Answer:
1 and 9
Step-by-step explanation:
By the Triangle Inequality Theorem, the sum of two side lengths of a triangle is always greater than the length of the third side.
In other words, in a triangle with side lengths 
and 
we always have 
Applying this to this question, the other side length, 
must satisfy the following inequalities:
Solving these inequalities gives
Combining these solutions, we have 
Therefore, the length of the third side falls between 1 and 9.
Number 2 is the correct answer
ANSWER
EXPLANATION
The period refers to the interval over which the function completes one full cycle.
The given function completed four cycles in on the the interval.
[-π,π]
The period is
Simplify;
The last choice is correct.
Answer:
Step-by-step explanation:
When two angles are complementary, their angle lengths add up to 90°.
Therefore, we can make the equation
Now we can solve for x.
Since the measure of ∠4 is just x°, and we know x is 33, that means ∠4 is 33°.
We also have the expression for ∠3, 
. Since we know x is 33, we can substitute it into the expression.
Hope this helped!
Whenever you face the problem that deals with maxima or minima you should keep in mind that minima/maxima of a function is always a point where it's derivative is equal to zero.
To solve your problem we first need to find an equation of net benefits. Net benefits are expressed as a difference between total benefits and total cost. We can denote this function with B(y).
B(y)=b-c
B(y)=100y-18y²
Now that we have a net benefits function we need find it's derivate with respect to y.
Now we must find at which point this function is equal to zero.
0=100-36y
36y=100
y=2.8
Now that we know at which point our function reaches maxima we just plug that number back into our equation for net benefits and we get our answer.
B(2.8)=100(2.8)-18(2.8)²=138.88≈139.
One thing that always helps is to have your function graphed. It will give you a good insight into how your function behaves and allow you to identify minima/maxima points.
