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Arte-miy333 [17]
3 years ago
6

Suppose the supply function for a certain item is given by S(q)= (q+6)2 and the demand funtion is given by D(q)= (1000)/(q+6).

Mathematics
1 answer:
nasty-shy [4]3 years ago
7 0

Answer: The equilibrium point is where; Quantity supplied = 100 and Quantity demanded = 100

Step-by-step explanation: The equilibrium point on a demand and supply graph is the point at which demand equals supply. Better put, it is the point where the demand curve intersects the supply curve.

The supply function is given as

S(q) = (q + 6)^2

The demand function is given as

D(q) = 1000/(q + 6)

The equilibrium point therefore would be derived as

(q + 6)^2 = 1000/(q + 6)

Cross multiply and you have

(q + 6)^2 x (q + 6) = 1000

(q + 6 )^3 = 1000

Add the cube root sign to both sides of the equation

q + 6 = 10

Subtract 6 from both sides of the equation

q = 4

Therefore when q = 4, supply would be

S(q) = (4 + 6)^2

S(q) = 10^2

S(q) = 100

Also when q = 4, demand would be

D(q) = 1000/(4 + 6)

D(q) = 1000/10

D(q) = 100

Hence at the point of equilibrium the quantity demanded and quantity supplied would be 100 units.

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An irrigation system (sprinkler) has a parabolic pattern. The height, in feet, of the spray of water is given by the equation ℎ(
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  1. The irrigation system is positioned 9.5 feet above the ground to start.
  2. The spray reaches a maximum height of <u>84.5 feet</u> at a horizontal distance of <u>5 feet</u> away from the sprinkler head.
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<h3>How to determine the position?</h3>

Since the height (feet) of the spray of water is given by this equation h(x) = -x² + 10x + 9.5, we can logically deduce that the irrigation system is positioned 9.5 feet above the ground to start.

<h3>How to determine the maximum height?</h3>

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Maximum distance = 10.87 feet.

Read more on maximum height here: brainly.com/question/24288300

#SPJ1

<u>Complete Question:</u>

An irrigation system (sprinkler) has a parabolic pattern. The height, in feet, of the spray of water is given by the equation h(x) = -x² + 10x + 9.5, where x is the number of feet away from the sprinkler head (along the ground) the spray is.

1. The irrigation system is positioned____ feet above the ground to start.

2. The spray reaches a maximum height of ____feet at a horizontal distance of feet away from the sprinkler head.

3. The spray reaches all the way to the ground at about_____ feet away​

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