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Slav-nsk [51]
2 years ago
5

two positive numbers x and y, with the maximum value 4, add up to 5. what is the difference between the maximum and minimum valu

e of the product x2y3

Mathematics
1 answer:
Svetach [21]2 years ago
5 0

Answer:

  92

Step-by-step explanation:

Since the sum of the two numbers is 5, we can represent one of them by x and the other by 5-x. Then the desired product is ...

  x²(5-x)³

A graphing calculator can show the extreme values of this on the interval 1 ≤ x ≤ 4. The maximum is 108 at x=2; the minimum is 16 at x=4.

The difference between the maximum and minimum is 108-16 = 92.

_____

If you like, you can take the derivative and set it to zero.

  f(x) = x²(5 -x)³

  f'(x) = 2x(5 -x)³ +x²(-3)(5-x)² = x(5 -x)²(2(5-x) -3x)

  f'(x) = 5x(5-x)²(2-x)

This will be zero for x=0, x=5, and x=2. The points at x=0 and x=5 represent minima in the product. The values x=0 and x=5 are not in the domain of interest. The point at x=2 represents a maximum.

To find the function extremes on an interval, we need to evaluate the function where the derivative is zero, and also at the ends of the interval. So, the function values of interest are ...

  f(1) = 1²·4³ = 64

  f(2) = 2²·3³ = 108 . . . . product maximum

  f(4) = 4²·1³ = 16 . . . . . . product minimum

The difference between the maximum and minimum is 92.

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7.
Agata [3.3K]

Answers:

  • prime number = {2,3,5}
  • composite number = {4,6}
  • number less than four = {1,2,3}
  • number more than or equal to three = {3,4,5,6}

====================================================

Explanation:

The list of all possible outcomes on a single standard die is {1,2,3,4,5,6}. The curly braces indicate set notation.

A prime number is a number where its only factors are 1 and itself. The value 1 is not prime, and it's not composite either.

Something like 3 is prime because its only factors are 1 and 3. Something like 4 is composite because 4 = 2*2. A composite value has factors other than 1 and itself.

Parts (iii) and (iv) are fairly straight forward. You simply list items less than four for part (iii) and you list items that are three or greater for part (iv).

5 0
3 years ago
Two decimals that are equivalent to 3.200
AleksAgata [21]

Answer:

Two or more decimal numbers are said to be equivalent decimals, when they name the same value (or same amount). For example, the decimals: 0.2 = 0.20 = 0.200 = 0.2000 etc. Thus by successive addition of zeros after the decimal part of the number after the decimal point means the same number and hence are equivalent. Therefore, the decimals: 5.3, 5.30, 5.300, 5.3000 etc are all equivalent.

Step-by-step explanation:

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5 0
2 years ago
Solve: (a)(9a + 4) = 0.
Monica [59]

Answer:

a = -4/9

Step-by-step explanation:

(9a + 4) = 0

Subtract 4 from each side

9a + 4-4 = 0-4

9a = -4

Divide each side by 9

9a/9 = -4/9

a = -4/9

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