Answer:
The answer is A, (1,2).
Step-by-step explanation:
Hope this helps!
8x-4(x+1) = 0
x =1
y = 1 + 1
y = 2
(x,y) = (1,2)
2 = 1 + 1
8 x 1 - 4 x 2 = 0
Simplify
2 = 2
0 = 0
Solution = (1 , 2)
Answer:
(-3, 16)
Step-by-step explanation:
If it is reflected off the y - axis, the x coordinates change.
It becomes (-3, 16)
Mr.Jones charges $800 per lesson and requires 3 lessons
That means mr Jones will charge Samantha 800x3 = $2400 in total.
Mr. Police charges $62 per lesson and requires 4 lessons,
62x4 = $248 in total.
Since mr. Police charges less than mr.Jones, it would be a better deal for Samantha.
IN CASE YOU WROTE THE QUESTION WRONG AND MR JONES CHARGES $80 PER LESSON
In that case it would be 80x3 = $240 in total
mr jones would charge less now and it would be better deal for Samantha.
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 :)
