<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:
6.5 square units
Step-by-step explanation:
There are MANY ways to do this problem, most of them involving breaking it into 3 or four shapes. But this one is easier if you do most of it by taking out the squares and half squares.
Squares - 3
Half squares - 4 (totals 2 squares)
Triangle - 1 - 1/2bh = 1/2x1x3 = 1.5
TOTAL = 3+2+1.5=6.5
Answer:
= 1.75
Step-by-step explanation:
7/6 divided by 6
= 7/36
7/36 = x/9
Cross multiply fractions:
36x = 63
Divide each side by 36:
x = 7/4 or 1.75
Answer:
The answer is 3
Step-by-step explanation:
I used the equation y/x. (Use the differences between two rows.)
Answer:
2
Use the prime factorization:
7 * 5 * 1 = 35
7 * 5 * 2 = 70
