Find parametric equations for the tangent line to the helix with parametric equations x = 5 cos(t) y = 4 sin(t) z = t at the point (0, 4, π/2). solution the vector equation of the helix is r(t) = 5 cos(t), 4 sin(t), t , so r'(t) = . the parameter value corresponding to the point (0, 4, π/2) is t = , so the tangent vector there is r'(π/2) = . the tangent line is the line through (0, 4, π/2) parallel to the vector , 0, , so by these equations its parametric equations are the following. x = y = 4 z =

Aplane is taking off from bangladesh headed to new york city. at the same time, a plane from new york city is headed to bangladesh is also taking off. the plane bound to new york city is traveling at 600 mph, while the plane traveling to bangladesh is traveling at 400 mph. how far from new york city will the two planes meet if the distance between new york city and bangladesh is 8,000 miles?

Someone answer this asap rn for ! a discount store’s prices are 25% lower than department store prices. the function c(x) = 0.75x can be used to determine the cost c, in dollars, of an item, where x is the department store price, in dollars. if the item has not sold in one month, the discount store takes an additional 20% off the discounted price and an additional $5 off the total purchase. the function d(y) = 0.80y - 5 can be used to find d, the cost, in dollars, of an item that has not been sold for a month, where y is the discount store price, in dollars. create a function d(c(x)) that represents the final price of an item when a costumer buys an item that has been in the discount store for a month. d(c(x)) =

If rs 900 amounts to rs 1044 in 4 years, what sum will amount to 1368 in 3 1/2 years at the same rate