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3 years ago

Explain why -11 is less than -7, but |-11| is greater than |-7|

Mathematics

2 answers:

kolezko [41]3 years ago

6 0

Because the absolute value makes anything positive so -11 to 11 and -7 to 7 which would mean that 11 >7 and -11<-7

Ber [7]3 years ago

5 0

When looking at the -7 and -11 it's like looking at a timeline you see the numbers from left to right so you would look at the -11 first and then the -7. whenever a number has the two lines it's the absolute value so you would ignore the negative signs and it would just be the number.

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Let $v$ denote the speed of the ship, and let $t$ denote the duration of the trip. The magnitude of the displacement of this ship would be $v\, t$ .

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The hypothenuse of the right triangle in this diagram represents the displacement of the ship, with a length of $v\, t$ . The dashed horizontal line segment represents the distance that the ship has travelled to the west (which this question is asking for.) The angle opposite to that line segment is exactly $29^{\circ}$ .

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$\begin{aligned}& \text{opposite (to $\theta$)} \\ =\; & \text{hypotenuse} \times \frac{\text{opposite (to $\theta$)}}{\text{hypotenuse}} \\ =\; & \text{hypotenuse} \times \sin (\theta) \\ =\; & v\, t \, \sin(\theta) \\ =\; & v\, t\, \sin(29^{\circ})\end{aligned}$ .

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$\begin{aligned} & v\, t\, \sin(29^{\circ}) \\ =\; & 20\; \frac{\text{nautical mile}}{\text{hour}} \times 6\; \text{hour} \times \sin(29^{\circ}) \\ \approx\; & 58.2\; \text{nautical mile}\end{aligned}$ .

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