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Gemiola [76]
3 years ago
6

Astronomy: At is closest approach, Mars is about 5.6X10^7 km from Earth and its apparent size is about 0.00012 radians. What is

the approximate diameter of Mars?
Mathematics
2 answers:
algol133 years ago
7 0
6700 km  
For this problem, there are two basic ways of solving it and both will give approximately the same answer. The easiest way is to simply ignore the slight difference in length of the adjacent leg of the right triangle and hypotenuse and calculate the arc tangent. The equation is 
tan θ = opp/adj 
adj * tan θ = opp 
5.6x10^7 km *0.000120000000576 = opp 
6.720000032256x10^3 = opp 
6720 km = opp  
So the diameter of Mars is about 6700 km.  
The other way is to actually acknowledge that the hypotenuse and adjacent leg are different lengths and divide the apparent size by 2 for performing the trig, then double the result. So: 
tan θ = opp/adj 
adj * tan θ = opp 
5.6x10^7 km * 0.000060000000072 = opp
 5.6x10^7 km * 0.000060000000072 = opp 
3.360000004032x10^3 = opp
 3.360000004032x10^3 * 2 = diameter
 6.720000008064x10^3 = diameter 
 And you may notice the digits at the end of the results do differ. But they're so insignificant, that the final results in both cases is the same. So to 2 significant digits, the diameter of Mars is 6700 km.
Mariana [72]3 years ago
6 0
1.) D = 2pi * d * A / 360 degrees; Where:
   pi = 3.14;
   d = distance or 56,000,000 km (5.6x10^7 to standard notation)
   A = angular size in degrees or .00688 degrees (.00012 radian to degrees)

  D = 2(3.14) * 56,000,000 * .00688 / 360
      = 6.28 * 385,280 / 360
      = 2,419,558.4 / 360
 D  = 6,720.996 or 6,721

Therefore, 6,721 km. is the approximate diameter of Mars.
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find the volume of a cylinder whose base has a diemeter of 11 and whose height is 12.5. use 3.14 and round your answer to the ne
atroni [7]
Volume = π (3.14)×22^2×12.5 = 18,997 inches³
3 0
3 years ago
NEED THESE ANSWERED ASAP SO I CAN GRADUATE THIS WEEK
babunello [35]

For this case we must solve each of the equations proposed:

A) -6 (2s-1) = 30

We apply distributive property to the terms within parentheses:

-12s + 6 = 30

Subtracting 6 from both sides of the equation we have:

-12s = 24

Dividing between -12 on both sides of the equation:

s = \frac {24} {- 12}s = -2

B) -3m = -5 (m-8)

We apply distributive property to the terms within parentheses:

-3m = -5m + 40

We add 5m on both sides of the equation:

2m = 40

Dividing between 2 on both sides of the equation:

m = \frac {40} {2}\\m = 20

C) 7 (2-g) = 49

We apply distributive property to the terms within parentheses:

14-7g = 49

We subtract 14 from both sides of the equation:

-7g = 35

Dividing between -7 on both sides of the equation:

g = \frac {35} {- 7}\\g = -5

D) -7 (3w + 4) = 14

We apply distributive property to the terms within parentheses:

-21w-28 = 14

We add 28 to both sides of the equation:

-21w = 42

Dividing between -21 on both sides of the equation:

w = \frac {42} {- 21}\\w = -2

Answer:

s = -2\\m = 20\\g = -5\\w = -2

6 0
3 years ago
Read 2 more answers
You are planning a May camping trip to Denali National Park in Alaska and want to make sure your sleeping bag is warm enough. Th
Goshia [24]

The probability that this bag will be warm enough on a randomly

selected May night at the park is 0.8106 ⇒ answer C

Step-by-step explanation:

You are planning a May camping trip to Denali National Park in Alaska

and want to make sure your sleeping bag is warm enough.

The average low temperature in the park for May follows a normal

distribution

The given is:

1. The mean is 32°F

2. The standard deviation is 8°F

3. One sleeping bag you are considering advertises that it is good for

   temperatures down to 25°F (x ≥ 25)

At first let us find the z-score

∵ z = (x - μ)/σ, where x is the score, μ is the mean, σ is standard deviation

∵ μ = 32°F , σ = 8°F , x = 25°F

- Substitute these values in the rule

∴ z = \frac{25-32}{8}=-0.875

Now let us find the corresponding area of z-score in the normal

distribution table

∵ The corresponding area of z = -0.875 is 0.18943

∵ For P(x ≥ 25) the area to the right is needed

∵ P(x ≥ 25) = 1 - 0.18943 = 0.8106

∴ P(x ≥ 25) = 0.8106

The probability that this bag will be warm enough on a randomly

selected May night at the park is 0.8106

Learn more:

You can learn more about mean and standard deviation in brainly.com/question/6073431

#LearnwithBrainly

3 0
3 years ago
Last one: which expression is equivalent?
Lady_Fox [76]
It is b 4/3+2/3 is 6/3 and 6/3 divided by 1/3 is 2/3x
5 0
2 years ago
Will mark Brainliest<br><br>1/4 ÷ 7/1 =
____ [38]
1/4 divided by 7/1 equals 1/28
7 0
2 years ago
Read 2 more answers
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