Answer:
$7,200
Step-by-step explanation:
r=p × n
where
r=revenue
p = price per item
n = number of items sold
A change in price changes quantity ( number sold)
Variable x changes with price, then
Let
p+x=a dollar price increase
p-x= a dollar price decrease
n+x= an increase in quantity sold
n-x= a decrease in quantity sold
Therefore,
A $2 dollar increase in price=p+2x
2 decrease in room quantity sold= n-2x
Substituting in the above equation
r=(p+2x)*(n-2x)
P=$60
n=180
Then
r=(60+2x)*(180-2x)
r=10,800-120x+360x-4x^2
r=-4x^2-240x+10,800
Solve the quadratic equation
The maximum value of x in the vertex = - b/2*a
Where
b=240
a=-4
Value of x=-240/2*(-4)
X=30
r=-4x^2-240x+10,800
=-4(30)^2-240(30)+10,800
=-4(900)-7200+10,800
=3,600-7200+10800
=$7,200
The rate that maximises revenue=$7,200
Remark
If the two angles are complimentary they add up to 90°. So the first job is to find the third angle. In the diagram below, the third angle is labeled C, so you must find it first.
After that, you need to use the Pythagorean Theorem to solve for QC which at this point is not known.
After completing that, You need to find the cosine of P and Q so that they can be added together.
Step One
Find angle C
All triangles have 180°
P + Q are complementary. Given
P + Q = 90° Definition
P + Q + C = 180 Property of a triangle.
90 + C = 180 Subtract 90 from both sides.
C = 180 - 90
C = 90°
Step Two
Find QC
When you have a right triangle the Pythagorean Theorem can be used to find any missing side.
Sin(Q) = opposite / hypotenuse [See diagram]
Sin(Q) = 4/5 Given
a = 4
b = ??
c = 5
4^2 + b^2 = 5^2
16 + b^2 = 25 Subtract 16 from both sides.
b^2 = 25 - 16
b^2 = 9
Take the square root of both sides.
sqrt(b^2) = sqrt(9)
b = 3
Step 3
Define Cos(Q) and Cos(P)
Cos(Q) = adjacent side (3) over the hypotenuse (5)
Cos(Q) = 3/5
Cos(P) has the same basic definition. The adjacent side is 4 for angle P
Cos(P) = 4/5
Step Four
Add the two findings from Step 3
Cos(Q) + Cos(P) = 3/5 + 4/5 =
7/5 <<<<< Answer
Answer:
<u>note:</u>
<em><u>solution is attached in word form due to error in mathematical equation. furthermore i also attach Screenshot of solution in word due to different version of MS Office please find the attachment</u></em>
Answer:
here
Step-by-step explanation:
I don't think it simplifies, it should be 103/50
<h3>
Answer: 90 degrees</h3>
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Explanation:
This figure is a kite since we have two pairs of adjacent sides that are congruent, but not all sides are the same length.
One property of kites is that the diagonals are always perpendicular (this applies to rhombuses as well). This means angle 3 is 90 degrees.