5. A rectangle has one side on the x-axis, one side on the y-axis, and a corner on the graph of y = x²+1. (a) Use Linear Approximation of the area formula to estimate the increase in the area of the rectangle if the base grows from 2 to 2.3 inches. (b) Calculate exactly the increase in the area of the rectangle as the base grows from 2 to 2.3 inches. y = x²+1 2

Suppose that the 3 points (0,0,0), (1,1,1), and (a,b,c) lie in a unique plane P. The line passing through (0,0,0) and (1,2,a) is normal to P. What is a?

Encuentra el rango o imagen

Encontrar el rango o imagen

Encontrar el rango o imagen

8 9. (a) You have been asked to determine the least expensive route for a telephone cable which connects Andersonville with Beantown. If it costs $5000 per mile to lay the cable on land and $8000 per mile to lay the cable across the river and the cost of the cable is negligible, find the least expensive route. (b) What is the least expensive route if the cable costs $7000 per mile plus the cost to lay it. cable B river 2

6. (a) You have been asked to bid on the construction of a square-bottomed box with no top which will hold 100 cubic inches of water. If the bottom and sides are made from the same material, what are the dimensions of the box which uses the least material? (Assume that no material is wasted.) (b) Suppose the box in part (a) uses different materials for the bottom and the sides. If the bottom material costs 5¢ per square inch and the side material costs 3¢ per square inch, what are the dimensions of the least expensive box which will hold 100 cubic inches of water?

Find parametric equations of the line tangent to the curve generated by r(t)=(t²+In(t −1), 3e²-4,4t-3) at the point (4,3,5). The velocity of a particle at time t is v(t) = (4t, 2t+1,6t²). At time t=1, the particle is at the point (-1,3,2). Find the position of the particle when t=3. Let C be the portion of the graph of y = 1—1—x³-x²+3 (a) Calculate the curvature of C at the point (0,3). (b) Find the point(s) on C at which the curvature is zero. Find the length of the curve generated by the position function r(t)=(2lnt,t,?) for 1≤t≤2. An object is fired from ground level with an initial speed of 100 ft/sec and an angle of elevation of 30°. Find the horizontal distance (range) traveled by the object. Round to the nearest tenth of a foot.

15. You own a small airplane which holds a maximum of 20 passengers. It costs you $100 per flight from St. Thomas to St. Croix for gas and wages plus an additional $6 per passenger for the extra gas required by the extra weight. The charge per passenger is $30 each if 10 people charter your plane (10 is the minimum number you will fly), and this charge is reduced by $1 per passenger for each passenger over 10 who goes (that is, if 11 go they each pay $29, if 12 go they each pay $28, etc.). What number of passengers on a flight will maximize your profits?