Search
Assume that random guesses are made for seven multiple choice questions on an SAT test, so that there are n=7 trials, each with probability of success (correct) given by p=0.55. Find the indicated probability for the number of correct answers.
Find the probability that the number x of correct answers is fewer than 4.
If H and K is subgroup prove H intersection K is subgrop.
Example of metric space but not norm
Let (u,v)=u^2-v^2,y(u,v)=2uv.
Find the the Jacobian determinant,J(u,v).
Determine which of the following
pairs of functions are independent. Using the Jacobian matrix
a) u= x cos y and v=x sin y;
b)u= x + y and v= y/x+y;
c)u=x-2y and v=x^2 +4y^2-4xy+3x-6y;
d)u= x + 2y and v= x^2-y^2+2xy-x
Tshego won R165000 and decided to deposit 65% of this amount in an account earning 8,25% interest per year, compounded every four months. What is the accumulated amount after five years?
dy/dx = 5y + (e ^−2x)(y^−2)
<e> Find the equation of the sphere touching the plane 8𝑥 + 5𝑦 + 3𝑧 + 1 = 0 at (3, −1, −1) and cutting the sphere 𝑥2 + 𝑦2 + 𝑧2 − 2𝑥 + 𝑦 − 𝑧 − 6 = 0 orthogonally.
<e> 3. A firm can produce a good either by (i) a labor intensive technique, using 8 units of labor and 1 unit of capital or (ii) a capital intensive technique using 1 unit of labor and 2 units of capital. The firm can arrange up to 200 units of labor and 100 units of capital. Note that the firm produce goods X and Y in process land 1 and 2 respectively. Its objective is to maximize profit by selling the good.
i) Construct the objective function and the constant inequalities.
ii) By drawing the graphs of the linear constraints, find the optimal solutions.
iii) Find the solution using the simplex methods.
<e> find the turning points and point of inflection on the curve, y=x5-5x4+5x3-1
