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Approximate the definite integral using the trapezoidal rule for the given value of n. Give the result accurate to 3 decimal places. (a) sin ( x ) dx n = 6 . Jo 1.95409 (b) Find the upper bound for the absolute value of the error based on [f"(x) | and Theorem 1. LETIS (c) Find the exact value of the definite integral. 2The velocity v, in meters per second, of an object at time t, in seconds, is given in the table below. 0.5 1.5 2 2.5 3 v(t) 5.3 57 6.2 7.3 6.8 Use the trapezoidal rule to approximate the distance s, in meters, traveled by the object from f = 0 to t = 3.Determine whether the integral converges or diverges; if it converges, evaluate. (If the quantity diverges, enter DIVERGES. Do not use the a symbol in your answer.) dx x 4 + 25x 2 XFind the area (if it Is possible) of the region between the graph of y = (3x _ 5)3/2 and the x-axis to the right of x = 7. (If not possible, enter IMPOSSIBLE. Do not use the a symbol in your answer.) X xAn object is thrown vertically upward with an initial velocity of 10 m/sec from a height of 1 meters. In meters, find the highest point it reaches, (Round your answer to three decimal places.) x m Find when it hits the ground. (Enter your answer in seconds, Round your answer to three decimal places.) 2.136Solve the differential equation. 2xy + 8x + (x2- 9) = 0 dx XFind the unique solution to the differential equation that satisfies the stated condition. dy dx with y (1 ) = 2Find the unique solution to the differential equation that satisfies the stated condition. dy _ 2x + sec (x) with r(0) = -9 dx 2yFind the unique solution to the differential equation that satisfies the stated condition. dy - In(x) with y(1) = 3 dx xyRadium decays exponentially; it has a half-life of 1,600 years. Find a formula for the amount, q(t), remaining from 70 mg of pure radium after t years. q(t) = x After how many years will there be 30 mg left? (Round your answer to the nearest year.) X yrSuppose that $30,000 is invested in an account for which interest is compounding continuously at 3.14%. What is the value after 5 years? After 10 years? (Round your answers to two d 5 years 10 years $ After how many years will the original investment be doubled? (Round your answer to two decimal places.) yrThe Lincoin wheat penny was designed by Victor D. Brenner in 1909. Currently, the most valued penny is the 1909 S VDB penny. It was minted in San Francisco and only 484,000 were minted with the initials on the back. In 2015, the S VDB penny in uncirculated condition is worth $3,200. When will it be worth $5,0007 (Round your answer to the nearest year.)The population of the United States has grown at different rates over ten-year increments as shown by the following table. Year Population of U.S. 1930 123.1 million 1940 132.1 million 1950 152.3 million 1960 180.7 million If the maximum supportable population of the U.S. is 600 million people, use the logistic model to predict the population (in millions of people) of the U.S. in 2030 by using the following years as data points. (Round your ama "s to one decimal place) (a) using 1930 and 1940 as data points X million people (b) using 1950 and 1960 as data points * million people Compare/contrast/explain the different results. The growth rate from part (a) is --Select-- @ the growth rate from part (b)