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3 years ago

A space shuttle orbits Earth one time in 90 minutes. How many times does orbit earth in six hours?

2 answers:

5 0

90 minutes =1.5 hours=one orbit
Divide 6 by 1.5 because this will help you see how many orbits can be made in 6 hours (since 1.5 hours=1 orbit)
6/1.5=4
Therefore the space shuttle orbits around the Earth 4 times in 6 hours.
Hope this helps!

Otrada [13]3 years ago

3 0

6 divided by 1.5 = 4

The shuttle orbits earth 4 times in 6 hours.

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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

Step-by-step explanation:

* Lets explain how to solve the problem

- The function f(x) = 4x² - 6x + 6

- To find f(x + h) substitute x in the function by (x + h)

∵ 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

- Lets find $\frac{f(x+h)-f(x)}{h}$

∵ 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

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

∴ $\frac{f(x+h)-f(x)}{h}=8x+4h-6$

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

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