Designer wants to create a whisper chamber in the shape of an ellipse. He has a warehouse space with a longest length of 30 feet which he decides will be the major axis of his elliptical chamber. He determines the best spots for his guest to stand to experience his whisper chamber will be 4 feet from the center of the warehouse space, which will act as the foci. How far out from the center along the minor axis should he built his whisper chamber.

28.9 feet

Step-by-step explanation:

From the above question, we have obtained the following values:

Major axis of elliptical chamber = 30 feet

Note that length of the major axis of an elliptical chamber = 2a

Hence, 2a = 30

a = 30/2

a = 15 feet

Focus or foci = c = 4 feet

Length of the minor axis =2b = ??

The formula =

c² = a² - b²

b² = a² - c²

b²= 15² - 4²

b² = 225 - 16

b² = 209

b = √209

b = 14.456832295 feet

How far out from the center along he minor axis should he built his whisper chamber = Length of the minor axis

= 2 × b

= 2 × 14.456832295 feet

= 28.91366459 feet

Approximately = 28.9 feet

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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