CPhill

You're close, maththis.......

If he's at 74.5 ft and he dives 80 ft...shouldn't we get a negative answer???

As, Melody says......try it again.....

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Let me amend this slightly......your answer actually could be expressed as a positive.....it's just that your math is a little "off"

Notice that the only thing that can make this 0 is when the numerator on the left side = 0

So

cos 2Θ = 0

And the cosine is equal to 0 at 90, 270, 450 and 630 degrees......so dividing each by 2, we have

45, 135, 225 and 315  degrees.......(and notice that the sin ≠ 0 at any of these values, so the denominator of the fraction isn't 0 at any of these values, either !!!)

No..we don't usually like to do too much "guessing" on here....

Since all the points lie on a line, the slope between them will be the same. So the slope between (-2, -4) and (0, 0) = [-4 - 0]/ [-2, 0] = -4/-2 = 2

So, using this, the slope between (0, 0) and (4, a) = 2  ....and we have..

[a - 0] / [4 - 0] = 2   → a/4 = 2  → (multiply both sides by 2)......a = 8.

Similarly.......

[18 - 0 ] / [ b - 0] =  2  →  18/2 = b → 9 = b

And that's it .....(without the guesswork .....!!!)

Every positive integer can be written as a power on some base > 1.

To see this, let "a" be some positive interger.

Then, using logs and assuming that b > 1, we have.....

log_b a = x  ...... which says, exponentially, that

b^x = a

And we have written "a" in terms of a power on a base > 1

Well...what's 5 times 4  ???

And what's 5 + 2 ???

Put the first answer over the second.....there's your final answer....

18 / 694

Well, 18 is almost 20 .....   and  694 is almost 700

So. 20/700 = 2/70 = 1/35

Out of 10 children, 7 are boys. So, since we have 3 sets of 10 children, these 3 sets must have 3 X 7 = 21 boys.

f(x) = x^1/3

Using the Power Rule, we have

f '(x)  = (1/3)x ^-2/3

5^(1/2)  = √5       ....this is definitely an irrational number....!!!!!

There is no unique solution to this. Let x be the number of  24 cent stamps and y be the number of 39 cent stamps.  So we have the following linear equation.

.24x + .39y = 16.80

Several possible solutions are (18, 32), (31, 24), (44,16),(70, 0).......(there may be other integer solutions, as well)......