If you're like me and don't remember hyperbolic identities (especially involving inverse functions) off the top of your head, recall the definitions of the hyperbolic cosine and sine:
Then differentiating yields
so that by the chain rule, if
then
Now, let , so that (•) .
Recall that
and so the derivative of tanh(<em>x</em>) is
where the last equality follows from the hyperbolic Pythagorean identity,
Differentiating both sides of (•) implicitly with respect to <em>x</em> gives
So, the derivative we want is the somewhat messy expression
and while this could be simplified into a rational expression of <em>x</em>, I would argue for leaving the solution in this form considering how <em>y</em> is given in this form from the start.
In case you are interested, we have
and you can instead work on differentiating that; you would end up with
Answer:
-3.5 -3, -2 1/2, -2, 2.5
Step-by-step explanation:
The probability of matching the first one correctly is 1/3 .
Then there are only two baby-pix left, so ...
The probability of matching the second one correctly is 1/2 .
Then there's only one baby-pic left, so ...
The probability of matching the third one correctly is 1 .
So the probability of matching all three correctly is
(1/3) x (1/2) x (1) = 1/6 = (16 and 2/3) percent .
Answer: No, Asher is incorrect. Instead of subtracting 4 from both sides, you should divide by 4. As a result, x should equal 16, not 60.
Divide by 4 to both sides.
Answer:
A)4
Step-by-step explanation:
Assuming all edges are integral values
The most basic right angles triangle with integral edges is
(3,4,5)
as it obeys pythogores theorem
which is
Now, double each edge,it will still remain a right angled triangle since it will still obey pythogores theorem
so the edges are (4,6,10)
⇒4 cm is the short leg of a integral right triangle with hypotenuse 10 cm