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Diano4ka-milaya [45]
3 years ago
10

Use Natural Logarithms to solve the equation

Mathematics
1 answer:
Rus_ich [418]3 years ago
7 0

Answer:

A) 0.106

Step-by-step explanation:

8e^3x + 4 = 15

Subtract 4 from each side

8e^3x + 4-4 = 15-4

8e^3x  = 11  

Divide each side by 8

8/8e^3x = 11/8

e^(3x) = 11/8

Take the natural log of each side

ln(e^(3x)) = ln(11/8)

3x = ln(11/8)

Divide by 3

3x/3 = 1/3 ln(11/8)

x = 1/3 ln(11/8)

x =.106151244

To the nearest thousandth

x = .106

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Which number produces an irrational number when multiplied by 1/3
MArishka [77]

We can simply observe that.

  1. 0.777... is rational, because it is a number with infinite but repeating decimal part.
  2. 1/3 is rational, because it's the division between two integers
  3. -\sqrt{16}=-4, so this is rational as well.

Since the product of two rational numbers is always rational, we have that

0.\bar{7}\cdot \dfrac{1}{3},\quad \dfrac{1}{3}\cdot \dfrac{1}{3},\quad -4\cdot \dfrac{1}{3}

are all rationals, since they are the product of two rationals.

On the other hand, we have

\sqrt{27}=\sqrt{9\cdot 3}=3\sqrt{3}

and thus

3\sqrt{3}\cdot \dfrac{1}{3}=\sqrt{3}

which is irrational.

3 0
3 years ago
15y^-11/3y^-11, show steps I need help please don't understand how to do it.
tester [92]
One may note, you never quite asked anything per se, ahemm, if you meant simplification.

\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\
a^{-{ n}} \implies \cfrac{1}{a^{ n}}
\qquad \qquad
\cfrac{1}{a^{ n}}\implies a^{-{ n}}
\qquad \qquad 
a^{{{  n}}}\implies \cfrac{1}{a^{-{{  n}}}}\\\\
-------------------------------\\\\
\cfrac{15y^{-11}}{3y^{-11}}\implies \cfrac{15}{3}\cdot \cfrac{y^{-11}}{y^{-11}}\implies 5\cdot y^{-11}\cdot y^{+11}\implies 5\cdot y^{-11+11}
\\\\\\
5y^0 \implies \boxed{5}
8 0
3 years ago
Perform the following food service calculation.
swat32

320 guests / 5 servings per can = 64 cans required

3 0
2 years ago
Answers needed as soon as possible
Naily [24]
Basically the answer is 6, if you'd like an explanation, let me know. :)
6 0
3 years ago
Read 2 more answers
A spinner is divided into 4 equal sections colored red, green , blue and orange . Ennis spins the spinner. What is the probabili
zavuch27 [327]

Answer:

By thinking logically,here's hint: there are only 4 equal sections and 4 colors,all of them equal to=

\frac{4}{4}

no matter what color you take,for example green is 1/4,red is 1/4 as well.Eventually the answer is:the probability of orange color is 1/4 too.

7 0
3 years ago
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