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Chapter 6: Problem 47
The rectangular coordinates of a point are given. Find polar coordinates of each point. Express \(\theta\) in radians. $$(5,0)$$
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A force is given by the vector \(\mathbf{F}=3 \mathbf{i}+2 \mathbf{j} .\) The force moves an object along a straight line from the point (4,9) to the point \((10,20) .\) Find the work done if the distance is measured in feet and the force is measured in pounds.
Find \(\text {pro}_{\mathbf{w}} \mathbf{V}\) Then decompose v into two vectors, \(\mathbf{v}_{1}\) and \(\mathbf{v}_{2},\) where \(\mathbf{v}_{1}\) is parallel to \(\mathbf{w}\) and \(\mathbf{v}_{2}\) is orthogonal to \(\mathbf{w}.\) $$\mathbf{v}=3 \mathbf{i}-2 \mathbf{j}, \quad \mathbf{w}=\mathbf{i}-\mathbf{j}$$
Two buildings of equal height are 800 feet apart. An observer on the street between the buildings measures the angles of elevation to the tops of the buildings as \(27^{\circ}\) and \(41^{\circ} .\) How high, to the nearest foot, are the buildings?
A force of 4 pounds acts in the direction of \(50^{\circ}\) to the horizontal. The force moves an object along a straight line from the point (3,7) to the point \((8,10),\) with distance measured in feet. Find the work done by the force.
Let $$\mathbf{u}=-\mathbf{i}+\mathbf{j}, \quad \mathbf{v}=3 \mathbf{i}-2 \mathbf{j}, \quad \text { and } \quad \mathbf{w}=-5 \mathbf{j}$$ Find each specified scalar or vector. $$\operatorname{proj}_{\mathbf{u}}(\mathbf{v}-\mathbf{w})$$
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