THIS IS THE COMPLETE QUESTION BELOW
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
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If a sample of gas is a 0.622-gram, volume of 2.4 L at 287 K and 0.850 atm. Then the molar mass of the gas is 7.18.
<h3>What is an ideal gas equation?</h3>
The ideal gas equation is given below.
The equation can be written as
Where M is the molar mass, P is the pressure, V is the volume, R is the universal gas constant, T is the temperature, and m is the mass of the gas.
Then the molar mass of a 0.622-gram sample of gas has a volume of 2.4 L at 287 K and 0.850 atm.
V = 2.4 L = 0.0024
P = 0.85 atm = 86126.25 Pa
T = 287 K
m = 0.622
R = 8.314
Then we have
Then the molar mass of the gas is 7.18.
More about the ideal gas equation link is given below.
brainly.com/question/4147359
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