 18 = -8\). We can get the real remainder by adding -8 to 19, which equals 11. the remainder is \(\boxed{11}\).  

Hope this helps,

- PM

 Wow!

Same with mine :D

(3/5)^3  =  3^3 / 5^3  =  27 / 125

Let the bottom left vertex of the right triangle lie at (0,0).....so.....the square will touch two sides of the triangle

Let the height of the right triangle = 5 and the base length = 12

And the endpoints of the hypotenuse lie at (0,12) and (5,0)

And the equation of the line conecting these two points is given by :

y = -(12/5)x + 12  (1)

And the diagonal of the square will be the segment lying on the line y = x    (2)

Find the x coordinate  intersection of  (1) and (2)  ..... this will be the length of the side of the square

So we have

- (12/5)x + 12  =  x      add -(12/5) to both sides

12 =  (17/ 5) x       multiply both sides by  5/17

60/17  units =   the side of the square

192,600

I found this with a quick internet search:

Is kinetic friction equal to applied force?

If the externally applied force (F) is equal to the force of kinetic friction, Fk, then the object slides at constant velocity, and the coefficient of friction involved is called the coefficient of kinetic friction, μk.

I think that applies to STATIC friction, but kinetic friction force and force to move object w/out accel are the same as I recall.

\(\sqrt{-27} = \sqrt{-1}\sqrt{27} = i 3\sqrt{3}\)

Dr. Joule is pushing a 75 kg refrigerator across the floor at a constant velocity. The coefficient of friction is 0.36 and he moves the refrigerator 3.5 meters. Solve for Force of Friction \(F_f\) and pushing Force \(F_p\).

Hello Guest!

\(F_p=m\times g = 75kg\times 9.81\frac{m}{s^2}=735.75\frac{kgm}{s^2}\times\frac{Ns^2}{kgm}\\ \color{blue }F_p=735.75N\)

\(F_f=F_p\times \mu_k=735.75N\times 0.36\\ \color{blue}F_f=264.87N\)

\(W=F_f\times s=264.87N\times 3.5m \times \frac{J}{Nm}\\ \color{blue}W=927.045J\)

  !

But if the forces are equal but opposite, doesn't that mean that the object hasn't moved at all?

If there is no acceleration, then the forces are balanced....the pushing force is exactly the same in magnitude as the force of the KINETIC friction.      264 N     although it is in the OPPOSITE direction as the frictional force.

4 kg is 4000 gm

4000 - 2570 = 1430 gm  = 1.43 kg = how much more the dog weighs (until the dog EATS the cat !)

Hang on just a sec ILT

1/10 * 2/10 = 2/100   =  1/50

        When you MULTIPLY fractions the numerator AND denominator get multiplied ...alike or not.

-6x+5y = 1

6x+4y = -10

Just add these and we get

9y = -9   divide both sides by   9

y  = -1

Sub this into either equation to find x

6x + 4(-1) = - 10

6x - 4 = -10      add 4 to both sides

6x = - 6     divide both sides by 6

x = - 1

Nope    ...2  x 6  =   12

2/10's because you multiply the denominator by the denominator and the numirator by the numirator wich is 1*2=2

and the denominators if the same would again stay the same giving you 2/10's

We don't have "7" on a die....

So....which other one pairs a letter and a number ??

would be B?

Is it D??