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- The force on a particle is described by 8x3 - 6 at a point x along the axis. What is the work done in moving the particle from the origin to x = 5.a) Help determine the dimensions of the least expensive cylindrical that can hold 100 cubic inches if the materials cost 2¢, 5¢ and 3¢, respectively, for the top, bottom and sides.b) Help find how do the dimensions of the least expensive can change if the bottom material costs more than 5¢ per square inch?Suppose that 2 J of work is needed to stretch a spring fromits natural length of 30 cm to a length of 42 cm.(a) How much work is needed to stretch the spring from35 cm to 40 cm?
- a particle moves along a straight line with an acceleration of a= 4sin pye t divided by 2 m/s square. if the displacement at t= 0 is 0, and initial velocity= 8 divided by pye, find i. acceleration after 2 seconds ii. velocity after 2 seconds iii. displacement after 2 secondsQ1) Explain the process of parametrisation and also write 3 application ?A particle moves in a straight line such that its acceleration when at position x (with respect to a given coordinate system) is given by: a = 7x2 + 3 If its velocity, v, at position x = 0 is given by v(0)= 2, what is the velocity of the particle when at position x? Give your answer in terms of x.
- If the rocket exploded at the peak of the projectile, part I falls at distance less than d to the center-of-mass, so part II must fall to a distance Choose answer larger than d to the center-of-mass smaller than d to the center-of-mass exactly d to the center-of-massFind the work done in emptying the tank in example 4. If the tank water is pumped to a level 1.00 meters above the top of the tank and the water is initially 4.00 meters deep.An open top rectangular tank with square bases is to have a volume of 10 cubic meters. The material for its bottom cost P 150.00 per square meter, and that for the sides is P 60.00 per square meter. Determine the most economical dimensions of the tank.
- Obtain the general solution using variation of parameters y''+y = (csc³x) (cotx)A basketball player makes a successful shot from the free throw line. Suppose that the path of the ball from the moment of release to the moment it enters the hoop is described by y = 2.15 + 2.09x −0.41x2,0 ≤ x ≤ 4.6 where x is the horizontal distance (in meters) from the point of release, and y is the vertical distance (in meters) above the floor. Use a CAS or a scientific calculator with a numerical integration capability to approximate the distance the ball travels from the moment it is released to the moment it enters the hoop. Round your answer to two decimal places.Plz ans as soon as possible don’t provide any explanation