Answer:
Option D (7, -3)
Step-by-step explanation:
We know that the general equation of an ellipse has the form:
Where the point (h, k) are the coordinates of the center of the ellipse
In this case the equation of the ellipse is:
Then
So The coordinates of the center of the ellipse are (7, -3)
The answer is 16 cm (or 0.16 m).
The scale is the ratio of the model to the real thing.
So, in the scale 1:50, the model is 1, while the real thing is 50.
Now, just make a proportion:
the model : the real thing = the model dimension : the real thing dimension
1 : 50 = x : 8m
From here:
x = 8m * 1 / 50 = 0.16 m = 0.16 * 100 cm = 16 cm.
Imagine the path of the tip of the pendulum as an arc of a circle. The circle would have a radius of 4 feet and the arc would be 20 degrees. To calculate the length of the arc, you need to find 20 degrees of the circumference.
Length of Arc = 2*pi*R*Degree of arc/360
Length of Arc = 2*pi*4*20/360
Length of Arc = 8pi * 1/18
Length of Arc = 4/9 pi feet
<span>Length of Arc ~ 1.396263402 feet
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Answer:
7. 1520.53 cm²
8. 232.35 ft²
9. 706.86 m²
10. 4,156.32 mm²
11. 780.46 m²
12. 1,847.25 mi²
Step-by-step explanation:
Recall:
Surface area of sphere = 4πr²
Surface area of hemisphere = 2πr² + πr²
7. r = 11 cm
Plug in the value into the appropriate formula
Surface area of the sphere = 4*π*11² = 1520.53 cm² (nearest tenth)
8. r = ½(8.6) = 4.3 ft
Plug in the value into the appropriate formula
Surface area of the sphere = 4*π*4.3² = 232.35 ft² (nearest tenth)
9. r = ½(15) = 7.5 m
Surface area of the sphere = 4*π*7.5² = 706.86 m² (nearest tenth)
10. r = ½(42) = 21 mm
Plug in the value into the formula
Surface area of hemisphere = 2*π*21² + π*21² = 2,770.88 + 1,385.44
= 4,156.32 mm²
11. r = 9.1 m
Plug in the value into the formula
Surface area of hemisphere = 2*π*9.1² + π*9.1² = 520.31 + 260.15
= 780.46 m²
12. r = 14 mi
Plug in the value into the formula
Surface area of hemisphere = 2*π*14² + π*14² = 1,231.50 + 615.75
= 1,847.25 mi²
Using the 45°-45°-90° triangle theorem, find the value of h, the height of the wall. C. 13 ft
