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bearhunter [10]
3 years ago
14

1. A ship sails at a constant speed of 20 km/hr. The ship leaves port and sails 20 degrees north of east for 2 hours. The ship t

hen changes direction and sails 10 degrees west of north for 1 hours. At the end of this trip how far is the ship from the starting port ?
Mathematics
1 answer:
andre [41]3 years ago
6 0
The ship sails at 20 km / h.
 So
 20 km / h x 2 h = 40 km
 The boat moves 40 km to the northeast.
 Then, in the same way:
 20 km / h x 1 h = 20 km.
 The ship moves 20 km northwest.
 We solve this problem using vectors. In this case, we must perform the sum of two vectors a and b
 a) magnitude = 40 km and direction 20 degrees east
 b) magnitude = 20 km and direction 10 degrees northwest
 In Cartesian coordinates, these vectors are written as:
 a) 40sin (20º) i + 40cos (20º) j = 13,68i + 37,59j
 b) -20sin (10th) i + 20cos (10th) j = -3,473i + 19,70j
 The displacement vector of the ship would be the sum of a + b
 a + b = 10,207i + 57,29j Finally, the magnitude of the a + b vector will tell us how far the ship is
 √(10.21² + 57.29²) = 58.92km
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Paper depot is swnding out 28 trucks to deliver paper to customers today. Each truck is being loaded with 3 cases of paper. 283
Stells [14]

Answer:

84 cases

Step-by-step explanation:

Given that:

Number of trucks: 28

Paper cases each truck can load = 3

Total cases of white paper = 283

So the cases delivered will be = 28 *3 = 84 cases will be delivered today

i hope it will help you!

4 0
4 years ago
A boat is 122 meters from the base of a lighthouse. The lighthouse is 34 meters tall. The angle formed with the lighthouse and s
mojhsa [17]

Answer:

about 16°

Step-by-step explanation:

Make sure your calculator is in degree mode.

Drawing the right triangle, we see that the shorter leg is 34 meters, and the longer leg is 122 meters. So the angle of elevation is:

\tan( \alpha )  =  \frac{34}{122}

\alpha  =  { \tan }^{ - 1}  \frac{34}{122}  = 15.57

3 0
3 years ago
What is x in 3.6x=1.6x+24
Ipatiy [6.2K]

Answer:

x=12

Step-by-step explanation:

3.6x=1.6x+24

We simplify the equation to the form, which is simple to understand

3.6x=1.6x+24

We move all terms containing x to the left and all other terms to the right.

+3.6x-1.6x=+24

We simplify left and right side of the equation.

+2x=+24

We divide both sides of the equation by 2 to get x.

x=12

7 0
3 years ago
What are the range values of the function f (x ) = 3x + 4 for the domain values {-5, -1, 0, 2, 7}?
Airida [17]

Answer:

Range values are:

{-11, 1, 4, 10, 25}

Step-by-step explanation:

Domain values are the possible x values that can be entered into the function, or the inputs.  Range values are the y values, or the outputs. By inserting every value in the set into the function, we get the outputs (y values)

-15 + 4 = -11

-3+4 = 1

0 + 4 = 4

6 + 4 = 10

21 + 4 = 25

Remember to put them in order.

7 0
3 years ago
Given the following diagram, find the missing measure.<br>*​
BigorU [14]

Option C:

x = 30

Solution:

The given image is a triangle.

angle 1, angle 2 and angle 3 are interior angles of a triangle.

angle 4 is the exterior angle of a triangle.

m∠4 = 2x°, m\angle2=\frac{4}{3}x^\circ, m∠3 = 20°

Exterior angle theorem:

<em>In triangle, the measure of exterior angle is equal to the sum of the opposite interior angles.</em>

By this theorem,

m∠4 = m∠2 + m∠3

$2x^\circ=\frac{4}{3}x^\circ+20^\circ

Subtract \frac{4}{3}x^\circ on both sides of the equation.

$2x^\circ-\frac{4}{3}x^\circ=20^\circ

To make the denominator same and then subtract.

$\frac{6}{3}x^\circ -\frac{4}{3}x^\circ=20^\circ

$\frac{2}{3}x^\circ =20^\circ

Multiply by \frac{3}{2} on both sides of the equation.

x° = 30°

x = 30

Hence option C is the correct answer.

6 0
4 years ago
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