How do I solve this question

Determine the domain and range of the function . f(x)=2 3√ 108^2x {x| all real numbers}; {y| y > 0} {x| all real numbers}; {y

Gala2k [10]

Answer:

Domain : {x | all real numbers} ; Range: {y | y > 0}

Step-by-step explanation:

The function can be written as :

$f(x)=\sqrt[\frac{2}{3}]{108^{2\cdot x}}\\\\\implies f(x)=(108)^{(\frac{3}{2})^{2\cdot x}}$

Now, since x is exponent so it can take any real values. So, its domain of f(x) is all real numbers

But value of f(x) can not be less than 1 because for x = 0 the value of f(x) is 1 and also for any values of x, the value of f(x) can never be less than 1

So, Range of f(x) is all real numbers greater than 0

Hence, Domain and Range of f(x) is given by :

Domain : {x | all real numbers} ;

Range: {y | y > 0}

4 0

2 years ago

Read 2 more answers

Please help with 15, 17 and 19

Irina-Kira [14]

Given:

15. $\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)$

17. $\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)$

19. $2^{\log_2100}$

To find:

The values of the given logarithms by using the properties of logarithms.

Solution:

15. We have,

$\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)$

Using property of logarithms, we get

$\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)=1$ $[\because \log_aa=1]$

Therefore, the value of $\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)$ is 1.

17. We have,

$\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)$

Using properties of logarithms, we get

$\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)=-\log_{\frac{3}{4}}\left(\dfrac{3}{4}\right)$ $[\because \log_a\dfrac{m}{n}=-\log_a\dfrac{n}{m}]$

$\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)=-1$ $[\because \log_aa=1]$

Therefore, the value of $\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)$ is -1.

19. We have,

$2^{\log_2100}$

Using property of logarithms, we get

$2^{\log_2100}=100$ $[\because a^{\log_ax}=x]$

Therefore, the value of $2^{\log_2100}$ is 100.

6 0

2 years ago

The life of a semiconductor laser at a constant power is normally distributed with a mean of 7,000 hours and a standard deviatio

Scrat [10]

This question not incomplete

Complete Question

The life of a semiconductor laser at a constant power is normally distributed with a mean of 7,000 hours and a standard deviation of 600 hours. If three lasers are used in a product and they are assumed to fail independently, the probability that all three are still operating after 7,000 hours is closest to? Assuming percentile = 95%

Answer:

0.125

Step-by-step explanation:

Assuming for 95%

z score for 95th percentile = 1.645

We find the Probability using z table.

P(z = 1.645) = P( x ≤ 7000)

= P(x<Z) = 0.95

After 7000 hours = P > 7000

= 1 - P(x < 7000)

= 1 - 0.95

= 0.05

If three lasers are used in a product and they are assumed to fail independently, the probability that all three are still operating after 7,000 hours is calculated as:

(P > 7000)³

(0.05)³ = 0.125

7 0

2 years ago

Plzzzz help!!! Due tomorrow!!!

-Dominant- [34]

Answer:

Quad One: A

Quad Two: C

Quad Three: B

Quad Four: E

Hope This Helps! Have A Nice Night!!

5 0

2 years ago

Read 2 more answers

Which side is adjacent to

Akimi4 [234]

Answer:

Answer is on the pic

Step-by-step explanation:

I hope it's helpful!

4 0

2 years ago