The given equations are

(1)

(2)
When t=0, obtain

Obtain derivatives of (1) and find x'(0).
x' (t+1) + x - 4√x - 4t*[(1/2)*1/√x = 0
x' (t+1) + x - 4√x -27/√x = 0
When t=0, obtain
x'(0) + x(0) - 4√x(0) = 0
x'(0) + 9 - 4*3 = 0
x'(0) = 3
Here, x' means

.
Obtain the derivative of (2) and find y'(0).
2y' + 4*(3/2)*(√y)*(y') = 3t² + 1
When t=0, obtain
2y'(0) +6√y(0) * y'(0) = 1
2y'(0) = 1
y'(0) = 1/2.
Here, y' means

.
Because

, obtain

Answer:
The slope of the curve at t=0 is 1/6.
Thw answer is -51
Found through long division
Set
f
(
x
)
=
0
f(x)=0.
If the polynomial function is not given in factored form:
Factor out any common monomial factors.
Factor any factorable binomials or trinomials.
Set each factor equal to zero and solve to find the
x
x- intercepts.
The length is 13 and the width is 6. The way I figured it out is: find two factors of the area (that if multiplied with each other, they equal the area) and see which ones add up and then get multiplied by two to find the perimeter. I found 6 and 13 and then added them together to get 19. Then I multiplied 19 by two and got 38. This is how I have always done it idk.
Your answer is length = 13 and width = 6.
hope this helps :)
74233 + 58490 = 132723
74233 increased by 58490 is 132723