1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
seraphim [82]
3 years ago
14

A jogger runs 140 m due west, then changes direction for the second leg of her run. At the end of the run, she is 374 m away fro

m the starting point at an angle of 20o north of west. What were the length and direction of her second displacement?

Mathematics
1 answer:
USPshnik [31]3 years ago
8 0

Answer:

The length of her second displacement = 247.12 m.

The direction of her second displacement = 31.24° from west.

Step-by-step explanation:

As per the question,

From the figure as drawn below,

Let the starting point be O. After running 140 m due west, she reached at point A.

∴ OA = 140 m

And At the end of the run, she is 374 m away from the starting point at an angle of 20° north of west.

∴ OP = 374 m

We have to find the distance AP = x.

By using the cosine rule in triangle OAP

cos \theta = \frac{OA^{2}+OP^{2}-AP^{2}}{2\times OA\times OP}

After putting the given value, we get

cos 20= \frac{140^{2}+374^{2}-x^{2}}{2\times 140\times 374}

x^{2}=140^{2}+374^{2} - 2\times 140\times 374\times cos 20

  ∴ x = 247.12 m  

Hence,the length of her second displacement = 247.12 m.

Again,

By using the cosine rule in triangle OAP, we get

cos \alpha = \frac{OA^{2}+AP^{2}-OP^{2}}{2\times OA\times AP}

After putting the given value, we get

cos \alpha = \frac{140^{2}+247.12^{2}-374^{2}}{2\times 140\times 247.12}

∴ α = 148.759°

Hence, the  direction of her second displacement = 180° - α = 180° - 148.759 = 31.24° from west.

You might be interested in
HELP TIMED TEST!!!!!!
aalyn [17]

Answer:

-4 and 9

Step-by-step explanation:

factored

(x - 9)(x + 4) = 0

with   this  x*x - 5x - 36 = 0

so  x = 9  or  x = -4

7 0
3 years ago
A right regular pentagonal prism has a base edge length 14 cm, and height 12 cm. Identify the volume of the prism to the nearest
maks197457 [2]

Answer:

4046.56 cm3

Step-by-step explanation:

The base is made by 5 isosceles triangles, with one side of 14 cm, and the opposite angle of \frac{360} 5 = 72°. Each of the other angle is \frac{180-72} {2} =54°. From there, you can calculate the height of each base triangle as in \frac {h} 7 = tan54 or 9.634...cm.

Your volume will be 5 * \frac  {(14 * 9.634)} 2 * 12 = 4046.56 cm^3

7 0
3 years ago
Plz help ASAP! I will mark brainliest if correct
MaRussiya [10]
A = L^2
A = L^2 = 2^2 + 4^2 (Pythagorean’s theorem)
A = L^2 = 20
Therefore the area of the square is 20 units square.
5 0
3 years ago
Read 2 more answers
Monique drew a square and inscribed circle on a sheet of paper, as shown below
Irina-Kira [14]
If you know the area of the square is 256 and the area of the circle is 200.96 you subtract 200.96 from 256 and you get 55.04 is the area of the square that is not covered by the circle. so 55.04/256  because that will give you the percent of the area that is outside that circle but inside the square and you get .215 or 21.50%
4 0
2 years ago
Find the slope of the line that passes through (4, 9) and (1, 4).
alexandr1967 [171]

We can use the points (1, 4) and (4, 9) to solve.

Slope formula: y2-y1/x2-x1

= 9-4/4-1

= 5/3 or 1 2/3

Best of Luck!

5 0
3 years ago
Other questions:
  • Isla walked 3/4 miles each way to and from the school Wednesday. How many miles did Isla walk that day?
    10·2 answers
  • Consider the function f(x, y) = x2 + xy + y2 defined on the unit disc, namely, d = {(x, y)| x2 + y2 ≤ 1}. use the method of lagr
    15·1 answer
  • P(2,4),parallel to y=-3×+4
    6·1 answer
  • From the top of a 210 foot lighthouse located at sea level, the keeper spots a boat at an angle of depression of 23 degrees
    15·1 answer
  • How many cupcakes can I make with 16 cups of batter into each cupcake
    9·2 answers
  • FIRST TO AWNSER GETS BRAINLEST! Koji is installing a rectangular window in an office building. The window is 8 2/3 feet wide and
    5·1 answer
  • Help!!!!!!!!!!!!!!! Please
    9·1 answer
  • An architect diagrams two sidewalks to go between the pool, grass, and seating areas as shown below
    10·1 answer
  • Help pls show brainly
    7·2 answers
  • *PLZ HELP* This goes for all questions...>...Given the following word problems, write an inequality that models the problem,
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!