The scale that maps Figure A onto Figure B is 1:3 1 4 . Enter the value of x.

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

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4 0

3 years ago

Balance the equation

loris [4]

On the right side, there are

• 2•2 = 4 atoms of Nb

• 2•5 = 10 atoms of O

so among the reactants on the left, the reaction is balanced as

4 Nb + 5 O₂ → 2 Nb₂O₅

7 0

2 years ago

Danielle earns a 7.25% commission on everything she sells at the electronics store where she works. She also earns a base salary

Nikitich [7]

Answer:

Last week her sales were $4500.

Step-by-step explanation:

Given:

Danielle earns a 7.25% commission on everything she sells at the electronics store where she works.

She also earns a base salary of $750 per week.

Her total earnings for the week were $1,076.25.

Now, to find her sales last week.

Let the sales of last week be $x.$

Base salary = $750.

Total earnings = $1076.25.

So, we deduct the base salary from the total earnings first:

$1076.25-750$

$=326.25.$

Thus, the rest of the earnings is $326.25 which is the 7.25% commission on sales.

Now, to get the sales of last week we put an equation:

$7.25\%\ of\ x=326.25$

$\frac{7.25}{100} \times x=326.25$

$\frac{7.25x}{100} =326.25$

Multiplying both sides by 100 we get:

$7.25x=32625$

Dividing both sides by 7.25 we get:

$x=4500.$

The sales of last week = $4500.

Therefore, last week her sales were $4500.

7 0

3 years ago

7+(53-3^{4} )/\sort{16}

topjm [15]

Answer: 7+(53-3^{4} )/sqrt{16} = 0

Solution:

7+(53-3^{4} )/sqrt{16} =

7+(53-3*3*3*3)/4 =

7+(53-81)/4 =

7+(-28)/4 =

7-7 =

0

4 0

3 years ago

PLS HELPPP ASAP

Mars2501 [29]

Yes they are similar! Both share the same angle of 61° then 20x5 is 100 just like 17x5 is 85!!

6 0

3 years ago