I need help on this one!!! Please helppppppp!
1 answer:
Answer:
Step-by-step explanation:
For pi i use the estimate 3.14
First find the radius of the sphere using the formula circumference= pi * diameter
then divide both sides of the equation by d to get the diameter, which is about 86.94.
To get the radius, divide the diameter by 2, which equals 43.47.
Use the formula to get the surface area, which is, rounded to the nearest number, is 23,734 feet
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Answer:
Step-by-step explanation:
<h3>Given expression</h3>sin²5° + sin²10° + sin²15° +... sin²85° + sin²90°
<h3>Concept:</h3>sin²x + cos²x = 1
sin(x) = cos (90 - x)
<u />
<u>There are in total these terms:</u>
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90
<u>In total, there are 18 terms, and the first one matches with the second to the last one:</u>
5 -- 85
10 -- 80
.
.
.
40 -- 50
<u />
<u>There are 2 terms left over:</u>
sin²45 and sin²90
<h3>Convert the first half of the sine terms (sin²5 - sin²40) to the cosine terms</h3>sin²5 = cos² (90 - 5) = cos²85
sin²10 = cos² (90 - 10) = cos²80
.
.
.
sin²40 = cos² (90 - 40) = cos²50
<h3>Simplify the 16 grouped terms </h3><em>i.e. sin²85 and cos²85</em>
Using the concept of sin²x + cos²x = 1
sin²85 + cos²85 = 1
sin²80 + cos²80 = 1
.
.
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sin²50 + cos²50 = 1
Total = (16/2) × 1 = 8 × 1 = 8
<h3>Evaluate the 2 terms that are left over</h3>sin²45 = (sin45) (sin45) = (√2 / 2) (√2 / 2) = 1/2
sin²90 = (sin90) (sin 90) = (1) (1) = 1
<h3>Add all the terms together</h3>Hope this helps!! :)
Please let me know if you have any questions