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Vinil7 [7]
3 years ago
15

Guys omg I will give 30 point please I'm stuck ​

Mathematics
1 answer:
IRINA_888 [86]3 years ago
8 0
<h3>Answer:   -10</h3>

=================================================

Work Shown:

First we need to evaluate f(3)

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

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

f(3) = -(3)^2 + 2(3) ... replace every x with 3; apply PEMDAS to simplify

f(3) = -9 + 6

f(3) = -3

Then we subtract 7 from both sides

f(3) - 7 = -3 - 7

f(3) - 7 = -10

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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.

Refer to the diagram attached. The direction {\rm S$29^{\circ}$W} means 29^{\circ} west of south. Thus, start with the south direction and turn towards west (clockwise) by 29^{\circ} to find the direction of the displacement of the ship.

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}.

Since the hypotenuse is of length v\, t, the dashed line segment opposite to the \theta = 29^{\circ} vertex would have a length of:

\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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