The gravitational pull of the Moon is not as great as that on Earth. In fact, if a person checks their weight on the Moon, it will be only 16
of their weight on Earth.
A graph is shown in the xy-plane, and is labeled as Weight on Earth Versus Weight on Moon. The x-axis is labeled as Weight on Earth left parenthesis pounds right parenthesis, and the y-axis is labeled as Weight on Moon left parenthesis pounds right parenthesis. The values on the x-axis range from 0 to 180 in increments of 20, and the values on the y-axis range from 0 to 32 in increments of 4. A line starts from the origin, goes up, and passes through (60, 10).
A. If a person weighs 12 pounds on the Moon, how much does the person weigh on Earth? Explain your answer.
B. If a person weighs 126 pounds on Earth, how much does the person weight on the Moon? Explain your answer.
A. If a person weighs 12 pounds on the Moon, using the graph, we can read the value on the y-axis which corresponds to 12 pounds on the Moon. The line passing through (60,10) gives us the weight on Earth for that corresponding value on the y-axis which is approximately 96 pounds. So, the person weighs 96 pounds on Earth if they weigh 12 pounds on the Moon.
B. If a person weighs 126 pounds on Earth, we can locate 126 pounds on the x-axis and find the corresponding value on the line passing through (60,10). From the graph, we can see that the line intersects the x-axis at approximately 140 pounds on Earth. Therefore, the person would weigh approximately 16 pounds on the Moon if they weigh 126 pounds on Earth.
A. If a person weighs 12 pounds on the Moon, according to the graph, we can see that the line passes through the point (60, 10). This means that at 10 pounds on the Moon, the person would weigh 60 pounds on Earth. Since the line is a straight line, we can assume that the relationship between weight on Earth and weight on the Moon is linear. So, we can use the slope of the line to find the weight on Earth corresponding to 12 pounds on the Moon. By using the equation of a line, we can calculate:
Weight on Earth = (Weight on Moon / slope) + y-intercept
Using the given point (60, 10) on the line, we can calculate the slope as:
slope = (10 - 0) / (60 - 0) = 10 / 60 = 1/6
Substituting the values into the formula, we get:
Weight on Earth = (12 / (1/6)) + 0
Weight on Earth = (12 * 6) + 0
Weight on Earth = 72 pounds
Therefore, if a person weighs 12 pounds on the Moon, they would weigh 72 pounds on Earth.
B. If a person weighs 126 pounds on Earth, we can use the same line on the graph to find the corresponding weight on the Moon. Again, we can use the equation of the line:
Weight on Earth = (Weight on Moon / slope) + y-intercept
Substituting the values:
126 = (Weight on Moon / (1/6)) + 0
(Weight on Moon / (1/6)) = 126
Weight on Moon = 126 * (1/6)
Weight on Moon = 21 pounds
Therefore, if a person weighs 126 pounds on Earth, they would weigh 21 pounds on the Moon.
A. To determine how much the person weighs on Earth given a weight of 12 pounds on the Moon, we can use the graph provided.
We can see from the graph that the line passes through the point (60, 10). This means that when a person weighs 60 pounds on Earth, they weigh 10 pounds on the Moon.
Since the line on the graph is linear, we can use a ratio to find the weight on Earth given a weight on the Moon.
The ratio of weight on the Moon to weight on Earth is 16:1, as stated in the problem.
Using this ratio, we can set up a proportion to find the weight on Earth:
(Weight on Moon) / (Weight on Earth) = 16 / 1
Plugging in the known values:
12 / (Weight on Earth) = 16 / 1
Cross multiplying:
12 * (1) = 16 * (Weight on Earth)
Simplifying:
12 = 16 * (Weight on Earth)
Dividing both sides by 16:
(Weight on Earth) = 12 / 16 = 0.75 pounds
Therefore, if a person weighs 12 pounds on the Moon, they would weigh 0.75 pounds on Earth.
B. To determine how much the person weighs on the Moon given a weight of 126 pounds on Earth, we can use the same graph and ratio.
Using the given ratio of 16:1, we can set up a proportion:
(Weight on Moon) / (Weight on Earth) = 1 / 16
Plugging in the known values:
(Weight on Moon) / 126 = 1 / 16
Cross multiplying:
(Weight on Moon) * (16) = 126 * (1)
Simplifying:
16 * (Weight on Moon) = 126
Dividing both sides by 16:
(Weight on Moon) = 126 / 16 = 7.875 pounds
Therefore, if a person weighs 126 pounds on Earth, they would weigh approximately 7.875 pounds on the Moon.
A. To find out how much a person weighs on Earth if they weigh 12 pounds on the Moon, we can use the provided graph. Start by locating the point (12, ?) on the y-axis, which represents a weight of 12 pounds on the Moon. Then, follow the line that passes through (60, 10) until it intersects with the y-axis. The point where it intersects gives the weight on Earth.
In this case, we can see that the line intersects the y-axis at approximately 30. Therefore, if a person weighs 12 pounds on the Moon, they would weigh around 30 pounds on Earth.
B. Similarly, to determine how much a person weighs on the Moon if they weigh 126 pounds on Earth, we can use the graph. Locate the point (126, ?) on the x-axis, which represents a weight of 126 pounds on Earth. Then, trace the line that goes through (60, 10) until it intersects with the x-axis. The point where it intersects gives the weight on the Moon.
In this case, we can observe that the line intersects the x-axis at approximately 96. Hence, if a person weighs 126 pounds on Earth, they would weigh around 96 pounds on the Moon.