By Green's theorem,
where 
is the circle 
and 
is the interior of , or the disk 
.
Convert to polar coordinates, taking
Then the work done by 
on the particle is
Vertex form formula: y = a(x-h)^2 +k, with vertex (h,k)
There are multiple ways to find the vertex. One way is to find the roots and then find the x value exactly in between them, because this parabola is symmetrical.
0 = (x - 3)(x + 2), so x = 3 and -2. The point directly in the middle is x = 1/2 = h
To find the y value of the vertex, plug in 1/2 to the equation.
(1/2)^2 - 2(1/2) + 5 = 4.25 = k
y = (x - 0.5)^2 + 4.25
Answer:
Step-by-step explanation:
p=sec0+tan0
=1/cos0 + sin0/cos0
=(1+sin0)/cos0
square both sides
(1+sin)^2 /cos^2 = p^2
(1+sin)^2/(1 - sin^2 ) = p^2
(1+sin)^2/((1-sin)(1+sin)) = p^2
(1+sin)/(1-sin)=p^2
1+sin=p^2-p^sin
sin+p^2sin=p^2-1
sin(1+p^2)=(p^2-1)
sin=(1-p^2)/(1+p^2)
cosec=1/sin
=(1+p^2)/(1-p^2)
<u></u><u>The correct answer is 47.5%, or 0.475.</u>
Explanation:
The empirical rule states that in any normal distribution:
68% of data will fall within 1 standard deviation of the mean;
95% of data will fall within 2 standard deviations of the mean; and
99.7% of data will fall within 3 standard deviations of the mean.
The mean is 500 and the standard deviation is 100. This means that 700 is 2 standard deviations away from the mean:
(700-500)/100=200/100=2.
We know that 95% of data will fall within 2 standard deviations from the mean. However, included in the 95% is data less than the mean and greater than the mean. Since we are only concerned with the scores from 500 to 700, we only want the half that is greater than the mean:
95/2 = 47.5%, or 0.475.
Answer:
Option C: 6(7 * 7)
Step-by-step explanation:
There are six faces of the cube. Since each face is 7 by 7 units, there are 6(7 *7) units total.
