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MrRissso [65]
2 years ago
12

Marco can paddle his canoe at a rate of 6 miles per hour on unmoving water. However, today Marco is canoeing down (with the curr

ent), and then back up (against the current), a river that's moving at a rate of 1 mile per hour, so the current affects his rate of speed. If it takes Marco 6 total hours to go x miles downstream and then return to his starting point, how far downstream does he travel?
A) 1.25 miles
B) 2.5 miles
C) 5 miles
D) 17.5 miles
Mathematics
1 answer:
Radda [10]2 years ago
3 0

Answer:

S = v1 t1 = 7 t1    traveling downstream

S = v2 t2 = 5 t2    traveling upstream

7 t1 = 5 t2

7 (6 - t2) = 5 t2     since t1 + t2 = 6

42 - 7 t2 = 5 t2

t2 = 42 / 12 = 3.5 hrs so t1 = 2.5 hrs

S = 7 t1 = 7 * 2.5 = 17.5 mi

Also, S = 5 t2 = 5 * 3.5 = 17.5 mi

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This table represents a quadratic function with a vertex at (1, 1). What is the
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The average rate of change on the interval (5, 6) is 9. So the correct option is D.

<h3>How to find the average rate of change on the interval?</h3>

Here we want to find the average rate of change of f(x), the function on the table, on the interval (5, 6).

This is just:

r = \frac{f(6) - f(5)}{6 - 5}

f(x) = a*x^2 + b*x + c

I we look at the table we see that:

f(1) = 1 = a + b + c

f(2) =2 =  4a + 2b + c

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This is a system of equations.

If we subtract the second and first functions, we get:

2 - 1 = (4a + 2b +c) - (a + b + c)\\1 = 3a + b = a + b + c

From that we take two relations:

1 - 3a = b\\2a = c

Now we can replace these two in the last equations so we get:

5 = 9a + 3b + c\\\\5 = 9a + 3*(1 - 3a) + 2a\\\\5 = 9a + 3 - 9a + 2a\\\\5 = 3 + 2a\\\\5 - 3 = 2a\\\\2 = 2a\\\\a = 1

Now that we know the value of a:

c = 2a = 2*1 = 2\\\\b = 1 - 3a = 1 - 3 = -2

The quadratic equation is:

f(x) = x^2 - 2x + 2

Evaluating this in x = 6 we get:

f(6) = 6^2  - 2*6 + 2 = 26

And from the table we know that f(5) = 17, then the average rate of change is:

r = \frac{f(6) - f(5)}{6 - 5} = \frac{26-17}{1} = 9

The correct option is D.

If you want to learn more about average rates of change:

brainly.com/question/8728504

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