(18-7x)+1= -9 Hope this helps ^^
Since you haven't identified this figure, I'm going to assume that it's a rectangle.
The Perimeter of a rectangle of length L and width W is P = 2L + 2W.
Here you are given the Perimeter and the length, and are to find the width, W.
Solving the above equation for W, we get P - 2L = 2W.
Dividing by 2 (to isolate that W), we get
P
-- - L = W
2
Substitute P= 6 yds and L = 6 feet (or 2 yds), find W (in yards).
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: 6 5/6
Step-by-step explanation:
Solve for a:
a + 7/6 = 8
Put each term in a + 7/6 over the common denominator 6: a + 7/6 = (6 a)/6 + 7/6:
(6 a)/6 + 7/6 = 8
(6 a)/6 + 7/6 = (6 a + 7)/6:
(6 a + 7)/6 = 8
Multiply both sides of (6 a + 7)/6 = 8 by 6:
(6 (6 a + 7))/6 = 6×8
(6 (6 a + 7))/6 = 6/6×(6 a + 7) = 6 a + 7:
6 a + 7 = 6×8
6×8 = 48:
6 a + 7 = 48
Subtract 7 from both sides:
6 a + (7 - 7) = 48 - 7
7 - 7 = 0:
6 a = 48 - 7
48 - 7 = 41:
6 a = 41
Divide both sides of 6 a = 41 by 6:
(6 a)/6 = 41/6
6/6 = 1:
Answer: a = 41/6 or a= 6 5/6
16 days since 2/5 is 0.4 and there was 40 days then 2/5 * 40 is 16
