Answer:
10.5
Step-by-step explanation:
Answer:
x = 0.5
Step-by-step explanation:
Given
2(x + 1.25) = 3.5 ← divide both sides by 2
x + 1.25 = 1.75 ( subtract 1.25 from both sides )
x = 0.5
Answer:
6
Step-by-step explanation:
Using Euclid's algorithm, we divide the larger by the smaller. If the remainder is zero, the divisor is the GCF. Otherwise, we replace the larger with the remainder and repeat.
18 ÷ 12 = 1 r 6
12 ÷ 6 = 2 r 0 . . . . the GCF is 6
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You can also factor the numbers and see what the common factors are.
18 = 2·3·3
12 = 2·2·3
The common factors are 2·3 = 6.
In the factorizations, we see 2 to powers of 1 and 2, and we see 3 to powers of 1 and 2. The GCF is the product of the common factors to their lowest powers: (2^1)(3^1) = (2)(3) = 6
A) Demand function
price (x) demand (D(x))
4 540
3.50 810
D - 540 810 - 540
----------- = -----------------
x - 4 3.50 - 4
D - 540
----------- = - 540
x - 4
D - 540 = - 540(x - 4)
D = -540x + 2160 + 540
D = 2700 - 540x
D(x) = 2700 - 540x
Revenue function, R(x)
R(x) = price * demand = x * D(x)
R(x) = x* (2700 - 540x) = 2700x - 540x^2
b) Profit, P(x)
profit = revenue - cost
P(x) = R(x) - 30
P(x) = [2700x - 540x^2] - 30
P(x) = 2700x - 540x^2 - 30
Largest possible profit => vertex of the parabola
vertex of 2700x - 540x^2 - 30
When you calculate the vertex you find x = 5 /2
=> P(x) = 3345
Answer: you should charge a log-on fee of $2.5 to have the largest profit, which is $3345.
