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    Calculating masses of unknown quantities of reactants.

    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...
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    Evaluating an Inverse Trigonometric Function

    Homework Statement Evaluate sin^-1(cos70°) Homework Equations The Attempt at a Solution sin^-1(cos70°)=θ sinθ=cos70° sinθ=1/2 sinθ=∏/3
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    Derivative of Trigonometric Functions

    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...
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    Write the polar form of a complex number in the form of a+ib

    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.
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    Prove whether or not a transformation is one to one.

    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...
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    Use exponential notation to form a+ib

    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...
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    Finding a transition matrix

    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...
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    Determine if a transformation is linear.

    Homework Statement Please see attached files and let me know if I am correct or not. Homework Equations The Attempt at a Solution
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    Isolating a variable in an exponent

    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...
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    Modifying an equation to plot a straight line.

    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...
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    For what value(s) of x does A^-1 exist.

    [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...
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    Finding values of k in a system of linear equations.

    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...
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    Order of calculations in a matrix problem.

    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.
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    Solving a system with the inverse of a matrix.

    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...
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    Proving a thermal conductivity/resistance formula.

    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...
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    Find the final internal energy of a gas.

    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...
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    Solving a logarithmic equation.

    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)...
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    Find the points on a graph at which the tangent line is parallel

    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...
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    Justify if a mass is negligible.

    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...
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    Finding a limit when assigned restrictions to f(x)

    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...
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    Tension on a string between two masses.

    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...
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    Magnitude and direction of net force acting on a charge.

    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...