https://file.aiquickdraw.com/mathbot/file/17289751571981979b4a2.jpg

In the image you provided, I see the following economic equations and questions related to market equilibrium:

1. **Demand function (Qd)**:  
   \[
   Qd = 20 - 8P^2
   \]
   
2. **Supply function (Qs)**:  
   \[
   Qs = 10P^2 + P + 20
   \]

### Questions asked:
1. **Kesetimbangan pasar** (Market equilibrium): Find the market equilibrium.
2. **Pajak sebesar 10** (Tax of 10): Analyze the effect of a tax of 10 on the equilibrium.
3. **Kesetimbangan setelah pajak** (Equilibrium after tax): Determine the new equilibrium after the tax is imposed.

### Step-by-Step Solution for Question 1 (Market Equilibrium):
At equilibrium, the quantity demanded (Qd) is equal to the quantity supplied (Qs):
\[
Qd = Qs
\]

Substitute the given functions for Qd and Qs:
\[
20 - 8P^2 = 10P^2 + P + 20
\]

Simplify the equation:
\[
20 - 8P^2 = 10P^2 + P + 20
\]
Subtract 20 from both sides:
\[
-8P^2 = 10P^2 + P
\]
Move all terms to one side:
\[
-8P^2 - 10P^2 - P = 0
\]
\[
-18P^2 - P = 0
\]

Factor the equation:
\[
P(-18P - 1) = 0
\]

This gives two solutions:
\[
P = 0 \quad \text{or} \quad P = -\frac{1}{18}
\]

Since price (P) cannot be negative, the equilibrium price is **P = 0**.

### Equilibrium Quantity:
Substitute \(P = 0\) into either the demand or supply function (I'll use the demand function):
\[
Qd = 20 - 8(0)^2 = 20
\]
Thus, the equilibrium quantity is **Q = 20**.

Would you like to proceed with the other questions (tax and new equilibrium) or need more details on this part? Let me know!

---

Here are 5 related questions to extend your understanding:
1. What happens if there is a shift in demand or supply curves?
2. How do taxes affect consumer and producer surplus in this scenario?
3. What is the effect of a price floor or ceiling on equilibrium?
4. How does elasticity of demand and supply affect the burden of tax?
5. What would happen if the tax imposed was larger than 10?

**Tip**: When solving quadratic equations, always check if the solutions are realistic (e.g., non-negative prices).

In the image, the user is asked to find market equilibrium and analyze the effect of a tax. The equations provided are:

1. Demand function: Qd = 20 - 8P^2
2. Supply function: Qs = 10P^2 + P + 20

Questions:
1. Find the market equilibrium.
2. Analyze the effect of a tax of 10.
3. Determine the new equilibrium after the tax.

Learn how to find market equilibrium using the demand and supply functions with a quadratic equation. This problem also involves analyzing the effect of a tax of 10 and determining the new equilibrium after the tax. Suitable for high school students in Grades 10-12.

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