Answer you cheating idiot
Step-by-step explanation:
Answer: A. $0.60
Step-by-step explanation:
The prices for which the carpets were sold are
1) 100 square feet for $67
2) 200 square feet for $130
3) 400 square feet for $240
4) 800 square feet for $504. We would determine the unit cost per square foot for each of them. It becomes
1) 1 square feet costs 67/100 = $0.67
2) 1 square feet costs 130/200 = $0.65
3) 1 square feet costs 240/400 = $0.6
4) 1 square feet costs 504/800 = $0.63
The unit cost per square foot of carpet for the worst deal is $0.6
This is quite a complex problem. I wrote out a really nice solution but I can't work out how to put it on the website as the app is very poorly made. Still, I'll just have to type it all in...
Okay so you need to use a technique called logarithmic differentiation. It seems quite unnatural to start with but the result is very impressive.
Let y = (x+8)^(3x)
Take the natural log of both sides:
ln(y) = ln((x+8)^(3x))
By laws of logarithms, this can be rearranged:
ln(y) = 3xln(x+8)
Next, differentiate both sides. By implicit differentiation:
d/dx(ln(y)) = 1/y dy/dx
The right hand side is harder to differentiate. Using the substitution u = 3x and v = ln(x+8):
d/dx(3xln(x+8)) = d/dx(uv)
du/dx = 3
Finding dv/dx is harder, and involves the chain rule. Let a = x+ 8:
v = ln(a)
da/dx = 1
dv/da = 1/a
By chain rule:
dv/dx = dv/da * da/dx = 1/a = 1/(x+8)
Finally, use the product rule:
d/dx(uv) = u * dv/dx + v * du/dx = 3x/(x+8) + 3ln(x+8)
This overall produces the equation:
1/y * dy/dx = 3x/(x+8) + 3ln(x+8)
We want to solve for dy/dx, achievable by multiplying both sides by y:
dy/dx = y(3x/(x+8) + 3ln(x+8))
Since we know y = (x+8)^(3x):
dy/dx = ((x+8)^(3x))(3x/(x+8) + 3ln(x+8))
Neatening this up a bit, we factorise out 3/(x+8):
dy/dx = (3(x+8)^(3x-1))(x + (x+8)ln(x+8))
Well wasn't that a marathon? It's a nightmare typing that in, I hope you can follow all the steps.
I hope this helped you :)
Answer:
d
Step-by-step explanation:
it's the answer because it's the answer and it makes sense because I know it does
Answer:
C is the closest one but it should be -472 instead -475
Step-by-step explanation:
just insert X in the formulas and compare to P
