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Basic Algebra


Please see attachment for equation to be solved.

Gradients of vectors expressions

See attached file for full problem description. f = r.k/|r^3| What is the gradient of f? Show that for vectors v and r and constant vector a we get: if v=(a.r)r Div(v) = 4(a.r) Curl(v) = a x r

Polynomial Interpolation Question

16. Let P_2(x) be the quadratic polynomial interpolating f(x) at the evenly space point x_0, x_1 = x_0 + h, x_2 = x_0 + 2h. Derive formulas for the error: f'(x_i) - P'_2(x_i), i = not zero, 1, 2 Assume f(x) is three times continuously differentiable, give commutable bounds for these errors. Hint: use the error formula


I need to solve a system of vector loop equations, using the Newton-Raphson method and find the (x,y) coordinates of the coupler point. This problem (NEW ATTACHMENT) is listed in "Applied Numerical Methods for Engineers and Scientists" by Singiresu S. Rao: problem 2.3, page 139.

Polynomial Interpolation - Newton's method

(i) Use the tabulated data and Newton's method of divided differences to (a) calculate the degree three interpolating polynomial based on x_0, x_1, x_2, x_3 and (b) calculate the degree four interpolating polynomial based on x_0, x_1, x_2, x_3, x_4. x_k || 0 | -1 | 1 | 3 | 2 y_k || 5 | 15 | 3 | 47 | 9 (Use exact arithmeti

Create a relational algebra expression for each of the seven queries

The following tables form part of a database held in a relational DBMS: Hotel (hotelNo, hotelName, city) Room (roomNo, hotelNo, type, price) Booking (hotelNo, guestNo, dateFrom, dateTo, roomNo) Guest (guestNo, guestName, guestAddress) where Hotel contains hotel details and hotelNo is the primary key; Room contains room d

What was the total training cost?

Nine salespersons attended an 8-hour products conference. The average hourly rate of pay for the 9 employees is $9.86. The sales manager, at an annual salary of $44,800,conducted the 1-day session after a 1-day prep session. Lunch was provided at a cost of $11.80 per person. What was the total training cost? a.$709.92 b.$117

7 Assorted Logarithm Problems

Please see the attached file for the fully formatted problems. A. i) Find the natural logarithms of the values given as Items 8 and 9 on the worksheet. (Give your answer to 3d.p. where appropriate). ii) Refer to Item 10 on your worksheet. Using common logarithms find the value of 'x' and check your answer by numerical subst

Algebra 2

1. Find all zeros for f(x)=x^4-15x^3+70x-156 2. Solve 3^x+2=65 Round your answer 3 decimal places. 3. Solve 6^4x+5=3^7x-1 Round your answer 3 decimal places. 4. Solve logx=4.952 Round your answer to 3 decimal places. 5. Solve 2^3x=3^4x-2 Round your answer to 3 decimal places. Please