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.
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Related Questions
Could someone help please
Answers
Step-by-step explanation:
1. x/3-2=6
x-6=18
x=18+6
x=24
2. x/5+1=5
x+5=25
x=25-5
x=20
Answer:
x = 24 , x = 20
Step-by-step explanation:
(a)
[tex]\frac{x}{3}[/tex] - 2 = 6 ( add 2 to both sides )
[tex]\frac{x}{3}[/tex] = 8 ( multiply both sides by 3 to clear the fraction )
x = 24
(b)
[tex]\frac{x}{5}[/tex] + 1 = 5 ( subtract 1 from both sides )
[tex]\frac{x}{5}[/tex] = 4 ( multiply both sides by 5 to clear the fraction )
x = 20
Write 110 as a product of primes
Answers
Answer:
The prime factorization of 110 is: 2 x 5 x 11.
What is the area of this figure?
Answers
Answer:
84mm
Step-by-step explanation:
square = LxW = 6x6 =36
triangle = bxh/2 = 6x8/2 =24
add together 24x2+36=84
Ryan and Taylor are both saving money to buy new video game equipment. Ryan's savings plan can be modeled by the function s= 15m + 50 where m represents the number of months since Ryan started his plan, and s represents the amount of money saved in dollars. The table shown represents Taylor's savings plan.
Taylor's Savings Plan --- In the file (Picture).
a. Ryans rate of change is_________Taylor's rate of change.
b. Ryans starting balance is _________Taylor's starting balance.
Answers
a. Ryan's rate of change is $15 per month;
Taylor's rate of change is $20 per month
b. Ryan's starting balance is $50;
Taylor's starting balance is $25.
Recall:
A linear function is modelled by the equation, y = mx + b, where m is the rate of change and b is the initial value (starting value).Rate of change = change in y/change in xRyan's Savings Plan Function:
s = 15m + 50
Thus, the starting value (starting balance) modelled by this function is $50
The slope/rate of change is $15 per month
Taylor's Savings Plan:
Given the table, the starting value will be the amount saved (initial value) at 0 number of months.
Therefore, Taylor's starting balance is: $25Using (0, 25) and (1, 45) find the rate of change:
Rate of change = (45 - 25)/(1-0) = 20/1 = $20In summary:
a. Ryan's rate of change is $15 per month;
Taylor's rate of change is $20 per month
b. Ryan's starting balance is $50;
Taylor's starting balance is $25.
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Cory has $24 more than twice as much as Stan. Together they have $150. How much money does each have?
Stan has $50 and Cory has $74
Stan has $42 and Cory has $108
Stan has $63 and Cory has $87
Stan has $108 and Cory has $42
Answers
Answer: B Stan has $42 and Cory has $108.
Step-by-step explanation:
The awnser is Stan has $42 and Cory has $108 and $108 + $42 = $150.
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Are these geometric shapes ASA, SSS, SAS or None?
I WILL GIVE BRAINLIEST TO BEST ANSWER!
refer to image.
Answers
Answer:
4)ASA
6) ASA
2) SSS
8) SAS
Step-by-step explanation:
numbers 4 and 6 are ASA because we have 2 congruent angles and one congruent side. Also, they r in the pattern angle, side, angle. Which makes it ASA
number 2 is SSS because all 3 sides are congruent
number 8 is SAS because because there are 2 congruent sides and one congruent angle. They are seen in the pattern side, angle, side. Which makes it SAS
hope that helps and I apologize about earlier
have a wonderful day!
Answer:
2) None, 4) ASA, 6) ASA, 8) ASAStep-by-step explanation:
#2We have two parallel sides.
This gives us two pairs of alternate interior angles and one pair of vertical angles.
In total 3 congruent angles. This is not enough to state congruence.
None
#4We have two pairs of congruent angles and an included common side.
This is good to state the triangles are congruent by ASA
#6Similarly to above question, we have two pairs of congruent angles and an included common side.
This is good to state the triangles are congruent by ASA
#8We have one pair of congruent sides and the parallel sides gives us two pairs of alternate interior angles and a pair of vertical angles.
We can state the triangles are congruent by ASA as the congruent side is included.
Grade 4c left their school at7:30 am for their trip to the market. They return at 10:45 am how much time did they spend on the trip?
Answers
Step by step explanation:
10:45
-7:30
———
3:15
evaluate –3(–5)(–1)(3)
Answers
Answer:
-45
Step-by-step explanation:
I think one way you could do it is:
1. –3(–5) = 15
2. (–1)(3) = -3
3. (15) (-3) = -45
I used a calculator pls let me know if im incorrect
1) If
[tex] \frac{1}{a + 1} + \frac{1}{b + 1} + \frac{1}{c + 1} = 2[/tex]
[tex]then \: {a}^{2} + {b}^{2} + {c}^{2} is[/tex]
Option :-
[tex]a) \frac{3}{4} [/tex]
[tex]b) \frac{1}{3} [/tex]
[tex]c) \frac{27}{16} [/tex]
[tex]d) \frac{4}{3} [/tex]
● NEED GENUINE ANSWER
●DON'T SPAM OTHERWISE ANSWER WILL BE REPORT
Answers
The sum of the square of the constants is 3/4
Given the equation [tex]\frac{1}{a+1} +\frac{1}{b+1} +\frac{1}{c+1} =2[/tex]
The partial form of the equation is given as:
[tex]\frac{1}{a +1} = 2\\[/tex]Solve for the constant "a"
[tex]\frac{1}{a +1} = 2\\a+1 = \frac{1}{2} \\a = \frac{1}{2} - 1\\a =-\frac{1}{2}[/tex]
Hence [tex]a=b=c=-\frac{1}{2} \\[/tex]
Taking the square of the constant, we will have:
[tex]a^2 + b^2 + c^2 =(-1/2)^2 +(-1/2)^2+(-1/2)^2\\a^2 + b^2 + c^2 =1/4 + 1/4 + 1/4\\a^2 + b^2 + c^2 =3/4[/tex]
Hence the sum of the square of the constants is 3/4
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Answer -the sum of the square of the consonants is 3/4
Hey y’all, please help me
Answers
What percent is equivalent to 24/50?
24%
48%
50%
52%
Answers
Answer:
48%
Step-by-step explanation:
24 is almost 25 which is half of 50 you it would be 48%, hope this helps!:)
What is the circumference of the top of the water buoy? Round your answer to the nearest tenth.
37.7 feet
28.3 feet
113.0 feet
84.8 feet
Answers
Answer:16.3 inches. What is the area of this plate? Use 3.14 for pi. Round to the nearest whole number.
Step-by-step explanation:
Write an equation in slope intercept for a line that passes through (2,2)
Answers
Answer:
any line can pass through the point (2,2) so there needs to be a second point
Step-by-step explanation:
Solve for x
3x+7=28
Answers
Answer:
X=7
Step-by-step explanation:
Answer:
x = 7Step-by-step explanation:
3x + 7 = 28=> 3x = 28 - 7=> 3x = 21=> x = 7Conclusion:
Therefore
x = 7.Hoped this helped.
[tex]GeniusUser[/tex]
How is 25:5 and 10:2 equivalent
Answers
Answer: yes !!
Step-by-step explanation:
first we have to simplify
25:5 = 5:1
10:2 = 5:1
yes, they are
When two ratios are in proportion the ratios are said to be equivalent.
The ratios 25:5 and 10:2 are equivalent because they are in proportion.
What is a ratio?It is the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
We have,
25:5 and 10:2
The ratio must be in proportion to be equivalent.
25:5 = 25/5 = 5 / 1
10:2 = 10/2 = 5/1
25:5 = 10:2
25/5 = 10/2
(5x5) / 5 = (5x2) / 2
5/1 = 5/1
We see that the ratio is equivalent.
Thus,
The ratios 25:5 and 10:2 are equivalent because they are in proportion.
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#SPJ2
6 remainder 1 as a fraction
Answers
1. Each of 9 friends chooses her favorite positive integer
a. The median of the chosen number is 91, what is the smallest the average of the 9 chosen numbers could be?
b. The median of the chosen number is 91, is there an limit to how large the aerge of the chosen numbers can be? If so, what is the largest the average can be?
c. The average of the chosen number is 91, what is the smallest the median of the 9 chosen numbers could be?
d. The average of the chosen numbers is 91. What is the largest the median of the chosen numbers could be?
Answers
Answer:
a) 1
b) There is no limit to which the largest number can be because we are only given information about the median.
c) 1
d) 90
Write 6(2x + 4) – 2(x + 7) +5 in the form a(bx+c)
where a, b and c are integers
and a > 1
Answers
Answer:
5(x + 3)
Step-by-step explanation:
6(2x + 4) - 2(x + 7) + 5
12x + 24 - 2x - 14 +5
10x + 24 - 9
10x + 15
5(x + 3)
Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 in his account by the end of the summer. If there are 10 weeks in the summer, how much can Keith spend each week to have at least $200 in his account? Let x represent how much he can spend each week.
options:
x>30
x>70
x≤70
x≤30
Answers
Answer:
x≤30
Step-by-step explanation:
he can spend no more than $30 a week
what is 25% off $27
Answers
Answer:
6.75 $
Step-by-step explanation:
25%
= 25 / 100
= 1 / 4
25% of $ 27
= ( 1 / 4 ) x ( 27 )
= ( 1 x 27 ) / 4
= 27 / 4
= 6.75 $
Answer:
$20.25
Step-by-step explanation:
If t=100, find 2t + 1
Answers
HELP!!!
‐9z = ‐207
Please solve this with math explanations and NOT just the answer! Whoever explains first will get brainly!
Answers
Answer:
23
Step-by-step explanation:
this is because
the equation is saying -9time something = -207
so
you would -207 divided by -9
which gives you 23
so
z=23
A gaming computer system and additional equipment was purchased for $2,000. The system and equipment depreciate in value by 10% each year.
After how many years will the computer have a value less than $1,000?
A. 1
B. 3
C. 7
D. 8
Answers
2000-200 = 1800
1800-180 = 1620
1620 - 162 = 1458
1458- 148.8 = 1309
1309 - 130.9 = 1178
1178- 117.8 = 1060.2
1060 - 106 = 954
= 7 years
The value of the car is $956.5938 after 7 years and this can be determined by using arithmetic operations.
Given :
A gaming computer system and additional equipment was purchased for $2,000. The system and equipment depreciate in value by 10% each year.The following steps can be used in order to determine the total number of years will the computer have a value of less than $1,000:
Step 1 - The 10% of $2000 is $200. So, the value of the car after 1 year is $1800.
Step 2 - The 10% of $1800 is $180. So, the value of the car after 2 years is $1620.
Step 3 - The 10% of $1620 is $162. So, the value of the car after 3 years is $1458.
Step 4 - The 10% of $1458 is $145.8. So, the value of the car after 4 years is $1312.2.
Step 5 - The 10% of $1312.2 is $131.22. So, the value of the car after 5 years is $1180.98.
Step 6 - The 10% of $1180.98 is $118.098. So, the value of the car after 6 years is $1062.882.
Step 7 - The 10% of $1062.882 is $106.2882. So, the value of the car after 7 years is $956.5938.
Therefore, the correct option is C).
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Hey y’all, please help me with this.
Answers
Answer:
Select all numbers greater to or equal to 48. (48, 49, 51, 53, 58)
x ≥ 48
Step-by-step explanation:
If you divide both sides by two because you have a 2x and you need to get a single x, you would get x ≥ 48 (96 divided by 2) you would select all numbers greater to or equal to 48.
Answer:
48, 49, 51, 53, 58
Step-by-step explanation:
Equivalent inequality
96 ≤ 2x
Which expression can be used to find the product of 57 x 44?
Answers
Answer:2508
Step-by-step explanation:
over what interval function is this graph constant
Answers
this is the next question
Solve: 1/2÷0.2
Answers
Answer:
2.5
Step-by-step explanation:
Willie's school is selling tickets to a play. On the first day of ticket sales the school sold 5 adult
tickets and 1 student ticket for a total of $80. The school took in $240 on the second day by
selling 14 adult tickets and 6 student tickets. Find the price of an adult ticket and the price of a
student ticket.
Answers
Answer:
Step-by-step explanation:
A I think sorry if I’m wrong
What did Diocletian do to change the way the Roman Empire was ruled?How would we add -3 + (-9) on the number line?
Answers
The sum of three consecutive odd numbers is 153 find the number
Answers
Answer:
Divide the no. by three
Step-by-step explanation:
153÷3 = 51
so, 51+51+51 = 153
Answer:
an odd number can be expressed as 2n+1 (2n would be even, add 1 = odd)
first number = 2n+1
second number = 2n+3 -> skip + 2 because it would make it even
third number = 2n+5
2n+1+2n+3+2n+5=153
6n+9=153
6n=144
n=24
24*2+1=48+1=49
24*2+3=48+3=51
24*2+5=48+5=53
the numbers are 49, 51, and 53.