A population of goblins was counted at 290 goblins in 1980. A later study showed that the population of goblins had grown to 1476 goblins by 2015. The goblins live in a valley with a large amount of food and no predators,
so we may assume exponential growth. Round all answers to 4 decimal places.

It is given that the quadratic equation hx²-3x+k=0, where h and k are constants, has roots [tex] \beta \: and \: 2 \beta [/tex]express h in terms of k

Find a parametrization for the curve「and determine the work done on a particle moving along γ in r3 through the force field f: r^3--r^3'where f(x, y,z) = (1,-x, z) and (a) im (γ) is the line segment from (0,0,0) to (1,2,1) (b) im (γ) is the polygonal curve with successive vertices (1,0,0), (0,1,1), and (2,2,2) (c) im (γ) is the unit circle in the plane z = 1 with center (0,0,1) beginning and ending at (1,0,1), and starting towards (0,1,1)

Thomas buys a cardboard sheet that is 8 by 12 inches. let x be the side length of each cutout. what is the size of the cutout he needs to make so that he can fit the most marbles in the box?