The demand equation for a product is p=90000/400+3x where p is the price (in dollars) and x is the number of units (in thousands). Find the average price p on the interval 40 ≤ x ≤ 50.

Answer

$168.27

Step by step Explanation

Given p=90000/400+3x

With the limits of 40 to 50

Then we need the integral in the form below to find the average price

1/(g-d)∫ⁿₐf(x)dx

Where n= 40 and a= 50, then if we substitute p and the limits then we integrate

1/(50-40)∫⁵⁰₄₀(90000/400+3x)

1/10∫⁵⁰₄₀(90000/400+3x)

If we perform some factorization we have

90000/(10)(3)∫3dx/(400+3x)

3000[ln400+3x]₄₀⁵⁰

Then let substitute the upper and lower limits we have

3000[ln400+3(50)]-ln[400+3(40]

30000[ln550-ln520]

3000[6.3099×6.254]

3000[0.056]

=168.27

the average price p on the interval 40 ≤ x ≤ 50 is

=$168.27

8 0

3 years ago

Joanie runs the concession stand for the school's baseball games. At each game, the best selling items are pretzels and hot dogs

Elenna [48]

X is pretzels and y is hot dogs
3x + 2y=195
x +15 =y

3x + 2(x+15)=195
5x=165
x=33
D

4 0

2 years ago

Factor the quadratic expression as the product of two binomials x^2-3x-10

vovikov84 [41]

X^2+2x-5x-10
x(x+2)-5(x+2)

(x-5)(x+2)

6 0

3 years ago