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 is 72
n = 5
a = 10 m
r = 6.88191 m
R = 8.50651 m
A = 172.048 m2
P = 50 m
x = 108 °
y = 72 °
When n = 1 first term = -6
n = 2 second term = 0
n = 3 third term = 6
n = 4 4th term = 12
so we have an Arithmetic sequence first term = -6 and common difference = 6
Sum 14 terms = (14/2)[2*-6 + (14-1)*6]
= 462 answer
I(interest rate)=P(principle)R(rate)T(time)
I=112*1400*1
I=$156800
Answer:
40°, 60° and 80°
Step-by-step explanation:
sum the parts of the ratio, 2 + 3 + 4 = 9 parts
Divide 180° ( sum of angles in a triangle) by 9 to find the value of one part of the ratio.
180° ÷ 9 = 20° ← value of 1 part of the ratio , then
2 parts = 2 × 20° = 40°
3 parts = 3 × 20° = 60°
4 parts = 4 × 20° = 80°
The angles in the triangle are 40°, 60°, 80°