Answer:
The correct option is C
Step-by-step explanation:
if f(x)= x3 + x2 - 20x
Replace f(x) by y
y = x3 + x2 - 20x
0 =x3 + x2 - 20x
x3 + x2 - 20x = 0
Take out x as a common:
x(x2+x-20)=0
Find factors of x2+x+20.
x(x^2+4x-5x-20) = 0
x{x(x+4)-5(x+4)}=0
x(x+4)(x-5)=0
Set x= 0
x=0 , x+4=0 , x-5 =0
x=0, x=0-4 , x=0+5
x=0, x= -4, x=5
x=(0,5,-4)
The correct option is C....
10 divided by 5 equals 2
9 divided by 3 equals 3
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:
45 Handshakes.
Step-by-step explanation:
10 people shake hands.
So, each person will shake hands with 9 other people.
Total number of handshakes = 90/2 = 45
The answer to the first part is 172 plants per row with a remainder of 3 plants
The answer to the second part is, Martin knows that 7 goes into 700 100 times, 7 goes into 490 70 times, and 7 goes into 17 twice with a remainder of 3. He then adds 100 70 and 2 together to get 172 with a remainder of 3.
