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Bad White [126]
3 years ago
7

3x^3-2x^2-147x+98=(ax-c)(bx+d)(bx-d) where a,b,c and d positive integers. Work out the value of a,b,c and d

Mathematics
1 answer:
Alexxx [7]3 years ago
6 0

Expand the right side:

(ax-c)(bx+d)(bx-d)=(ax-c)(b^2x^2-d^2)

=ab^2x^3-b^2cx^2-ad^2x+cd^2

Notice that 98 = 2 * 7 * 7, so we have c=2 and d=7.

Then

-ad^2=-147\implies a=\dfrac{147}{49}=3

and

ab^2=3\implies b^2=1\implies b=1

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Jeremy wants to construct an open box from an 18-inch square piece of aluminum. He plans to cut equal squares, with sides of x i
serious [3.7K]

a.

The volume of the box V = 4x³ - 72x² + 324x

Since the dimensions of the square piece of paper are 18 inches each, and we cut out a length x from each side to give a total length of 2x cut from each side. So, each dimension is L = 18 - 2x.

Since the height of the open box is x and its base is a square, the volume of the open box ix V = L²x

= (18 - 2x)²x

= (324 - 72x + 4x²)x

= 324x - 72x² + 4x³

The volume of the box V = 4x³ - 72x² + 324x

b.

The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.

  • the length of the box, L = 12 inches,
  • the width of the box = 12 inches
  • and the height of the box, x = 3 inches.

Since the volume of the box is 432 cubic inches,

V = 324x - 72x² + 4x³

324x - 72x² + 4x³ = 432

4x³  - 72x² + 324x - 432 = 0

x³  - 18x² + 81x - 108 = 0

A factor of the expression is x - 3

So, x³  - 18x² + 81x - 108 ÷ x - 3 = x² - 15x + 36

So,  x³  - 18x² + 81x - 108 = (x² - 15x + 36)(x - 3) = 0

Factorizing the expression x² - 15x + 36 = 0

x² - 3x - 12x + 36 = 0

x(x - 3) - 12(x - 3) = 0

(x - 3)(x - 12) = 0

So,  x³  - 18x² + 81x - 108 = (x - 3)(x - 3)(x - 12) = 0

So, (x - 3)²(x - 12) = 0

(x - 3)² = 0 and (x - 12) = 0

x - 3 = √0 and x - 12 = 0

x - 3 = 0 and x - 12 = 0

x = 3 twice and x = 12

Since x = 3 is the minimum value, the minimum value of x = 3.

Since the length of the box, L = 18 - 2x

= 18 - 2(3)

= 18 - 6

= 12 inches

The width of the box = L = 12 inches

The height of the box = x = 3 inches.

So,

The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.

  • the length of the box, L = 12 inches,
  • the width of the box = 12 inches
  • and the height of the box, x = 3 inches.

Learn more about volume of a box here:

brainly.com/question/13309609

6 0
2 years ago
How do you estimate the quotient of 6.1 divided by 8
Alisiya [41]
Detecting...
<span>
</span>Your answer would be:
0.7625



8 0
3 years ago
Read 2 more answers
Have a wonderful day and here are free pts to make your day better &lt;3<br> 12 x 7 = ?
Rom4ik [11]

Answer:

its 84 but tysm thats so sweet

Step-by-step explanation:

4 0
3 years ago
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(x−3)÷9=11<br> help idk how to do this
Bess [88]

Answer:

102

Step-by-step explanation:

papa math will help you

x−3

9

=11

Step 1: Multiply both sides by 9.

x−3

9

=11

(

x−3

9

)*(9)=(11)*(9)

x−3=99

Step 2: Add 3 to both sides.

x−3+3=99+3

x=102

Answer:

x=102

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https://www.mathpapa.com/algebra-calculator.html?q=(x%E2%88%923)%5Cdiv9%3D11

x−3

9

=11

Step 1: Multiply both sides by 9.

x−3

9

=11

(

x−3

9

)*(9)=(11)*(9)

x−3=99

Step 2: Add 3 to both sides.

x−3+3=99+3

x=102

Answer:

x=102

Close Ad

Back to Algebra Calculator »

Share this page

Share URL:

https://www.mathpapa.com/algebra-calculator.html?q=(x%E2%88%923)%5Cdiv9%3D11

x−3

9

=11

Step 1: Multiply both sides by 9.

x−3

9

=11

(

x−3

9

)*(9)=(11)*(9)

x−3=99

Step 2: Add 3 to both sides.

x−3+3=99+3

x=102

Answer:

x=102

Close Ad

Back to Algebra Calculator »

Share this page

Share URL:

https://www.mathpapa.com/algebra-calculator.html?q=(x%E2%88%923)%5Cdiv9%3D11

6 0
3 years ago
Simplify using order of operations(PEMDAS):<br><br>(2^3x6)-3^2
Vladimir [108]
(2^3 \cdot 6) - 3^2=(8 \cdot 6)-9=48-9=39
8 0
3 years ago
Read 2 more answers
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