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Determine the truth value of the compound proposition given that p is a false statement, q is a true statement, and r is a true statement.
1. p disjunction (negation q disjunction r)
2. r conjunction negation (p disjunction r)
Determine whether each sentence is a proposition or not. Write P if it is a proposition and N if not.
1. Star Wars: The Force Awakens is the greatest movie of all time.
2. Have a fun trip.
3. Do you like to read?
4. x2 = 25
5. x = x + 1
D. Consider the following sets:
U= {1, 2, 3, 4, 5, 6, 7, 8, }, A= {1, 2, 3, 4, 5, 7}, B= {1, 5, 6, 7}, C= {1, 2, 3, 6}
16-20. Illustrate the Venn Diagram for the sets A, B, and C.
(3) (i) A broken pipe at an oil rig off the east coast of Trinidad produces a circular oil slick that is S meters thick at a distance x meters from the break. It difficult to measure the thickness of the slick directly at the source owing to excess turbulence, but for x 0 they know that 2 3 2 5 2 3 ( ) 2 x x S x x x x If the oil slick is assumed to be continuously distributed, how thick is expected to be at the source? (ii) If 2 4 7 ( ) 4 1 x f x x 1 2 2 4 x x , determine whether the function f x( ) is continuous throughout its domain?
Demonstrate the stages of early number learning
Water is poured into a vessel of the form of a straight circular cone. If the vessel is installed with the <<sharp>> end down then the distance from the water level to the base of the cone is 1 m. When the vessel was turned over, it turned out that the distance from the water level to the <<sharp>> end of the vessel is root(3, 13) * m . Find the height of the vessel; give your answer in meters, rounded to two decimals if needed. The volume of a cone can be found by the V = 1/3 * S * h formula , where S is the area of its base and h is its height.
Determine the smallest positive root of the following equation: f(x) = x5 – 2x2 – 4x - 16 = 0 The root should be correct up to two decimal places, using (a) Regula-falsi method (b) Newton-Raphson method (c) Bisection method (d) Secant method
Discuss the standard unit's goals of measurement.
Consider the following matrix equation.
( "\\begin{matrix}\n 2 & -1 & 0 \\\\\n 1 & 2 & -1 \\\\\n 0& 1&3\n\\end{matrix}" ) ( "\\begin{matrix}\n x1 \\\\\n x2 \\\\\nx3\n\\end{matrix}" ) = ( "\\begin{matrix}\n 2 \\\\\n 1 \\\\\n3\n\\end{matrix}" )
Solve the equation by using Thomas algorithm.
Will an interpolating polynomial of degree n, interpolating n+1 points, be always uniquely
determined? Will an interpolating polynomial of degree n+1, interpolating n points, be always uniquely determined?
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