ANSWER
EXPLANATION
From the graph, the coordinates of Y are:
We want to find the image of this point after a dilation by a scale factor of -½ about the origin.
The rule for the dilation is :
To find the coordinates of Y', we plug the coordinates of Y.
The first choice is correct.
This is a linear differential equation of first order. Solve this by integrating the coefficient of the y term and then raising e to the integrated coefficient to find the integrating factor, i.e. the integrating factor for this problem is e^(6x).
<span>Multiplying both sides of the equation by the integrating factor: </span>
<span>(y')e^(6x) + 6ye^(6x) = e^(12x) </span>
<span>The left side is the derivative of ye^(6x), hence </span>
<span>d/dx[ye^(6x)] = e^(12x) </span>
<span>Integrating </span>
<span>ye^(6x) = (1/12)e^(12x) + c where c is a constant </span>
<span>y = (1/12)e^(6x) + ce^(-6x) </span>
<span>Use the initial condition y(0)=-8 to find c: </span>
<span>-8 = (1/12) + c </span>
<span>c=-97/12 </span>
<span>Hence </span>
<span>y = (1/12)e^(6x) - (97/12)e^(-6x)</span>
Answer:
84%
Step-by-step explanation:
What we must do is calculate the z value for each value and thus find what percentage each represents and the subtraction would be the percentage between those two values.
We have that z is equal to:
z = (x - m) / (sd)
x is the value to evaluate, m the mean, sd the standard deviation
So for 190000 we have:
z = (190000 - 200000) / (10000)
z = -1
and this value represents 0.1587
for 230000 we have:
z = (230000 - 200000) / (10000)
z = 3
and this value represents 0.9987
we subtract:
0.9987 - 0.1587 = 0.84
Which means that it represents 84% of the houses
A^2 + 16^2 = 20^2
(Third one)
The answer is the point of intersection, (2,1)