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
Gnoma [55]
3 years ago
8

8. A cable car travels 2236 m to climb a mountain that is 1000 m high. It then travels 1414 m to descend 1000 m on the other sid

e of the mountain. A tunnel goes straight through the mountain, from the starting point to the endpoint of the cable car's journey. How long is the tunnel?

Mathematics
1 answer:
frutty [35]3 years ago
4 0

Answer:

3000 m

Step-by-step explanation:

Using Pythagoras theorem

2236^2=1000^2+|AB|^2\\|AB|^2=2236^2-1000^2\\|AB|^2=3999696\\|AB|=\sqrt{3999696} \\=1999.9

Similarly

1414^2=1000^2+|BC|^2\\|BC|^2=1414^2-1000^2\\|BC|^2=999696\\|BC|=\sqrt{999696} \\=999.7m

Length of the Tunnel = |AB|+|BC|

=1999.9+999.7

=2999.6

=3000 m

You might be interested in
Jake drove 300 miles from his house to a soccer tournament. This graph shows the distance Jake had traveled (m) and the time tha
Bad White [126]

Part A. The trip starts at 8am which corresponds to 0 hrs, point (0hr, 0mi)

2hrs later it's 10am. .point (2hr, 140mi)

The average speed is the slope between 0 and 2 hrs. Remember the slope formula m = Δy/Δx  

m = (140 - 0) / (2 - 0)  

m = 70 mph

Part B. Average speed from 11am - 2pm  

11am is point (3hr, 140mi)  

2pm is point (6hr, 300mi)  

As you can see from the graph, the speed or slope changes at 1pm (5,260). You Can just use the start and end points.

m  = (300-140) / (6-3)  

m = 160/3

53.3 mph

* It comes out the same solution as if you average the two different slopes. 2hrs at 60mph + 1 hr at 40mph = (120 + 40)/3 = 160/3  

Part C.  Total average speed = total distance / total time driving

He went 70 mph for 2 hrs

stopped for an hour (slope is zero, no speed)

60 mph for 2hrs

40mph for 1 hr

300mi /5hr = 60mph

Part D. No Question....

7 0
3 years ago
Suppose that 4 fair coins are tossed. Let Equals The event that exactly 2 coins show tails and Equal The event that at least 2 c
faust18 [17]

Answer:

a) P ( E | F ) = 0.54545

b) P ( E | F' ) = 0

Step-by-step explanation:

Given:

- 4 Coins are tossed

- Event E exactly 2 coins shows tail

- Event F at-least two coins show tail

Find:

- Find P ( E |  F )

- Find P ( E | F prime )

Solution:

- The probability of head H and tail T = 0.5, and all events are independent

So,

                    P ( Exactly 2 T ) = ( TTHH ) + ( THHT ) + ( THTH ) + ( HTTH ) + ( HHTT) + ( HTHT)  = 6*(1/2)^4 = 0.375

                    P ( At-least 2 T ) = P ( Exactly 2 T ) + P ( Exactly 3 T ) + P ( Exactly 4 T) = 0.375 + ( HTTT) + (THTT) + (TTHT) + (TTTH) + ( TTTT)

      = 0.375 + 5*(1/2)^4 = 0.375 + 0.3125 = 0.6875

- The probabilities for each events are:

                    P ( E ) = 0.375

                    P ( F ) = 0.6875

- The Probability to get exactly two tails given that at-least 2 tails were achieved:

                    P ( E | F ) = P ( E & F ) / P ( F )

                    P ( E | F ) = 0.375 / 0.6875

                    P ( E | F ) = 0.54545

- The Probability to get exactly two tails given that less than 2 tails were achieved:

                    P ( E | F' ) = P ( E & F' ) / P ( F )

                    P ( E | F' ) = 0 / 0.6875

                    P ( E | F' ) = 0                

6 0
3 years ago
3x-2y=10. 4x-y=6. solve each of the pair of simultaneous linear equation by substitution method ​
brilliants [131]

Answer:

x = 2/5, y= -22/5

Step-by-step explanation:

4x−y=6;3x−2y=10

Step: Solve4x−y=6for y:

4x−y+−4x=6+−4x(Add -4x to both sides)

−y=−4x+6

-y/-1 = -4x +6 over -1 (Divide both sides by -1)

y=4x−6

Step: Substitute4x−6for y in 3x−2y=10:

3x−2y=10

3x−2(4x−6)=10

−5x+12=10(Simplify both sides of the equation)

−5x+12+−12=10+−12(Add -12 to both sides)

−5x=−2

-5x/-5 = -2/5 (Divide both sides by -5)

x=  2 /5

Step: Substitute  2/ 5  for x in y=4x−6:

y=4x−6

y=4 ( 2/ 5 ) −6

y=  −22 /5

(Simplify both sides of the equation)

x = 2/5, y= -22/5

4 0
3 years ago
What is the surface area of a sphere with a diameter of 6 ft
Aleksandr-060686 [28]

Answer: 113.1ft²

Step-by-step explanation:

The answer is 113.1ft²

7 0
3 years ago
Answer and simplify 6(p+6)-3(p+3)
Finger [1]

Answer:

3p + 27

Step-by-step explanation:

simplify the expression.

6 0
3 years ago
Read 2 more answers
Other questions:
  • 153000 in standard form?
    10·1 answer
  • Simplify: (4a + 2b)(a - b)
    12·1 answer
  • $27 for 12 avocados HELP ME PLZ 14 POINTS
    5·1 answer
  • The Gonzalez family is taking a cruise that costs $3,082.24 for a family of four. How much does it cost perperson?
    15·1 answer
  • What is true about the graph of the equation y=6?
    12·1 answer
  • In an SLR camera, photographers look from the viewfinder through which of the following?
    12·1 answer
  • taka is playing a game of darts. she scores 52 points. in the game she is playing, she gets a -3 score each time she misses the
    15·1 answer
  • If the class started at 11:30 A.M. and ended at 12:25 P.M., how long did the class last?
    14·2 answers
  • Find the equation of the line that is perpendicular to y = - 1/3 x + 2 and passes though the point (-5,2)
    9·1 answer
  • Write your answer as a fraction or whole number.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!