Homework Statement
Calculate the number of moles and mass of BaCl2 and NaCl in the original mixture.
Homework Equations
We prepared a solution of 0.35M Na2SO4. We then obtained an unknown mixture of BaCl2•2H2O and NaCl, weighed 1 g and added it to 200 mL of water and 10 mL HCl. Finally we...
Homework Statement
d/dx(sec(x)/1+tan(x)
Evaluate at x=∏/6
Homework Equations
The Attempt at a Solution
((1/cos(x))(1+tan(x))-(sec(x))(sin(x)/cos(x)))/(1+tan(x))^2
((1/cos(x))-(sec(x))(sin(x)/cos(x)))/(1+tan(x))
I used the quotient rule and reduced what I could. Have I done this...
Homework Statement
4{cos(13∏/6)+isin(13∏/6)}
= 4((√3/2)+(i/2))
= 2√3+2i
Homework Equations
The Attempt at a Solution
This is an example from my textbook. The part which I do not understand is how to convert the cos and sin of radians into those fractions. Any help is greatly appreciated.
Homework Statement
Let T: R3 -> M22 by
T\begin{bmatrix}
a \\
b \\
c
\label{T}
\end{bmatrix}
=
\begin{bmatrix}
a-b & b-c \\
a+b & b+c\\
\end{bmatrix}
Is this transformation one-to-one?
Homework Equations
The Attempt at a Solution
I am not really certain...
Homework Statement
Use exponential notation to write (√3-i)(1+i√3) in the form a+ib.
Homework Equations
The Attempt at a Solution
Let (√3-i) = z1
r1=|z1|=√((√3)2-i2)
=√(3-1)
=√2
Therefore,
√3=√2cosθ and -1=√2sinθ
cosθ = √3/√2 and sinθ = -1/√2
θ= arcsin(-1/√2)
θ= -∏/4...
Homework Statement
Let B = {(1,1,1),(1,2,2),(2,3,4)} be an ordered basis of R3, and let B` be the standard basis of R3.
Find the transition matrix from B to B` and use it to find the coordinates of (1,2,3)T with respect to B.
Homework Equations
The Attempt at a Solution
Is it...
Homework Statement
So I had to find out
N=Noe-ux
Where No=1.5,e is the elementary charge, u=-0.068 and x=0.07
I came to the answer 1.221
Now I need to find x if u =-0.036, N=1.221 and No remains 1.5
Homework Equations
The Attempt at a Solution
I reduce the equation to the following...
Homework Statement
Show all the steps required to modify the equation so that the plot yields a straight line.
N/N0=e\ -ux
This equation demonstrates the fraction radiation absorbed by a material, where "N0" is the number of incident photons from the radioactive source without any absorbed...
[b]1. Homework Statement
Let A =
(x+1 2 )
(x+5 x+1)
For what value(s) of x, if any, does A-1 exist?
Homework Equations
The Attempt at a Solution
So let me see if I get the gist of this. An n x n matrix is invertible if and only if rank (A) = n. So unless there is...
Homework Statement
For what value(s) of k does the system of linear equations below have a unique solution?
2x+(k-1)y = 6
3x+(2[I]k+1)y= 9
Homework Equations
The Attempt at a Solution
I'm uncertain how to even go about tackling this problem. Given how all the other problems...
Homework Statement
(A+2D)T
Homework Equations
The Attempt at a Solution
I believe this would become AT+2DT. My only question then is, do I multiply the transpose of matrix D by 2, or multiply matrix D by two and then take the transpose? Thank you.
Homework Statement
a)Use Gauss-Jordan elimination to find the inverse of A =
[ 2 1 4 ]
[ 1 1 2 ]
[ -2 -3 -2 ]
b) Use the result from part a) to find the solution of the following system.
5x+2y-3z = 5
x+y-z = -1
-3x-y+2z = 2
Homework Equations
The Attempt...
Homework Statement
The figure below shows a block that consists of two materials with different thicknesses l 1 and l 2 and different thermal conductivities λ1 and λ2. The temperatures of the outer surfaces of the block are Thigh and Tlow, as shown in the figure. Each face of the block has a...
Homework Statement
A thermally isolated container is filled with 2.3 mol of an ideal gas at T = 0°C.The gas is then compressed from 1.9 m3 to 0.3 m3. What is the final internal energy U of the gas? (Assume the process occurs at constant pressure.)
Homework Equations
U=3/2nRT
U=Q+W
W=pΔV...
Homework Statement
log3x+log3(2x+1)=1
Solve for x.
Homework Equations
The Attempt at a Solution
log3((2x+1)x)=1
3log3((2x+1))=31
(2x+1)x=3
2x2+x=3
2x2+x-3=0
Using the quadratic formula
x= (-1±√(12-4(2)(-3)))/(2(2))
= (-1±√(1+24))/(4)
= (-1±√25)/(4)
= (-1±5)/(4)...
Homework Statement
Find the points on the graph y=x^3/2 - x^1/2 at which the tangent line is parallel to y-x=3.
Homework Equations
The Attempt at a Solution
First I found that the derivative of y=x^3/2 - x^1/2 is 1x.
I then rewrote the other line as y = 3+x and found the...
Homework Statement
A standard man holds an object of mass m = 3 kg on the palm of the hand with the arm stretched, as shown in the figure below.
(a) Use the torque equilibrium equation to determine the magnitude of the force F that is exerted by the biceps muscle, when a = 32 cm,b = 6 cm,and...
Homework Statement
Suppose 0 ≤ f(x) ≥ 1 for all x, find lim x→0 x^4f(x)
Homework Equations
The Attempt at a Solution
I'm very uncertain about how to go about doing this.
lim x→0 x^4 f(x) = 0^4 (0)
= 0
lim x→0 x^4 f(x) = 1^4 (1)
=1...
Homework Statement
The figure below shows an object of mass m1 = 1.1 kg on an inclined surface. The angle of the inclined surface is θ = 31° with the horizontal. The object m1 is connected to a second object of mass m2 = 6.10 kg on a horizontal surface below an overhang that is formed by the...
Homework Statement
Four charges,
q1 = +195 µC, q2 = +60 µC, q3 = −145 µC, and q4 = +21 µC,
are fixed at the corners of a 4 m by 5 m rectangle, as illustrated in the figure below. What are the magnitude and the direction of the net force acting on q1? (Assume the x-axis extends from q1 to...