You arrive in my class 45 seconds after leaving math which is 90 meters away. How fast did you travel?
1 answer:
You might be interested in
Given :
Natalie is going mountain biking. She can buy a bike for $250 or she can rent a bike for $30 an hour.
In both cases, she must also rent a helmet for $5 an hour.
To Find :
Which inequality shows the number of hours Natalie must bike for the cost of buying a bike to be less than renting a bike.
Solution :
Let, after t hours total money required is ( if she rent bike ).
T = 30t.
Money required to purchase bike , M = $250.
For cost of buying a bike to be less than renting a bike :
Hence, this is the required solution.
Answer:
See expla below
Step-by-step explanation:
Given the demand function:
q = D (x) = 943 - 17 x
a) Find the elasticity:
Find the derivative of the demand function.
D'(x)= -17
Thus, elasticity expression is:
Elasticity expression =
b) At what price is the elasticity of demand equal to 1?
This means E(x) = 1
Substitute 1 for E(x) in the elasticity equation:
Cross multiply:
Collect like terms
x = 27.74
Elasticity at the price of demand = 1 is 27.74
c) At what prices is the elasticity of demand elastic?
This means E(x) > 1
Therefore,
Cross multiply:
Collect like terms
x > 27.74
The elasticity of demand is elastic at x > 27.74
d) At what prices is the elasticity of demand inelastic?
This means E(x) < 1
Therefore,
Cross multiply:
Collect like terms
x < 27.74
The elasticity of demand is inelastic at x < 27.74
e) At what price is the revenue a maximum:
Total revenue will be:
R(x) = x D(x)
= x (943 - 17x)
= 943x - 17x²
R(x) = 934 - 17x(price that maximizes total revenue)
Take R(x) = 0
Thus,
0 = 943 - 17x
17x = 943x
Total revenue is maximun at x= 27.74 per cookie
f) At x = 21 per cookie, find the price:
Thus,
R (21) = (943 * 21) - (17 * 21²)
= 19803 - 7497
= 12306
At x = 27.74, find the price:
R(27.74) = (943 * 27.74) - (17 - 27.74²)
= 26158.82 - 13081.63
= 13077.19
We can see the new price of cookie causes the total revenue to decrease.
Therefore, with a small increase in price the total revenue will decrease.