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RoseWind [281]
3 years ago
14

Given the following three points, find by hand the quadratic function they represent.

Mathematics
1 answer:
RideAnS [48]3 years ago
3 0

Answer:

The equation is;

f(x) = -2·x² + 5·x - 1

Step-by-step explanation:

The general form of a quadratic equation  or function f(x) is, f(x) = y = a·x² + b·x + c

Given that the points representing the quadratic function are;

(-1, -8), (0, -1), (1, 2) which  are of the form (x, y)

When x = -1, f(x) = y = -8

Plugging in the above values into the general form of a quadratic function, we have;

-8 = a·(-1)² + b·(-1) + c = a - b + c

-8  = a - b + c.........................(1)

When x = 0, y = -1, we have;

-1 = a·(0)² + b·(0) + c = c

c = -1.......................................(2)

When x = 1, y = 2, which gives;

2 = a·(1)² + b·(1) + c = a + b + c

2 = a + b + c........................(3)

Adding equation (1) to equation (3), we have;

-8 + 2 = a - b + c + a + b + c

-8 + 2 = 2·a + 2·c

From equation (2) c = -1, we get;

-8 + 2 = -6 = 2·a + 2·c = 2·a + 2 × (-1)

-6 = 2·a - 2

-4 = 2·a

a = -2

From equation (3), we have

2 = a + b + c

Substituting the values of a, and c gives;

2 = -2 + b - 1

b = 2 + 2 + 1 = 5

b = 5

The equation is therefore;

f(x) = -2·x² + 5·x - 1.

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Anton [14]

Answer:

  • k = 0.006
  • T = 48 °F

Step-by-step explanation:

The initial temperature difference of 72 -34 = 38 °F is reduced to a difference of 72 -41 = 31 °F after 35 minutes. The exponential term in the temperature expression could have the factor ...

  (31/38)^(t/35) = e^(-kt)

Taking the natural log, we find ...

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To the nearest thousandth, this is ...

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Using this in the equation for temperature, we have ...

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Filling in the desired value for t (80), we find the turkey temperature after 80 minutes to be about

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The value of k is about 0.006, and the turkey temperature is about 48 °F.

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Answer:

See below  

Step-by-step explanation:

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A negatively charged particle has an electric field associated with it.

The field lines spread out radially from the centre of the point. They are represented by arrows pointing in the direction that a positive charge would move if it were in the field.

Opposite charges attract, so the field lines point toward the centre of the particle.

For an isolated negative particle, the field lines would look like those in Figure 1 below.

If two negative charges are near each other, as in Figure 2, the field lines still point to the centre of charge.

A positive charge approaching from the left is attracted to both charges, but it moves to the closer particle on the left.

We can make a similar statement about appositive charge approaching from the left.

Thus, there are few field lines in the region between the two particles.

(b) Coulomb's Law

The formula for Coulomb's law is

F = (kq₁q₂)/r²

It shows that the force varies inversely as the square of the distance between the charges.

Thus, the force between the charges decreases rapidly as they move further apart.

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