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
n200080 [17]
3 years ago
14

Two ants, Ant M and Ant B, often compete with each other to see which can be the first to grab a sweet morsel of food. Ant B, th

e faster runner of the two, always runs at twice the speed of Ant M. One day they both saw a particularly inviting crumb of bread 100 cm directly to the east of Ant M. At that moment Ant B happened to be some distance straight north of Ant M's position. At the signal "1, 2, 3, GO!" they both ran to the crumb of bread, arriving at the same moment. A tie! So they decided to share it. Your task for this problem is to determine just how far north of Ant M Ant B was at the start of this race. Bonus: What if Ant B started directly northeast of Ant M? Then how far apart were the two ants

Mathematics
1 answer:
NeX [460]3 years ago
3 0

Answer:

a) Ant B was 173.2 cm away from ant M along the northern line/in the northern direction.

b) Ant B was 257.8 cm away from ant M along the northeastern line/in the northeastern direction.

Step-by-step explanation:

Let the speed of ant M be x

The speed of ant B = 2x

Let the distance between the two ants be d

The diagram of the situation described in the first part of the question is drawn in the first image attached to the question.

The position of ant B, ant M and the crumb of bread form a right angled triangle as shown in the first image attached.

Using Pythagoras theorem, the distance between ant B and the crumb of bread is given as

√(d² + 100²]

Speed = (distance)/(time)

Time = (distance)/(speed)

It is given in the question that the time taken for the two ants to reach the crumb of bread is exactly the same.

For ant M

Time = (100/x)

For ant B

Time = [√(d² + 100²)]/2x

Time = Time

[√(d² + 100²)]/2x = 100/x

√(d² + 100²) = 200

(d² + 100²) = 200²

d² = 40000 - 10000 = 30000

d = 173.2 cm

b) Determine the distance between the two ants if ant B is directly northeast from ant M

The image of the description is shown in the second attached image to this solution.

The distance between ant B and the crumb of bread can be obtained using cosine rule

Distance between ant B and the crumb of bread = √[d² + 100² - (2×d×100×cos 45°)]

The distance gives √[d² + 100² - 141.42d]

Using the speed, distance, time relation used in (a)

Time for ant M to reach crumb of bread

Time = (100/x)

Time for any B to reach crumb of bread

Time = (√[d² + 100² - 141.42d])/2x

They both reach the crumb at the same time

Time = Time

(√[d² + 100² - 141.42d])/2x = 100/x

√[d² + 100² - 141.42d] = 200

d² + 100² - 141.42d = 200²

d² - 141.42d + 10000 - 40000 = 0

d² - 141.42d - 30000 = 0

Solving the quadratic equation

d = 257.8 cm or - 116.4 cm

Since distance cannot be negative,

d = 257.8 cm

You might be interested in
Solve (4x^4-7-6x^2) (2x^2 4x^4 8)
kotykmax [81]
Your answer can only be simplified to
256x^10 - 384^8 - 448^6 
5 0
3 years ago
If f and g are functions of time, and at time t = 2, f equals 5 and is rising at a rate of 6 units per second, and g equals 7 an
Yuliya22 [10]

Answer:

f/g at t =3 will be 9/8

d/ddx(f(x)/g(x))=f'(x)d(x)-f(x)g'(x)/(g'(x))^2

rate of change=(6*8)+(9*9)/9^2

rate of change =43/27=1.5925

8 0
3 years ago
Read 2 more answers
You and your brother are reading the same novel. You want to get ahead of him in the book, so you decide to read 30 minutes long
NemiM [27]

the equation would be y = 30 + x and if your brother will read for 15 minutes then you'll read for 45 minutes i believe.

6 0
3 years ago
Please help i don’t know how to do this
laila [671]

Answer:

1.) 25

2.)81

3.)49

Step-by-step explanation:

(I recommend getting a Texas instruments TI-84 you can just plug in the numbers and it does it for you :)

4 0
3 years ago
Which point is a solution to the system of inequalities graphed here? y ≤ 2x 2 y ≥ -5x 4
Mandarinka [93]

The point that is a solution to the system of inequalities is (5, 0)

<h3>How to determine the points on the solution?</h3>

The system of inequalities is given as:

y ≤ 2x + 2

y ≥ -5x + 4

Next, we test the given options.


From the list of options, we have

(x, y) = (5, 0)

Substitute (x, y) = (5, 0) in y ≤ 2x + 2 and y ≥ -5x + 4

y ≤ 2x + 2

0 ≤ 2 * 5 + 2

0 ≤ 12 -- this is true

y ≥ -5x + 4

0 ≥ -5 * 5 + 4

0 ≥ -21 -- this is true

Since both results are true, then it means that the point that is a solution to the system of inequalities is (5, 0)

Read more about system of inequalities at:

brainly.com/question/24372553

#SPJ1

<u>Complete question</u>

Which point is a solution to the system of inequalities graphed here? y ≤ 2x + 2

y ≥ -5x + 4

A. (1,6)

B. (-6,0)

C. (0,5)

D. (5,0)

7 0
2 years ago
Other questions:
  • The perimeter of a right triangle is 24 meters, and the area is 24 square meters. The lengths of the sides are each multiplied b
    8·1 answer
  • certain electronics manufacturer found that the marginal cost C to produce x DVD/Blu- ray players can be found using the equatio
    13·1 answer
  • Henry took out a 4 year loan for 5,000 and payed 4.2% simple annual interest. Ingrid took out a 6 year loan for 5,000 and payed
    8·1 answer
  • Create a histogram for the data set. Click and drag on the horizontal axis to adjust the bar heights.
    5·2 answers
  • The y-intercept of the line whose equation is 2x + y = 4 is -2 2 4
    6·2 answers
  • (4 x 10^2) + 120.5<br> What’s the answer to this
    12·1 answer
  • The slope of the line whose equation is 3x - 2y = 4 is 2/3 3/2 -2
    6·1 answer
  • Can you show work for B?
    6·1 answer
  • Answer please.........
    14·1 answer
  • Select the correct inequality to make a true statement.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!