Various mathematical equations and formulas shown in different colors.

Let’s go through each equation one by one and solve for the variable if possible. Some equations are just formulas (like the circle equation or slope-intercept form), so we’ll note that too.

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1. z = √8.6

This is already solved for z. We can leave it as is, or approximate:

√8.6 ≈ 2.93 (since 2.93² = 8.5849, close to 8.6)

But unless asked to approximate, we can keep it exact:
→ z = √8.6

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2. (x - h)² + (y - k)² = r²

This is the standard formula for a circle with center (h, k) and radius r.
It’s not an equation to solve — it’s a general formula.
→ No solution needed; it’s a definition.

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3. y = mx + b

This is the slope-intercept form of a line. Again, this is a formula, not something to solve unless values are given.
Later we’re told m = 4, but no x or b or y value is given here, so we can’t solve further yet.
→ Just a formula for now.

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4. y^(1/3) = 17

This means the cube root of y equals 17.

To solve for y, cube both sides:

(y^(1/3))³ = 17³
→ y = 17 × 17 × 17

Calculate step by step:

17 × 17 = 289
289 × 17 = ?

Break it down:
289 × 10 = 2890
289 × 7 = 2023
Add them: 2890 + 2023 = 4913

→ y = 4913

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5. m = 4

Already solved.
→ m = 4

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6. y = 3x²

This is a quadratic equation. Without a specific x or y value, we can’t solve for a number. It’s just a relationship between y and x.
→ Formula only.

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7. P = 3Q

Again, without knowing Q or P, we can’t find a numerical value. It’s a proportional relationship.
→ Formula only.

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Now, let’s collect all the actual solutions we found:

- From y^(1/3) = 17 → y = 4913
- From z = √8.6 → z = √8.6 (or approx 2.93 if needed)
- m = 4 → m = 4

The rest are formulas, not solvable without more info.

Since the problem says “solve the problem accurately,” and there are multiple expressions, I assume we’re to solve any that can be solved numerically.

The only fully solvable equation with a unique numeric answer is:

y^(1/3) = 17 → y = 4913

Also, z = √8.6 is technically solved, but it’s irrational. If they want decimal, we can give it, but usually in math problems like this, unless specified, we leave radicals exact.

But looking again — maybe the task is to identify which ones can be solved? Or perhaps just solve what’s possible?

Wait — actually, re-reading the user instruction: “Solve the problem accurately.” And the image has several equations. But none say “find x” or “find y” except implicitly.

However, in context, since y^(1/3)=17 is the only one that gives a clean integer solution when solved, and others are either formulas or require approximation, I think the main solvable part is that one.

But let me double-check: Is there any other equation that can be combined?

We have y = mx + b and m=4, but no x or b or y given — so no.

We have y = 3x² — again, no values.

P = 3Q — no values.

So only two things we can compute numerically:

- y from y^(1/3)=17 → 4913
- z = √8.6 → approximately 2.93, but exactly √8.6

But perhaps the problem expects us to list all solved variables?

Looking at the colors and layout — maybe it’s just a collection, and we’re to solve each that can be solved.

In that case:

Final answers per solvable equation:

- z = √8.6
- y = 4913 (from y^(1/3)=17)
- m = 4

Others are formulas.

But since the instruction says “solve the problem”, singular, maybe they mean the entire set? That doesn’t make sense.

Alternatively, perhaps the student is supposed to recognize which are solvable and solve those.

I think safest is to provide the numerical solutions where possible.

Let me verify y = 17³ again:

17² = 289
289 × 17:

200×17 = 3400
80×17 = 1360
9×17 = 153
Total: 3400 + 1360 = 4760; 4760 + 153 = 4913 → correct.

And √8.6: let's calculate more precisely.

2.93² = 8.5849
2.932² = ? 2.93² = 8.5849, plus 2*2.93*0.002 + (0.002)^2 ≈ 0.01172 + 0.000004 ≈ 0.011724 → total ≈ 8.5966 — still less than 8.6

2.933² = 2.93² + 2*2.93*0.003 + (0.003)^2 ≈ 8.5849 + 0.01758 + 0.000009 ≈ 8.602489 — a bit over.

So √8.6 ≈ 2.9326 or something. But again, unless asked, better to leave as √8.6.

Given that, and since the problem likely wants exact answers where possible, I'll present:

For y^(1/3) = 17 → y = 4913

That’s the clearest numerical solution.

Perhaps the problem is to solve for y in that red equation.

Looking back at the image description — the red text is y^(1/3)=17 and y=3x², purple is P=3Q, etc.

But no indication which one to prioritize.

Another thought: maybe "solve the problem" means to evaluate or simplify each expression? But most are already simple.

I think the only non-trivial solution is y = 4913 from the cube root equation.

To be thorough, let's see if any combination is implied.

For example, if we had y = mx + b and m=4, and say y=4913, then 4913 = 4x + b, but we don't know b or x.

Similarly, y=3x² and y=4913 would give x² = 4913/3, but again, not asked.

So probably, the intended solvable part is y^(1/3)=17.

Moreover, in many such images, the colored equations are separate problems.

Given that, and to follow instructions strictly, I'll provide the solution for the equation that yields a definite number.

Final Answer:
4913