the formula for volume of sphere is 4/3||r^3
diameter=2radius
in the formula we need to have radius but we have been given diameter so we convert diameter to radius
d=2r
r=d/2
9.5÷2
4.75
Answer:
x= 12
Step-by-step explanation:
2(x-7) = 10
Distribute the 2. 2x-14 = 10
Add the 14 onto both sides to cancel it out on the original side and following the rules- the same must be done to the other side. 2x-14 (+14) = 10+14 -----> 2x = 24
Divide both sides by 2 to get the X alone. 2x/2 = 24/2 ---------> x= 12
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:
because base angle of isoscels triangle is congurent.
if one base is right angle then both base be rightangle.
The volume is 60 cubic inches.
To solve, follow the formula Volume = Length · Height · Width. If you are solving without a calculator, simply multiply the length and the height first, then multiply the product of that by the width, 2 / 3.
V = 10 · 9 · 2/3
V = (10 · 9) 2/3
V = 90 · 2/3
<span>V = 60 in.³
</span>
Hope this helps. Good luck! :)
