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2 years ago

Divide using synthetic division: (3x^3+2x^2-32x+2)÷(x-3)

1 answer:

6 0

3x^3+2x^2-32x+2 | x-3
-----------------
-3X^3+9x^2 3x^2 +11x+1
-------------------------
/ 11x^2-32x+2
-11x^2+33x
------------------
/ x+2
-x+3
-------
/ 5
⇒ (3 x^3+2X^2-32x+2) : (x-3)= 3x^2+11x+1 rest 5

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If two circles have the same circumference what do you know about their area

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If the circumference is half of the perimeter than the area for both circles would be half of them find one circles area and half it

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3 years ago

Miranda enlarged a picture twice as shown below, each time using a scale factor of 3.

lyudmila [28]

Answer:

The area of the second enlargement is 1,944 square inches

The area of the second enlargement is (3 squared) squared times the original area.

The ratio of the area of the first enlargement to the area of the original equals the square of the scale factor

Step-by-step explanation:

<u><em>Verify each statement</em></u>

1) The area of the first enlargement is 72 square inches.

The statement is false

Because

we know that

The original dimensions of the rectangle are

length 6 inches and width 4 inches

First enlargement

Multiply the original dimensions by a scale factor of 3

$Length: 6(3)=18\ inches\\Width: 4(3)=12\ inches$

The area of the first enlargement is

$18(12)=216\ in^2$

2) The area of the second enlargement is 1,944 square inches

The statement is true

Multiply the dimensions of the first enlargement by a scale factor of 3

$Length: 18(3)=54\ inches\\Width: 12(3)=36\ inches$

The area of the second enlargement is

$54(36)=1,944\ in^2$

3) The area of the second enlargement is (3 squared) squared times the original area.

The statement is true

Because

The original area is 24 square inches

$[(3^2)]^2(24)=1,944\ in^2$

4) The area of the second enlargement is 3 times the area of the first enlargement

The statement is false

Because

$3(216)=648\ in^2$

$648\ in^2 \neq 1,944\ in^2$

5) The ratio of the area of the first enlargement to the area of the original equals the square of the scale factor

The statement is true

Because

The square of the scale factor is 3^2=9

and the ratio is equal to

$\frac{216}{24}=9$

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3 years ago

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1 year ago

Solve the following absolute value inequality. 3x - 727 x < 16 X > [?]

RUDIKE [14]

Answer:

-2

Step-by-step explanation:

3|x-7|<= 27

then |x-7|<=27/3=9

hence, -9<=x-7<=9

therefore, -2<=x<=16

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3 years ago

A cylinder shaped can needs to be constructed to hold 600 cubic centimeters of soup. The material for the sides of the can costs

PSYCHO15rus [73]

Answer:

the dimensions that minimize the cost of the cylinder are R= 3.85 cm and L=12.88 cm

Step-by-step explanation:

since the volume of a cylinder is

V= π*R²*L → L =V/ (π*R²)

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Cost = cost of side material * side area + cost of top and bottom material * top and bottom area

C = a* 2*π*R*L + b* 2*π*R²

replacing the value of L

C = a* 2*π*R* V/ (π*R²) + b* 2*π*R² = a* 2*V/R + b* 2*π*R²

then the optimal radius for minimum cost can be found when the derivative of the cost with respect to the radius equals 0 , then

dC/dR = -2*a*V/R² + 4*π*b*R = 0

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replacing values

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then

L =V/ (π*R²) = 600 cm³/(π*(3.85 cm)²) = 12.88 cm

therefore the dimensions that minimize the cost of the cylinder are R= 3.85 cm and L=12.88 cm

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3 years ago