# Search results

1. ### Margin of error in a t-distribution

This is not a homework problem. I am working on an experiment and I need to know how many samples (n) I need to achieve a margin of error (e) below 2%. Looking through a statistics text book they provide a calculation for e using z-distributions, but not t-distributions. Replacing...
2. ### Finding the Basis?

In a solution to an old exam the prof found a basis of a 5x5 matrix by simply subtracting the transpose of A from A aka(A - A^T) and then found the basis for the null for the now much simplified matrix. Is that a general guideline I can follow? If so it would make my life a lot easier.
3. ### Finding the Basis?

Find a basis for and calculate the dimension of nullA: A = [1 2 7]T, [1 1 2]T, [-2 0 6]T, [0 1 -10]T, [4 -5 -7]T Like most algebra texts mine has pages and pages of proofs with hardly a single example tying it together. Here is what I think I know: If the determinant does not equal 0...
4. ### Vector spaces, Spans and Matrix Determinants

I think I have something mixed up so if someone can please point out my error. 1. the set of all linear combinations is called a span. 2. If a family of vectors is linearly independent none of them can be written as a linear combination of finitely many other vectors in the collection. 3. If...
5. ### How can you find two different values for sin^-1(0.750)?

I am working on a statics question and one of the angles is sin^-1(0.750) which I calculate as 48.6 degrees though the book gives 131.41 degrees If I calculate sin(48.6) it equals 0.750 If I calculate sin(131.41) it equals 0.750 Clearly there is some relation or rule that I am unaware of...
6. ### Determine the length of l (equilibrium)

A ring of negligible size is subjected to vertical force P. Determine the required length l of the cord AC such that tension acting in AC is TAC. Also, what is the force acting in cord AB? P = 300N, d = 0.2m (distance between A & B), angle ABC = 45 degrees, TAC = 250N The graph...
7. ### Structural Formulas for all the (C5H11OH) alcohols

Given: Draw structural formulas for all the alcohols that have the molecular formula C5H11OH. Name each one and classify them as primary, secondary, or tertiary alcohols. Describe how they are formed and give two uses for this type of alcohol. Solution: I am still at the naming portion but...
8. ### Equilibrium equations

Write the equations for the equilibrium, showing a) the reaction between H and CrO4 to produce Cr2O7 and H2O b) the reaction between OH and Cr2O7 to reproduce CrO4 and H2O c) a summation equation showing both H and OH in the equilibrium reaction between CrO4 and Cr2O7 First I found the...
9. ### Equilibrium (water and ethanol)

Ethanol and water are completely miscible; that is, they dissolve in each other in all proportions a) When two substances are mixed, is randomness increased or decreased? b) Heat is liberated in the disolving process. Does the tendency toward minimum energy favour the seperated pure...
10. ### Rate law for the reaction

Mixture-----[I-] (mol/L)---[S2O8^2] (mol/L)---Time (s) 1---------------0.10--------------0.050-------------20 2---------------0.075-------------0.050-------------28 3---------------0.050-------------0.050-------------41 4---------------0.025-------------0.050-------------84...
11. ### Use binomial theorem to prove

Use binomial theorem to prove C(n,0) - 3(C(n,1)) + 9(C(n,2) - 27(C(n,3) + ... + (-3)^n(C(n,n) = (-2)^n From looking at the data given b = (-3) so a = 1 so (-2)^n = (1-3)^n With this I know the equation in sigma notation and could probably prove the theorem through mathematical induction but...
12. ### Proof #2

If a circle has an area of t square units and radius r, then a circle with area 2t square units has a radius 2r a) State whether or not the statement is true, Justify your answer. b) If it is not true, rewrite the statement so that it is true. 50 = (4)(4)(pi) 100 = (5.6)(5.6)(pi) 5.6/2 does...
13. ### Determine the remainders when dividing their squares by four

Randomly select eight odd integers of less than 1000 a) Determine the remainders when dividing their squares by four, and tabualte your results b) Make a conjecture about your findings c) test your conjecture with at least five larger integers d) Prove of justify the conjecture you make. n...
14. ### Solve each linear system using row reduction

3x+3y+3z=3 x+y+z=-1 3 3 3 | 3 1 1 1 |-1 1 1 1 | 0 0 0 0 | 1 x = -y -z y = 1 Substitute y into x, x = -1 -z Let z = t, tER Then x = -1 -t, y = 1 The corresponding vector equation of the line intersection is: (x,y,z) = (-1, 1, 0) + t(-1, 0, 1) Does that look right...
15. ### Area of a Triable with three vertices

Determine the area of a triangle with vertices A(1,0,-5), B(-2,2,3) and C(-3,1,-1). 1/2|a x b| |a x b| = (1, 0, -5) x (-2, 2, 3) = ((0)(3) - (2)(-5), (-5)(-2) - (3)(1), (1)(2) - (-2)(0)) = (10, 7, 4) |(10, 7, 4)| = sqr(10^2 + 7^2 + 4^2) = sqr(165) (1/2)(sqr(165)) = 6.42 Therefore the area...
16. ### Determine the values of a and c on a line.

A line is defined by the equations x = 3-4t, y = 8t, and z = 6+t a) Determine the vector and symmetric equations of the line b) Determine the values of a and c if the point (a, 2, c) lies on the line. I have part a) solved: (x,y,z) = (3,0,6) +t(-4,8,1) (3-x)/4 = y/8 = z-6/1 I am a...
17. ### Anti-Commutative Law

Prove that anti-commutative law for the cross product: a * b = -(b * a) The question looks easy enough except that I can not find a definition of the anti-commutative law anywhere. I can find countless references to it but not a single definition. Can some one give me a run down on what the...
18. ### Cross Product and Dot Product

Use two methods to determine a unit vector perpendicular to both (2,1,-3) and (-1, 7, 4) Using Cross Product: Let v be a perpendicular vector to the given vectors v = a*b = (2,1,-3)(-1,7,4) =((1)(4)-(7)(-3), (-3)(-1)-(4)(2), (2)(7)-(-1)(1)) =(4+21, 3-8, 14+1) =(25, -5, 15) = (5, -1...
19. ### Binding energy of a nucleon virus an electron

The energy that binds an orbiting electron to the hydrogen nucleus is 13.4 eV. Calculate the ratio of the binding energy per nucleon to the binding energy per electron in deuterium. Which part is held more tightly, the electron or the neutron? I already worked out the average binding energy...
20. ### Nautralization Reactions

Write equations for the neutralization reactions that result in the formation of the following salts: lithium carbonate H2CO3 + LiO2 --> LiCO3 + H2O copper (II) chlorate 2HClO3 + CuO --> Cu(ClO3)2 + H2O aluminium sulphate 2Al(OH3) + 3H2SO4 + 10H2O --> Al2(SO4)3 * 16H2O ammonium...
21. ### Proper Length

"proper" Length What speed would the spaceship have to travel for its relative length to be half its “proper” length Given: Lo = 67m L = 33.5 Required: v Analysis: L = (Lo)(sqr(1-(v^2)/(c^2))) Now, I calculate v = sqr((1-(L/Lo)^2)(c^2)) however that gives me an non-real anwer...
22. ### Angles of Nodal Lines (Two point light source)

A two-point source operates at a frequency of 1.0Hz to produce an interference pattern in a ripple tank. The sources are 2.5cm apart and the wavelength of the waves is 1.2 cm. Calculate the angles at which the nodal lines in the pattern are located far from the sources. (assume the angles...
23. ### Work done to move a test charge

A test charge of +1.0*10^-6 C is 40cm from a charged sphere of 3.2*10^-3 How much work is required to move it there from a point 1.0*10^2 m away from the sphere? GIVEN: q1 = +1.0*10^-6 C q2 = 3.2*10^-3 C r1 = 1.0*10^2 m r2 = 0.40 m Required: W Analysis: Ee=(k*q1*q2)/r delta...
24. ### The meaning of u (Mu)?

You are observing the effects of a single point charge with a magnitude of +4.3uC Calculate the strength of the electric field 3 cm away from the charge (in any direction I am curious as to the meaning of u (mu) in the above question. I am sure they would not have included it arbitrary...
25. ### Coulomb's Law (positive & negative charges)

I need to draw a single point charge with a magnitude of +4.3 C (coulomb's) I want to make sure that I am doing this right so: If one electron equals 1.602*10^-19 C than +4.3 C is actually a negative charge and therefore -4.3 C would be a positive charge. Is this right or do i have it...
26. ### Direction of a satellite in a circular orbit

A satellite is designed to orbit Earth at an altitude above its surface that will place it in a gravitational field with a strength of 4.5 N/kg a) Calculate the distance above the surface of Earth at which the satellite must orbit b) Assuming the orbit is circular calculate the...
27. ### Total Energy of a satellite

Calculate the total energy of a geosynchronous satellite (one that orbits over a fixed spot) with a mass of 1500kg, orbiting Earth at a height of 325km with an orbital speed of 5000m/s This question is starting to drive me a little mad. First of all, the satellite can't be in a...
28. ### Applied Force

In many neighbourhoods, you might see parents pulling youngsters in a four-wheeled wagon. The child and the wagon have a combined mass of 50kg and the adult does 2.2 x10^3 J of work pulling the two 60m at a constant speed. The coefficient of friction for the surfaces in contact is 0.26...
29. ### Volume - Volume Calculations

Suppose that you want to prepare 2.00*10^3 L of ammonia gas, NH3 , from the reaction of hydrogen gas with nitrogen gas. What volume of hydrogen and nitrogen do you need? Assume that the temperature and pressure remain constant during the reaction. 3H2(g) + N2(g) -> 2 NH3(g) V H2 =...
30. ### Centrifuge acceleration expressed in terms of gravity

A Biophysicist wants to separate sub-cellular particles with an analytic ultra-centrifuge. The biophysicist must determine the magnitude of the centripetal acceleration provided by the centrifuge at various speeds and radii. Calculate the magnitude of the centripetal acceleration at 8.4 cm...