Answer:
y(x) = 7e^(5x)
Step-by-step explanation:
The question says that the slope of the curve at every point P is five times the y-coordinate of P. This means that
dy/dx = 5y
Refer to solutions of differential equations, dy/dt = ky, being in the form of y(t) = y(0) e^(kt)
Using the above stated law now, we can relate to our equation, saying that
y(x) = y(0) e^(5x)
The point given from the question is, (0, 7). This also means that y(0) = 7. So finally, we can have
y(x) = 7e^(5x)
And that is our needed equation of the curve
Solution
write the division as a fraction = 12y^4-4y^3 - 6y^2 + 36y - 22 over y-3 multiplied by r over y-3
r ×(2y^4 - 4y^3- 16y^2 + 36y- 22) over (y-3)^2
2ry^4 - 4ry^3 - 16ry^2 + 36ry - 22r over (y-3)^2
C: B:
3 0
6 9
9 18
12 27
All you had to do was plug in the value for c or b and solve. You can tell this is most likely correct because you see patterns for both variables. C is going up by threes, while b is going up by nines.
Similarities: They both are polynomials of degree 2, both of their graphs is a parabola, both have either 2 or 0 real solutions, they are both continuous functions over R
<span>(DOS= difference of two squares, PST=perfect square trinomial </span>
<span>Differences: PST has three terms, whereas the difference of squares has 2. PST's factors are both the same, whereas DOS's elements are conjugates of each other. DOS can always be factored into two distinct polynomials with rational coefficients, whereas PST has two same polynomial factors.</span>
