two mountain bikers leave from the same parking lot and head in opposite directions on two different trails. the first rider goes 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?
Answers
Applying the required rule or theorem, it can be concluded that the second biker is farther from the parking lot. The distance of the bikers to the parking lot are:
i. First biker = 17.0 km
ii. Second biker = 20.22 km
The path of travel of both bikers would form a triangle. Applying the Pythagoras theorem to the path of the first biker would give his distance from the starting point. While applying the cosine rule to the path of second rider would gives his distance to the starting point.
Thus,
a. To determine the distance of the first biker from the parking lot.
Let the required distance be represented by x. Applying the Pythagoras theorem, we have:
[tex]hyp^{2}[/tex] = [tex]adj 1^{2}[/tex] + [tex]adj 2^{2}[/tex]
[tex]x^{2}[/tex] = [tex]8^{2}[/tex] + [tex]15^{2}[/tex]
= 64 + 225
= 289
x = [tex]\sqrt{289}[/tex]
= 17
x = 17 km
Thus, the first biker is 17.0 km from the starting point.
b. To determine the distance of the second biker from the parking lot.
Let the required distance be represented by x. So that applying the cosine rule, we have:
[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2ab Cos θ
[tex]x^{2}[/tex] = [tex]8^{2}[/tex] + [tex]15^{2}[/tex] - 2(15*8) Cos (180 - 20)
= 64 + 225 - 240 Cos 160
= 289 - 240 * -0.5
[tex]x^{2}[/tex] = 289 + 120
= 409
x = [tex]\sqrt{409}[/tex]
= 20.2237
x = 20.22 km
Thus, the second biker is 20.22 km from the starting point.
Therefore, the second biker is farther from the parking lot.
A sketch of the path of travel for the two bikers is attached for more clarifications.
Visit: https://brainly.com/question/22699651
Related Questions
1.What is the domain of this graph?____
Answers
Answer:
x=2
Step-by-step explanation:
Java 1
Question 14
If x is 5 and y is 10, what will the output of the following code be?
return x > y;
a. true
b. false
c. 10
d. 5
e. 0
Answers
Answer:
it will return 10
Step-by-step explanation:
As you can see 5 = x ad y = 10. So is say's x is lesser than 10 so 10 will be the ne to return
Gordon types 2,584 words in 38 minutes.
Answers
Answer:
Gordon types 68 words per minute
Step-by-step explanation:
2584/38=68
what is 26x54 PLSSSSSSSSSSSS
Answers
Answer:
1404
Step-by-step explanation:
Answer:
1404
Step-by-step explanation:
If you need assistance with problems like these, try breaking it up!
Instead of 26*54, try doing 26*50 + 26*4
Having "wholer" numbers will help the process.
A school is arranging a field trip to the zoo. The school spends 515.84 dollars on passes for 30 students and 2 teachers. The school also spends 282.90 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
Answers
Answer:
26.16
Step-by-step explanation:
Given the function f described by fly)=9y2 + 7y-6, find the function values.
f(-5) = 0
(Simplify your answer. Type an integer or a fraction.)
Answers
Answer:
f(- 5) = 184
Step-by-step explanation:
Substitute y = - 5 into f(y) , that is
f(- 5) = 9(- 5)² + 7(- 5) - 6
= 9(25) - 35 - 6
= 225 - 41
= 184
can someone please help with this?
Answers
What are the slopes to
3x+6=30
&
4y+2x+9
Answers
3. Using the number line below, list the following numbers in increasing order:
1.1, -1.9, .4, -.6
Answers
60 minutes is 20% of minutes?
Answers
Answer:
300
Step-by-step explanation:
Let the value that we are trying to find be x.
If 60 is 20% of x, then we have the following equation:
1/5x = 60.
Then, we can multiply by 5 to get:
x = 300
Answer:
20 percent of 60 minutes is 1/3
Step-by-step explanation:
I'm not sure if that is what you're asking, but if it is I hope it helps!
8x - 2y = - 8 5x - 4y = 17
Answers
Answer:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Point Form:
( − 3 , − 8 )
Equation Form:
x =- 3 , y = − 8
Step-by-step explanation:
2⎜x - 7/2⎟ + 3 > 4
Pls
Answers
Answer: x<3 or x>4
Step-by-step explanation: 2|x-7/2|+3+-3>4+-3 2|x-7/2|/2>1/2 x+|−7/2|+7/2>1/2+7/2 x>4 or x+|−7/2|+7/2<−1/2+7/2 x<3
-1.3x=3.9
Solve for x
Answers
Answer:
x = -3
Step-by-step explanation:
The equation is : -1.3x=3.9
We can divide both sides by -1.3
-1.3x/-1.3=-3.9/-1.3
We get
x=-3
Answer:
x =-3
Step-by-step explanation:
divide -1.3 to both sides
Find the measure of angle Y.
Answers
Answer:
Y = 62°
Step-by-step explanation:
The sum of angles in a triangle is 180°.
W + X + Y = 180°
(4n -9°) + (7n -16°) +(6n -16°) = 180°
17n -41° = 180° . . . . . . . . . . simplify
17n = 221° . . . . . . . . . . add 41°
n = 13° . . . . . . . . . . divide by 17
Then the measure of Y is ...
Y = 6n -16° = 6(13°) -16° = 78° -16°
Y = 62°
_____
The other angles are W = 43°, X = 75°.
Angles of a triangle adds to 180° .
===============================> W + X + Y = 180°
=> (4n-9°) + (7n-16°) + (6n-16°) = 180°
=> 17n-41° = 180°
=> 17n = 180° + 41°
=> 17n = 221°
=> n = 221/17
=> n = 13°
The measure of Y is,=> 6n-16° = 6(13°) -16° = 62°
Y = 62°
HELPPPPP I ONLY HAVE AN HOUR & ITS 7:23
Answers
Answer:
x=17
Step-by-step explanation:
angle O is equal to angle M.
This means (5x-10)=75
add 10 degrees to both sides
5x=85
divide both sides by 5
x=17
A pancake recipe calls for 4 eggs and 12 cups of flour. How many cups of flour would you need for a single egg?
Answers
Answer:
3
Step-by-step explanation:
i'd say 3
i divided 12 by 4 and then multiplied by one, since that is the amount of eggs we want
good luck! <3
May I please receive help?
Answers
[tex]h = 2 \sqrt{2} [/tex]
[tex]c = \frac{8}{ \sqrt{3} } = \frac{8 \sqrt{3} }{3} \\ [/tex]
indentify the range, y=2x + 6
Answers
x
can take any value, the Domain of this equation is the set of all Real Numbers:
{
R
}
Because this is a simple linear transformation, the Range of this equation is also the set of all Real Numbers:
{
R
}
Find the size of unknown angles
Answers
Answer:
hope it helps.
plzz give me brainliest
Mrs. Hill went to get an oil change, because she has a 20% off coupon. F the oil change is $35.00, how much is the discount? In problem #1, how much does Mrs. Hill have to pay?
Answers
Answer:
28
Step-by-step explanation: 20% off $35 is equal to (20 x 20) / 100 = 7. So if you buy an item at $35 with 20% discounts, you will pay $28 So the Discount would be 7 Dollars
What is the value of x?
74
138
69
148
Answers
Answer:
69
Step-by-step explanation:
All angles add up to 180 in a triangle.
Hope that helps
- The triangle has two sides that are the same
Angles in a triangle add up to 180.
The two angles at the base of an isoceles triangle are equal, therefore:
180 - 42 = 138 (Sum of the angles at the base)
138 / 2 = 69 (One of the equal angles)
So x = 69.
After Lois picks a value for b, Clark must solve the equation 2x + 7 - x = 4x + 2b – 3x - 3b.
Clark uses Lois's b, then tries to solve the equation by repeatedly guessing values of x until he guesses
the right one. However, for every x he picks, the left side is always 3 more than the right side. What
value of b did Lois give Clark?
Answers
The value of b that Lois give Clark will be -7
Given the expression 2x + 7 - x = 4x + 2b – 3x - 3b.First, we need to find the value of b from the expression.Rearrange;
2x + 7 - x = 4x + 2b – 3x - 3b.
x + 7 = x + 2b - 3b
2b - 3b = 7
-b = 7
b = -7
Substitute b = -7 into the expression and find the value of x;
2x + 7 - x = 4x + 2(-7) – 3x - 3(-7)
x + 7 = 4x - 3x - 14 + 21
x + 7 = x + 7
Since for every x he picks, the left side is always 3 more than the right side, the equation becomes;
x + 7 = x + 3x + 7
x + 7 = 4x + 7
x - 4x = 0
-3x = 0
x = 0
Hence the value of b that Lois give Clark will be -7
Learn more on equations here: https://brainly.com/question/16450098
I need help and I can’t find any sadly. Help!!
Answers
1 = Given
2 = Addition Property of Equality
3 = Division Property of Equality
Can a shape have the perimeter be the same as the area?
Answers
Answer:
In geometry, area is the 2-dimensional space or region occupied by a closed figure, while perimeter is the distance around a closed figure i.e. the length of the boundary. Two shapes may have the same perimeter, but different areas or may have the same area, but different perimeters.
Step-by-step explanation:
Answer maybe
Step-by-step explanation:
Christian's mom made some cookies. Christian ate 3\9 of the cookies and gabriel ate 1\3 of them. What fraction of the cookies were left?
Answers
Answer:
1/3 of the cookies remain
Step-by-step explanation:
Christian ate 3/9 of the cookies, which can be simplified into 1/3
Gabriel ate the other 1/3
Therefore, there are only 1/3 of the cookies remaining
I’m stuck on this question, can anybody help?
Answers
Answer: 1/4
Step-by-step explanation:
Noon is 12:00
Supposing that each number is one hour
15 minutes = 1/4 hrs
And therefore 12:15 PM is represented as 1/4
Divide 75 by -25.
12
Answers
Answer: 6.25
Step-by-step explanation:
Will mark Brainliest for the correct answer:
Classify EACH expression as a polynomial or not a polynomial.
(just screenshotted since its a lot to type)
Answers
Step-by-step explanation:
#1 is polynomial of degree 4#2 is polynomial of degree 3#3 NOT a polynomial, variable as fraction#4 NOT a polynomial, radical variable#5 is polynomial of degree 5#6 NOT a polynomial, negative exponentLet's see
Yes, Polynomial having degree 4Yes Polynomial having degree 3No, Fraction onlyNo,radical expressionYes,Of degree 5No12 cm
5 cm
4 cm
15 cm
The area of the trapezium shown
above is
Answers
Answer:
120cm
Step-by-step explanation:
hope it helps pls mark brainliest
120cm² is the area of the trapezium. The two pairs of different sides of a parallelogram are parallel, making it a specific example of a trapezium.
What is trapezium?A trapezium is indeed a quadrilateral having four straight sides, four corners, and one pair of opposing sides that are parallel to the other pair and the other pair that are not1,2,3,4,5. Bases refers to the parallel sides, whereas Legs 1, 2, 3, and 4 refer to the non-parallel sides.
The two pairs of different sides of a parallelogram are parallel, making it a specific example of a trapezium4. The Trapezium is one of the most popular shapes; when drawn on paper, it creates a two-dimensional shape that resembles a table. A water glass, a lighting fixture, a flower pot, or boats are examples of items that have a trapezium shape.
Area of trapezium =1/2×(sum of parallel sides)×height
= 1/2×(5+4)×12
= 120cm²
Therefore, 120cm² is the area of the trapezium.
To know more about trapezium, here:
https://brainly.com/question/27929782
#SPJ7
Your question is incomplete but most probably your full question was,
The area of the trapezium shown below is
What is the length of the unknown side of the right triangle? (1 point)
A right triangle with hypotenuse x and legs 21 and 20
A)21
B)29
C)400
D)441
Answers
Answer:
B)29
Step-by-step explanation:
[tex] {x}^{2} = {21}^{2} + {20}^{2} [/tex]
[tex] {x}^{2} = 441 + 400[/tex]
[tex] {x}^{2} = 841[/tex]
[tex]x = \sqrt{841} [/tex]
[tex]x = 29[/tex]
Answer:
B
Step-by-step explanation:
Using Pythagoras' identity
The square on the hypotenuse is equal to the sum of the squares on the two legs, that is
x² = 21² + 20 ² = 441 + 400 = 841 ( take square root of both sides )
x = [tex]\sqrt{841}[/tex] = 29 → B