Beneficial tips on vibration of rectangular plates

Calculus Problems Help?
Question 1:Confirm that f and g are inverses by showing that f(g(x))=x and g(f(x))=x.f(x)=x+4/x and g(x)=4/x -1Question 2:An airplane leaves Los Angeles for Denver at a speed of 430 mph. Thirty minutes later, a plane going from Denver to Los Angeles leaves Denver, which is 850 miles from Los Angeles, at a speed of 510 mph. When they meet, how far are they from Denver? Answer choices belowa. 60 milesb. 345 milesc. 120 milesd. 300 milesQuestion 3:The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in inches: M(x)=20x – x^2. What vibration of rectangular plates rainfall produces the maximum number of mosquitoes? Answer choices belowa. 400 inchesb. 10 inchesc. 0 inchesd. 20 inchesQuestion 4:An open-top rectangular box has a square base and it will hold 256 cubic centimeters (cc). Each side has length x cm and height y cm. The box’s surface area is given by S(x)= 1024/x+x^2. Estimate the minimum surface area and the value x that will yield it. Answer choices belowa. 108 cm when x = 8cmb. 192 cm when x = 8cmc. 256 cm when x = 6cmd. 256 cm when x = 8cmQuestion 5:A flare fired from the bottom of a gorge is visible only when the flare is above the rim. If it is fired with an initial velocity of 208 ft/sec, and the gorge is 672 ft deep, during what interval can the flare be seen? Answer choices belowa. 60a. (-2, ∞)b. (-∞, -7)U(-6,-2)c. (-∞,-6)d. (-7,-6)U(-2,∞)Question 7:The period of vibration P for a pendulum varies directly as the square root of the length L. If the period of vibration is 2.5 seconds when the length is 25 inches, what is the period when L=6.25 inches? Answer choices belowa. 3.25 secondsb. 3 secondsc. 2.75 secondsd. 1.25 seconds
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vibration of rectangular plates