Search & Filtering
Solve the equation √3sin𝜃−cos𝜃=0 for −180°≤𝑥≤180°
Solve the equation 8sin^2𝑥−7=2cos𝑥 for 0≤𝑥≤360°, giving your answers to 1 decimal place.
Prove:
a. (sin𝑥+cos𝑥)^2 ≡1+2sin𝑥cos𝑥
b. (1+sin𝑥+ cos𝑥)^2 ≡2 (1+sin𝑥) (1+cos𝑥)
c. (6−cos^2𝜃)/(sin^2𝜃+5) ≡1
An organization is interested in the analysis of two products that can be produced from the idle time of labour, machine and investment. It was notified on the investigation that the labour requirement of the first and the second products was 4 and 5 units respectively and the total available man-hours were 48. Only the first product required machine hour utilization of one hour per unit and at present only 10 spare machine hours are available. The second product needs one unit of by-product per unit and the daily availability of the by-product is 12 units. According to the marketing department, the sales potential of the first product cannot exceed 7 units. In a competitive market, the first product can be sold at a profit of Rs.6 and the second product at a profit of Rs.10 per unit. Formulate the problem as a linear programming model. Also determine graphically the feasible region. Identify the redundant constraints if any.
Solve the following equations by Elimination method, Substitution method and Graphing method.
1. 2𝑥 + 3𝑦 = 8
5𝑥 − 3𝑦 = −1
2. 2𝑥 +5y = 19
x − 2y = −4
3. 𝑦 = 5 − 2𝑥
4𝑥 + 3𝑦 = 13
4. 𝑦 = 2𝑥 − 3
𝑦 = − 2/3𝑥 + 5
Suppose that A, B, and C are sets such that A ⊆ B and B ⊆ C. Show that A ⊆ C.
Use a Venn diagram to illustrate the set of all months of the year whose names do not contain the letter Y in the
set of all months of the year.
Heights of the students in a class are given in the distribution below:
5' - 5'2" 10
5'2" - 5'4" 40
5'4" - 5'6" 25 .
Find:
1. Skewness and Kurtosis
three cans of beans and five cans of soup weigh 700g.
four cans of beans weigh 300g.
what is thr weight of five cans of beans and three cans of soup?.
X=28 ; n=100
