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3 years ago

Find the equilibrium point for the pair of supply and demand functions. Demand: q=18/x Supply: q=x/2

Mathematics

1 answer:

storchak [24]3 years ago

5 0

Answer:

The equilibrium point is at x = 6

Step-by-step explanation:

Given

$Demand (q) = \frac{18}{x}$

$Supply (q) = \frac{x}{2}$

Required

Determine the equilibrium point

The equilibrium point is determined by

$Demand = Supply$

Substitute values for Demand and Supply

$\frac{18}{x} = \frac{x}{2}$

Cross Multiply

$x * x = 18 * 2$

$x^2 = 36$

Take positive square root of both sides

$x = 6$

Hence;

The equilibrium point is at x = 6

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Use distributive property to find product 5×3087

katrin [286]

Answer:

15,435

Step-by-step explanation: thts the anwser

5 0

3 years ago

Two boats depart from a port located at (–8, 1) in a coordinate system measured in kilometers and travel in a positive x-directi

miss Akunina [59]

Answer:

$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

Step-by-step explanation:

1st boat:

Parabola equation:

$y=ax^2 +bx+c$

The x-coordinate of the vertex:

$x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=1\\ \\b=-2a$

Equation:

$y=ax^2 -2ax+c$

The y-coordinate of the vertex:

$y_v=a\cdot 1^2-2a\cdot 1+c\Rightarrow a-2a+c=10\\ \\c-a=10$

Parabola passes through the point (-8,1), so

$1=a\cdot (-8)^2-2a\cdot (-8)+c\\ \\80a+c=1$

Solve:

$c=10+a\\ \\80a+10+a=1\\ \\81a=-9\\ \\a=-\dfrac{1}{9}\\ \\b=-2a=\dfrac{2}{9}\\ \\c=10-\dfrac{1}{9}=\dfrac{89}{9}$

Parabola equation:

$y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}$

2nd boat:

Parabola equation:

$y=ax^2 +bx+c$

The x-coordinate of the vertex:

$x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=0\\ \\b=0$

Equation:

$y=ax^2+c$

The y-coordinate of the vertex:

$y_v=a\cdot 0^2+c\Rightarrow c=-7$

Parabola passes through the point (-8,1), so

$1=a\cdot (-8)^2-7\\ \\64a-7=1$

Solve:

$a=-\dfrac{1}{8}\\ \\b=0\\ \\c=-7$

Parabola equation:

$y=\dfrac{1}{8}x^2 -7$

System of two equations:

$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

7 0

3 years ago

Read 2 more answers

Raquel can type 63 words every minnute.Rick type then Raquel in 135 minute?Circle the letter of the correct answer.A 1350 B 4599

lozanna [386]

Answer: 1350

Step-by-step explanation:

Here is the correct question.

Raquel can type an average of 63 words per minute. Rick can type 73 words per minute. how many more words can Rick type than Raquel in 135 minutes? Jared chose B as the correct answer. How did he get that answer? Jared said the answer is 4599. How did he get that answer?

Rick's word per minute= 73

Raquel's word per minute= 63

Ricks word in 135minute= 73×135 = 9855

Raquel's word in 135 minutes=63×135 = 8505

=9855 - 8505

= 1350

Rick can type 1350 more words than Raquel in 135 minutes.

Jared's answer is wrong. He got the answer by multiplying 63 by 73 which gives 4599.

8 0

3 years ago

Read 2 more answers

Solve: 3-x+1=2 Thank youuuu ‍♀️

timurjin [86]

Answer:

Step-by-step explanation:

3 - x + 1 = 2 combine like terms

-x + (3 + 1) = 2

-x + 4 = 2 subtract 4 from both sides

-x +4 - 4 = 2 - 4

-x = -2 change the signs

x = 2

5 0

3 years ago

Read 2 more answers

The value of a bank account, y, increases by 5% each year, x. If the initial value of the account is $800, which equation repres

Mashcka [7]

Answer:

Equation to represent the situation = $800=Y(1.05)^X$

Step-by-step explanation:

Given:

Initial investment = Y

Growth rate (r) = 5% = 5 / 100 = 0.05

Number of year (n) = X year

Amount after X year = $800

Find:

Equation to represent the situation:

Computation:

$Amount = Initial\ investment (1+r)^n\\\\800 = Y (1+0.05)^X\\\\800 = Y (1.05)^X\\\\$

Equation to represent the situation = $800=Y(1.05)^X$

6 0

3 years ago