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2 answers:
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Answer:
D
Step-by-step explanation:
Given
=
, then
=
=
= 262144 → D
Question is not complete. Complete question is;
Mount Belinda is the highest point in the South Sandwich Islands, with a peak at about 1,370 meters above sea level. The South Sandwich Trench, which lies about 100 kilometers (62 miles) to the east of the South Sandwich Islands, is about 8,428 meters below sea level (at its lowest point).
Part A: What is the difference in elevations between Mount Belinda and the South Sandwich Trench?
Part B: Is the elevation halfway between the peak of Mount Belinda and the South Sandwich Trench above sea level or below sea level? Give your explanation without calculating the exact value.
Part C: What elevation is halfway between the peak Mount Belinda and the South Sandwich Trench?
Answer:
A) 100478.86 metres
B) Explained below.
C) 50239.43 metres
Step-by-step explanation:
I have attached an image showing the elevations as depicted in the question.
MB represents peak of Mount Belinda while SS represents lowest point of South Sandwich Islands.
A) Now, total vertical distance from peak of MB to lowest point of SS is;
8428 + 1370 = 9798 metres
Since the horizontal distance between MB and SS is 100000 metres, then we can use pythagoras theorem to find the Elevation between MB and SS.
If the Elevation is x.
Thus;
x = √(9798² + 100000²)
x = 100478.86 metres
B) The Elevation between peak of MB and lowest point of SS will be halfway below the sea level because the distance from the lowest point of SS from the sea level is 5 times bigger than the distance from peak of MB to the sea level.
C) The halfway Elevation between peak MB and lowest SS will be;
100478.86/2 = 50239.43 metres
Subtract 14x from both sides to get
Subtract 12 from both sides to get
Now we have moved all terms involving x on one side, and all constant terms on the other. We can simplift both sides, i.e. sum like terms, to get
Now we have to divide both sides by 6. When dealing with inequality you have to be careful about dividing both sides by the same constant: if the constant is negative, the inequality side switches (i.e. ). But this is not the case since 6 is positive, so we mantain the inequality sign:
on the other. We can simplift both sides, i.e. sum like terms, to get
Evaluate left and right hand side: