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2 years ago

Sinθ/cosθtanθ=1how is this identity true?

Mathematics

1 answer:

Yakvenalex [24]2 years ago

7 0

Answer:

This is actually not an identity.

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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)?

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

4 0

3 years ago

Identifying rate of chang

trasher [3.6K]

There is no question content here but I can still help just add a picture

If you want to know how to identify the rate of change here's how.

If we use only the beginning and ending data, we would be finding the average rate of change over the specified period of time. To find the average rate of change, we divide the change in the output value by the change in the input value.

Hope this helps sum!

5 0

3 years ago

What adds to 12 but multiplies to 9

kotykmax [81]

The numbers are irrational, so they can't be written exactly.
Rounded to the nearest thousandth, they are

11.196
and
0.804 .

11.196 + 0.804 = 12
11.196 x 0.804 = 9.002...

7 0

3 years ago

Read 2 more answers

What is the product of 1.54 and 2.6?

34kurt

Answer:

the product of 1.54 and 2.6 is 4.004. I think

4 0

3 years ago

When the function is given in vertex form y=a(x-h)2+k, how is the vertex found?

Nat2105 [25]

Once you have it in that form, you just read off the values of h and k

For instance, if you had y = 2(x-3)^2 + 5, then h = 3 and k = 5. So the vertex is (h,k) = (3,5)<span />

3 0

3 years ago

Read 2 more answers

Sinθ/cosθtanθ=1how is this identity true?​

Sinθ/cosθtanθ=1how is this identity true?