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3 years ago

Rewrite lnx=4 as an exponential equation rewrite as a logarithmic equation: e^8=y

1 answer:

5 0

$\bf \textit{exponential form of a logarithm} \\\\ \log_a b=y \implies a^y= b\qquad\qquad a^y= b\implies \log_a b=y \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ln(x)=4\implies log_e(x)=4\implies e^4=x \\\\\\ e^8=y\implies log_e(y)=8\implies ln(y)=8$

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Let w = 4. Enter >, <, or = to compare the expressions. 3w² + 1 10w + 8

Svetach [21]

Answer: ≥ without the line on the bottom.

Step-by-step explanation:

I am assuming the expression you are talking about are

$3w^{2} +1$ and $10w+8$ .

If we were to replace w with 4 and calculate, we will find the answer:

$3*4^{2} +1=3*16+1=48+1=49$

$10*4+8=40+8=48$

Since the first expression, $3w^{2} +1$ , is bigger than the second expression, the correct symbol to use is ≥ without the line on the bottom.

6 0

2 years ago

A chain saw requires 5 hours of assembly and a wood chipper 4 hours. A maximum of 40 hours of assembly time is available. The pr

iris [78.8K]

So first you need to by the chain saw and the chipper for $380. It should only take you about 9 hours to assemble it. And lets say that the 31 hours you were looking for the best of the best chain saw and chipper.

8 0

3 years ago

Two glass containers are shown. Both are right rectangular prisms. Container 1 is filled with water and Container 2 is empty.

dmitriy555 [2]

9514 1404 393

Answer:

18 in

Step-by-step explanation:

The volume of each container is the product of its dimensions:

V = LWH

We can let h represent the unknown height of Container 2. The volumes are equal when ...

32·18·12 = 24·16·h

(32·12·18)/(16·24) = h =18 . . . . . divide by the coefficient of h, simplify

The missing height of Container 2 is 18 inches.

6 0

3 years ago

Valentin [98]

Answer 20 are left

Step-by-step explanation:

6 0

3 years ago

What are the points of discontinutity y=(x-3)/x^2-12x+27

madreJ [45]

Answer:

$(3, -\frac{1}{6})$

Step-by-step explanation:

We can rewrite the equation as

$y = \frac{x - 3}{(x - 3)(x - 9)}$

Notice that we have $x - 3$ in both the numerator and the denominator, so it looks like we can divide it out. However, what if $x - 3$ is $0$ ? Then we would have $y = \frac{0}{0 \times (x - 9)} = \frac{0}{0}$ , which is undefined. So although it looks like the numerator and denominator can be simplified, the resulting function we would get from simplification would not have the same behavior as this one (since such a function would be defined for $x = 3$ , but this one is not).

A point of discontinuity refers to a particular point which is included in the simplified function, but which is not included in the original one. In this case, the point which is not included in the unsimplified function is at $x = 3$ . In the simplified version of the function, if we plug in $x = 3$ , we get

$y = \frac{1}{((3) - 9)} = -\frac{1}{6}$

So the point $(3, -\frac{1}{6})$ is our only point of discontinuity.

It's also important to distinguish between specific points of discontinuity and vertical asymptotes. This function also has a vertical asymptote at $x = 9$ (since it causes the denominator to be 0), but the difference in behavior is that in the case of the asymptote, only the denominator becomes 0 for a specific value of $x$

5 0

3 years ago

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