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
faltersainse [42]
3 years ago
5

On the standard coordinate grid at initial moment, ship Tiger is at the position (0, 795), ship Lion is at the position (985, 0)

. Tiger sails along the straight line to the position (1229, 0). At the same time, Lion sails along the straight line to the position (0, 1039). Lion will reach her destination in one hour, Tiger – in two hours.
a) Find the point of intersection of the paths of the ships.
b) At what time from the moment of departure each of the ships will pass the point of intersection of the paths.
c) At what time (in minutes after departure) the distance between Lion and Tiger will be the shortest?
d) What is the shortest distance between Lion and Tiger?
e) What will be the positions of both ships at the moment when the distance between them is the shortest?
Mathematics
1 answer:
elena-14-01-66 [18.8K]3 years ago
6 0

Answer:

A) (380, 640)

B) ship Tiger: Time = 0.96 hours

Ship Lion: Time = 0.62 hours

C) Ship Tiger = 57.6 minute

Ship Lion = 37.2 minutes

D) Distance = 533 metres

E) Ship Tiger (0, 795)

Ship Lion (1039,0)

Step-by-step explanation:

From the question, we can form the equation of the straight line from the initial and final position of the two ships. Using the general linear equation Y = mx + c. that is

Ship Tiger

Initial position (0, 795)

Final position (1229, 0)

M = (0 - 1229)/795

M = - 1.55

1229 = -1.55(0) + C

C = 1229

Hence the equation of the line for ship Tiger will be

Y = - 1.55x + 1229 ...... (1)

Ship Lion

Initial position (985, 0).

Final position (0, 1039).

M = 1039/ -985 = - 1.05

0 = -1.05(985) + C

0 = - 1039 + C

C = 1039

The equation of the line for ship Lion will be

Y = - 1.05(x) + 1039..... (2)

At the point of intersection of the paths of the ships, they will have common Y and X. Hence equation 1 is equal to equation 2

- 1.55x + 1229 = -1.05(x) + 1039

1.55(x) - 1.05(x) = 1229 - 1039

0.5x = 190

X = 190/0.5 = 380

Substitute x in equation 1

Y = -1.55(380) + 1229

Y = -589 + 1229

Y = 640

Therefore the point of intersection of the paths of the ships is (380, 640)

B) given that Lion will reach her destination in one hour, Tiger – in two hours.

Ship Tiger

distance = root(795^2 + 1229^2)

Distance = 1463.7

Speed = distance/time

Speed = 1463.7/2 = 731.9 m/s

Distance at the point of intersection will be

Distance = root(380^2 + (640-1229)^2)

Distance = root(144400 + 346921)

Distance = 700.9

Speed = distance/time

Time = distance /speed

Time = 700.9/731.9

Time = 0.96 hours

Ship Lion

distance = root(985^2 + 1039^2)

Distance = 1431.69

Speed = distance/time

Speed = 1431.69/1 = 1431.69

Distance at the point of intersection will be

Distance = root((380 - 985)^2 + (640)^2)

Distance = root(775625)

Distance = 880.7 meters

Speed = distance/time

Time = distance /speed

Time = 880.7/1431.69

Time = 0.615 hours

C) the time in minute the distance between Lion and Tiger will be the shortest will be

Ship Tiger: 0.96 × 60 = 57.6 minute

Ship Lion: 0.62 × 60 = 36.9 minutes

D) The shortest distance between Lion and Tiger will be achieved by using pythagorean theorem for the the distances at the point of intersection

Root (880.7^2 - 700.9^2)

Distance = 533 metres

E) the positions of both ships at the moment when the distance between them is the shortest will be the initial position of both ships

That is

Ship Tiger

Initial position (0, 795)

Ship Lion

Initial position (985, 0).

You might be interested in
Solve for p: 3p-2=2p/5+p-2/3<br><br>please help ASAP<br>Best answer will be marked brainliest ​
Reika [66]
P=5/6


Mark brainliest please


Hope this helps you
7 0
2 years ago
Read 2 more answers
I have an F I need help
Vikentia [17]

Answer:

I think it's B

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Yann will be x years old y years from now. How old was he z years ago?
erastova [34]
Here we can change the variables to real numbers, just to make things easier for us. For the sake of calculation, let’s say that x=10, y=6, and z=1.

So, y years from now, Yann will be x years old. If we plug in our randomly chosen numbers, we get that Yann will be 10 years old 6 years from now. This means that today, he would be x-y years old, or 10-6, so 4 years old today.
Next we ask how old he was z years ago, or in this case, 1 year ago. We know that if you’re 4 years old now, you were 3 years old last year. In other words, you’re 4-1 years old, or x-y-z years old.

Your answer is x-y-z.
8 0
3 years ago
What is the product of 41 and 8.4 x 10^4 expressed in scientific notation?​
LenaWriter [7]

Answer:

3.44 x 10^6

Step-by-step explanation:

41 x 8.4 = 344.4

344.4 x 10^4 = 3.44 x 10^4+2

6 0
2 years ago
A rectangle measures 15 cm by 4 cm what's it's area
schepotkina [342]
The way you find area is multiplying width times height, so you have to multiply 15 by 4 which equals 60. Therefore the answer is 60
5 0
3 years ago
Other questions:
  • Find the derivative of y=sin^(2)(x)cos^(2)(x)
    9·1 answer
  • eva and Liam are reading a novel in their English class. Liam has read 17 pages less than eva has. if they had read 265 pages co
    8·2 answers
  • M increased by 5 is what
    6·2 answers
  • Find the length of a diagonal of a rectangle if the length of the rectangle is 24 cm and its width is 10 cm. A) 22 cm B) 26 cm C
    7·2 answers
  • Help me find Angle AJL
    14·1 answer
  • Evaluate the following:
    8·1 answer
  • Which of the following questions would use the calculation
    15·1 answer
  • In a class, there are 18 girls and 14 boys. If the teacher selects two students at random to attend a party with the principal,
    15·1 answer
  • If S lies between R and T, RT=21, RS=2X+5, and ST=3x-4. Find RS and ST
    10·2 answers
  • Express the sum or difference as a product. sin 4x - sin 6x
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!