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3 years ago

Translate this equation into a verbal sentence. 4(a + b) = 9a

Mathematics

1 answer:

EastWind [94]3 years ago

8 0

Answer:

Four times a plus b equals nine times a

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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

Solve using the Factor Method:

Dima020 [189]

6x^2+12x=0 Factor out the greatest common factor which is 6x

6x(x+2)=0

So the there are two solutions, when x=0 and x=-2

The points are, (0,0) and (-2,0)

And they expressed it as {0, -2}

4 0

4 years ago

What does 1/9-(-2/5-8/9) equal?

babunello [35]

1/9 - (-2/5 - 8/9) = 1/9 + 2/5 + 8/9 = 1 + 2/5 = 7/5 or 1 2/5

6 0

4 years ago

What formula to use <br> Answer

77julia77 [94]

Check the picture below.

now, since we know what "f" is, let us use the CNT triangle with the small COR one.

$\bf \cfrac{36+f+30}{36}=\cfrac{48+32+g}{48}\implies \cfrac{36+24+30}{36}=\cfrac{48+32+g}{48} \\\\\\ \cfrac{90}{36}=\cfrac{80+g}{48}\implies \cfrac{5}{2}=\cfrac{80+g}{48}\implies 240=160+2g \\\\\\ 80=2g\implies \cfrac{80}{2}=g\implies 40=g$

4 0

4 years ago

Solve this equation -2x + 8 = 22

hichkok12 [17]

I got you :)

-2x + 8 = 22

Subtract 8 from both sides....

-2x = 14 Divide by 2 on both sides....

8 0

3 years ago