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The accompanying figure shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 2 units long. a) Express the y-coordinate of P in terms of x. (You might start by writing an equation for the line AB.) b) Express the area of the rectangle in terms of x. P(x, ?)

The accompanying figure shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 2 units long. a) Express the y-coordinate of P in terms of x. (You might start by writing an equation for the line AB.) b) Express the area of the rectangle in terms of x. P(x, ?)

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter8: Areas Of Polygons And Circles
Section8.5: More Area Relationships In The Circle
Problem 9E
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The accompanying figure shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 2 units long. a) Express the y-coordinate of P in terms of x. (You might start by writing an equation for the line AB.) b) Express the area of the rectangle in terms of x. P(x, ?)
Transcribed Image Text:The accompanying figure shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 2 units long. a) Express the y-coordinate of P in terms of x. (You might start by writing an equation for the line AB.) b) Express the area of the rectangle in terms of x. P(x, ?)
A power plant sits next to a river where the river is 250 mt wide. To lay a new cable from the plant to a location in the city 2 km downstream on the opposite side costs $180 per meter across the river and $100 per meter along the land. -2 km- P City 250 mi Power plant NOT TO SCALE a) Suppose that the cable goes from the plant to a point Q on the opposite side, and that the point P is directly opposite to the plant. Write a function C(x) that gives the cost of laying the cable in terms of the distance x.| b) Generate a table of values to determine if the least expensive location for point Q is less than 300 m or greater than 300 m from point P.
Transcribed Image Text:A power plant sits next to a river where the river is 250 mt wide. To lay a new cable from the plant to a location in the city 2 km downstream on the opposite side costs $180 per meter across the river and $100 per meter along the land. -2 km- P City 250 mi Power plant NOT TO SCALE a) Suppose that the cable goes from the plant to a point Q on the opposite side, and that the point P is directly opposite to the plant. Write a function C(x) that gives the cost of laying the cable in terms of the distance x.| b) Generate a table of values to determine if the least expensive location for point Q is less than 300 m or greater than 300 m from point P.
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