For this specific question, we need to formulate an equation that accurately reflects the provided data concerning the diameters of specific circles. From the information given, the first term is 2.5 cm, and the difference between the first two terms is 0.6 cm. This same difference applies to the following terms, indicating that the sequence is arithmetic, with the first term as 2.5 cm and a common difference of 0.6 cm. Based on the variables specified in this problem, the equation representing the given sequence is: f(n) = 2.5 + (n - 1)(0.6).
The equations we work with are f(x)=4x-3 and g(x)=x³-x²-4x+4. The intersections of these functions occur at f(x)=g(x). Using graphing technology, the figures are displayed in the attached image; the solutions to the equations are approximate values: x=-2.781, which rounds to -2.8, x=0.862 rounds to about 0.9, and x=2.919 rounds to 2.9.
Let’s break it down:
The nine-digit number is structured as nnn,nnn,nnn
To be divisible by 100, the final two digits must be 00
In the hundred thousands position, the digit is 7
The digit in the millions place must be an even and prime number, which is 2(the only even prime)In the hundreds place, the digit is 0 (the freezing point of water at 0 °C)
The ten millions place digit is three times that of the millions position, which is 6(calculated as 2x3)
And in the thousands place, the digit is 8 (equivalent to 8 fluid ounces per cup)
Finally, the hundred millions position is 1 (the only number that divides evenly into every number)
Thus, the number is 162,708,000
