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3 years ago

Helppppp meeeeeeplzzzzzzzzzz

Mathematics

1 answer:

ss7ja [257]3 years ago

6 0

<1 and <5 are corresponding angles

answer
C. corresponding angles

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(a) Find the domain off (x) = ln(ex − 3).<br> (b) Find F −1 and its domain.

Anettt [7]

Answer:

a) The domain of f(x) is $x > 1.1$ .

The inverse function is:

$y = \ln{(e^{x} + 3)}The domain is all the real values of x.Step-by-step explanation:(a) Find the domain off f(x) = ln(e^x − 3)The domain of f(x) = ln(g(x)) is g(x) > 0. That means that the ln function only exists for positive values.So, here we have[tex]g(x) = e^{x} - 3$

So we need

$e^{x} - 3 > 0$

$e^{x} > 3$

Applying ln to both sides

$\ln{e^{x}} > \ln{3}$

$x > 1.1$

So the domain of f(x) is $x > 1.1$ .

(b) Find F −1 and its domain.

$F^{-1}$ is the inverse function of f.

How do we find the inverse function?

To find the inverse equation, we change y with x to form the new equation, and then we isolate y in the new equation. So:

Original equation:

f(x) = y = \ln{e^{x} - 3}

New equation

$x = \ln{e^{y} - 3}$

Here, we apply the exponential to both sides:

$e^{x} = e^{\ln{e^{y} - 3}}$

$e^{y} - 3 = e^{x}$

$e^{y} = e^{x} + 3$

Applying ln to both sides

$\ln{e^{y}} = \ln{e^{x} + 3}$

The inverse function is:

$y = \ln{e^{x} + 3}$

The domain is

$e^{x} + 3 > 0$

$e^{x} > -3$

$e^{x}$ is always a positive number, so it is always going to be larger than -3 no matter the value of x. So the domain are all the real values.

5 0

3 years ago

How do i sovle number 48

Jet001 [13]

The price reduced from 250 to 200, so it is -50

3 0

4 years ago

Read 2 more answers

Write three fractions equivalent to

Bogdan [553]

Answer:

I. think it is12, 6, 2, 1

8 0

3 years ago

If you measure a tds of 1.4%, and you used a brew ratio of 15, what is the percent extraction?

sweet-ann [11.9K]

Answer: the extraction is 18.2%.

Explanation:

Let's see few definitions:
TDS = Total Dissolved Solids = solids dissolved in the brew
PE = Percent Extraction = percent of solids extracted from the dry coffee grounds

The percent extraction can be calculated by the formula:
PE = TDS × Rm

where
Rm = ratio between the mass of the brew and the mass of dry grounds

Now, you need to consider the following facts:
1) every 1g of coffee absorbs 2g of water
2) the given brew ratio is 1:15, which means that for every 1g of grounds we use 15g of water

Let's call
x = grams of coffee grounds we want to use
Therefore the mass of the brew will be:
m(brew) = water we use - water absorbed by the coffee
= 15·x - 2·x
= 13·x

Therefore,
Rm = m(brew) / x
= 13·x / x
= 13

Hence, the percent of extraction will be:
PE = <span> TDS × Rm
= 1.4 </span>× 13
= 18.2

4 0

3 years ago

Which equation can be used to find mArc M N? mArc M N + 150 = 180 mArc M N + 150 = 360 mArc M N – 150 = 180 mArc M N – 150 = 360

olga2289 [7]

Answer:

Step-by-step explanation:

trust me

8 0

3 years ago

Read 2 more answers