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zysi [14]
3 years ago
6

Given that the quadratic equation has equal roots (k^2-1)x^2-2kx-3k-1=0

Mathematics
1 answer:
Alik [6]3 years ago
7 0

Answer:

(See explanation for further details)

Step-by-step explanation:

The real expression is:

(k^{2}-1)\cdot x{{2} - 2\cdot k \cdot x - 3\cdot k + 1 = 0

The general equation for the second-order polynomial is:

x = \frac{2\cdot k \pm \sqrt{4\cdot k^{2}-4\cdot (k^{2}-1)\cdot (-3\cdot k + 1)}}{k^{2}-1}

This condition must be observed for the case of a quadratic equation with equal roots:

4\cdot k^{2} - 4\cdot (k^{2}-1)\cdot (-3\cdot k + 1) = 0

k^{2} + (k^{2}-1)\cdot (3\cdot k + 1) = 0

k^{2} + 3\cdot k^{3} - 3\cdot k - k^{2}-1 = 0

3\cdot k^{3} - 3\cdot k - 1 = 0

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Basile [38]

Using an exponential function, it is found that the bottle contains 255,960 atoms of tritium after 11 years.

<h3>What is an exponential function?</h3>

A decaying exponential function is modeled by:

A(t) = A(0)(1 - r)^t

In which:

  • A(0) is the initial value.
  • r is the decay rate, as a decimal.

In this problem:

  • The bottle initially contained 450,000 tritium atoms, hence A(0) = 450000.
  • The amount decays by about 5% per year, hence r = 0.05.

Thus, the equation is given by:

A(t) = A(0)(1 - r)^t

A(t) = 450000(1 - 0.05)^t

A(t) = 450000(0.95)^t

After 11 years, the amount is given by:

A(11) = 450000(0.95)^{11} = 255960

The bottle contains 255,960 atoms of tritium after 11 years.

More can be learned about exponential functions at brainly.com/question/25537936

8 0
2 years ago
Sara poured 3/4 of the juice from a 2 liter bottle while serving guests at a party how many Juice in liters is still left in the
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There is now 1/4 or half a liter left of juice still.
6 0
3 years ago
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Step-by-step explanation:

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write the standard form of the equation of the circle with the given center and radius (6,4), r= square root of 7
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The standard form of the equation of a circle is (x-6)^{2}+(y-4)^{2}=7.

Solution:

Center of the circle = (6, 4)

Radius of the circle = \sqrt{7}

<u>To find the equation of the circle:</u>

General formula for the equation of a circle

(x-h)^{2}+(y-k)^{2}=r^{2}

where (h, k) is the center of the circle and r is the radius of the circle.

Here, h = 6, k = 4 and r = \sqrt{7}

(x-6)^{2}+(y-4)^{2}=(\sqrt{7}) ^{2}

(x-6)^{2}+(y-4)^{2}=7

Hence the standard form of the equation of a circle is (x-6)^{2}+(y-4)^{2}=7.

3 0
3 years ago
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