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olchik [2.2K]
3 years ago
8

Look at photo NEED HELP ASAP EXPLAIN ANSWER

Mathematics
1 answer:
Dahasolnce [82]3 years ago
3 0

Answer:

x = 2

Step-by-step explanation:

Angles ABN and NBC are adjacent angles and sum up to angle ABC

  • 23x + 63x + 3 = 175
  • 86x = 175 - 3
  • 86x = 172
  • x = 172/86
  • x = 2
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According to one cosmological theory, there were equal amounts of the two uranium isotopes 235U and 238U at the creation of the
FromTheMoon [43]

Answer:

6 billion years.

Step-by-step explanation:

According to the decay law, the amount of the radioactive substance that decays is proportional to each instant to the amount of substance present. Let P(t) be the amount of ^{235}U and Q(t) be the amount of ^{238}U after t years.

Then, we obtain two differential equations

                               \frac{dP}{dt} = -k_1P \quad \frac{dQ}{dt} = -k_2Q

where k_1 and k_2 are proportionality constants and the minus signs denotes decay.

Rearranging terms in the equations gives

                             \frac{dP}{P} = -k_1dt \quad \frac{dQ}{Q} = -k_2dt

Now, the variables are separated, P and Q appear only on the left, and t appears only on the right, so that we can integrate both sides.

                         \int \frac{dP}{P} = -k_1 \int dt \quad \int \frac{dQ}{Q} = -k_2\int dt

which yields

                      \ln |P| = -k_1t + c_1 \quad \ln |Q| = -k_2t + c_2,

where c_1 and c_2 are constants of integration.

By taking exponents, we obtain

                     e^{\ln |P|} = e^{-k_1t + c_1}  \quad e^{\ln |Q|} = e^{-k_12t + c_2}

Hence,

                            P  = C_1e^{-k_1t} \quad Q  = C_2e^{-k_2t},

where C_1 := \pm e^{c_1} and C_2 := \pm e^{c_2}.

Since the amounts of the uranium isotopes were the same initially, we obtain the initial condition

                                 P(0) = Q(0) = C

Substituting 0 for P in the general solution gives

                         C = P(0) = C_1 e^0 \implies C= C_1

Similarly, we obtain C = C_2 and

                                P  = Ce^{-k_1t} \quad Q  = Ce^{-k_2t}

The relation between the decay constant k and the half-life is given by

                                            \tau = \frac{\ln 2}{k}

We can use this fact to determine the numeric values of the decay constants k_1 and k_2. Thus,

                     4.51 \times 10^9 = \frac{\ln 2}{k_1} \implies k_1 = \frac{\ln 2}{4.51 \times 10^9}

and

                     7.10 \times 10^8 = \frac{\ln 2}{k_2} \implies k_2 = \frac{\ln 2}{7.10 \times 10^8}

Therefore,

                              P  = Ce^{-\frac{\ln 2}{4.51 \times 10^9}t} \quad Q  = Ce^{-k_2 = \frac{\ln 2}{7.10 \times 10^8}t}

We have that

                                          \frac{P(t)}{Q(t)} = 137.7

Hence,

                                   \frac{Ce^{-\frac{\ln 2}{4.51 \times 10^9}t} }{Ce^{-k_2 = \frac{\ln 2}{7.10 \times 10^8}t}} = 137.7

Solving for t yields t \approx 6 \times 10^9, which means that the age of the  universe is about 6 billion years.

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3 years ago
Find the zero of the function f(x) = -8x + 4.<br> NEED HELP FAST DONT HAVE MUCH TIME
Paladinen [302]

Answer:

1/2

Step-by-step explanation:

5 0
3 years ago
What addition expression is equivalent to<br> 3-(-7)?
Lesechka [4]

Answer:

3 - (-7)

= 3 + 7.

Step-by-step explanation:

A double negative  is equivalent to a plus.

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3 years ago
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10x−15=−5x−20 Solve for x.
Nesterboy [21]
The answer would be -5x-20+15/10 



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3 0
3 years ago
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Which expression is equivalent to -7(y-2)
soldi70 [24.7K]

Hello!

Distributive property: a(b+c)=ab+ac

a=-7, b=y, c=2

-7y-(-7)*2

Minus and plus sign.

-7y+7*2

Then multiply by the numbers.

7*2=14

\boxed{=-7y+14}

Hope this helps!

Thanks!

Have a great day!

5 0
3 years ago
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