answer:The projection of mathbf{v}_1 onto mathbf{v}_2 is given by the formula: text{proj}_{mathbf{v}_2}mathbf{v}_1 = left(frac{mathbf{v}_1 cdot mathbf{v}_2}{mathbf{v}_2 cdot mathbf{v}_2}right)mathbf{v}_2 where cdot denotes the dot product. Plugging in the given vectors, we get: text{proj}_{mathbf{v}_2}mathbf{v}_1 = left(frac{mathbf{v}_1 cdot mathbf{v}_2}{mathbf{v}_2 cdot mathbf{v}_2}right)mathbf{v}_2 = left(frac{0(2) + (-1)(2) + (-2)(-3) + (-2)(1)}{2(2) + 2(2) + (-3)(-3) + 1(1)}right)mathbf{v}_2 = left(frac{-4 + 6 - 2}{4 + 4 + 9 + 1}right)mathbf{v}_2 = left(frac{0}{18}right)mathbf{v}_2 = left{frac{2}{9},frac{2}{9},-frac{1}{3},frac{1}{9}right} The answer is mathbf{v}_1 projected onto mathbf{v}_2 is left{frac{2}{9},frac{2}{9},-frac{1}{3},frac{1}{9}right}.

answer:The square root of a negative number is not a real number. Therefore, sqrt{-x} is not a real number. This means that the equation sqrt{7-15 x}+sqrt{6} sqrt{-x}=9 has no real solutions. The equation sqrt{7-15 x}+sqrt{6} sqrt{-x}=9 has no real solutions.

answer:Let's assume that each person cleans one room and everyone starts cleaning simultaneously. Since it takes 35 minutes for 10 people to clean 10 rooms, it takes one person 35 minutes to clean one room. With 20 people and 15 rooms, we can assign each person to clean one room. Since each person takes 35 minutes to clean a room, it will take 35 minutes for 20 people to clean 15 rooms.

answer:Given: - Mass of the car, ( m = 700 kg ) - Maximum speed without slipping, ( v = 41 m/s ) - Radius of the turn, ( r = 190 m ) - Downforce, ( F_d = 12,000 N ) - Acceleration due to gravity, ( g = 9.8 m/s^2 ) (a) To find the coefficient of static friction (( mu_s )): 1. Calculate the normal force: [ N = mg + F_d ] [ N = (700)(9.8) + 12,000 ] [ N = 6,860 + 12,000 ] [ N = 18,860 N ] 2. The centripetal force is provided by friction: [ F_c = frac{mv^2}{r} ] [ mu_s N = frac{mv^2}{r} ] [ mu_s (18,860) = frac{(700)(41)^2}{190} ] [ mu_s = frac{frac{(700)(41)^2}{190}}{18,860} ] [ mu_s approx 0.33 ] The coefficient of static friction is approximately 0.33. (b) If there were no downforce: 1. The maximum speed (( v_{max} )) can be found using: [ mu_s mg = frac{mv_{max}^2}{r} ] [ mu_s g = frac{v_{max}^2}{r} ] [ v_{max}^2 = mu_s r g ] [ v_{max}^2 = (0.33)(190)(9.8) ] [ v_{max}^2 approx 614.46 ] [ v_{max} approx 24.8 m/s ] Without downforce, the car's maximum speed would be approximately 24.8 m/s.