An object is suspended by two cables attached at a single point. The force applied on one cable has a magnitude of 125 pounds and acts at an angle of 37°. The force on the other cable is 75 pounds at an angle of 150°.Part A: Write each vector in component form. Show all necessary work.Part B: Find the dot product of the vectors. Show all necessary calculations Part C: Use the dot product to find the angle between the cables. Round the answer to the nearest degree. Show all necessary calculations.

An airplane flies at 500 mph with a direction of 135° relative to the air. The plane experiences a wind that blows 60 mph with a direction of 60°.Part A: Write each of the vectors in linear form. Show all necessary calculations.Part B: Find the sum of the vectors. Show all necessary calculations. Part C: Find the true speed and direction of the airplane. Round the speed to the thousandths place and the direction to the nearest degree. Show all necessary calculations.

Use sigma notation to write the sum. Σ EM i=1 - n 2 4n + n n

Vectors t = 3i + 7j, u = 2i − 5j, and v = −21i + 9j are given.Part A: Find the angle between vectors t and u. Show all necessary calculations. Part B: Choose a value for c, such that c > 1. Find w = cv. Show all necessary work.Part C: Use the dot product to determine if t and w are parallel, orthogonal, or neither. Justify your answer.

A small company of science writers found that its rate of profit (in thousands of dollars) after t years of operation is given by P'(t) = (5t + 15) (t² + 6t+9) ³. (a) Find the total profit in the first three years. (b) Find the profit in the sixth year of operation. (c) What is happening to the annual profit over the long run? (a) The total profit in the first three years is $ (Round to the nearest dollar as needed.)

Find the area between the curves. x= -2, x = 7, y=2x² +3, y=0 Set up the integral (or integrals) needed to compute this area. Use the smallest possible number of integrals. Select the correct choice below and fill in the answer boxes to complete your choice. A. 7 [[2x² +3] dx -2 B. [[ ] dx+ -2 7 S [ ] dx The area between the curves is (Simplify your answer.)

The rate at which a substance grows is given by R'(x) = 105e0.3x, where x is the time (in days). What is the total accumulated growth during the first 2.5 days? Set up the definite integral that determines the accumulated growth during the first 2.5 days. 2.5 Growth = (105e0.3x) dx 0 (Type exact answers in terms of e.) Evaluate the definite integral. Growth= (Do not round until the final answer. Then round to one decimal place as needed.)

Find the total area of the shaded regions. y 18- 16- 14- 12- 10- 8- 6- y=ex+1-e 4- 2- 0- 2 3 4 5 -2 -4- X ☑ The total area of the shaded regions is (Type an integer or decimal rounded to three decimal places as needed.)

The graph of f(x), shown here, consists of two straight line segments and two quarter circles. Find the 19 value of f(x)dx. 小 Srxdx. 19 f(x)dx y 7 -7 2 12 19 X ☑