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<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.
Write algorithm using pseudocode and flowchart that uses while loops to perform the
following steps:
i. Prompt the user to input two integers: firstNum and secondNum note that firstNum
must be less than secondNum.
ii. Output all odd numbers between firstNum and secondNum.
iii. Output the sum of all even numbers between firstNum and secondNum.
iv. Output the numbers and their squares between firstNum and secondNum.
v. Output the sum of the square of the odd numbers between firstNum and secondNum.
b. Redo Exercise (a) using for loops.
c. Redo Exercise (a) using do. . .while loops.
<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
<e> Congratulations! You are hired in a business organization. In this company the market research department that you are the member recommended to manufacture and market a promising new product (x). After extensive surveys, the research department supported the recommendation with the demand function:
Dx = f (p) = 60 – 3 P
Where Dx is quantity demanded at price P during a month. Financial department has brought the cost function and is given by
C(x) = 72 + 6x
Now the team leader of the market research department ordered you to manipulate the following problems.
Express revenue as a function of X
Expresses profit as a function of X
<e> Solve the first order linear inhomogeneous differential equation using the bernoulli method
(2x+1)y,=4x+2y
<e> Gerry needs a loan of 8000 € for his holiday trip. The loan period is 1 year and the payments are made quarterly. The loan has fixed principal payment and the interest rate is 3.8 % p.a. How much money Gerry needs for the third payment?
Two small conducting and identical spheres A and B have charges -25 nC and +15 nC, respectively. They are separated by a distance of 0.02 m. (a) What is the magnitude of the electric force between the two spheres? Is this force attractive or repulsive? (b) The spheres are then allowed to touch each other and then separated. What is the magnitude of the force between the two spheres? Is this a repulsive force or an attractive force?
<e> Evaluate the integral ∮c= 1 /(z-1)(z-2)(z-4) dz where C is |z| = 3 ?
<e> Show that if P and Q are vector Subspaces of a vector space V then P ∩ Q is also a vector subspace of V.
#339914 on Dec 2023