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3 years ago

Solve the equations below. Give exact solutions only. Show your work.

Mathematics

1 answer:

Nikolay [14]3 years ago

4 0

Step-by-step explanation:

remember, the general formula to solve a quadratic equation ax² + bx + c = 0 is

x = (-b ± sqrt(b² - 4ac))/(2a)

I think there is a typo, and this should be

5x² - 7x = 72

5x² -7x - 72 = 0

x = (7 ± sqrt(49 - -1440))/10 = (7 ± sqrt(1489))/10

x1 = (7 + sqrt(1489))/10

x2 = (7 - sqrt(1489))/10

x(x + 2) = 5

x² + 2x - 5 = 0

x = (-2 ± sqrt(4 - -20))/2 = (-2 ± sqrt(24))/2 =

= (-2 ± sqrt(4×6))/2 = (-2 ± 2×sqrt(6))/2 =

= -1 ± sqrt(6)

x1 = -1 + sqrt(6)

x2 = -1 - sqrt(6)

3x² + 2x - 4 = 0

x = (-2 ± sqrt(4 - -48))/6 = (-2 ± sqrt(52))/6 =

= (-2 ± sqrt(4×13))/6 = (-2 ± 2×sqrt(13))/6 =

= (-1 ± sqrt(13))/3

x1 = (-1 + sqrt(13))/3

x2 = (-1 - sqrt(13))/3

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A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 3 inches. The height of the cone is 18 inc

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Given that, cylinder and a cone have the same diameter: 8 inches

Diameter = 8 inches

Radius is diameter divided by 2

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Radius = 4 inches

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$volume = \pi r^2 h$

Radius = 4 inches

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Substituting the values, we get

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Thus volume of cylinder is 150.72 cubic inches

Volume of cone:

$volume = \frac{\pi r^2h}{3}$

Radius = 4 inches

The height of the cone is 18 inches

height = 18 inches

Substituting the values, we get

$volume = \frac{3.14 \times 4^2 \times 18}{3}\\\\volume = 3.14 \times 16 \times 6\\\\volume = 301.44$

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Volume of cylinder is 150.72 cubic inches

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On observing the volume of cylinder and cone, we find that two times the volume of cylinder is volume of cone

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Thus the relationship between the volume of this cylinder and this cone is that two times the volume of cylinder is volume of cone

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