What is the slope of a line that goes through the points (1, -5) and (-3, 2)?

In an attempt to escape a desert island, a castaway builds a raft and sets out to sea. The wind shifts a great deal during the d

nikdorinn [45]

Answer:

R = 7,34 km

Ф = 63,43° north of east

Step-by-step explanation:

Let´s analyze each movement and find its perpendicular components. Then, we are going to add the components along the x and y axes to get the resultant and finally to calculate its magnitude and direction.

To determine the perpendicular components, we will use right triangles trigonometrics ratios.

Please see images for each displacement in attached file.

Displacement A: 2.50 km and 45° north of west

Ax= AcosФ = 2.50cos45° = 1.77 km (neg. direction)

Ay= AsenФ = 2.50sen45° = 1.77 km (pos. direction)

Displacement B: 4.70 km and 60° south of east

Bx= BcosФ = 4.70cos60° = 2,35 km (pos. direction)

By= BsenФ = 4.70sen60° = 4,07 km (neg. direction)

Displacement C: 1.30 km and 25° south of west

Cx= CcosФ = 1.30cos25° = 1,18 km (neg. direction)

Cy= CsenФ = 1.30sen25° = 0.55 km (neg. direction)

Displacement D: 5.10 km due east (0°)

Dx= DcosФ = 5.10 km (pos. direction)

Dy= DsenФ = 0 km

Displacement E: 1.70 km and 5° east of north

Ex= EsenФ = 1.70sen5° = 0,15 km (pos. direction)

Ey= EcosФ = 1.70cos5° = 1.69 km (pos. direction)

Displacement F: 7.20 km and 55° south of west

Fx= FcosФ = 7.20cos55° = 4.13 km (neg. direction)

Fy= FsenФ = 7.20sen55° = 5.90 km (neg. direction)

Displacement G: 2.80 km and 10° north of east

Gx= GcosФ = 2.80cos10° = 2.76 km (pos. direction)

Gy= GsenФ = 2.80sen10° = 0.49 km (pos. direction)

Now, we add the components along the x- and y- axis to find the components of the resultant (R):

Rx = Ax + Bx + Cx + Dx + Ex + Fx + Gx

Ry = Ay + By + Cy + Dy + Ey + Fy + Gy

Therefore,

Rx= (-1.77)+(2.35)+(-1.18)+(5.10)+(0.15)+(-4.13)+(2.76)

Ry= (1.77)+(-4.07)+(-0.55)+(0)+(1.69)+(-5.90)+(0.49)

Note: minus (-) symbol to negative directions

Rx = 3.28 km

Ry = - 6.57 km

Let´s use the Theorem of Pythagoras to find the magnitud ot the resultant:

$R = \sqrt{Rx^{2} +Ry^{2} }$

$R =\sqrt{(3.28)^{2}+(-6.57)^{2} }$

R = 7,34 km

To find the direction of the resultant:

tanФ = $\frac{Ry}{Rx}$

tanФ = $\frac{6.57}{3.28}$

tanФ = 2.00

Ф = tan-1 (2.00)

Ф = 63,43° north of east

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3 0

3 years ago

Of all the people that attend movies 67% are in the 12-29 age group. At one theater, 300 people attended a showing of a certain

suter [353]

67 multiplied by 3 is 201, so there is 201 people in the age group 12-29. Also, 67% is approximately two thirds, and we can see that reflected in our answer.

6 0

3 years ago

Are the following lines parallel? y = -3x + 1 y = 4 - 3x

PIT_PIT [208]

Answer:

Simple! The answer is yes.

Step-by-step explanation:

Simply put the equations into Desmos graphing calculator and it will show you that the equations are parallel. :))

4 0

3 years ago

What is 3.116372 rounded to the nearest hundred thousandths place?

Neporo4naja [7]

Answer: 3.11637

Explanation: The hundred thousandths place is in the fifth place after the decimal. To avoid remembering this, you can simply note that the first place after the decimal is the tenths. You simply keep progressing as you would in whole numbers.

For example 10 becomes 100 when a zero is added. This zero is always added right beside the first zero and indicates the hundreds place.

Furthermore, the general rule for rounding is if the number after the preferred rounding place is 4 or less, the number remains the same. 5 or more means it goes up by one digit.

4 0

3 years ago

Read 2 more answers

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (x,y) be the unkno

makkiz [27]

Step-by-step explanation:

Hey, there!!

Here, one point is A(10,8) and P(8,5) is the midpoint.

Let B(x,y) be the another end point.

Now,

Using midpoint formulae,

$p(x.y) = \frac{x1 + x2}{2} . \frac{y1 + y2}{2}$