<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: A. 30+(-12)+70
Step-by-step explanation:
Commutative property of addition is given by : a+b = b+a , where a and b can be any expression of real numbers.
It basically changes the order of the so that simplification of any expression becomes easier.
In A. we use this property as
30+(-12)+70 = 30+[(-12)+70]
= 30 + [70+(-12)] [we switched order of (-12) and 17]
= 30+70-12
= 100-12
= 88
The rest of the expression already arranged accordingly, there is no need to apply commutative property to change the order of the numbers.
So the correct option is A. 30+(-12)+70.
Area of smaller triangle:
Area of larger triangle:
Area of inner rectangle:
Total area:
I believe the next three terms are -20, -26, -32 if it goes down by 6
she drove 40 mph & 60 mph
60 +40 = 100
100/2 = 50
so she drove an average of 50 mph
