Acone has a volume of 50π in3 and a diameter of 10 in. wilson states that a cylinder with the same height and diameter has the same volume. which statement explains whether or not wilson is correct?

  A cylinder in which h = 6 and d = 10 has a volume of 150π in³, therefore, Wilson is incorrect.

Step-by-step explanation:

You know that the cylinder has 3 times the volume of a cone of the same diameter and height, so only the last two answer choices make any sense. In order to determine which one, we must find the height of either figure.

The volume of the cylinder is ...

  V = πr²h = (π/4)d²h = π/4·(10 in)²h = 150π

  h = 150π/(25π) = 6 . . . . inches

The height of the cylinder/cone is 6 inches, so the last answer choice pertains:

 A cylinder in which h = 6 and d = 10 has a volume of 150π in³, therefore, Wilson is incorrect.

if the diameter of the cone is 10, then its radius is half that or 5.

so then, a cone with that volume and radius has a height of 6.  However, a cylinder also with a radius of 5 and a height of 6, has a volume of 150π.

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

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