The weekly volume (in liters) of milk produced in a farm is given by v(x)=x3+21x2-1480x, where x is the number of cows. Find the number of cows that corresponds to a total production of 1500 liters of milk in a week

30 cows

Step-by-step explanation:

The given parameters are;

v(x) = x³ + 21·x² - 1480·x

Where x = The number of cows

V(x) = The weekly volume (in liters) of milk produced

The number of cows that corresponds to a total production of 1500 liters of milk in a week is given as follows;

1,500 = x³ + 21·x² - 1480·x

x³ + 21·x² - 1480·x = 1,500

x³ + 21·x² - 1480·x - 1,500 = 0

x³ + 21·x² - 1480·x - 1,500 = 0

We observe that x = -1 is a solution of the above equation, as follows;

(-1)³ + 21·(-1)² - 1480·(-1) - 1,500 = 0

Therefore, (x + 1) is a factor of x³ + 21·x² - 1480·x - 1,500, which by long division gives;

  x² + 20·x - 1500

(x³ + 21·x² - 1480·x - 1,500)/(x + 1)

        x³ + x²

           20·x² - 1480·x - 1500

           20·x² + 20·x        

                       -1500·x - 1500

                      -1500·x - 1500

Therefore, the other factors is x² + 20·x - 1500, which gives;;

x² + 20·x - 1500 = (x - 30) × (x + 50)

Therefore;

x³ + 21·x² - 1480·x - 1,500 = 0

Which gives;

(x - 30) × (x + 50) × (x + 1) = 0

The solutions are x = 30, or x = -50, or x = -1

Therefore, the only possible solution is the number of cows = x = 30 cows.

answer: sorry i can't you.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.