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3 years ago

5

The exponential function g, represented in the table, can be written as g(x)=a times b^x x g, left parenthesis, x, right parenth

esis, equals, a, dot, b, start superscript, x, end superscript. xxx g(x)g(x)g, left parenthesis, x, right parenthesis 000 121212 111 222 Complete the equation for g(x)g(x)g, left parenthesis, x, right parenthesis. g(x)=g(x)=

2 answers:

boyakko [2]3 years ago

8 0

Answer:

12 times (3/4) ^x

Step-by-step explanation:

Vikki [24]3 years ago

5 0

On khan academy the answer is g(x)=12( $\frac{1}{6}$ )^x

:)

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Physics students were modeling the height of a ball once it was dropped from the top of a 10 foot ladder. The

julsineya [31]

Answer:

<em>Interval notation: [0, 2.236]</em>

<em>Set Builder notation: </em> $\{t\ |\ 0\le t\le 2.236\}$

Step-by-step explanation:

Given that:

Equation of height of the ball dropped from a height of 10 foot, as:

$h(t) = 10 - 2t^2$

Where $t$ is the time since the ball was dropped.

To find:

The domain of the function in Interval and set builder notation.

Solution:

<em>Domain of a function </em>is defined as the set of valid input values that can be given to the function for which the function is defined.

Here, input is time.

We can not have negative values for time.

Therefore, starting value for time will be <em>0 seconds</em>.

And the value of height can not be lesser than that of 0 ft.

$0= 10 - 2t^2\\\Rightarrow 2t^2=10\\\Rightarrow t^2=5\\\Rightarrow t =2.236\ seconds$

Maximum value for time can be 2.236 seconds.

Therefore the domain is:

<em>Interval notation: [0, 2.236]</em>

<em>Set Builder notation: </em> $\{t\ |\ 0\le t\le 2.236\}$

4 0

3 years ago

It has been reported that men are more likely than women to participate in online auctions. In a recent survey, 65% of responde

vivado [14]

Answer:

0.84 or 84%

Step-by-step explanation:

Let 'n' be number of people who took the survey, the number of men who answered the survey is 0.45n. The number of men who answered the survey and have participated in online auctions is 0.38n. Therefore, choosing from the population of men who took the survey (0.45n) the probability that a respondent had participated in an online auction is:

$P =\frac{0.38n}{0.45n}\\P=0.84$

8 0

3 years ago

Solve the equation: X to the 4th power - 81=0

Musya8 [376]

$x^4-81=0\\
x^4=81\\
x^4=3^4 \vee x^4=(-3)^4\\x=3 \vee x=-3$

5 0

3 years ago

You were given a free ticket for a boat ride for you and 2 people of your choice. Sadly,5 of your friends want to

givi [52]

✨Jokes on you I only have two friends✨

6 0

3 years ago

The indicated function y1(x is a solution of the given differential equation. use reduction of order or formula (5 in section 4.

Taya2010 [7]

Given a solution $y_1(x)=\ln x$ , we can attempt to find a solution of the form $y_2(x)=v(x)y_1(x)$ . We have derivatives

$y_2=v\ln x$
${y_2}'=v'\ln x+\dfrac vx$
${y_2}''=v''\ln x+\dfrac{v'}x+\dfrac{v'x-v}{x^2}=v''\ln x+\dfrac{2v'}x-\dfrac v{x^2}$

Substituting into the ODE, we get

$v''x\ln x+2v'-\dfrac vx+v'\ln x+\dfrac vx=0$
$v''x\ln x+(2+\ln x)v'=0$

Setting $w=v'$ , we end up with the linear ODE

$w'x\ln x+(2+\ln x)w=0$

Multiplying both sides by $\ln x$ , we have

$w' x(\ln x)^2+(2\ln x+(\ln x)^2)w=0$

and noting that

$\dfrac{\mathrm d}{\mathrm dx}\left[x(\ln x)^2\right]=(\ln x)^2+\dfrac{2x\ln x}x=(\ln x)^2+2\ln x$

we can write the ODE as

$\dfrac{\mathrm d}{\mathrm dx}\left[wx(\ln x)^2\right]=0$

Integrating both sides with respect to $x$ , we get

$wx(\ln x)^2=C_1$
$w=\dfrac{C_1}{x(\ln x)^2}$

Now solve for $v$ :

$v'=\dfrac{C_1}{x(\ln x)^2}$
$v=-\dfrac{C_1}{\ln x}+C_2$

So you have

$y_2=v\ln x=-C_1+C_2\ln x$

and given that $y_1=\ln x$ , the second term in $y_2$ is already taken into account in the solution set, which means that $y_2=1$ , i.e. any constant solution is in the solution set.

4 0

3 years ago