The general form of a solution of the differential equation is already provided for us:
where 
. We now want to find a solution 
such that 
and 
. Therefore, all we need to do is find the constants 
and 
that satisfy the initial conditions. For the first condition, we have:
For the second condition, we need to find the derivative 
first. In this case, we have:
Therefore:
This means that we must solve the following system of equations:
If we add the equations above, we get:
If we now substitute 
into either of the equations in the system, we get:
This means that the solution obeying the initial conditions is:
Indeed, we can see that:
which do correspond to the desired initial conditions.
Answer:
−72x
Step-by-step explanation:
Answer:
Onaje is correct.
Step-by-step explanation:
To start, total up how many shirts we have, and multiply them by <em>t</em>. Since they are the same price, we now have a total for how many shirts they bought. This proves the second and third equations that they wrote. If you take the easy way and just add them, you'll still have 25<em>t</em>, making Onaje's expression correct.
EDIT: Just saw you need why it's incorrect for Paula, just hold on.
So for Paula, it's simple why she is incorrect. If you look at the third equation she wrote, she's adding 25 to 2t, which is completely incorrect, and will come up with a different result than 16t + 9t.
Hope this helps.
Answer:
Step-by-step explanation:
The triangle would end up back where it started. It is hard to explain without a graph. If you have graph paper, you might want to try drawing this out. Say that the original points are at A (1,2) B (2,0) and C(0,0). Now, when we reflect the points over the x axis, they will be the same distance below the x that the points original were about the x axis. Since A was 2 units above the axis, it will now be 2 units below at (1, -2). Points B and C will stay on the x axis and will remain in place at B(2.0) and C(0,0). Since these points are on the line, they were not above the x axis, so they will now not be below the x axis.
Now, we are going to reflect the triangle over the y axis. Since C (0,0) is already on the y axis, it will not move. It will remain there. Since B(2,1) is two units to the right of the y axis, when we flip it, it will now be 2 units to the left of the y axis B (-2,0). Point C will move one unit to the left of the y axis to become (-1,2).
The last thing left it to rotate this final triangle 180 degrees. Since a circle is 360 degrees and 180 is half of a circle, it does not matter if we rotate clockwise or counter-clockwise. If you could trace our new triangle and put a plus sign at the origin (0,0). You would put your pencil on the origin and rotate the two turns at the plus sign. This would put your triangle right back to the beginning. So the original value of B would be the same. In this case C ((2,0)
Answer:
9000
Step-by-step explanation:
SI=PRT/100
P=SI 100/RT
=[ 1800×100]÷ 20
= 180000÷20
= 9000
