Answer:
4
Step-by-step explanation:
4 is way off of the other numbers.
Answer:
Step-by-step explanation:
Given that the 45% of the population of a city are men and 15% are children . The number of women is 64,400 . And we need to find the number of children . Here ,
So the percentage of women will be equal to [ 100 - ( 45 -15) ]% = [ 100 - 60 ]% = 40% .
So let us take the total number of people be x . So ,
<u>The </u><u>percentage</u><u> of</u><u> </u><u>children </u><u>=</u><u> </u><u>1</u><u>5</u><u>%</u><u> </u><u>:</u><u>-</u>
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:
√(110 - n)
Step-by-step explanation:
This can't be simplified. All we can do here is re-write "square root of 110 - n" symbolically, which comes out to √(110 - n). The parentheses are essential for clarity.