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
DedPeter [7]
2 years ago
11

two mountain bikers leave from the same parking lot and head in opposite directions on two different trails. the first rider goe

s 8km due east, then rides due south for 15km. The second rider goes 8km due west, then changes directions and rides 20 degrees west of due north for 15km. Both riders have been traveling for 23km, but which one is further from the parking lot?
Mathematics
1 answer:
sveta [45]2 years ago
7 0

Applying the required <em>rule </em>or <em>theorem</em>, it can be concluded that the second biker is <u>farther</u> from the <em>parking lot</em>. The distance of the bikers to the <em>parking lot</em> are:

i. First biker = 17.0 km

ii. Second biker = 20.22 km

The <u>path</u> of travel of both bikers would form a triangle. Applying the <u>Pythagoras</u> theorem to the path of the <em>first</em> biker would give his <u>distance</u> from the starting point. While applying the <u>cosine</u> rule to the path of <em>second</em> rider would gives his <u>distance</u> to the starting point.

Thus,

a. <u>To determine the distance of the first biker from the parking lot.</u>

Let the required <em>distance </em>be represented by x. Applying the Pythagoras theorem, we have:

hyp^{2} = adj 1^{2} + adj 2^{2}

x^{2} = 8^{2} + 15^{2}

   = 64 + 225

   = 289

x = \sqrt{289}

  = 17

x = 17 km

Thus, the <u>first</u> biker is 17.0 km from the <em>starting</em> point.

b. <u>To determine the distance of the second biker from the parking lot.</u>

Let the required <em>distance</em> be represented by x. So that applying the cosine rule, we have:

c^{2} = a^{2} + b^{2} - 2ab Cos θ

x^{2} = 8^{2} + 15^{2} - 2(15*8) Cos (180 - 20)

    = 64 + 225 - 240 Cos 160

    = 289 - 240 * -0.5

x^{2} = 289 + 120

   = 409

x = \sqrt{409}

 = 20.2237

x = 20.22 km

Thus, the <u>second</u> biker is 20.22 km from the <em>starting</em> point.

Therefore, the second biker is <u>farther</u> from the <em>parking lot</em>.

A sketch of the path of travel for the two bikers is attached for more clarifications.

Visit: brainly.com/question/22699651

You might be interested in
-6x-6y =18 6x-3y=27 its supposed to be solving systems by elimination by adding or subracting, im really confused.
Lera25 [3.4K]

Answer:

y = -5

x = 2

Step-by-step explanation:

The computation is show below:

Given that

-6x - 6y = 18

6x - 3y = 27

Now if we solved both equation so

-9y = 45

y = -5

And, x is

-6x - 6(-5)  = 18

-6x + 30 = 18

-6x = 18 - 30

-6x = -12

x = 2

3 0
3 years ago
-2 with a exponent six
DIA [1.3K]
-2^{6} &#10;&#10; =  -2 with a exponent six
Well Exponents mean that you multiply the number 6 times. 
Soo..
-2^{6} = -2 x -2 x -2 x -2 x -2 x -2 = 64 

So <span>-2^{6} = 64 
</span>
Good Luck! :)

5 0
3 years ago
Read 2 more answers
Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? Select t
Pepsi [2]

Answer:

Step-by-step explanation:

Two lines are perpendicular if the first line has a slope of m and the second line has a slope of \frac{1}{-m}.

With this information, we first need to figure out what the slope of the line is that we're given, and then we can determine what the slope of the line we're trying to find is:

5x - 2y = -6

-2y = -5x - 6

y = \frac{5}{2}x + 3

We now know that m = \frac{5}{2} for the first line, which means that the slope of the second line is m = \frac{-2}{5}. With this, we have the following equation for our new line:

y = \frac{-2}{5}x + C

where C is the Y-intercept that we now need to determine with the coordinates given in the problem statement, (5, -4):

y = \frac{-2}{5}x + C

(-4) = \frac{-2}{5}(5) + C

-4 = -2 + C

C = -2

Finally, we can create our line:

y = \frac{-2}{5}x - 2

5y = -2x - 10

2x + 5y = -10

8 0
3 years ago
Read 2 more answers
What are the nouns in this sentence?
fgiga [73]

Answer:

A noun is most commonly taught a person, place, or thing and sometimes idea. In this sentence, it would be Magazine, Americans, and carbohydrates. And if smith is also part of the sentence, he is a person, so its also a noun. :) Happy learning friend

3 0
2 years ago
URGENT PLEASE!!!!!!!!!!!!
kondaur [170]

Answer:

i got 178

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Other questions:
  • What is the measure of angles g
    12·2 answers
  • The average mark of candidates in an aptitude test was 128.5 with a standard deviation of 8.2.Three scores extracted from the te
    13·1 answer
  • if juanita and her friends made nine friendship bracelets in three hours how many could they make in 15 hours? which proportion
    15·2 answers
  • the compound interest of a sum of money for 1 year and 2 years are rs 450 and rs 945 respectively. find the rate of interest com
    14·1 answer
  • /19
    6·1 answer
  • I have 4418 pieces of corn but there are <br>3 rows how many are in each row
    12·2 answers
  • Multiply or divide as indicated.
    6·1 answer
  • Y= 4x +6 (x=3) Substitution
    12·2 answers
  • Mariah made a down payment on a van. Which of the following is true because of the down payment?
    6·2 answers
  • Mr.arswan prepares a mixture for a science experiment. He measures 10.5 grams of wood shavings,150 grams of iron filings, and 18
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!