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deff fn [24]
2 years ago
8

Match the correct angle measurement with its letter from the diagram.

Mathematics
1 answer:
igor_vitrenko [27]2 years ago
5 0

Answer:

<C=48 because 90-42=42 as in the other side of the triangle.

<B=42 because vertical angles are always congruent.

<B+<D=90 because <D is 48 because it is vertical to <C

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3 years ago
When a sprinkler is installed in the ground, the spray of water goes up and falls in the pattern of a parabola. The height, in i
Westkost [7]

Answer:

(1) 256 inches

(2) 5 feet

(3) 400 inches

(4) 10 feet

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(1) The function that gives the height in inches of the spray of water at a distance <em>x</em> from the sprinkler head is given as follows;

h(x) = 160·x - 16·x²

At x = 2 feet, we have;

h(2) = 160 × 2 - 16 × 2² = 256

Therefore, the height of the spray water at a horizontal distance of 2 feet from the sprinkler head h(2) = 256 inches

(2) The x-coordinate, x_{max}, of the maximum point of a parabola given in the form, y = a·x² + b·x + c is found using the following formula;

x_{max} = -b/(2·a)

The x-coordinate, x_{max}, of the maximum point of the given equation of the parabola, h(x) = 160·x - 16·x², (a = -16, b = 160) is therefore;

x_{max} = -160/(2 × (-16)) = 5

Therefore, the number of feet along the way, the function will reach maximum height, x_{max} = 5 feet

(3) The function, h(x) = 160·x - 16·x², will reach maximum height, h_{max}, at x = 5, therefore;

h_{max} =  h(5) = 160 × 5 - 16 × 5² = 400

The maximum height of the spray, h_{max} = 400 inches

(4) The water is at ground level where h(x) = 0, therefore;

At ground level, h(x) = 0 = 160·x - 16·x²

160·x - 16·x² = 0

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By zero product rule, we 16·x = 0, or (10 - x)  = 0, from which we have;

x = 0, or x = 10

The water is at ground level at x = 0 and x = 10 feet, therefore, the water will hit the ground again (the second time after leaving the sprinkler head at x = 0) at x = 10 feet.

7 0
3 years ago
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