From home, Mary’s work is two thirds along the way to training. Training is 2.5km from work. Mary normally goes to work, then tr
aining and then home again. However, today she forgot her shoes. How far will Mary travel in total today if she has to go home before training to get her shoes?
1 answer:
First thing to do is to illustrate the problem, Since it was mentioned that work was along the way to training, the order is shown in the picture. Mary's home and workplace are nearer compared to her training center. It is also mentioned that the distance between work and home, denoted as x, is 2/3 of the total distance from home to training. The total distance is (x + 2.5). Thus,
x = 2/3(x+2.5)
x = 2/3 x + 5/3
1/3 x = 5/3
x = 5 km
Thus, the distance from home to work is 5 km. This means that Mary has to walk this distance twice to return home to get her shoes. Then, she will travel again the total distance of 5+2.5 = 7.5 km to get to her training center. So,
Total distance = 2(5km) + 7.5 km
Total distance = 17.5 km
x = 2/3(x+2.5)
x = 2/3 x + 5/3
1/3 x = 5/3
x = 5 km
Thus, the distance from home to work is 5 km. This means that Mary has to walk this distance twice to return home to get her shoes. Then, she will travel again the total distance of 5+2.5 = 7.5 km to get to her training center. So,
Total distance = 2(5km) + 7.5 km
Total distance = 17.5 km
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Answer:
Step-by-step explanation:
Component form of a vector is given by , where
represents change in x-value and
represents change in y-value. The magnitude of a vector is correlated the Pythagorean Theorem. For vector
, the magnitude is
.
190 degrees counterclockwise from the positive x-axis is 10 degrees below the negative x-axis. We can then draw a right triangle 10 degrees below the horizontal with one leg being , one leg being
, and the hypotenuse of the triangle being the magnitude of the vector, which is given as 9.
In any right triangle, the sine/sin of an angle is equal to its opposite side divided by the hypotenuse, or longest side, of the triangle.
Therefore, we have:
To find the other leg, , we can also use basic trigonometry for a right triangle. In right triangles only, the cosine/cos of an angle is equal to its adjacent side divided by the hypotenuse of the triangle. We get:
Verify that
Therefore, the component form of this vector is