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The EuroDish: Concentrated Solar Power for Remote Areas

The EuroDish is a high-efficiency parabolic reflector that uses concentrated sunlight to generate electricity in remote areas. It heats helium to 650°C, powering the engine and providing a sustainable energy solution.

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The EuroDish: Concentrated Solar Power for Remote Areas

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  1. The EuroDish, developed to provide electricity in remote areas, uses a parabolic reflector to concentrate sunlight onto a high-efficiency engine located at the reflector’s focus. The sunlight heats helium to 650°C to power the engine. EXAMPLE 3 Solve a multi-step problem Solar Energy •Write an equation for the EuroDish’s cross section with its vertex at (0, 0). •How deep is the dish?

  2. EXAMPLE 3 Solve a multi-step problem SOLUTION STEP 1 Write an equation for the cross section. The engine is at the focus, which is | p | = 4.5 meters from the vertex. Because the focus is above the vertex, pis positive, so p = 4.5. An equation for the cross section of the EuroDish with its vertex at the origin is as follows: x2 = 4py Standard form, vertical axis of symmetry x2 = 4(4.5)y Substitute 4.5 for p. Simplify. x2 = 18y

  3. Find the depth of the EuroDish. The depth is the y- value at the dish’s outside edge. The dish extends = 4.25 meters to either side of the vertex (0, 0), so substitute 4.25forxin the equation from Step 1. 8.5 2 vertex (0, 0), so substitute 4.25 for xin the equation from Step 1. 1.0 y EXAMPLE 3 Solve a multi-step problem STEP 2 x2 = 18y Equation for the cross section (4.25)2 = 18y Substitute4.25forp. Solve for y.

  4. ANSWER The dish is about 1 meter deep. EXAMPLE 3 Solve a multi-step problem

  5. for Example 3 GUIDED PRACTICE 9. Microwaves A parabolic microwave antenna is 16 feet in diameter. Find an equation for the cross section of the antenna with its vertex at the origin and its focus 10 feet to the right of its vertex. Then find the antenna’s depth.

  6. for Example 3 GUIDED PRACTICE SOLUTION STEP 1 Write an equation for the cross section. Because the focus is right of the vertex, so p = 10. An equation for the cross section of the Antenna with its vertex at the origin is as follows: y2 = 4px Standard form, vertical axis of symmetry y2 = 4(10)x Substitute 4.5 for p. Simplify. y2 = 40x

  7. ANSWER Find the depth of the antenna. The depth is the x- value at the antenna outside edge. The antenna extends = 8 feet to either side of the vertex (0,0), so substitute 8foryin the equation from Step 1. The antenna is 1.6 ft deep. 16 2 1.6 x for Example 3 GUIDED PRACTICE STEP 2 y2 = 40x Equation for the cross section (8)2 = 40x Substitute8forp. Solve for x.

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