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nalin
5 days ago
11

You are watering a garden. The height h (in feet) of water spraying from the garden hose can be modeled by h(x)=−0.1x2+0.7x+3, w

here x is the horizontal distance (in feet) from where you are standing. You raise the hose so that the water hits the ground 1 foot farther from where you are standing. Write a function that models the new path of the water.
Mathematics
1 answer:
lawyer [4K]5 days ago
3 0

Answer:

g(x) = -0.1x^2 + 0.5x + 3.6

Step-by-step explanation:

Given

h(x) = -0.1x^2 + 0.7x + 3

Required

Find the updated function

The problem specifies that the water should land 1 ft further away.

This means we need to use x + 1

Consequently, in the initial function, we will replace x with x + 1 in h(x) = -0.1x^2 + 0.7x + 3

Thus, we obtain:

h(x + 1) = -0.1(x + 1)^2 + 0.7(x + 1) + 3

Expand the Parenthesis

h(x + 1) = -0.1(x + 1)(x + 1) + 0.7(x + 1) + 3

h(x + 1) = -0.1(x^2+2x+1) + 0.7(x + 1) + 3

h(x + 1) = -0.1x^2-0.2x-0.1 + 0.7x + 0.7 + 3

Combine Like Terms

h(x + 1) = -0.1x^2-0.2x + 0.7x + 0.7 + 3-0.1

h(x + 1) = -0.1x^2 + 0.5x + 3.6

The resulting function is:

g(x) = h(x + 1) = -0.1x^2 + 0.5x + 3.6

g(x) = -0.1x^2 + 0.5x + 3.6

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17 days ago
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Answer:

840

Step-by-step explanation:

As the arrangement matters, we apply the permutations formula to find the solution.

Permutations formula:

The count of possible arrangements of x items chosen from a total of n items is defined by this formula:

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For this problem:

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