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ExtremeBDS [4]
3 years ago
12

What is the range of the function on the graph

Mathematics
1 answer:
Tanzania [10]3 years ago
6 0

Answer:

All real numbers greater than or equal to -2.

Step-by-step explanation:

The range is the set of values of the y-coordinates of the points on the graph.

The smallest y-coordinate is -2. All real numbers greater than equal to -2 are the range.

Answer: All real numbers greater than or equal to -2.

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10.) The measure of angle 1 is 131° according to the Alternate Interior Angles Theorem. The measure of angle 2 is 49° because 180° - 131° = 49°. I can do this because of the Linear Pair Postulate.

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6 0
3 years ago
Let f be a differentiable function such that f(1)=π and f'(x)=√x^3+6. what is the value of f(5)?
natali 33 [55]

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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