If 0.4 kg cost 4. 0 dollar
than 1.kg will cost x dollar
x = (1 * 4)/0.4 = 10 dollars
1 kg tomatoes cost 10 dollars
The answer is 51 (not sure of the measurement unit). Assuming you mean the football hits the ground when it's kicked and lands somewhere downfield, y would be 0 (y means height from the ground, and if something is on the ground, it has no height. Hence, the 0). Set the equation equal to 0 and factor to solve for x. 0 = -.03x(x-51). 0 = -.03x and x = 0, or 0 = x-51 and x = 51
◉ 
Before performing any calculation it's good to recall a few properties of integrals:
So we apply the first property in the first expression given by the question:
![\small \sf{\longrightarrow\int ^3_{-2} [2f(x) +2]dx= 2 \int ^3 _{-2} f(x) dx+ \int f^3 _{2} 2dx=18}](https://tex.z-dn.net/?f=%5Csmall%20%5Csf%7B%5Clongrightarrow%5Cint%20%5E3_%7B-2%7D%20%5B2f%28x%29%20%2B2%5Ddx%3D%202%20%5Cint%20%5E3%20_%7B-2%7D%20f%28x%29%20dx%2B%20%5Cint%20f%5E3%20_%7B2%7D%202dx%3D18%7D)
And we solve the second integral:
Then we take the last equation and we subtract 10 from both sides:
And we divide both sides by 2:
Then we apply the second property to this integral:
Then we use the other equality in the question and we get:
We substract 8 from both sides:
• 
follows from the fact that the cosine function is
-periodic, which means
. Roughly speaking, this is the same as saying that a point on a circle is the same as the point you get by completing a full revolution around the circle (i.e. add
to the original point's angle with respect to the horizontal axis).
If you make another complete revolution (so we're effectively adding
) we get the same result:
. This is true for any number of complete revolutions, so that this pattern holds for any even multiple of
added to the argument. Therefore
for any integer
.
Next, because
, it follows that
is also true for any integer
. So we have
The rest follows from considering either case and solving for
.
