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professor190 [17]
2 years ago
11

The height of a tree is 42 inches. After 6 years the height is 15 feet 6 inches. How many inches did the tree grow each year?

Mathematics
1 answer:
statuscvo [17]2 years ago
6 0
<h3><u>Given :-</u></h3>

<u />

  • Height of the tree = 42 inches.
  • Height of the tree after 6 years = 15 feet 6 inches.

<h3><u>To Find :-</u></h3>

<u />

  • Number of inches the tree grew each year.

<h3><u>Solution :-</u></h3>

<u />

Height of the tree after 6 years,

→  15 feet 6 inches = 186 inches.

→  186 - 42 = 144 inches.

Height of the tree after 1st year = 144/6 = 64

∴ The tree grows 24 inches in each year.

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Find and simplify each of the following for
WINSTONCH [101]

Answer:

(A) f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6

(B) f(x + h) - f(x) = 8xh + 4h² - 6h

(C) \frac{f(x+h)-f(x)}{h}=8x+4h-6

Step-by-step explanation:

* Lets explain how to solve the problem

- The function f(x) = 4x² - 6x + 6

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∵ f(x) = 4x² - 6x + 6

∴ f(x + h) = 4(x + h)² - 6(x + h) + 6

- Lets simplify 4(x + h)²

∵ (x + h)² = (x)(x) + 2(x)(h) + (h)(h) = x² + 2xh + h²

∴ 4(x + h)² = 4(x² + 2xh + h²) = 4x² + 8xh + 4h²

- Lets simplify 6(x + h)

∵ 6(x + h) = 6(x) + 6(h)

∴ 6(x + h) = 6x + 6h

∴ f(x + h) = 4x² + 8xh + 4h² - (6x + 6h) + 6

- Remember (-)(+) = (-)

∴ f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6

* (A) f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6

- Lets find f(x + h) - f(x)

∵ f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6

∵ f(x) = 4x² - 6x + 6

∴ f(x + h) - f(x) = 4x² + 8xh + 4h² - 6x - 6h + 6 - (4x² - 6x + 6)

- Remember (-)(-) = (+)

∴ f(x + h) - f(x) = 4x² + 8xh + 4h² - 6x - 6h + 6 - 4x² + 6x - 6

- Simplify by adding the like terms

∴ f(x + h) - f(x) = (4x² - 4x²) + 8xh + 4h² + (- 6x + 6x) - 6h + (6 - 6)

∴ f(x + h) - f(x) = 8xh + 4h² - 6h

* (B) f(x + h) - f(x) = 8xh + 4h² - 6h

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∵ f(x + h) - f(x) = 8xh + 4h² - 6h

∴ \frac{f(x+h)-f(x)}{h}=\frac{8xh + 4h^{2}-6h}{h}

- Simplify by separate the three terms

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∴ \frac{f(x+h)-f(x)}{h}=8x+4h-6

* (C) \frac{f(x+h)-f(x)}{h}=8x+4h-6

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