3 feet make one yard.
Multiplying 3 by 10 gives 30 feet.
Dividing 30 by 7 gives approximately 4.2.
Answer: 4 ropes can be cut.
Since partial ropes cannot be counted, only 4 full ropes are possible.
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 shadow's length measures 96.6. To find the distance, you can use a right-angle triangle method if you know the angle of elevation. Here, (a) is the adjacent side, (b) is the hypotenuse, and (c) is the opposite side. We know that the adjacent side (a) equals 40, while the opposite side (b) is unknown. The tangent of the angle θ is given by opposite/adjacent; thus, tan 67° = opposite/40. Therefore, the opposite side equals tan 67° multiplied by 40, leading to an adjacent length of 96.6.
Based on a table of values, the outputs of f(x) for whole numbers are 0, 1, 4, 9, 16, 25, 36, and further. Meanwhile, for the same inputs, g(x) generates outputs of 1, 2, 4, 8, 16, 32, and 64. It is evident that g(x) consistently doubles its outputs, leading to numbers that surpass those produced by f(x). The exponential function, g(x), experiences a constant multiplicative change rate, allowing it to accelerate more quickly compared to the quadratic function.
(ed. just click all of them)
