Hooke's law states that f = -kx where f is the force by the spring, k is the spring constant, and x is the displacement (distance). write equation for the force by a spring with a spring constant of 30 n/m and an unknown displacement.

Divide the following fractions 3/4 ÷ 2/3 1/2 8/9 9/8 2

Arley is building a model of a city map. in one part of the city, three roads form a right triangle, which harley draws as triangle abc, with the following measures: m∠b=90° and m∠a=30°. in his scale model, the hypotenuse of triangle abc, ac¯¯¯¯¯¯¯¯, has a length of 817−−√ cm. what is the value of a (the length of bc¯¯¯¯¯¯¯¯)?

Elizabeth claims that the fourth root of 2 can be expressed as 2^m since (2^m)^n = 2. find the values of m and n for the case where elizabeth's claim is true.