In ΔPQR, the measure of ∠R=90°, RQ = 16, PR = 63, and QP = 65. What ratio represents the cosine of ∠Q?
1 answer:
Answer:
Cos Q = 16/65
Step-by-step explanation:
In this question, we have a triangle and we have the information above supplied. We are being tasked with getting the ratio of the cosine.
To do this, we shall be making reference to a diagrammatic representation of the information supplied. Please do check the attachment section for this.
Looking at this triangle, we can see that one of the angles measure 90, what this means is that what we are dealing with is a right-angled triangle.
Now to get the answer in the question, we have to define what is meant by the cosine. The cosine is a trigonometric ratio of the adjacent to the hypotenuse.
In this case, our adjacent is 16 while our hypotenuse is the longest side which is 65.
Hence, Cos Q = 16/65
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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.
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.