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
never [62]
3 years ago
12

A boat on the ocean is 2 mi from the nearest point on a straight? shoreline; that point is 15 mi from a restaurant on the shore.

A woman plans to row the boat straight to a point on the shore and then walk along the shore to the restaurant. Complete parts?(a) and? (b) below.
a. If she walks at 3? mi/hr and rows at 2? mi/hr, at which point on the shore should she land to minimize the total travel? time?

Let x be the distance between the nearest point on shore and the point she lands on shore. If T is the time it takes her to get to the? restaurant, what is the objective ?function?

b. If she walks at 3? mi/hr, what is the minimum speed at which she must row so that the quickest way to the restaurant is to row directly? (with no? walking)?
Mathematics
1 answer:
Sladkaya [172]3 years ago
6 0

Answer:

a) x  =  0,70 miles

T  =  1/2* (√4 + x²)  +( 15 - x )/3   Objective Function to minimize

b) V(min)  = 2.59 m/hr

Step-by-step explanation:

Let assume the boat is in Point A,  she lands in point B, and R  is the restaurant

Let call  x distance between the point O in  which perpendicular line from the boat get to shoreline, and the point were she land.

We know  distance is

d = v*t       ⇒  t = d/v

She rows at 2 miles/hr  and walk at 3 miles /hr

According to that she takes

c (hypotenuse) of right triangle  AOB/ 2 rowing

and  15 - x /3  walking

Total time is:

T  =  c/2  + ( 15-x )/3          c =√(2)² + x²     ⇒  T = [√(2)² + x²  ] /2  +  ( 15-x )/3  

T  =  1/2* (√4 + x²)  +( 15 - x )/3   (1)

And that is  the Objective function to minimize

a) Taking derivatives on both sides of the equation we get

T´(t)  =  x /( √4 + x²)  - 1/3    ⇒   T´(t)  = 0     x /( √4 + x²)  - 1/3 = 0

3*x - √( √4 + x²) = 0     ⇒  3*x  =  √( √4 + x²)

Squaring both sides

9x²  =  4 + x²     ⇒  8x²  = 4       x² = 1/2      x  =  0,70 miles

If we plug this value in the Objective function we will get the minimum time

1/2* (√4 + x²)  +( 15 - x )/3    ⇒ [√ 4  + 0,5] /2 +  14,3/3 = T (min)

T(min)  =  1.06 + 4.77  = 5.83 hr

Distance L (hypotenuse of right triangle AOR)

L = √(2)²  + (15)²   L  = 15,13 miles

And that distance have to be traveled at least in 5.83 hr rowing

Then  as  v = d/t      V(min)  =  15.13/ 5.83   ⇒    V(min)  = 2.59 m/hr

You might be interested in
What is 103,2727,495 in expanded form
Rzqust [24]
Do u mean 103,272,485?
4 0
3 years ago
Pls help look at the picture to answer th questions
bonufazy [111]

Answer:

Step-by-step explanation:

B, y=5x

7 0
3 years ago
Read 2 more answers
ANSWER FOR BRAINLIEST:
AlekseyPX

Step-by-step explanation:

<em><u>I </u></em><em><u>thin</u></em><em><u>k</u></em><em><u> </u></em><em><u>mode</u></em><em><u>,</u></em><em><u>range</u></em><em><u> </u></em><em><u>and</u></em><em><u> </u></em><em><u>median</u></em><em><u> </u></em><em><u>dpo</u></em><em><u> </u></em><em><u>ako</u></em><em><u> </u></em><em><u>sure</u></em>

3 0
2 years ago
Why did the farmers daughter watch the lazy cows
artcher [175]
Because she was bored
3 0
3 years ago
Read 2 more answers
Solve using substitution<br>x-2y =2<br>3x+4y=3​
lorasvet [3.4K]

Answer:

7/5, y = -3/10

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Other questions:
  • What is the surface area of a sphere if its volume is 288π cubic inches? Leave your answers in terms of π. A. 216π in² B. 144π i
    7·1 answer
  • ALGEBRA 1 HELP!!<br> The answer is correct, I just need the work for both. *giving brainliest!
    9·2 answers
  • Solve these equations.<br><br> |x-7|=x-7<br><br> pls help!
    13·1 answer
  • What is the prime number of 24
    12·2 answers
  • What is fifty four times eighty nine?
    7·2 answers
  • An ogive shown cumulative frequency and always overlays a pareto chart. true or false
    14·1 answer
  • The value of your quarters (in cents) is a function of , the number of quarters you have. Write an equation that represents this
    10·1 answer
  • What is the measure of the missing angle?)<br><br>Please explain how u got the answer so I can learn
    6·2 answers
  • Solve by elimination and show all steps please <br><br><br> 3x=2y-7, 2x-y=10
    11·2 answers
  • Find the H.C.F,a square -bsquare and a+b whole square
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!