Detailed derivation:
dA/dt = 6 - 0.02A
dA/dt = -0.02 (A - 300)
Rearranging terms.
dA / (A - 300) = -0.02 dt
Integrate both sides.
ln(A - 300) = -0.02t + C
Isolate A.
A - 300 = Ce^(-0.02t)
A = 300 + Ce^(-0.02t)
Apply initial condition to determine C.
50 = 300 + Ce^(-0.02 × 10)
50 = 300 + Ce^(-0.2)
-250 = Ce^(-0.2)
C = -250e^(0.2)
A = 300 - 250e^(0.2)e^(-0.02t)
A = 300 - 250e^(0.2 - 0.02t)
The equation Y - (-8) = -6 (x-2) is accurate, but the rest are not.
This simplifies to y + 8 = -6x + 12.
Then, applying the subtraction of 8 yields y = -6x + 4, which is the correct slope-intercept form.
The train descends at twice the speed compared to its ascent, and it travels at 2/3 of the speed uphill relative to flat terrain.
If its speed downhill is measured at 120 miles per hour, its uphill speed would be 120 divided by 2, equaling 60 miles per hour, and its speed on flat ground would be 60 divided by (2/3), simplified to (60 times 3) divided by 2, resulting in 90 miles per hour.
Consequently, for the train to cover 45 miles on flat terrain, the time required is calculated as 45 divided by 90, which is equal to 0.5 hours, or 30 minutes.
2x^2 - y = -5
x + y = 8
----------------adding gives us
2x^2 + x = 3 <==
** It's important to note that 2x^2 and x cannot be combined, because they are not like terms.
Answer:
Area= 247 feet²
Volume= 1235 feet³
Step-by-step explanation:
The storage pod features a rectangular base measuring 19 feet by 13 feet, with a flat ceiling height of 5 feet above.
Calculating the area of the floor yields: length multiplied by width
Length = 19 feet
Width = 13 feet
Area = 19*13
Area = 247 feet²
The volume of the pod can be found by multiplying the area by the height
Height of the pod = 5 feet
Area = 247 feet²
Volume = 247*5
Volume = 1235 feet³
