A set of books that are each 1.5 inches wide are being organized on a bookshelf that is 36 inches wide. How many books can fit o
1 answer:
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Result is x³
On further squaring x³, he got = (x³)²
Pi() is the ratio of circumference to diameter for any circle.
Perimeter is the distance around a circle.
Circumference of circle .
Perimeter of circle
What is circle ?
A circle is a spherical shape without boundaries or edges.
A circle is a closed, curved object with two dimensions in geometry.
Consider two small arcs AB and CD of two circles of radii x and y units, both of which make an angle of measure θ at the centers P and Q respectively.
For smaller values of θ, the arc length AB is almost equal to the length of the line segment . Similarly, arc CD ≅
.
Using the SAS rule of triangle similarity, we can say that APB and CQD are similar triangles because their angles are the same and their ratios are AP: PB = CQ: QD = 1: 1. So, it stands to reason that AB: AP = CD: CQ.
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radius if this constant equals some value.
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Answer:
1. <u>Cost per customer</u>: 10 + x
<u>Average number of customers</u>: 16 - 2x
3. $10, $11, $12 and $13
Step-by-step explanation:
<u>Given information</u>:
- $10 = cost of buffet per customer
- 16 customers choose the buffet per hour
- Every $1 increase in the cost of the buffet = loss of 2 customers per hour
- $130 = minimum revenue needed per hour
Let x = the number of $1 increases in the cost of the buffet
<u>Part 1</u>
<u></u>
<u>Cost per customer</u>: 10 + x
<u>Average number of customers</u>: 16 - 2x
<u>Part 2</u>
The cost per customer multiplied by the number of customers needs to be <u>at least</u> $130. Therefore, we can use the expressions found in part 1 to write the <u>inequality</u>:
<u>Part 3</u>
To determine the possible buffet prices that Noah could charge and still maintain the restaurant owner's revenue requirements, solve the inequality:
Find the roots by equating to zero:
Therefore, the roots are x = 3 and x = -5.
<u>Test the roots</u> by choosing a value between the roots and substituting it into the original inequality:
As 144 ≥ 130, the <u>solution</u> to the inequality is <u>between the roots</u>:
-5 ≤ x ≤ 3
To find the range of possible buffet prices Noah could charge and still maintain a minimum revenue of $130, substitute x = 0 and x = 3 into the expression for "cost per customer.
[Please note that we cannot use the negative values of the possible values of x since the question only tells us information about the change in average customers per hour considering an <em>increase </em>in cost. It does not confirm that if the cost is reduced (less than $10) the number of customers <em>increases </em>per hour.]
<u>Cost per customer</u>:
Therefore, the possible buffet prices Noah could charge are:
$10, $11, $12 and $13.