when looking at two buildings at the same time length of the buildings' shadows varies directly as their height, meaning there is a rate of shadow length per building height. If a 7-story building has a 27.65 m long shadow, using a proportion determine how many stories high would a building be if it casts a shadow that is 19.75 m long.
Show all calculations, steps, and/ or explain your answer.
To solve this problem, we can set up a proportion using the given information.
Let x represent the number of stories in the building.
The proportion can be set up as:
(shadow length of 7-story building) / (height of 7-story building) = (shadow length of x-story building) / (height of x-story building)
Substituting the given values:
27.65m / 7 stories = 19.75m / x stories
To solve for x, we cross-multiply:
27.65 * x = 19.75 * 7
27.65x = 138.25
Dividing both sides of the equation by 27.65:
x = 5
Therefore, a building that casts a 19.75m long shadow would be approximately 5 stories high.
when looking at two buildings at the same time length of the buildings' shadows varies directly as their height, meaning there is a rate of shadow length per building height. If a 7-story building has a 27.65 m long shadow, using a proportion determine how many stories high would a building be if it casts a shadow that is 19.75 m long with all diagram
Show all calculations, steps, and/ or explain your answer.
To solve this problem using a proportion, we can set up the equation:
(shadow length of building 1) / (height of building 1) = (shadow length of building 2) / (height of building 2)
Let's label the variables:
Shadow length of building 1 = S1
Height of building 1 = H1
Shadow length of building 2 = S2
Height of building 2 = H2
Given:
S1 = 27.65 m (shadow length of the 7-story building)
H1 = 7 stories (height of the 7-story building)
S2 = 19.75 m (shadow length for the building we want to find the height of)
H2 = ?
Using the proportion equation, we have:
S1 / H1 = S2 / H2
Substituting the given values:
27.65 / 7 = 19.75 / H2
To solve for H2, we cross-multiply:
27.65 * H2 = 19.75 * 7
27.65H2 = 138.25
Dividing both sides of the equation by 27.65 to solve for H2:
H2 = 5
Therefore, the building that casts a 19.75m long shadow would be approximately 5 stories high.
Jack went on a hike for 2 hours and 15 minutes. According to his fitness watch, he burned 1013 calories during the hike. Brooke went to a 45 minutes high-impact aerobic class. According to her fitness watch, she burned 347 calories. Compare the rate at which jack and brooke burn calories. Conclude who burns calories at a higher rate.
Show all calculations, steps, and/ or explain your answer.
To compare the rate at which Jack and Brooke burn calories, we can calculate their calorie burn rates per minute.
Jack's hike duration: 2 hours 15 minutes = 2 * 60 minutes + 15 minutes = 135 minutes
Jack's calorie burn rate: 1013 calories / 135 minutes = 7.505 calories/minute
Brooke's aerobic class duration: 45 minutes
Brooke's calorie burn rate: 347 calories / 45 minutes = 7.711 calories/minute
Comparing the calorie burn rates, we see that Brooke burns calories at a higher rate of 7.711 calories per minute compared to Jack's rate of 7.505 calories per minute. Therefore, Brooke burns calories at a higher rate than Jack.
To solve this problem, we can set up a proportion using the given information.
Let "x" represent the number of stories in the building we want to find.
The proportion we can set up is:
Height of the 7-story building / Length of the shadow of the 7-story building = Height of the x-story building / Length of the shadow of the x-story building.
We know that the 7-story building has a height of 7 stories and a shadow length of 27.65 m. The x-story building has an unknown height (x stories) and a shadow length of 19.75 m.
So, the proportion becomes:
7 / 27.65 = x / 19.75
To solve for x, we can cross-multiply:
7 * 19.75 = 27.65 * x
138.25 = 27.65 * x
Now we can isolate x by dividing both sides of the equation by 27.65:
138.25 / 27.65 = x
x ≈ 5
Therefore, the x-story building would be approximately 5 stories high if it casts a shadow that is 19.75 m long.
To solve this question, we can set up a proportion using the relationship between the height of the building and the length of its shadow. Let's call the unknown height of the building "x", and the length of its shadow "19.75 m".
We know that the length of the shadow varies directly with the height of the building, and the given information states that a 7-story building has a 27.65 m long shadow.
So, we can set up the following proportion:
7-story building height / 27.65 m = x-story building height / 19.75 m
To find the value of "x", we can cross-multiply and solve for it.
7-story building height * 19.75 m = 27.65 m * x-story building height
139.25 m = 27.65 m * x
Next, isolate "x" by dividing both sides of the equation by 27.65 m:
139.25 m / 27.65 m = x
Simplifying the calculation:
5 = x
Therefore, the building would be 5 stories high if it casts a shadow that is 19.75 m long.