Answer:
C. 1.214
Step-by-step explanation:
P(t) = 2 + 5 tan⁻¹(t/2)
When P(t) = 6, the value of t is:
6 = 2 + 5 tan⁻¹(t/2)
4 = 5 tan⁻¹(t/2)
4/5 = tan⁻¹(t/2)
tan(4/5) = t/2
t = 2 tan(4/5)
t ≈ 2.059
The instantaneous rate of change of P(t) is dP/dt:
dP/dt = 5 / (1 + (t/2)²) × 1/2
dP/dt = 5 / (1 + t²/4) × 1/2
dP/dt = 20 / (4 + t²) × 1/2
dP/dt = 10 / (4 + t²)
At t = 2.059:
dP/dt ≈ 1.214
Here's a graph:
desmos.com/calculator/7leerprg4i
Answer:
Step-by-step explanation:
c=1/4(A-3c)
4c = A-3c
7c = A
c = A/7
One is 25/20,another one is 20/16
Y = 15
180 = 142 + 2y + 8
180 = 150 + 2y
30 = 2y
y = 15
x = 30.5
142 = 4x + 20
122 = 4x
x = 30.5
<span>The perimeter of the area is the length of the fence.
Perimeter = x + y + y. This can be simplified to
Perimeter = x + 2y. You're told that the rancher has 100 m of fence, so the perimeter is 100 m:
100 = x + 2y (1)
The area of a rectangle is given by the formula A = length * width. The length in this case is x, and the width is y.
So, A = xy.
Solve equation (1) for y. Once you find the expression to which y equals, plug that for y into A = xy.
100 = x + 2y. Solve for y by subtracting both sides by x:
100 - x = 2y. Divide both sides by 2:
(100 - x)/2 = y
Substitute (100 - x)/2 for y into A = xy:
A = x[(100 - x)/2]
A = [x(100 - x)]/2
You can rewrite this as (100x - x²)/2 or 50x - (x²/2) or 50x - (1/2x²).
Hope that helped!</span>