Question 1

Which graph represents the solution set of the inequality x+2>6

Andreyy89

Answer:

x + 2 < 6

x < 4

d represents the inequality

3 0

2 years ago

Read 2 more answers

Given f(x) = (lnx)^3 find the line tangent to f at x = 3

kirill [66]

Explanation

We must the tangent line at x = 3 of the function:

$f(x)=(\ln x)^3.$

The tangent line is given by:

$y=m*(x-h)+k.$

Where:

• m is the slope of the tangent line of f(x) at x = h,

,

• k = f(h) is the value of the function at x = h.

In this case, we have h = 3.

1) First, we compute the derivative of f(x):

$f^{\prime}(x)=\frac{d}{dx}((\ln x)^3)=3*(\ln x)^2*\frac{d}{dx}(\ln x)=3*(\ln x)^2*\frac{1}{x}=\frac{3(\ln x)^2}{x}.$

2) By evaluating the result of f'(x) at x = h = 3, we get:

$m=f^{\prime}(3)=\frac{3}{3}*(\ln3)^2=(\ln3)^2.$

3) The value of k is:

$k=f(3)=(\ln3)^3$

4) Replacing the values of m, h and k in the general equation of the tangent line, we get:

$y=(\ln3)^2*(x-3)+(\ln3)^3.$

Plotting the function f(x) and the tangent line we verify that our result is correct:

Answer

The equation of the tangent line to f(x) and x = 3 is:

$y=(\ln3)^2*(x-3)+(\ln3)^3$

6 0

6 months ago

There are 84 students in the glee club there are 12 more boys than girls what is the ratio of the number of girls to the number

Masja [62]

Let us denote the number of boys in the glee club with X and the number of girls with Y.There are 84 students in the glee club, which means that the following equation can be written:X+Y=84We also now that there are 12 more boys than girls, so:X=Y+12We can rewrite the first equation like:(Y+12)+Y=842Y+12=842Y=62Y=62/2=31X=31+12=43So, the ratio of the number of girls to the number of boys is: Y/X=31/43
Read more on Brainly.com - brainly.com/question/4711779#readmore

5 0

2 years ago

Please solve and explain for number 2

chubhunter [2.5K]

The ratios as fractions are 6/8 and 9/11.
Since they are not compare because they have different denominators you must find the Least Common Multiple of the two fractions.
Since 8 and 11 both can go into 88, we can use that as our denominator.
6/8 times 11/11 equals 66/88 and 9/11 times 8/8 equals 72/88.
66/88 is less than 72/88.

Therefor, Mix B is the reddest mixture.

Hope this helped!! :)

8 0

2 years ago

in an election between two candidates one got 55% of the total valid votes 20% votes were invalid if the total number of votes w

timurjin [86]

Answer:

25%- 1875 Votes

7500 x 0.55 = 4125 (first candite valid votes)

7500 x 0.20 = 1500 (invalid)

first candite valid votes (55) + invalid votes (20) = 75% of total votes

first candite valid votes (4125) + invalid votes (1500 ) = 5625 of total votes

100 (total percent of votes) - 75 (total percent of votes) = 25% Votes Left

7500 (total number of votes) - 5625 (total number of votes) = 1875 Votes Left

7500 x 0.25 = 1875 (valid votes for the other candite)

4 0

2 years ago