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
The slope of the line is the velocity, or rate of change, of y with respect to x. In other terms, the slope tells you how much y will change for every change in x by one unit. For example if the slope, which is velocity, is 2. y will increase by two units every time x increases by one unit. Your graph is not pictured nor explained, so I cannot give you the specific context beyond the principle that the slope of a line is a constant velocity or rate of change.
-3x - 3/4 = 9
-3x - 3/4 + 3/4 = 9 + 3/4
-3x = 9 3/4
I change 9 3/4 to improper fraction
-3x = 39/4
-3x / -3 = 39/4 / -3
X = 39/4 x -1/3 (change division to multiplication so that you can complete the problem)
X = -39/12
You can convert that if you want to -3 3/12
So x = -3 3/12
Simplify to x = -3 1/4
1/5 = x/1100
5x = 1100
x = 1100 ÷ 5
x = 220
So 220 people named blue as fav.
3/10 = x/1100
3x = 1100
x = 1100 ÷ 3
x = 366.6666.... = 367
So 367 people chose red
