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lord [1]
3 years ago
13

Write as a square of a binomial: 1: 4x^2+12x+92: 10xy +0.25x^2+100y^2

History
1 answer:
oksano4ka [1.4K]3 years ago
6 0

Answer:

1) (2x + 3)^2

2) (.5x + 10y)^2

Explanation:

1) You know this has to be a squared term, so just look for the roots of the first and last terms. For the first term, \sqrt[2]{4x^{2} } = 2x and for the last term, \sqrt[2]{9} = 3. You can check either by FOIL or the Box Method and you will see that it comes out to the initial formula.

2) Once again, look for the square roots of the first and last terms. In this case, you have to sort the initial equation out so that it looks like a normal trinomial, this is what you get:

0.25x^{2} + 10xy + 100y^{2}

Then you just take the square roots of the first and last terms, which are 0.5x and 10y, respectively.

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A cone has a diameter of 8 units and a height of 8 units.Its radius is A. 2 B. 4 C. 8 D. 16 units, and its volume is A. 66.99 B.
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Question

1) A cone has a diameter of 8 units and a height of 8 units. Its radius is

A. 2 B. 4 C. 8 D. 16 units,

2) and its volume is A. 66.99 B. 133.97 C. 401.92 D. 535.89 cubic units.

3) A cylinder with the same height and radius as the cone will have a volume of A. 66.99 B. 133.97 C. 401.92 D. 535.89 cubic units.

4) If a sphere has the same radius as the cylinder, its volume is A. Half B. Two-thirds C. Four-thirds the volume of the cylinder

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1) B. 4 units

2) B. 133.97 cubic units

3) C. 401.92 cubic units

4) B. Two-thirds the volume of the cylinder.

Explanation:

1)In the above question, we are given the following values.

A cone has a diameter of 8 units and a height of 8 units. We are asked to find the radius.

The formula for radius = Diameter ÷ 2

The radius of the cone = 8 units ÷ 2 = 4 units.

2) We are asked to find the volume of the cone in question 1

Volume of the cone = 1/3πr²h

r = 4 units, h = 8 units, π = 3.14

= 1/3 × 3.14 × 4² × 8

= 133.97 cubic units.

3) We are asked to find the volume of a cylinder if it has same height and radius as the cone in question 1

Volume of a cylinder = πr²h

r = 4 units

h = 8 units

Volume of a cylinder = 3.14 × 4² × 8

= 401.92 cubic units.

4) If a sphere has the same radius as the cylinder, its volume is

The radius of the cylinder = 4 units

Volume of a sphere = 4/3πr³

π = 3.14

= 4/3 × π × 4³

= 268.08257311cubic units

Approximately = 268.08 cubic units.

The volume of the cylinder = 401.92 cubic units,

Two thirds of the volume of the cylinder = 2/3 × 401.92 = 268

Therefore, if a sphere has the same radius as the cylinder, its volume is 268.08 cubic units is Two-thirds the volume of the cylinder.

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