H (x) = -x+4 when h(x)=-3
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The volume of railway car is 216 cubic meters
<em><u>Solution:</u></em>
Given that, Railway car is shaped like a rectangular prism with a length of 18 meters, a width of 3 meters and a height of 4 meters
To find: volume of railway car
<em><u>The volume of rectangular prism is given as:</u></em>
Where,
"l" is the length and "w" is the width and "h" is the height of prism
From given question,
length = 18 meters
width = 3 meters
height = 4 meters
Substituting the values, we get
Thus volume of railway car is 216 cubic meters
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
.
.
.
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