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
snow_lady [41]
3 years ago
14

At noon, ship A is 130 km west of ship B. Ship A is sailing east at 30 km/h and ship B is sailing north at 20 km/h. How fast is

the distance between the ships changing at 4:00 PM?

Mathematics
2 answers:
Sergeeva-Olga [200]3 years ago
8 0

Answer:

36.1 km/h

Step-by-step explanation:

rate at which the distance is changing is given by relative velocity(vR)

Look at the diagram. THe diagram shows relative motion. From relative motion diagram, velocity vector diagram is drawn.

From velocity vector diagram, it can be seen that relative velocity or vR can be calculated using pythagoras theorem.

vR²= vA² + vB²

vR²= 30²+ 20²

vR= 36.1 km/h

lesya692 [45]3 years ago
7 0

Answer:

At 4:00pm, the distance between ship A and B is increasing at the rate of 16.12 km/hr

Step-by-step explanation:

The illustration forms a right angle triangle.  At noon the distance between ship A and Ship B is 130 km . But ship A is west of ship B . Ship A is sailing east towards the starting point of ship B which means the distance is shrinking  at 30 km/hr and ship B is sailing north at 20 km/hr .This means ship B distance is extending.

The distance covered by ship A is  

distance = speed × time

noon to 4 pm  =  4 hrs

distance = 30 × 4

distance = 120 km

The distance covered by ship B is  

distance = speed × time

distance = 20 × 4

distance = 80 km

The distance from Ship A present position to ship B after moving east is 130 km - 120 km = 10 km.

Using Pythagorean theorem

c = ?

a = 10 km

b = 80 km

c² = a² + b²

c² = 10² + 80²

c² = 100 + 6400

c² = 6500

c = √6500

The question ask us how fast is the distance between the ships changing at 4:00 pm. This means calculating the rate .

c² = a² + b²

differentiate with respect to time

2c(dc/dt) = 2a(da/dt) + 2b(db/dt)

divide through by 2

c(dc/dt) = a(da/dt) + b(db/dt)

since we are looking for the rate of c we make dc/dt subject of the formula

dc/dt = (a(da/dt) + b(db/dt)) / c

Note Ship A travelling to the east is shrinking. so the speed which is da/dt = - 30 km/hr

c = √6500

a = 10 km

b = 80 km

dc/dt =  10(-30) + 80(20) / √6500

dc/dt = (-300 + 1600)/√6500

dc/dt = 1300 /√6500

dc/dt = 1300/80.622577483

dc/dt = 16.1245154966 km / hr

At 4:00pm, the distance between ship A and B is increasing at the rate of 16.12 km/hr

You might be interested in
The next event requires each runner to jump 8 hurdles that are spaced 12.3 meters apart. If there are 15 meters from the startin
inessss [21]
The race is 111.6 m long.

8 hurdles spaced 12.3 m apart means 7 spaces that are 12.3 m in length; 7*12.3 = 86.1

Add to this the distance to the first hurdle and the distance from the last hurdle:
86.1+15+10.5 = 111.6 m
3 0
3 years ago
Haseena bought 1 pencil box, 4 pencils and 4 notebooks from a store. She paid Rs. 95 in all. Some ink fell on the bill that she
Rudik [331]

The price of the one notebook will be Rs. 10.6

  • Let the price of one notebook be x.

If Haseena bought 1 pencil box, 4 pencils and 4 notebooks from a store, with a total of Rs. 95 paid in all, then;

1x + 4x + 4x = 95

9x = 95

x = 95/9

x = 10. 6

Hence the price of the one notebook will be Rs. 10.6

Learn more on ratio here: brainly.com/question/20346769

8 0
2 years ago
As an aid to the establishment of personnel requirements, the director of a hospital wishes to estimate the mean number of peopl
GenaCL600 [577]

Answer:

n = 66.564

Step-by-step explanation:

  1. Because the population is unknown, we will apply the following formula to find the sample size:

n= (\frac{zS}{E} )^{2}

Where:

z = confidence level score.

S = standard deviation.

E = error range.

   2. We will find each of these three data and replace them in the formula.

"z" theoretically is a value that measures how many standard deviations an element has to the mean. For each confidence level there is an associated z value. In the question, this level is 99%, which is equivalent to a z value of 2.58. To find this figure it is not necessary to follow any mathematical procedure, it is enough to make use of a z-score table, which shows the values ​​for any confidence interval.

The standard deviation is already provided by the question, it is S = 100.

Finally, "E" is the acceptable limit of sampling error. In the example, we can find this data. Let us note that in the end it says that the director wishes to estimate the mean number of admissions to within 1 admission, this means that she is willing to tolerate a miscalculation of just 1 admission.

Once this data is identified, we replace in the formula:

n=(\frac{(2.58)(100)}{1} )^{2}

    3. The corresponding mathematical operations are developed:

n=(\frac{258}{1} )^{2}

n= (258)^{2}

n= 66.564

4 0
3 years ago
M= i + r ; solve for r
Alex777 [14]

Answer:

m - i = r

Step-by-step explanation:

In this question, you are solving for "r".

Solve:

M= i + r

We have to get "r" by itself, so subtract "i" from both sides.

m - i = r

Since we found what "r" is, we can't solve any further.

m - i = r would be your answer.

7 0
2 years ago
Pls help my last one ​
ikadub [295]

Answer:

7.59/ KG

Step-by-step explanation:

plss help me in my qwestion

7 0
2 years ago
Read 2 more answers
Other questions:
  • Please help!
    13·1 answer
  • Use the substitution method to solve each system of equations. Write the answer in ordered pairs.
    9·1 answer
  • Find the length of the segment. round to the nearest tenth of a unit P(1,2) Q(5,4)
    5·2 answers
  • What is- 2(10.50+6) +3(6.50+6) +7.50+ 2(6-5)
    14·1 answer
  • To convert 3 square feet to square centimeters, multiply 3 by 9.29 × 10-2 <br> True or False
    11·2 answers
  • Melanie spent four hours babysitting. She charges $16 upfront and then an additional charge per hour. The total amount she earne
    10·1 answer
  • The area of a rectangle a=1(w) is represented by the expression 24x6y15. If the width of the rectangle is 2x3y9, what is the l
    10·1 answer
  • 4x-4&lt;24 <br> I need this step by step PLZZZZZ
    10·1 answer
  • Are inverse functions? <br> f(x) = <br> 1<br> 3<br> x − 8, g(x) = 3x + 2
    13·1 answer
  • MATH HELP NEEDED PLEASE
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!