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Bad White [126]
3 years ago
7

3x^3-2x^2-147x+98=(ax-c)(bx+d)(bx-d) where a,b,c and d positive integers. Work out the value of a,b,c and d

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

Expand the right side:

(ax-c)(bx+d)(bx-d)=(ax-c)(b^2x^2-d^2)

=ab^2x^3-b^2cx^2-ad^2x+cd^2

Notice that 98 = 2 * 7 * 7, so we have c=2 and d=7.

Then

-ad^2=-147\implies a=\dfrac{147}{49}=3

and

ab^2=3\implies b^2=1\implies b=1

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The isotope cobalt-60 has a nuclear mass of 59.933820 u
Anit [1.1K]

To start this question, we should know what is the atomic number of cobalt. The atomic number (the number of protons) of Cobalt is Z =27.

Now, we know that a Cobalt 60 isotope means an isotope of Cobalt whose Atomic Mass is 60.

Thus, in a Cobalt 60 isotope, the number of neutrons in the nucleus are

60-Z=60-27=33

From the question we know that the given nuclear mass is 59.933820 u.

Now, the mass defect of Cobalt 60 can be easily calculated by adding the masses of the protons and the neutrons as per our calculations and subtracting the given nuclear mass from it.

Thus,

Mass Defect = (Number of Protons Mass of Proton given in the question) + (Number of Neutrons Mass of Neutron given in the question)-59.933820 u

\therefore 27\times 1.007825+33\times 1.008665-59.933820=0.5634 u

Thus, the required Mass Defect is 0.5634u.

In eV, the Mass Defect is 931.5MeV\times 0.5634=534.807 MeV

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3 years ago
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Bill has candy from trick-or-treating. He has 15 Reese's and 20 Kit-Kat's.
saul85 [17]

Answer:

15:35

Step-by-step explanation:

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What is the decimal equivalent of 13/4?
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3.25

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Please help asap<br> find 140% of 82
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Step-by-step explanation:

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9. Determine how long it takes for 80% of the material to decay.
Vilka [71]

Using an exponential function, it is found that it takes 18.6 days for 80% of the material to decay.

The amount of a substance after t days is modeled by:

A(t) = A(0)e^{-kt}

In which:

  • k is the decay rate, as a decimal.
  • A(0) is the initial amount.

The half-life is of 8 days, hence A(8) = 0.5A(0), and this is used to find k.

A(t) = A(0)e^{-kt}

0.5A(0) = A(0)e^{-8k}

e^{-8k} = 0.5

\ln{e^{-8k}} = \ln{0.5}

-8k = \ln{0.5}

k = -\frac{\ln{0.5}}{8}

k = 0.08664339757

Hence:

A(t) = A(0)e^{-0.08664339757t}

The time it takes for 80% of the material to decay it t for which A(t) = 0.2A(0), hence:

0.2A(0) = A(0)e^{-0.08664339757t}

e^{-0.08664339757t} = 0.2

\ln{e^{-0.08664339757t}} = \ln{0.2}

-0.08664339757t = \ln{0.2}

t = -\frac{\ln{0.2}}{0.08664339757}

t = 18.6

It takes 18.6 days for 80% of the material to decay.

To learn more about exponential functions, you can take a look at brainly.com/question/24906920

5 0
3 years ago
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