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3 years ago

11

Carlos is going on a boat tour. The boat will travel a total distance of 20 kilometers during the 5 dash hour tour. If the boat

travels at a constant speed during the tour, what distance in kilometers should the boat travel in 2 hours?

2 answers:

katen-ka-za [31]3 years ago

7 0

Answer:

8km

Step-by-step explanation:

Given parameters:

Distance covered during the first 5hours = 20km

Time taken to cover this distance = 5hours

Since ;

Speed = $\frac{distance}{time}$

Speed = $\frac{20}{5}$ = 4km/hr

Given also that the car traveled with a constant speed throughout the tour and we have found the speed to be 4km/hr;

Distance covered in 2hrs;

Distance = speed x time

= 4 x 2

= 8km

son4ous [18]3 years ago

4 0

8 km

Step-by-step explanation:

We begin by finding the speed of the tour boat;

Speed = distance/ time

= 20 / 5

= 4km/hr

To find distance traveled by the boat in 2 hrs;

Distance = speed * time

= 4 * 2

= 8 km

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We can use the fact that:

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In first quadrant (0 < θ < π/2), all six trigonometric functions are positive.
In second quadrant(π/2 < θ < π), only sin and cosec are positive.
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Here, the given function is:

$y= 3\cos(2(x + \pi/2)) - 2$

The options are:

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Checking all the options one by one:

Option 1: $y= 3\sin(2(x + \pi/4)) - 2$

$y= 3\sin(2(x + \pi/4)) - 2\\y= 3\sin (2x + \pi/2) -2\\y = -3\cos(2x) -2\\y = 3\cos(2x + \pi) -2\\y = 3\cos(2(x+ \pi/2)) -2$

(the last second step was the use of the fact that cos flips its sign after pi radian increment in its input)
Thus, this option is same as the given function.

Option 2: $y= -3\sin(2(x + \pi/4)) - 2$

This option if would be true, then from option 1 and this option, we'd get:
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which isn't true for all values of x.

Thus, this option is not same as the given function.

Option 3: $y= 3\cos(2(x + \pi/4)) - 2$

The given function is $y= 3\cos(2(x + \pi/2)) - 2 = 3\cos(2x + \pi) -2 = -3\cos(2x) -2$

This option's function simplifies as:

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Thus, this option isn't true since $\sin(2x) \neq \cos(2x)$ always (they are equal for some values of x but not for all).

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The given function simplifies to: $y= 3\cos(2(x + \pi/2)) - 2 = 3\cos(2x + \pi) -2 = -3\cos(2x) -2$

The given option simplifies to:

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Thus, this function is not same as the given function.

Thus, the function which is same as the function y = 3cos(2(x +π/2)) -2 is: Option A: y= 3sin(2(x + π/4)) - 2

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