<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>
I think it is fair becasue you have the chance to win more than to lose point if get 1 or 6 you dont get nothing so that not a lose
Answer:
y = 5.6
Step-by-step explanation:
Use Sine
Sine = 
Sine 45 = 
Sine of 18 is 0.309
0.309 = 
Multiply 18 on both sides
0.309 x 18 =
x 18
5.562 = y
Round to the nearest tenth:
5.562 = 5.6
Answer: 10
Step-by-step explanation:
Since integral from 1 to 4 of f(x) =10
To evaluate integral from 2 to 8 of 2 times f(2x), using substitution method
Let U = 2x, dU = 2dx, dx = dU/2
Evaluate the limit, upper limit gives dU = 2*4 = 8, lower limit gives dU = 2*1 = 2.
Since this limit are the same as the limit for the question,
Therefore, F(4) - F(1) = F(8) - F(2) = 10
Substituting dx=dU/2
Gives,
Integral from 2 to 8 of 2 times f(2x)= (1/2)(2)(F(8)-F(2)) = 10