By inspection, it's clear that the sequence must converge to
because
when
is arbitrarily large.
Now, for the limit as
to be equal to
is to say that for any
, there exists some
such that whenever
, it follows that
From this inequality, we get
As we're considering
, we can omit the first inequality.
We can then see that choosing
will guarantee the condition for the limit to exist. We take the ceiling (least integer larger than the given bound) just so that
.
Answer: x=45
STEPS:
1
Add the same term to both sides of the equation
2
Simplify
3
Multiply all terms by the same value to eliminate fraction denominators
4
Simplify
Answer:
1.) 
≈ 3.652
2.) I would say something about how the A in front of cos in the equation would change to 90, rather than stay 75 (in the equation for the step by step), but it would be easier to just use the Pythagorean theorem.
Step-by-step explanation:
I think we may have the same class so hopefully this helps:
1.) 
--> law of cosines formula.
--> plugged in numbers; when you draw the triangle, the included angle would be A, and the opposite side would be a. B and b, and C and c are opposite each other. In this case, a is the hypotenuse.
--> in between steps.
--> more simplifying.
--> answer
2.) This one is just an explanation: The 75 in the equation is the given angle, which is a. If this changes, it would just change in the equation too. And obviously, if it's 90 degrees, you can just use Pythagorean theorem a^2+b^2=c^2.
Good luck! :)
Answer:
e total number of minutes, m.
Step-by-step explanation:
The dependent variable is the variable in which the variable cannot stand by itself.
In this situation, the total number of minutes, m, equal 20 times the number of d.
m = 20d
d, is a variable which can be multiplied which states that it has a value, no matter what. On the other hand, m, requires d, to be there in order to have a value.
The answer is, m, the total number of minutes.
Step-by-step explanation:
