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3 years ago

14

What is the solution to the inequality below?

1 answer:

nexus9112 [7]3 years ago

5 0

Answer:

Quadratic Equations

A quadratic equation is one of the form ax2 + bx + c = 0, where a, b, and c are numbers, and a is not equal to 0.

Factoring

This approach to solving equations is based on the fact that if the product of two quantities is zero, then at least one of the quantities must be zero. In other words, if a*b = 0, then either a = 0, or b = 0, or both. For more on factoring polynomials, see the review section P.3 (p.26) of the text.

Example 1.

2x2 - 5x - 12 = 0.

(2x + 3)(x - 4) = 0.

2x + 3 = 0 or x - 4 = 0.

x = -3/2, or x = 4.

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Let f be a differentiable function such that f(1)=π and f'(x)=√x^3+6. what is the value of f(5)?

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The value of f(5) is 49.1

Step-by-step explanation:

To find f(x) from f'(x) use the integration

f(x) = ∫ f'(x)

1. Find The integration of f'(x) with the constant term

2. Substitute x by 1 and f(x) by π to find the constant term

3. Write the differential function f(x) and substitute x by 5 to find f(5)

∵ f'(x) = $\sqrt{x^{3}}$ + 6

- Change the root to fraction power

∵ $\sqrt{x^{3}}$ = $x^{\frac{3}{2}}$

∴ f'(x) = $x^{\frac{3}{2}}$ + 6

∴ f(x) = ∫ $x^{\frac{3}{2}}$ + 6

- In integration add the power by 1 and divide the coefficient by the

new power and insert x with the constant term

∴ f(x) = $\frac{x^{\frac{5}{2}}}{\frac{5}{2}}$ + 6x + c

- c is the constant of integration

∵ $\frac{x^{\frac{5}{2}}}{\frac{5}{2}}=\frac{2}{5}x^{\frac{5}{2}}$

∴ f(x) = $\frac{2}{5}$ $x^{\frac{5}{2}}$ + 6x + c

- To find c substitute x by 1 and f(x) by π

∴ π = $\frac{2}{5}$ $(1)^{\frac{5}{2}}$ + 6(1) + c

∴ π = $\frac{2}{5}$ + 6 + c

∴ π = 6.4 + c

- Subtract 6.4 from both sides

∴ c = - 3.2584

∴ f(x) = $\frac{2}{5}$ $x^{\frac{5}{2}}$ + 6x - 3.2584

To find f(5) Substitute x by 5

∵ x = 5

∴ f(5) = $\frac{2}{5}$ $(5)^{\frac{5}{2}}$ + 6(5) - 3.2584

∴ f(5) = 49.1

The value of f(5) is 49.1

Learn more:

You can learn more about differentiation in brainly.com/question/4279146

#LearnwithBrainly

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