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2 years ago

HELP PLEASE!!!

Mathematics

2 answers:

Marina CMI [18]2 years ago

8 0

Answer:

The maximum profit of $ 10277.32____ can be made when the selling price of the dog food is set to $ _34___ per bag.

Step-by-step explanation:

Profit = Revenue - Cost

P(x) = R(x) -C(x)

= -31.72x^2 + 2,030x -( -126.96x + 26,391)

Distribute the minus sign

= -31.72x^2 + 2,030x+126.96x - 26,391

Combine like terms

= -31.72 x^2 + 2156.96 x - 26391

This is a parabola. It is facing downwards. The maximum profits is at the vertex ( where the max is)

vertex = h = -b/2a = -(2156.96)/(2*-31.72) = -2156.96/-63.44=34

Evaluate P(x) at x=34 to determine the profit

P(34) = -31.72 (34)^2 + 2156.96 (34) - 26391

-36668.32+73336.64-26391

10277.32

Luba_88 [7]2 years ago

5 0

Answer:

Max profit is: $10,277.32

Selling price: $951.52

Step-by-step explanation:

Profit = Revenue - Cost

Profit = (-31.72x² + 2,030x) - (-126.96x + 26,391)

Profit = -31.72x² + 2156.96x - 26391

= -31.72(x² - 68x + 34² - 34²) - 26391

= -31.72(x² - 2(34)(x) + 34²) + 31.72(34²) - 26391

= -31.72(x - 34)² + 10277.32

Max profit is: $10,277.32

When x = 34

Revenue = -31.72(34²) + 2030(34)

= 32351.68 for 34 bags

Per bag:

32351.68/34

$951.52

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Write in terms of inequalities: (-13,4]

anzhelika [568]

9514 1404 393

Answer:

-13 < x ≤ 4

Step-by-step explanation:

The round bracket means the lower limit is not included in the interval. The square bracket means the upper limit is included.

-13 < x ≤ 4

8 0

2 years ago

Determine all prime numbers a, b and c for which the expression a ^ 2 + b ^ 2 + c ^ 2 - 1 is a perfect square .

kogti [31]

Answer:

The family of all prime numbers such that $a^{2} + b^{2} + c^{2} -1$ is a perfect square is represented by the following solution:

$a$ is an arbitrary prime number. (1)

$b = \sqrt{1 + 2\cdot a \cdot c}$ (2)

$c$ is another arbitrary prime number. (3)

Step-by-step explanation:

From Algebra we know that a second order polynomial is a perfect square if and only if $(x+y)^{2} = x^{2} + 2\cdot x\cdot y + y^{2}$ . From statement, we must fulfill the following identity:

$a^{2} + b^{2} + c^{2} - 1 = x^{2} + 2\cdot x\cdot y + y^{2}$

By Associative and Commutative properties, we can reorganize the expression as follows:

$a^{2} + (b^{2}-1) + c^{2} = x^{2} + 2\cdot x \cdot y + y^{2}$ (1)

Then, we have the following system of equations:

$x = a$ (2)

$(b^{2}-1) = 2\cdot x\cdot y$ (3)

$y = c$ (4)

By (2) and (4) in (3), we have the following expression:

$(b^{2} - 1) = 2\cdot a \cdot c$

$b^{2} = 1 + 2\cdot a \cdot c$

$b = \sqrt{1 + 2\cdot a\cdot c}$

From Number Theory, we remember that a number is prime if and only if is divisible both by 1 and by itself. Then, $a, b, c > 1$ . If $a$ , $b$ and $c$ are prime numbers, then $2\cdot a\cdot c$ must be an even composite number, which means that $a$ and $c$ can be either both odd numbers or a even number and a odd number. In the family of prime numbers, the only even number is 2.

In addition, $b$ must be a natural number, which means that:

$1 + 2\cdot a\cdot c \ge 4$

$2\cdot a \cdot c \ge 3$

$a\cdot c \ge \frac{3}{2}$

But the lowest possible product made by two prime numbers is $2^{2} = 4$ . Hence, $a\cdot c \ge 4$ .

The family of all prime numbers such that $a^{2} + b^{2} + c^{2} -1$ is a perfect square is represented by the following solution:

$a$ is an arbitrary prime number. (1)

$b = \sqrt{1 + 2\cdot a \cdot c}$ (2)

$c$ is another arbitrary prime number. (3)

Example: $a = 2$ , $c = 2$

$b = \sqrt{1 + 2\cdot (2)\cdot (2)}$

$b = 3$

4 0

2 years ago

Find the equation of the plane z = mx + ny + b which contains the points (0,0,6), (1,0,-3) and (0,2,5).

leonid [27]

The three points give you three equations, which you can solve by your favorite method.
.. 0m +0n +b = 6
.. 1m +0n +b = -3
.. 0m +2n +b = 5

(m, n, b) = (-9, -1/2, 6)
so the equation of the plane can be written as
.. z = -9x -1/2y +6

_____
In standard form, this would be
.. 18x +y +2z = 12