Determine the absolute error (as a decimal) and the relative error (as a percentage) in approximating th following integral using the trapezoidal rule with n = 4 subdivisions. √2 L √2x+6 dx 3 Absolute error (round to four decimals): Relative error (round to two decimals): %

Engr. Moncada is playing tennis. She hit the ball into the air at a certain height in meters given by the equation h(t)=-24t^2+120t, where t is the number of seconds elapsed since the ball was hit. How long does it take for the ball to hit the ground?* O O seconds 6 seconds 5 seconds O 3 seconds O 4 seconds

Make a substitution to express the integral as a rational function and then evaluate the integral. (Please show all steps and work)

The shaded region shown below is bounded by the functions f (x) = -3x² + 8 and g(x) = -1.5x + 6 and the x and y axes. Find the area of the shaded region using a calculator, rounding to the nearest thousandth. 10 2. 3

A person standing at the edge of a cliff throws a rock upward from a height of 170 ft above ground level with an initial velocity of 64 ft/s. Calculate the velocity of the rock when it is exactly 48 ft above the person's hand. Separate multiple answers with a comma. (Hint: Use h(t) = − 16t² +64t + 170 as the position function, where h is in feet, t in seconds. Ignore air resistance.) Answer ft/s Keypa- Keyboard Shortc

Q8 Find the integral: [√x+1d +1 da. Show all your work.

Simplify by rewriting F(t) using a negative exponent and no fractions. F(t) = (1/9t+1)^5

The velocity (in feet/second) of a projectile t seconds after it is launched from a height of 10 feet is given by v(t) = - 15.7t + 148. Approximate its height after 3 seconds using 6 rectangles. It is approximatley feet. (Round final answer to nearest tenth. Do NOT round until the final answer.)

A person standing at the edge of a cliff throws a rock upward from a height of 240 ft above ground level with an initial velocity of 48 ft/s. Calculate the velocity of the rock when it is exactly 32 ft above the person's hand. Separate multiple answers with a comma. (Hint: Use h(t) = − 16t² + 48t + 240 as the position function, where h is in feet, t in seconds. Ignore air resistance.) Answer ft/s Keyp- Keyboard Short

Evaluate the integral f dx /20x+2x² by completing the square and using trigonometric substitution.