Answer:
y = 
Step-by-step explanation:
If the equation of a function is in the form of y = h(x)
When the graph of this function is reflected across x-axis,
Transformed function will be,
y = -h(x)
Further reflected across y-axis, then the transformed function will be,
y = -h(-x)
By this rule,
Given equation when reflected across x-axis,
y = 
Further reflected across y-axis,
y = 
y = 
y =
Answer: 54678 years
Step-by-step explanation:
This can be solved by the following equation:
(1)
Where:
is the quantity of atoms of carbon-14 left after time 
is the initial quantity of atoms of C-14 in the mammal hide
is the rate constant for carbon-14 radioactive decay
is the time elapsed
On the other hand, has a relation with the half life 
of the C-14, which is 
:
(2)
Substituting (2) in (1):
(3)
Applying natural logarithm on both sides of the equation:
(4)
(5)
Isolating :
(6)
(7) This is the age of the mammal hide
Slope intercept form
y = mx+b
y = -7x + 9
m = -7
Refer to the figure shown below.
x = the width of the rectangle (meters)
y = the height of the rectangle (meters(
The fencing for the perimeter of the rectangle costs $30 per meter.
The two inner partitions cost $25 per meter.
The total cost of the fencing is
C = 2(x+y)*$30 + 2y*$25
= 60(x+y) + 50y
= 60x + 110y
Because the amount available to spend is $600, therefore
60x + 110y = 6000
or
6x + 11y = 600
That is,
y = (600 - 6x)/11 (1)
The area is
A = x*y (2)
Substitute (1) into (2).
A = (x/11)*(600 - 6x) = (1/11)*(600x - 6x²)
To maximize A, the derivative of A with respect to x is zero.
That is,
600 - 12x = 0
x = 600/12 = 50
From (1), obtain
y = (1/11)*(600 - 6*50) = 300/11 = 27.273
Because the second derivative of A with respect to x is negative, x=50, y = 27.273 will yield the maximum area.
The maximum area is
50*27.273 = 1363.64 m² = 1364 m² (nearest integer)
Answer: 1364 m² (nearest integer)
