First figure out how many times 9 can go into 25 **do the highest amount of times it can go in-
<span><span>9x1=9 </span><span>9x2=18 </span><span>9x3=27 </span><span>9x4=<span>36
nine can go in 2 times because 3 times would be way to much
so you're mixed number would be 2
now to figure out you're numerator do 25-18=7
Now it would be 2 7/25
so you're mixed number,then the numerator,finally denomantor ALWAYS stays the same.
*IF YOU'RE NUMERATOR AND DENOMANTOR CAN BE REDUCED THEN REDUCE</span></span></span>
Answer:
A
Step-by-step explanation:
horizontal component=18cos 36.9°≈14.39 m/s≈14.4 m/s
Vertical component=18 sin 36.9°≈10.81 m/s≈10.8 m/s
Answer:
84 degree
Step-by-step explanation:
the new supposed line is parallel to the given parallel lines..
Answer:
wilma is 22.5 mph
fred is 25.5 mph
Step-by-step explanation:
Time:40 minutes, or 2/3 hours
Speed:
Fred:x+3
Wilma: x
Distance:32 miles
2/3(x+x+3)=32
2/3(2x+3)=32
1 1/3x+2=32
4/3x=30
x=22.5
wilma is 22.5 mph
fred is 22.5+3= 25.5 mph
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 :)
