CPhill

Is the 12 being raised to the power of "x" or the power of (x-2) ??

Just put this into the on-site calculator.......it'll give you your answer...

If 5/7 are boys, than 2/7 must be girls.

Let x be the total number of students.

Then 2/7 of x = 300     or, in math terms

(2/7)x = 300        Multiply both sides by the reciprocal of (2/7) ⇒ (7/2)

x = 300(7/2) = 1050 = total students

Then.... the total students - the number of girls = the number of boys

So 1050 - 300 = 750      And that's the number of boys.

Note something else......if 2 parts of the 7 are girls = 300, then there must be 150 students in each "part"  

Then, since the boys are 5 "parts", then 5(150) = 750 !!!

Does that make sense??

Ok.........the total distance traveled by both trains is 340km - 30 km = 310km

Let the speed of the slower train be x

So the speed of the faster train is x + 5

So the rate of the first train (x) times the time it has traveled (2 hrs) = some distance

And the rate of the second train (x+5) times the time it has traveled (2 hrs) = some distance

And the distances combined is 310km

So

x(2) + (x+5)(2) = 310

2x + 2x + 10 = 310       Subtract 10 from both sides

4x = 300       Divide by 4

x = 75km/hr     And that's the rate of the slower train

And the faster train is traveling 5km/hr faster = 80km/hr

Let's blame it on.............zegroes!!!

(We know you did it, zegroes........confess...now!!)

You'd better give me a thumbs up........

Or I'll sic the Dinosaur on you............

And I mean it !!!

I think reinout-g made a slight mistake...it should be the tan of 18 degrees, not 28 degrees

OK, zegroes.....we have a right triangle......we know one side, the height of the tower which is 80 ft and we're trying to find the adjacent side, i.e., the distance the stake is from the tower.

So we have

tan 72 = opposite / adjacent

tan 72 = 80/ adjacent           multiply by "adjacent" on each side

adjacent * tan 72 = 80          divide by the tan 72 on both sides

(adjacent =   80 / tan 72 ) =   about 26 ft.

And that's how far the stake is from the tower base

I'll include a picture if you need it

Let the speed of the train be "x"

Then the speed of the plane is five times as fast plus 50km/hr = 5x + 50

Remember that Distance/Rate  = Time

And the time the train travels = Its Distance Traveled/Its rate  = 600/x

And the time the airplane travels = Its Distance Traveled/Its rate = 3500/(5x + 50)

But the times are equal....so

600/x = 3500/(5x + 50)

The easiest way to solve this is to just to take the cross products and set them equal, i.e.,

600(5x + 50) = 3500x       Expanding the left side, we have

3000x + 30000 = 3500x    Subtract 3000x from both sides

30000 = 500x                    Divide by 500 on both sides

60 = x   And that's the rate of the train in km/hr

And the plane's rate is 5(60) + 50 = 350km/hr

That appears to be impossible, rosala

If the speed of the airplane is five times that of the train, it would travel 5 times as far in the same time

But 3500 / 600 = about 5.8 times as far