Not completely sure if I understand the problems.
1) (3^{\sqrt2})^\sqrt2
(x^m)(x^n) = x^{m*n}
so,
3^{\sqrt2*\sqrt2}
Now just simplify it a little more.
2) 3^{3x} - 1 = 3^{x+2}
Possibly use ln to solve.ln(3^{3x} - 1) = ln(3^{x+2})
2xln3-(x+2)ln3 = ln1
ln3(2x-(x+2))=ln1
x =...
Haha. Thanks for all the help. Turns out the professor wanted us to solve it with calculator. Mesmerize would have been a better way to go. =P
g(x) = 1 + 4x - 10x^2 + x^4
(dy/dx) = 4 - 20x + 4x^3
Perfect, I think it was the basic concepts that helped. Just to verify:
I was able to simplify the first equation to y = 2x. Using that...
y = 2(6-2y)
y = 12 - 4y
5y= 12
y=12/5
Plug into x = 6-2y...
x = 6 - 2(12/5)
x = 1.2
So, (1.2, 2.4)
That seems right. Thank you.
[SOLVED] System of equations problem
I'm trying to brush up on my algebra and had difficulties with a problem.
Solve for (x,y): (x^-(2/3))(y^(2/3)) = (2x^(1/3))(y^-(1/3)) and 6 = x + 2y
I'm mainly having problems simplifying the first equation for y but got y=0. Any help?
[SOLVED] Local Max & Min problem
I'm having a real tough time finishing this problem. I have to find the local maxima and minima points for g(x).
g(x) = 1 + 4x - 10x^2 + x^4
(dy/dx) = 4 - 20x + 4x^3
I've been trying to factor it to get the max and min points, but I find it...
Problem: A 40kg, 5.0m long beam is supported by, but not attached to, the two posts in the figure. A 20kg boy starts walking along the beam. How close can he get to the right end of the beam without it falling over?
http://student.ucr.edu/~meliz003/phy.JPG
My answer:
\tau_net =...
Problem: Consider two identical ships, one loaded with a cargo of cork (which floats), and the other empty. Which ship displaces more water?
My answer:
V=V
m_1>m_2
and,
\rho_1=\frac{m_1}{V}
\rho_2=\frac{m_2}{V}
so,
\rho_1>\rho_2
\rho_1 displaces more water because the mass added...
Homework Statement
A 500g block is attached to a spring on a frictionless horizontal surface. The block is pulled to stretch the spring by 10cm, then gently released. A short time later, as the block passes through the equilibrium position, its velocity is 1m/s.
>A)What is the block's period of...