Let f be a function defined for t ≥ 0. Then the integral ℒ{f(t)} = [infinity] e−t f(t) dt 0 is said to be the Laplace transform of f, provided that the integral converges. to find ℒ{f(t)}. (Write your answer as a function of s.) f(t) = t sin(t)

Astudent draws two parabolas on graph paper. both parabolas cross the x-axis at (-4, 0) and (6,0). the y-intercept of thefirst parabola is (0, –12). the y-intercept of the second parabola is (0-24). what is the positive difference between the avalues for the two functions that describe the parabolas? write your answer as a decimal rounded to the nearest tenth.

Johnny rode his bike to a friends house 4 blocks down the street in his neighborhood. he immediately rode back home once he realized his friend was unable to play. what was his displacement for the total bike ride trip? what could you use as a reference point ? show the steps to solve this problem.

Consider the enlargement of the pentagon. what is the value of x, rounded to the nearest tenth? 2.1 centimeters 3.3 centimeters 7.0 centimeters 15.0 centimeters