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marysya [2.9K]
2 years ago
6

Mike is working on solving the exponential equation 37^x = 12; however, he is not quite sure where to start.

Mathematics
1 answer:
Rainbow [258]2 years ago
4 0

The solution of the given exponential equation is 0.688.

Given that Mike is working on solving the exponential equation 37ˣ = 12.

An exponential equation is an exponential equation where the power (or)  part of the exponent is a variable.

firstly, we have to slve this equation is by converting it to logarithmic form. Any exponential equation can be transformed into an equivalent logarithmic equation as follows:

aˣ = y

logₐy = x

Now, we will apply this transformation to our equation and we get

log₃₇12=x

Further, we will apply the change of base formula so that solution is written in terms of base 10 logs:

x=log12/log37

So, this is an exact answer to given equation, but we can simplify it further by using decimal approximation of it using a calculator. Remember that these logs are base 10:

x≈1.079/1.568

x=0.688

Hence, the solution of the given exponential equation 37ˣ=12 is 0.688.

Learn more about exponential equation from here brainly.com/question/24162621

#SPJ4

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insens350 [35]
The sea turtle's speed is
v_{t} = (27 \, \frac{km}{h} )*(1000 \, \frac{m}{km} )*( \frac{1}{60} \, \frac{h}{min} ) = 450 \, \frac{m}{min}

The girl's speed is
v_{g} = (14 \, \frac{dm}{s} )*( \frac{1}{10} \, \frac{m}{dm} )*(60 \, \frac{s}{min} ) = 84 \, \frac{m}{min}

The ratio of the turtle's speed to that of the girl is
\frac{v_{t}}{v_{g}} = \frac{450}{84} =5.357

Answer: 5.36 faster  (nearest hundredth)


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yaroslaw [1]

One way is...

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1. Find the probability of rolling a sum less than 4 or a
-Dominant- [34]
<h3>Answer:  13/36</h3>

=============================================================

Explanation:

Refer to the chart below. The values in red up top add to the values in blue along the left column to get the 6 by 6 grid of values inside. This represents all of the possible ways to add up values on a pair of dice. There are 6*6 = 36 outcomes.

Of those 36 outcomes, we have 13 outcomes where we roll less than a 4, or greater than 8

  1. outcome = 1+1 = 2
  2. outcome = 1+2 = 3
  3. outcome = 2+1 = 3
  4. outcome = 3+6 = 9
  5. outcome = 4+5 = 9
  6. outcome = 5+4 = 9
  7. outcome = 6+3 = 9
  8. outcome = 4+6 = 10
  9. outcome = 5+5 = 10
  10. outcome = 6+4 = 10
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  12. outcome = 6+5 = 11
  13. outcome = 6+6 = 12

These 13 results are shown in green boxes in the diagram.

Since we have 13 ways to get what we want, out of 36 total, the final answer as a fraction is therefore 13/36

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There are an infinite number of shapes, because a shape can have any number of sides. This is where we get into our laws of fractals. A fractal is a shape with an infinite perimeter and area, meaning that every level of infinity is another shape, but can be beat by another shape. However, this is all philosophical math and goes way beyond the context of your question.

To keep it short and simple, there are an infinite number of shapes in the world.
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Answer:

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Step-by-step explanation:

The converse of ...

  If P, then Q.

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Here, we have ...

  P = "x and y are natural numbers"

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So, the converse is ...

  If x-y is a natural number, then x and y are natural numbers.

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In this case, the converse is false.

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3 years ago
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