4. Suppose you are climbing a hill whose shape is given by the equation f(x, y) 360 – x2 – 0.1y², where x and y are measured in meters. You are standing at the point P(12, 10, 206) on the hill. (NOTE: Your answers might not seem realistic for an actual hill you can climb.) - (a) Find Vf at the point (12, 10). (b) From this point, in which direction is the slope the greatest? Give your answer as a unit vector, with all numbers exact (not decimal approxima- tions). (c) What is the rate of ascent in the direction of the greatest slope (found in part (b))? Give an exact answer (not a decimal approximation). (d) Suppose that the positive y-axis points north and the positive x-axis points east. If you walk directly southwest, will you be ascending or descending? At what rate? Give an exact answer or round your answer to three decimal places.

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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.