Recommendations Skill plans

Algebra 2

Q.5 Transformations of functions RSN

Find g(x), where g(x) is the translation 2 units left and 16 units down of f(x) = 5x - 1.

g(x) = 5x + 25

g(x) = 5x + 5

g(x) = 5x - 7

g(x) = 5x - 27

O

Two cannon balls weighing 18 kg and 24 kg are chained together and fired horizontally with a velocity of 165 m/s from the top of a 21-m wall. the chain breaks during the flight of the cannonballs and the 18-kg cannonball strikes the ground at t = 1.5 s, at a distance of 240 m from the foot of the wall, and 7 m to the right of the line of fire. determine the position of the other cannonball at that instant. neglect the resistance of the air.

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?

Ablock of mass m = 2.5 kg is attached to a spring with spring constant k = 740 n/m. it is initially at rest on an inclined plane that is at an angle of theta= 26 with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is uk = 0.17. in the initial position, where the spring is compressed by a distance of d = 0.16 m, the mass is at its lowest position and the spring is compressed the maximum amount. take the initial gravitational energy of the block as zero. the block's initial mechanical energy is 9.472 j.b. if the spring pushes the block up the incline, what distance l in meters will the block travel before coming to rest? the spring remains attached to both the block and the fixed wall throughout its motion.