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
ycow [4]
2 years ago
6

A cyclist travels 5 miles each way on a bike path. Travel in one direction is with a 4 mile per hour wind and travel back is aga

inst a 4 mile per hour wind. Part A: Write and simplify an equation for the amount of time t in hours it will take the cyclist to make the trip. Part B: What is the cyclist's total travel time, if she travels an average of 6 miles per hour without the wind?
Mathematics
1 answer:
Dahasolnce [82]2 years ago
3 0

Answer:

a. 10v/(v² - 16) b. 3 hours

Step-by-step explanation:

a. Write and simplify an equation for the amount of time t in hours it will take the cyclist to make the trip.

Let v be the speed of the cyclist without the wind. The speed of the cyclist with the 4 mile per hour wind in the direction of the wind is v' = v + 4. Since the distance travelled is 5 miles, and time, t = distance/speed, the time it takes to make this trip is t' = 5/(v + 4)

Let v be the speed of the cyclist. The speed of the cyclist with the 4 mile per hour wind against the direction of the wind is v" = v - 4. Since the distance travelled is 5 miles, and time, t = distance/speed, the time it takes to make this trip is t" = 5/(v - 4).

So, the total travel time, T = t' + t"

= 5/(v + 4) + 5/(v - 4)

= [5(v - 4) + 5(v + 4)]/[(v + 4)(v - 4)]

= [5v - 20 + 5v + 20)]/(v² - 4²)

= 10v/(v² - 16)

b. What is the cyclist's total travel time, if she travels an average of 6 miles per hour without the wind?

If v = 6 miles per hour, then

T = 10v/(v² - 16)

= 10(6)/(6² - 16)

= 60/(36 - 16)

= 60/20

= 3 hours

You might be interested in
Somebody, please help
SashulF [63]
F(x) can be written as:
f(x) = Asin(2x); where A is the amplitude and the period of the function is half that of a normal sin function.
f(π/4) = 4
4 = Asin(2(π/4))
4 = Asin(π/2)
A = 4
Amplitude of g(x) = 1/2 * amplitude of f(x)
A for g(x) = 2
g(x) = 2sin(x)
5 0
3 years ago
Specify what an individual unit is in each of the following studies. Then specify what two variables were measured on each unit.
r-ruslan [8.4K]

Answer:

a) Unit: College Student

Variables of measurement: Procrastination and illness habits.

b) Unit: SUV cars

Variables: Manufacturing and car damage for two car manufactures.

Step-by-step explanation:

We are given the following in the question:

In a research, a unit is a single individual or object that is measured.

a) A study finds that college students who often procrastinate tend to be sick more often than students who do not procrastinate.

Since college students are asked about procrastination, then the unit in this study is college students.

Unit: College Student

Variables of measurement: Procrastination and illness habits.

b) A study finds that sport utility vehicles (SUVs) made by one car manufacturer tend to be more heavily damaged in a crash test than SUVs made by a second car manufacturer.

Since all SUVs cars are considered, the unit in this research is  SUV cars

Unit: SUV cars

Variables: Manufacturing and car damage for two car manufactures.

7 0
3 years ago
Diagram below shows the curve of a quadratic function
uranmaximum [27]

Answer:

q = -8, k = 2.

r = -6.

Step-by-step explanation:

f(x) = (x - p)^2 + q

This is the vertex form of a quadratic where the vertex is at the point (p, q).

Now the x intercepts are at -6 and 2 and the curve is symmetrical about the line x = p.

The value of p is the midpoint of  -6 and 2 which is (-6+2) / 2 = -2.

So we have:

f(x) = 1/2(x - -2)^2 + q

f(x) = 1/2(x + 2)^2 + q

Now the graph passes through the point (2, 0) , where it intersects the x axis, therefore, substituting x = 2 and f(x) = 0:

0 = 1/2(2 + 2)^2 + q

0 = 1/2*16 + q

0 = 8 + q

q = -8.

Now convert this to standard form to find k:

f(x) = 1/2(x + 2)^2 - 8

f(x) = 1/2(x^2 + 4x + 4) - 8

f(x) = 1/2x^2 + 2x + 2 - 8

f(x) = 1/2x^2 + 2x - 6

So k = 2.

The  r  is the y coordinate when x = 0.

so r = 1/2(0+2)^2 - 8

=  -6.

3 0
3 years ago
Jennifer has a job that pays her $5200 per month. She also has to pay
Elena L [17]

Answer:

4394

5200 X 0.12 = 624 --> 5200 - 624 = 4576

5200 X 0.035 = 182

4576 - 182 = 4394

6 0
2 years ago
Find the value of the variable 10 45
Ratling [72]

Answer:

35.

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • Simplify (w^6c) (-3w^4c^3)
    6·1 answer
  • carmela cut a cake into 12 equal-sized pieces. She ate 2/12 of the cake and her brother ate 3/12 of the cake.What fraction of th
    11·2 answers
  • Find the simplified form of the expression. Give your answer in scientific notation. (3x10^8)(9x10^7)
    6·1 answer
  • In a school, the ratio of students of class 9 to that of class 10 is 3:2. 30% of the students of class 9 and 10%of the students
    5·1 answer
  • QUESTION 9
    11·1 answer
  • Describe the position of all the points on the number line that are
    6·1 answer
  • Pls pls helppppp if you help me i will give you 17 points. ^_^
    8·1 answer
  • -5x+2y=4 solved algebraically
    14·1 answer
  • Find the value of u to the nearest tenth of a centimeter
    9·1 answer
  • I know im terrible at math, dont tell me lol i need help this app is making this so much easier- 25 pts! fake answers will be de
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!