(x+1)y" -(x +2)y' + y=0;

The kinetic energy E of an object varies jointly with the object’s mass m and the square of the object’s velocity v . An object with a mass of 50 kilograms traveling at 16 meters per second has a kinetic energy of 6400 joules. What is the kinetic energy of an object with a mass of 70 kilograms traveling at 20 meters per second?

If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per second. What is the terminal velocity, and how long does it take the filter to reach 99 of terminal velocity? Use a table increment of 0.1 and given your answer to the nearest tenth of a second.

Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.

The path of flight (trajectory) of a football thrown by a quarterback is described by the +0) ². x² following function: y(x) = - where y = vertical position of football relative to the ground Linear model yo = vertical launch position of football relative to the ground horizontal position of football relative to launch position g=magnitude of gravitational acceleration vo = launch speed = launch angle relative to horizontal Which type of mathematical model is used here to describe the football's trajectory? Nonlinear model g 2v² cos² e Exponential model + (tan)x + yo Trigonometric model

Which of the following is the equation of a line tangent to the graph of f(x) = x* + 1 and parallel to the line y = 32x – 2? %3D - 16х — у 3 39 y = 32x + 39 O y + 47 = 32x 32x – y + 47 = 0

Find the first four derivatives of the following functions: with solution please.

Find the derivative of each function. h(x) = (4x³ + 8x)(16 – 5x) 145x7 – 240x4 – 192x* + 128 O -160x7 + 240x° – 128x² – 192 O 192x7 + 145x³ + 240x4 – 128 O -160x7 – 240x° + 192x² + 128

Differentiate the function. r(t) = (3t². + 8)i + r'(t) = (6t)i + +(12²) ₁ r'(t) = = (1²2); - 15 i + (6t)j r'(t) = (6t)i - r'(t) = (6)i + 15 25

(1 point) Differentiate y = Vx + Vx + vx. ||