The 10-kg double wheel with radius of gyration of 125mm about o is connected to the spring of stiffness k = 600 n/m by a cord which is wrapped securely around the inner hub. if the wheel is released from rest on the incline with the spring stretched 225 mm, calculate the maximum velocity v of its center o during the ensuing motion. the wheel rolls without slipping

Because light travels in a straight line and casts a shadow, isaac newton hypothesized that light is

The base of a 50-meter tower is at the origin; the base of a 50-meter tree is at (0, 50, 0). the ground is flat and the z-axis points upward. the following parametric equations describe the motion of six projectiles each launched at time t = 0 in seconds. (i) r (t) = (50 + t2)k (ii) r (t) = 2t2 j + 2t2k (iii) r (t) = 50 i + 50 j + (50 − t2)k (iv) r (t) = 2t j + (50 − t2)k (v) r (t) = (50 − 2t) i + 2t j + (50 − t)k (vi) r (t) = t i + t j + tk (a) which projectile is launched from the top of the tower and goes downward? at time t = , the projectile hits the ground at point (x, y, z) = . (b) which projectile hits the top of the tree?

For the below questions, consider a consumer that consumes two goods, x and z with the following utility function. u with bar on top space equals space x to the power of 1 third end exponent z to the power of 2 over 3 end exponent suppose initial values for income and the prices of goods x and z are y equals 90, p subscript x equals space 10, and p subscript z equals 15 respectively, then the price of good x falls to syntax error from line 1 column 89 to line 1 column 100. unexpected '\'.. what is the magnitude of the total effect