Hi there!


We can evaluate using the power rule and trig rules:
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

Therefore:
![\int\limits^{12}_{2} {x-sin(x)} \, dx = [\frac{1}{2}x^{2}+cos(x)]_{2}^{12}](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B12%7D_%7B2%7D%20%7Bx-sin%28x%29%7D%20%5C%2C%20dx%20%3D%20%5B%5Cfrac%7B1%7D%7B2%7Dx%5E%7B2%7D%2Bcos%28x%29%5D_%7B2%7D%5E%7B12%7D)
Evaluate:

5280 divided by 4224 equals 1.25
Assume that
a and b = the two legs of the right triangle.
c = the hypotenuse.
The area of the right triangle is 750 yd², therefore
(1/2)*a*b = 750
ab = 1500 (1)
The perimeter is 150yd, therefore
a + b + c = 150 (2)
Let the side fenced with wood be a, at $5/yd. Sides b and c are fenced with steel at $10/y. The total cost is $1200, therefore
5a + 10b + 10c = 1200
or
a + 2b + 2c = 240 (3)
From (2), obtain
c = 150 - a - b (4)
Substitute (4) into (3)
a + 2b + 2(150 - a - b) = 240
-a + 300 = 240
a = 60
From (1), obtain
60b = 1500
b = 25
From (4), obtain
c = 150 - 60 - 25 = 65
Answer:
A. The length of the leg fenced with wood is 60 yd.
B. The length of the leg fenced with steel is 25 yd.
Answer:
42
Step-by-step explanation:
Use LCM of 6 and 7 to find a number that is the same:
6 12 18 24 30 36 42
7 14 21 28 35 42
Since 42 shows up in both, the 42th voter gets a button and sticker.
Hope this helped.
Answer:
25.12 in^3.
Step-by-step explanation:
Volume of the cylinder = 3.14 * r^2 * h
= 3.14 * 2^2 * 8
The volume of the preserve
= 1/4 * 3.14 * 4 * 8
= 25.12 in^3.