<span>3down votefavoriteFind the area between the circles <span><span><span>x2</span>+<span>y2</span>=4</span><span><span>x2</span>+<span>y2</span>=4</span></span> and <span><span><span>x2</span>+<span>y2</span>=6x</span><span><span>x2</span>+<span>y2</span>=6x</span></span> using polar coordinates.I have found that the equation of the first circle, call it <span><span>C1</span><span>C1</span></span>, is <span><span>r=2</span><span>r=2</span></span> on the other hand, for <span><span>C2</span><span>C2</span></span>, I get that its equation is <span><span>r=6cosθ</span><span>r=6cosθ</span></span>. Then, to find the bounds of integration, I have found that their angle of intersection should be <span><span>θ=arccos(1/3)</span><span>θ=arccos(1/3)</span></span> and <span><span>θ=−arccos(1/3)</span><span>θ=−arccos(1/3)</span></span>. Then, to set up the double integral:<span><span>A=<span><span>∫<span>arccos(1/3)</span><span>−arccos(1/3)</span></span><span><span>∫2<span>6cosθ</span></span>rdrdθ</span></span></span><span>A=<span><span>∫<span>−arccos(1/3)</span><span>arccos(1/3)</span></span><span><span>∫<span>6cosθ</span>2</span>rdrdθ</span></span></span></span>However, when evaluating this integral with the calculator, I get a negative value. What would be the problem in this case? Thanks in advance for your help.</span>
Answer:
Step-by-step explanation:
12
rs st tw rt rw sw
13
sr sw tr st tw
14
tr and tw
sr and st
I'll depend on you to add the proper markings on the answer.
Answer: −1−3k
Step-by-step explanation:
Distribute:
(−3+4k)−1(−2+7k)
(-3+4k)+{2-7k}
Eliminate redundant parentheses:
(−3+4k)+2−7k
-3+4k+2-7k
Add the numbers:
−3+4k+2−7k
−1+4k−7k
Add the same term to both sides of the equation:
−1+4k−7k
−1−3k
It is important to understand the meaning of orthocenter in respect to a triangle first. Ii is actually the intersection of all the altitudes within a triangle. The altitudes can be drawn from an angle to the opposite side but the line should create a right angle with the side of the triangle. In case of obtuse triangle, the three lines would meet outside the triangle. I hope the answer helps.
Answers:
1. 74856 + 1489
= 76345
2. 42000/5
= 8400
3. 142100/10
= 14210
4. 2500 + (8-5)
2500 + 3
= 2503
5. 385 + (29 - 9)
385 + 20
= 405
6. 1780 - 643
= 1137
7. 4 x 2 + 30 / 5
4 x 2 + 6
8 + 6
= 14
8. 65743 - 754
= 64989
