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Artemon [7]
3 years ago
5

Logarithmic and Exponential Forms of Equations In Exercise, write the logarithmic equation as an exponential equation, or vice v

ersa.
In 12 = 2.4849...
Mathematics
1 answer:
Nata [24]3 years ago
6 0

Answer:

12 = e^{2.4849}

Step-by-step explanation:

For this case we have the following expression:

ln(12) = 2.4849

We need to remember that the natural log and the exponentiation with the base the euler number e are inverse operations, and if we apply exponentiation on both sides of the equation we got this:

e^{ln(12)} = e^{2.4849}

We have the identity operator for this e^{ln(x)}= x

12 = e^{2.4849}

And that would be our final answer for this case.

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The temperature at 6.00 am was - 12 the temperature increased by 1/2 each hour for 6 hours what was the temperature in degrees F
Illusion [34]

Answer: -9 degrees Fahrenheit

Step-by-step explanation:

Given: Temperature at 6:00 AM = -12 degrees Fahrenheit

Temperature increased each hour = \dfrac12 degrees Fahrenheit

Temperature increase in 6 hours = 6\times\dfrac12=3\text{ degrees Fahrenheit}

Temperature at noon = Temperature at 6:00 AM+Temperature increase in 6 hours

= -12+3 degrees Fahrenheit

= -9 degrees Fahrenheit

Hence, the temperature in degrees Fahrenheit at noon= -9 degrees Fahrenheit

8 0
2 years ago
What is the area of the trapezoid? The diagram is not drawn to scale.
Katyanochek1 [597]

Answer:

The area of trapezoid is 72 cm²

Step-by-step explanation:

Given : A trapezoid with given dimensions.

We have to find the area of trapezoid ABCD.

Consider the given trapezoid ABCD ,

AB = EF = 8 cm

and CE = FD = 4 cm

Then CD = CE + EF + FD = 4 + 8 + 4 = 16 cm

Thus, Area of trapezoid = \frac{1}{2}\cdot \text{(Sum of parallel sides)} \cdot height

here, height = 6 cm

and sum of parallel sides = AB + CD = 16 + 8 = 24 cm

Thus,  Area of trapezoid = \frac{1}{2}\cdot 24 \cdot 6

Simplify, we have,

Area of trapezoid = 72 cm²

Thus, The area of trapezoid is 72 cm²

8 0
3 years ago
Read 2 more answers
Write a system of inequalities using the given graph
ch4aika [34]

Take two points

  • (-2,1)
  • (0,-3)

Slope

  • m=-3-1/0+2=-4/2=-2

Parallel lines so slopes are equal

Only y intercept will vary

So both lines have y intercept at -3 and -1 respectively

The equations

  • y=-2x-3
  • y=-2x-1

Put (0,0) on first one

  • 0>-3

On second one

  • 0>-1

So as lines are dashed symbols remain >

The inequalities are

  • y>-2x-3
  • y>-2x-1
4 0
2 years ago
expression to approximate log a of x for all positive numbers a, b, and x, where a is not equal to 1 and b is not equal to one
amid [387]

Question:

Approximate log base b of x, log_b(x).

Of course x can't be negative, and b > 1.


Answer:

f(x) = (-1/x + 1) / (-1/b + 1)


Step-by-step explanation:

log(1) is zero for any base.

log is strictly increasing.

log_b(b) = 1

As x descends to zero, log(x) diverges to -infinity


Graph of f(x) = (-1/x + 1)/a is reminiscent of log(x), with f(1) = 0.


Find a such that f(b) = 1

1 = f(b) = (-1/b + 1)/a

a = (-1/b + 1)


Substitute for a:

f(x) = (-1/x + 1) / (-1/b + 1)

f(1) = 0

f(b) = (-1/b + 1) / (-1/b + 1) = 1




7 0
3 years ago
rodney bought a 25pound bag of dog food his dog eat 10and2/5poundsof foodinthe firstmounthand104/5poundsof the foodin the second
MakcuM [25]

Answer:

3⅘ lb  

Step-by-step explanation:

(a) <em>Amount eaten</em>

Eaten = 10⅖ + 10⅘

Think of pounds as pies. Each pie has 5 slices.

10⅖ pies = 10 pies + 2 slices = 50 slices + 2 slices = 52 slices

10⅘ pies = 10 pies + 2 slices = 50 slices + 4 slices = 54 slices

Eaten = 52 slices + 54 slices = 106 slices


(b) <em>Amount remaining</em>

Remaining = Original – Eaten

Original = 25 pies = 125 slices

Eaten = 106 slices

Remaining = 125 slices -106 slices

Remaining = 19 slices                 Convert slices to pies

Remaining = 15 slices + 4 slices

Remaining = 3 pies + 4 slices     Convert to mixed fraction

Remaining = 3⅘ pies                   Convert pies to pounds

Remaining dog food = 3⅘ lb

8 0
3 years ago
Read 2 more answers
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