Answer:
The incorrect statement is <em>A. Alpha and beta particles pose little or no hazard to human health.</em>
Step-by-step explanation:
Alpha particle - the nucleus of a helium atom, made up of two neutrons and two protons with a charge of +2. Certain radioactive nuclei emit alpha particles. Alpha particles generally carry more energy than gamma or beta particles, and deposit that energy very quickly while passing through tissue. Alpha particles can be stopped by a thin layer of light material, such as a sheet of paper, and cannot penetrate the outer, dead layer of skin. Therefore, they do not damage living tissue when outside the body. When alpha-emitting atoms are inhaled or swallowed, however, they are especially damaging because they transfer relatively large amounts of ionising energy to living cell.
Beta particles - electrons ejected from the nucleus of a decaying atom. Although they can be stopped by a thin sheet of aluminium, beta particles can penetrate the dead skin layer, potentially causing burns. They can pose a serious direct or external radiation threat and can be lethal depending on the amount received. They also pose a serious internal radiation threat if beta-emitting atoms are ingested or inhaled.
Therefore, <em>alpha and beta particles do pose affect the health of human beings.</em>
Until the concerns I raised in the comments are resolved, you can still set up the differential equation that gives the amount of salt within the tank over time. Call it
.
Then the ODE representing the change in the amount of salt over time is
and this with the initial condition
You have
![\dfrac{\mathrm d}{\mathrm dt}\left[e^{t/250}A(t)\right]=\dfrac25e^{t/250}(1+\cos t)](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dt%7D%5Cleft%5Be%5E%7Bt%2F250%7DA%28t%29%5Cright%5D%3D%5Cdfrac25e%5E%7Bt%2F250%7D%281%2B%5Ccos%20t%29)
Integrating both sides gives
Since
, you get
so the amount of salt at any given time in the tank is
The tank will never overflow, since the same amount of solution flows into the tank as it does out of the tank, so with the given conditions it's not possible to answer the question.
However, you can make some observations about end behavior. As
, the exponential term vanishes and the amount of salt in the tank will oscillate between a maximum of about 100.4 lbs and a minimum of 99.6 lbs.
(420 + 144) / 6 =
564/6 =
$ 94.....each person paid $ 94
First off, I think the equation should have a negative 9 in it originally and then you move it to the other side and it becomes positive.
You'll basically complete the square for two equations at the same time. Set it up like this:
(16x^2 + 96x) + (9y^2 - 18y) = 9
Divide everything by 16 to get the x^2 by itself, then divide everything by 9 to get y^2 by itself. You should end up with this.
(x^2 + 6x) + (y^2 - 2y) = 9/144
then complete the square by taking the second term of each polynomial, dividing by two, and squaring it.
For instance the first one will be 6/2 = 3^2 = 9
The next one will be 2/2 =1^2 = 1
Add these to numbers to the polynomials as well as to the other side of the equation to keep it equal. You should end up with this.
(x^2 + 6x+9) + (y^2 - 2y+1) = (9/144)+9+1
Then find a common denominator on the right side of the equals sign and add them all together to get:
(x^2 + 6x+9) + (y^2 - 2y+1) = 1449/144
Factor out the two polynomials
(x+3)^2 + (y-1)^2 = 1449/144
the center of the circle is (-3,1) according to the factored out polynomials and the radius will be the square root of the number on the right side of the equals sign = sqrt(1449/144) = 3.17
