Answer:
104
Step-by-step explanation:
There are two ways to do it, though we need to know how it is affected.
20+6=26
26+6=32
32+6=38
38+6=44
Thus, you are adding 6 for each term.
1. You do it manually...(yes.)
I'll number it one by one
1.20
2.26
3.32
4.38
5.44
6.50
7.56
8.62
9.68
10.74
11.80
12.86
13.92
14.98
15.104
The 15th term is 104.
2. This method is easier. As shown above, there is a pattern. We can apply it using this formula:
20+6(n-1)
You can get this formula from the facts that:
-you start off with an additional added 8
-you add 6 every time
-if we do it 6n then it would be incorrect, with an extra 6 for each
-the formula is correct; you can test it for terms 2,3,4,5 like this:
20+6=26
20+2x6=32
20+3x6=38
20+4x6=44
To find the 15th term, you can:
20+14x6=20+84=104.
X - the volume of the tank
The tank holds
375 liters when full.
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 :)
The left side
1.99999925
1.99999925
does not equal to the right side
1
1
, which means that the given statement is false.
Use the fomula a_(n)= a_(1)+ d(n-1)
