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3 years ago

Discrete math question. can you please make it easier to understand. thanks.

Mathematics

1 answer:

umka21 [38]3 years ago

4 0

Answer:

It doesn't exist

Step-by-step explanation:

The graph must follow the handshake lemma: the sum of odd vertex degrees must be an even number: 1+3+5=9

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PLEASE HELP!!!!<br> Which of these pair of functions are inverse functions?

Mamont248 [21]

Answer:

Option B and C are correct.

Step-by-step explanation:

Inverse function: If both the domain and the range are R for a function f(x), and if f(x) has an inverse g(x) then:

$f(g(x)) = g(f(x)) = x$ for every x∈R.

Let $f(x) = \frac{1}{2}(\ln(\frac{x}{2}) -1)$ and $g(x) = 2e^{2x+1}$

Use logarithmic rules:

$ln e^a = a$

$e^{lnx} = x$

$\ln a^b = b\ln a$

then, by definition;

$f(g(x)) = f(2e^{2x+1}) =\frac{1}{2}(\ln(\frac{2e^{2x+1}}{2})-1)$ = $\frac{1}{2}(\ln(e^{2x+1}}){-1) = \frac{1}{2} (2x+1-1) =\frac{1}{2}(2x) = x$

$g(f(x)) = g(\frac{1}{2}(\ln(\frac{x}{2}) -1)) = 2e^{2({\frac{1}{2}(\ln(\frac{x}{2}) -1})+1$ $2e^{(\ln(\frac{x}{2}) -1+1}=2e^{\ln(\frac{x}{2})} =2\cdot \frac{x}{2} = x$

Similarly;

for $f(x) = \frac{4 \ln(x^2)}{e^2}$ and $g(x) = e^{\frac{e^2 \cdot x}{8} }$

then, by definition;

$f(g(x)) = f(e^{\frac{e^2 \cdot x}{8}}) =\frac{4 \ln {(\frac{e^2 \cdot x}{8})^2}}{e^2}$ = $\frac{8 \ln {(\frac{e^2 \cdot x}{8})}}{e^2} =\frac{8\frac{e^2\cdot x}{8} }{e^2}=\frac{8e^2 \cdot x}{8e^2}=x$

Similarly,

g(f(x)) = x

Therefore, the only option B and C are correct. As the pairs of functions are inverse function.

3 0

3 years ago

Matilda is selling hand-painted vases at a craft fair. She will

sladkih [1.3K]

Answer:

14x>200+5.5, She must sell 15 or more vases

Step-by-step explanation:

14x>200+5.5

14x>205.5

x>14.68*

She must sell 15 or more vases

*You round up because you cannot sell a partial vase

7 0

3 years ago

I am struggling hard out with linear algebra in math level one

Elena L [17]

I would recommend "Introduction to Linear Algebra," by Gilbert Strang. It is a compact but very helpful textbook reference written by a well-known MIT professor. There is a corresponding online MIT course that is free, so that's a bonus. I am currently using it to study linear algebra with no class or previous experience, and I think it does a solid job of explaining things. Each section in the book has a set of questions for you to work through, and answers to selected questions appear in an appendix at the end of the book. Hope this helps!

4 0

3 years ago

Look at screenshotfghfdewefghbvfcdrftgbvfdrtfg

Brut [27]

61.67$ because you round the 7 up to the nearest hundredth

7 0

2 years ago

NEED SOME HELP HERE!!

Stolb23 [73]

Answer:

6 and 8

Step-by-step explanation:

Pythagorean theorem: a² + b² = c²

Given this,

(3x)² + (4x)² = 10²

9x² + 16x² = 100

25x² = 100

Divide both sides by 25

x² = 4

x = 2

Substitute this into 3x and 4x.

3x = 3 * 2 = 6

4x = 4 * 2 = 8

Thus, the answer is 6 and 8

5 0

2 years ago