Answer:
The country's population for the year 2030 is 368.8 million.
Step-by-step explanation:
The differential equation is:
Integrate the differential equation to determine the equation of P in terms of <em>t</em> as follows:
![\int\limits {\frac{1}{P(600-P)} } \, dP =k\int\limits {1} \, dt \\(\frac{1}{600} )[(\int\limits {\frac{1}{P} } \, dP) - (\int\limits {\frac{}{600-P} } \, dP)]=k\int\limits {1} \, dt\\\ln P-\ln (600-P)=600kt+C\\\ln (\frac{P}{600-P} )=600kt+C\\\frac{P}{600-P} = Ce^{600kt}](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7B%5Cfrac%7B1%7D%7BP%28600-P%29%7D%20%7D%20%5C%2C%20dP%20%3Dk%5Cint%5Climits%20%7B1%7D%20%5C%2C%20dt%20%5C%5C%28%5Cfrac%7B1%7D%7B600%7D%20%29%5B%28%5Cint%5Climits%20%7B%5Cfrac%7B1%7D%7BP%7D%20%7D%20%5C%2C%20dP%29%20-%20%28%5Cint%5Climits%20%7B%5Cfrac%7B%7D%7B600-P%7D%20%7D%20%5C%2C%20dP%29%5D%3Dk%5Cint%5Climits%20%7B1%7D%20%5C%2C%20dt%5C%5C%5Cln%20P-%5Cln%20%28600-P%29%3D600kt%2BC%5C%5C%5Cln%20%28%5Cfrac%7BP%7D%7B600-P%7D%20%29%3D600kt%2BC%5C%5C%5Cfrac%7BP%7D%7B600-P%7D%20%3D%20Ce%5E%7B600kt%7D)
At <em>t</em> = 0 the value of <em>P</em> is 300 million.
Determine the value of constant C as follows:
It is provided that the population growth rate is 1 million per year.
Then for the year 1961, the population is: P (1) = 301
Then 
.
Determine <em>k</em> as follows:
For the year 2030, P (2030) = P (70).
Determine the value of P (70) as follows:
Thus, the country's population for the year 2030 is 368.8 million.
This makes no sense.. the question doesn’t state how much he sold. It only states what he had and how much he sold them for.
Answer:
t=11/13
Step-by-step explanation:
Answer:
Imagine an easier version of this problem: You have a board 5 feet long that you must cut (divide, right?) into two equal parts. It is probably clear to you that you simply divide the length (5) by the number of parts you're dividing it into (2) to obtain the length of each piece (2.5 feet).
Use the same method for your problem 5 feet divided by 6 is 0.83 feet per piece.
We do not ordinarily divide feet into decimal portions, but instead into inches. Since an inch is 1/12 of a foot, you could simply say 5/6 = how many twelfths? or 5/6 = n/12 Solve this by inspection or by cross multiplying 5 times 12 equals n times 6. So n must equal 10, and your pieces of board are each 10 inches long.
Answer:
Step-by-step explanation:
Considering the polynomial 2x⁵ + 4x³ - 3x⁸. The polynomial is not yet in standard form. For a polynomial to be in standard form, the power of the variables must decrease as we progress to the right of the expression.
A) The polynomial in standard form is therefore<u> - 3x⁸ + 2x⁵ + 4x³</u>. <em>We can see that the power are reducing as we move through each terms i.e from 8 to 5 then to 3.</em>
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B) The degree of a polynomial is the maximum degree among all the terms of the polynomial. The term that has the maximum degree is -3x⁸. Hence, the degree of the polynomial is 8
C) There are only 3 terms in the polynomial given. The terms are separated by mathematical signs. The terms if the polynomial are 2x⁵, 4x³ and - 3x⁸.
D) The leading term of the polynomial is the term that comes first after rewriting the polynomial in standard format. Given the standard from of the polynomial given as -3x⁸ + 2x⁵ + 4x³, the leading term will be - 3x⁸
E) Given the leading term to be - 3x⁸, the leading coefficient of the polynomial will be the coefficient of the leading term. The coefficient of -3x⁸ is -3
