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gizmo_the_mogwai [7]
4 years ago
11

F(x) ==x² + 10x-a What is the vertex?

Mathematics
1 answer:
Tju [1.3M]4 years ago
8 0

Answer:

of

x

x

and

y

y

.

f

(

x

)

=

x

2

−

10

x

f(x)=x2-10x

Rewrite the equation in vertex form.

Tap for more steps...

y

=

(

x

−

5

)

2

−

25

y=(x-5)2-25

Use the vertex form,

y

=

a

(

x

−

h

)

2

+

k

y=a(x-h)2+k

, to determine the values of

a

a

,

h

h

, and

k

k

.

a

=

1

a=1

h

=

5

h=5

k

=

−

25

k=-25

Find the vertex

(

h

,

k

)

(h,k)

.

(

5

,

−

25

)

(5,-25)

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Answer:

Q(t) = Q_o*e^(-0.000120968*t)

Step-by-step explanation:

Given:

- The ODE of the life of Carbon-14:

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The expression for Q(t).

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- Assuming Q(t) satisfies:

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- Separate variables:

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- Integrate both sides:

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- Make the relation for Q:

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- Using initial conditions given:

                                       Q(0) = Q_o

                                       Q_o = C*e^(-r*0)

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- The relation is:

                                       Q(t) = Q_o*e^(-r*t)

- We are also given that the half life of carbon is t = 5730 years:

                                       Q_o / 2 = Q_o*e^(-5730*r)

                                        -Ln(0.5) = 5730*r

                                        r = -Ln(0.5)/5730

                                        r = 0.000120968          

- Hence, our expression for Q(t) would be:

                                       Q(t) = Q_o*e^(-0.000120968*t)                                    

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