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Amanda [17]
3 years ago
10

Light travels 300,000 km/s. The planet Mars is about 228,000,000 km from the sun. How would you find out how many minutes it tak

es light from the Sun to reach Mars?
Mathematics
1 answer:
miv72 [106K]3 years ago
5 0

Answer:

12.67 minutes

Step-by-step explanation:

Time taken is given by distance divided by speed

Given distance of 228, 000, 000 km and speed of light as 300, 000 km/s then time will be

Time=228, 000, 000/300, 000=760 seconds

Conversion

60 seconds make up 1 minute

760 seconds will be 760/60

Time=760/60=12.666666666666

Rounded off, this is 12.67 minutes

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A blind man wanders under a door into an empty room. After running into the walls repeatedly for a while, it stops to think and
Nostrana [21]

From the side where the man is located in the 10' by 12' rectangular room, we have;

A) 0.046

B) The average time to escape in first attempt is approximately 605.02 seconds

<h3>Which concept can be used to find the odds and time of escape?</h3>

A) From The given diagram, we have;

Width of the door = 10 - 6 - 2 = 2

Therefore, the door is 2 feet wide

Distance, d1, from the man to the side of the door closer to him is given by Pythagorean theorem as follows;

  • d1 = √(6² + 7²) = √(85)

From the furthest side of the door to the man, we have;

  • d2 = √(7² + 8²) = √(113)

According to the law of cosines, we have;

2² = 85+113 - 2×√(85)×√(113) cos(A)

Where angle <em>A </em>is the angle formed by the lines from the man to the closer and farther sides of the door.

2×√(85)×√(113) cos(A) = 85+113 - 2²

A = arccos((85+113 - 2²)/(2×√(85)×√(113)))

A = arccos (194/(2×√(9605)) ≈ 8.213°

The angle of the possible directions in which the man can turn is 180°.

Therefore;

The probability, <em>P(</em><em>E)</em>, of escaping in the first move is therefore;

  • P(E) = 8.213°/180° ≈ 0.046

B) Given that the man escapes in the first move, the shortest and longest distances the man moves are;

d1 = √(85) and d2 = √(113)

Speed of the man, <em>v </em>= 0.5 cm/sec

Therefore by unit conversion function of a graphing calculator;

  • v = (25/1524) ft./sec

The times taken are;

t1 = √(85)/(25/1524) ≈ 562.023

t2 = √(113)/(25/1524) ≈ 648.014.

Average time, <em>t </em>= (t1 + t2)/2

Which gives;

t = (562.023 + 648.014)/2 ≈ 605.02

The average time it takes the man to escape in first move is <em>t </em><em>≈</em> 605.02 seconds.

Learn more about Pythagorean theorem and probability here:

brainly.com/question/27180985

brainly.com/question/654982

brainly.com/question/24756209

#SPJ1

3 0
1 year ago
FOR 90 POINTS PLEASE HELP
miskamm [114]

Answer:

Question 1: RS=47

Question 2: x=6

Step-by-step explanation:

Question 1:

Step 1: 3x+5=2x+15+6x-37

Step 2: 3x+5=8x-22/2

Step 3: 3x+5=4x-11

Step 4: x=16

Step 5: 2(16)+15=32+15=47

<u>RS= 47</u>

<u />

Question 2:

Step 1: 7x+2+25x-14=180

Step 2: 32x-12=180

Step 3: 32x=192  (divide 32 from each side)

<u>x=6</u>

<u />

7 0
3 years ago
Simplify square root of x^2y^8
PSYCHO15rus [73]
Sqrt x^2 y^8
The index is 2 so divide power by index
x y^4
5 0
3 years ago
Each night, Abby recorded how many pages of a book she read before going to bed. Her data is as follows: 7, 9, 10, 6, 8, 12, 5,
aksik [14]

Answer:

mean = 12.9

median = 9.5

Step-by-step explanation:

mean = sum of all observations / total no. of observations

= 7+9+10+6+8+12+5+11+48+13 / 10

=129 / 10

= 12.9

median = middlemost no. after arranging in ascending order

= 5,6,7,8,9,10,11,13,48

=9 and 10

=9+10 / 2

= 19 / 2

= 9.5

8 0
3 years ago
The diameter of this circle is 12 inches. The diameter of the smaller circle is 8 inches. find the area of the SHADED region.
kolezko [41]

Answer:

so you multiply 12 by 8 =96

3 0
3 years ago
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