MATHEMATICS COLLEGE

Two cruise ships leave port at the same time. Ship A sails north at a speed of 20 mph while Ship B sails east at a speed of 40 mph. (a) Find an expression in terms of the time t (in hours) giving the distance D between two ships.
D(t) =



(b) Using the expression obtained in part (a), find the distance between the two ships 4 hr after leaving the port. (Round your answer to two decimal places.)
mi

Answers

Answer 1
Answer:

Answer:

a) D(t) =

b) 178.885 miles

Step-by-step explanation:

Ship A travels north at the rate of 20 mph.

Ship B travels east at the rate of 40 mph.

After t hours, Ship A is at a distance of 20t miles from the origin.

Similarly, Ship B is at a distance of 40t miles from the origin.

(a) Distance D(t) =

=

=

=

(b) Distance between the two ships when t = 4,

=

= miles

= 80 * 2.236

= 178.885 miles


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Consider this function. f(x) = |x – 4| + 6

If the domain is restricted to the portion of the graph with a positive slope, how are the domain and range of the function and its inverse related?

1.Since the domain of the original function is limited to x> 6, the range of the inverse function is y ≤ 6.
2.Since the domain of the original function is limited to x> 4, the range of the inverse function is y ≤ 1.
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Answers

Answer:

3. Since the range of the original function is limited to y> 6, the domain of the inverse function is x ≥ 6.

Step-by-step explanation:

The domain of a function is the range of its inverse, and vice versa. The only answer choice that expresses this relationship is choice 3.

__

Comment on the answer choice:

The slope of the function is undefined at x=4, so restricting the function domain to the portion with positive slope means the domain restriction of the function is x > 4. That also means the range restriction of the function is y > 6. The domain restriction of the inverse function is the same: x > 6, not x ≥ 6. The answer choice has an error.

Answer:

3. Since the range of the original function is limited to y> 6, the domain of the inverse function is x ≥ 6.

Step-by-step explanation:

Given absolute function,.

f(x) = |x-4|+6,

Since, an absolute function is defined for all real numbers,

So, the domain of f(x) is the set of all real numbers,

∴ Options (1) and (2) can not be true.

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|x-4| ≥ 0,

That is, f(x) ≥ 6,

Hence, the range ( possible value of output of a function ) of f(x) would be all real numbers greater than equal to 6,

I.e. Range of f(x) is, f(x) ≥ 6,

⇒ if y = f(x) ⇒ the range of the original function is limited to y > 6

∴ Option (4) can not be true,

Also, range of = Domain of

Hence, domain of is x ≥ 6.

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