An island is 3 mi from the nearest point on a straight shoreline; that point is 13 mi from a power station (see figure). A Utility company plans to lay electrical cable underwater from the island to the shore and then underground along the shore to the power station. Assume that is costs $2800imi to lay cable underwater and $1400imi to lay underground cable. At what point should the underwater cable meet the shore to minimize the cost of the project? Write an equation for the total cost. C, as a function of x, where x is the distance from the shoreline closest to the island and the point where the cable leaves the shore C- 2800 (9+) + 1400(13 - x) Iland (Type an expression.) Cable The interval of interest of the objective function is [0,13] (Simplify your answer. Type your answer in interval notation.) Station The cost is minimized when x is 3 mi. (Type an exact answer) -13 mi The minimum installation cost is S (Round to the nearest cent as needed.)

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.