Enter the ordered pair for point A in the boxes.

Finding an Equation of a Tangent Line In Exercise, use implicit differentiation to find an equation of the tangent line to the g

Karo-lina-s [1.5K]

Answer:

$y=\frac{4}{3}-\frac{x}{3e}$

Step-by-step explanation:

Equation of tangent line of given function at (e,1) is found by implicitly differentiating the given function w.r.to x

$y^{2}+ln(xy)=2\\\\y^{2}+ln(x)+ln(y)=2\\\\\frac{d}{dx}(y^{2}+ln(x)+ln(y))=\frac{d}{dx}(2)\\\\2y\frac{dy}{dx}+\frac{1}{x}+\frac{1}{y}\frac{dy}{dx}=0\\\\\frac{dy}{dx}(2y+\frac{1}{y})=-\frac{1}{x}\\\\\frac{dy}{dx}=-\frac{y}{x(2y^{2}+1)}\\\\at (e,1)\\\\\frac{dy}{dx}=-\frac{1}{e(2+1)}\\\\\frac{dy}{dx}=\frac{1}{3e}$

Equation of tangent line is

y-y₁=m(x-x₁)

at (e,1)

$y-1=-\frac{1}{3e}(x-e)\\\\y=1-\frac{1}{3e}(x-e)\\\\y=1+\frac{1}{3}-\frac{x}{3e}\\\\y=\frac{4}{3}-\frac{x}{3e}\\$

6 0

4 years ago

How do you solve 5h>4

blagie [28]

Answer:

any number equal or greater than 1

Step-by-step explanation:

5 time what is bigger the 4

8 0

4 years ago

If 10% of a number is 44, 5% of the number is

Musya8 [376]

Answer:

Step-by-step explanation:

10% of 44= 4.4

5% of 4.4=0.22

6 0

3 years ago

Read 2 more answers

Use long division to solve:<br> 2 )3.8

Natasha2012 [34]

The answer is about 0.5263

7 0

4 years ago

There are 16 kids on a soccer team. The players are either boys or girls, and they either prefer playing offense or defense. The

Mariana [72]

Answer:

$P(B|A)=\frac{2}{7}$

Step-by-step explanation:

The probability of $P(B|A)$ can be read as the probability of event B occurring given event A. In this question, event A occurs when the chosen player is a girl. There are 7 girls on the soccer team. Event B occurs when the chose player plays defense. Since $P(B|A)$ stipulates that event A already occurred, we want the probability of choosing a player who prefers defense from the 7 girls. There are 2 girls who prefer defense, hence $P(B|A)=\boxed{\frac{2}{7}}$ .

<u>Alternative:</u>

For dependent events $A$ and $B$ , the conditional probability of event B occurring given A is given by:

$P(B|A)=P(B\cap A)\div P(A)$

$P(B\cap A)$ indicates the intersection of $P(B)$ and $P(A)$ . In this case, it is the probability that both events occur. Since there are 16 kids on the soccer team and only 2 are girls and prefer defense, $P(B\cap A)=\frac{2}{16}=\frac{1}{8}$ . The probability of event A occurring (chosen player is a girl) is equal to the number of girls (7) divided by the number of kids on the team (16), hence $P(A)=\frac{7}{16}$ .

Therefore, the probability of event B occurring, given event A occurred, is equal to:

$P(B|A)=\frac{1}{8}\div \frac{7}{16},\\\\P(B|A)=\frac{1}{8}\cdot \frac{16}{7}=\boxed{\frac{2}{7}}$

5 0

3 years ago