Step-by-step explanation:
The exterior angles of an equilateral triangle will always have a measure of 120°.
I’m not entirely sure, but try Desmos or Symbolab calculators :)
Try to relax. Your desperation has surely progressed to the point where
you're unable to think clearly, and to agonize over it any further would only
cause you more pain and frustration.
I've never seen this kind of problem before. But I arrived here in a calm state,
having just finished my dinner and spent a few minutes rubbing my dogs, and
I believe I've been able to crack the case.
Consider this: (2)^a negative power = (1/2)^the same power but positive.
So:
Whatever power (2) must be raised to, in order to reach some number 'N',
the same number 'N' can be reached by raising (1/2) to the same power
but negative.
What I just said in that paragraph was: log₂ of(N) = <em>- </em>log(base 1/2) of (N) .
I think that's the big breakthrough here.
The rest is just turning the crank.
Now let's look at the problem:
log₂(x-1) + log(base 1/2) (x-2) = log₂(x)
Subtract log₂(x) from each side:
log₂(x-1) - log₂(x) + log(base 1/2) (x-2) = 0
Subtract log(base 1/2) (x-2) from each side:
log₂(x-1) - log₂(x) = - log(base 1/2) (x-2) Notice the negative on the right.
The left side is the same as log₂[ (x-1)/x ]
==> The right side is the same as +log₂(x-2)
Now you have: log₂[ (x-1)/x ] = +log₂(x-2)
And that ugly [ log to the base of 1/2 ] is gone.
Take the antilog of each side:
(x-1)/x = x-2
Multiply each side by 'x' : x - 1 = x² - 2x
Subtract (x-1) from each side:
x² - 2x - (x-1) = 0
x² - 3x + 1 = 0
Using the quadratic equation, the solutions to that are
x = 2.618
and
x = 0.382 .
I think you have to say that <em>x=2.618</em> is the solution to the original
log problem, and 0.382 has to be discarded, because there's an
(x-2) in the original problem, and (0.382 - 2) is negative, and
there's no such thing as the log of a negative number.
There,now. Doesn't that feel better.
Answer:<u> 9.42 inches</u>, 3π in terms of pi
Step-by-step explanation:
A full circle is 360 degrees, so if the segment has an arc of 120 degrees, it is 1/3 of a regular circle.
To find the area of a circle, we use the equation A = πr^2. In this case, we will divide the equation by 3 because we are only finding 1/ of a circle. So, our equation will be A = (πr^2)/3.
Using 3.14 for π:
A = (πr^2)/3.
A = (π3^2)/3
A = (π9)/3
A = 3π
A = 9.42
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<em>We will assume the tent is in the shape of a triangular prism.</em>
The volume of a triangular prism can be found with the following formula, where 
is the width at the base, 
is the height, and 
is the length.
Substitute in the known values.
Simplify — use multiplication.
Simplify — use division.
The volume — or in this case, the amount of living space — is 
.
