PROBLEM 17. [TIME ALLOWED = 5 MINUTES] State whether “n is divisible by 9” is (a) necessary, (b) sufficient, or (c) neither necessary nor sufficient for “n is divisible by 6”, where n is a natural number.
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- (Oceanography) The pressure, P, exerted on an underwater object can be determined by this formula: P=gh is the density of water, which is 1.94slug/ft3 . g is the acceleration caused by Earth’s gravity, which is 32.2ft/sec2. h is the object’s depth in the water in feet. a. Determine the units of P by calculating the units resulting from the right side of the formula. Check that your answer corresponds to the units for pressure listed in Table 1.1. b. Determine the pressure on a submarine operating at a depth of 2500 feet.PROBLEM 4. [TIME ALLOWED = 5 MINUTES] Give the negation of the following sentence: “It is hot today.”PROBLEM 13. [TIME ALLOWED = 5 MINUTES] Give the contrapositive, converse, and inverse of the following proposition: “If the number is positive, then its square is positive.”
- Problem 3. A gantep number is a positive integer whose sum of the digit is equal to 12.For example 5403 is a gantep number since 5+4+0+3 = 12.Write down the number of gantep numbers less than 100000?N(100000) =(Thermodynamics) The work, W, performed by a single piston in an engine can be determined by this formula: W=Fd F is the force provided by the piston in Newtons. d is the distance the piston moves in meters. a. Determine the units of W by calculating the units resulting from the right side of the formula. Check that your answer corresponds to the units for work listed in Table 1.1. b. Determine the work performed by a piston that provides a force of 1000 N over a distance of 15 centimeters.Computer Science f(x)= Sin(x) – x 3 + C Where C = Max [0.15, (69/100)] x20, (x is in radian). Apply the false position method three iterations to find the root of the function (Decide the starting values of Xl and Xu yourself)
- PROBLEM 11. [TIME ALLOWED = 5 MINUTES] Express the contrapositive in English of the following sentence: “I will buy the tickets only if you call.”PROBLEM 12. [TIME ALLOWED = 5 MINUTES] Give the contrapositive and converse of the following proposition: “If it is sunny, then I will go swimming.”H.W1/ Write an numerical programme to calculate the first derive for the following function y(x)=sin(4x)+cos(4x) in term of an analytic, central, forward and backward differences respectively. using 101 points from x=0 to x=4. and plot the estimates and the actual function derivatives.
- 4. Look up the Pythagorean theorem if you are not already familiar with it. Use the following formula to solve for c in the formula: c = √a2 + b2. Use the proper functions from the cmath header file. Be sure to output the result..Solve problem 23 please by following the directions.(Automotive) a. An automobile engine’s performance can be determined by monitoring its rotations per minute (rpm). Determine the conversion factors that can be used to convert rpm to frequency in hertz (Hz), given that 1rotation=1cycle,1minute=60seconds,and1Hz=1cycle/sec. b. Using the conversion factors you determined in Exercise 7a, convert 2000 rpm into hertz.