1. You con solve the quadratic equation x^2+20x+100=50<span> by following the proccedure below:
2. Pass the number 50 from the right member to the left member. Then you obtain:
x^2+20x+100-50=0
</span><span> x^2+20x+50=0
</span><span>
3. Then, you must apply the quadratic equation, which is:
x=(-b±√(b^2-4ac))/2a
</span><span>x^2+20x+50=0
</span><span>
a=1
b=20
c=50
4. Therefore, when you substitute the values into the quadratic equation and simplify ir, you obtain that the result is:
-10</span>±5√2 (It is the last option).
Answer:
wait so what is the numbers of distance they have swam?
Step-by-step explanation:
Answer: 10k
Step-by-step explanation:
Answer:
y= 25x+500
y=30x+400
20
standard machine
Step-by-step explanation:
just did it on edge!! :D
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 :)
