Assume that 0 a) 25/24 b) -25/24 c) 24/25 d) -24/25

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2/3 + y2/3 = 4 (−3 3 , 1)

vovikov84 [41]

Answer with Step-by-step explanation:

We are given that an equation of curve

$x^{\frac{2}{3}}+y^{\frac{2}{3}}=4$

We have to find the equation of tangent line to the given curve at point $(-3\sqrt3,1)$

By using implicit differentiation, differentiate w.r.t x

$\frac{2}{3}x^{-\frac{1}{3}}+\frac{2}{3}y^{-\frac{1}{3}}\frac{dy}{dx}=0$

Using formula : $\frac{dx^n}{dx}=nx^{n-1}$

$\frac{2}{3}y^{-\frac{1}{3}}\frac{dy}{dx}=-\frac{2}{3}x^{-\frac{1}{3}}$

$\frac{dy}{dx}=\frac{-\frac{2}{3}x^{-\frac{1}{3}}}{\frac{2}{3}y^{-\frac{1}{3}}}$

$\frac{dy}{dx}=-\frac{x^{-\frac{1}{3}}}{y^{-\frac{1}{3}}}$

Substitute the value x= $-3\sqrt3,y=1$

Then, we get

$\frac{dy}{dx}=-\frac{(-3\sqrt3)^{-\frac{1}{3}}}{1}$

$\frac{dy}{dx}=-(-3^{\frac{3}{2}})^{-\frac{1}{3}}=-\frac{1}{-(3)^{\frac{3}{2}\times \frac{1}{3}}}=\frac{1}{\sqrt3}$

Slope of tangent=m= $\frac{1}{\sqrt3}$

Equation of tangent line with slope m and passing through the point $(x_1,y_1)$ is given by

$y-y_1=m(x-x_1)$

Substitute the values then we get

The equation of tangent line is given by

$y-1=\frac{1}{\sqrt3}(x+3\sqrt3)$

$y-1=\frac{x}{\sqrt3}+3$

$y=\frac{x}{\sqrt3}+3+1$

$y=\frac{x}{\sqrt3}+4$

This is required equation of tangent line to the given curve at given point.

8 0

4 years ago

Last year the highest temperature in a city was recorded as 23ºC, and the lowest temperature was recorded as -10ºC. How many deg

DerKrebs [107]

33 degrees C

Step-by-step explanation:

On the integer scale, the numeric values can be added thus

23 to -10

23 to 0 and 0 to -10

23-0 = 23

0 -(-10) = 10

23 + 10 = 33

Thus, 33 degree C is the difference between the two temperatures.

5 0

3 years ago

The calculation of the mean of a population and the expected value of the probability mass function of a Random Variable (RV) ar

Zanzabum

Answer: Hello the options related to your question is missing attached below are the missing options.

A.) The probabilities of the RVs may be equal

B.) The sum of the probabilities of the RVs exceed 1

C.) This is an impossible occurrence

D.) The probabilities of the RVs must be equal

E.) None of the above

answer:

The probabilities of the RVs may be equal ( A )

Step-by-step explanation:

Given that the value of the population mean and the value of probability mass function of a set of random variables are similar

For the Random Variables : 100,200,300,400

The Probability mass function of RV = ( 100 + 200 + 300 + 400 ) / 4

Hence The probabilities of the RVs may be equal

3 0

3 years ago

At the movie theatre, child admission is $5.80 and adult admission is $9.60. On Thursday, 167 tickets were sold for a total sale

saveliy_v [14]

Answer:

93 adult tickets

Step-by-step explanation:

Let 'a' represent the number of adult tickets sold. Then total revenue was ...

9.60a +5.80(167 -a) = 1322

3.80a = 353.40 . . . . . . . . . . subtract 968.60, collect terms

a = 93 . . . . . . . . . . divide by 3.8

93 adult tickets were sold that day.

__

74 child tickets were sold

8 0

3 years ago

Which function , A or B has a greater rate of change ? Be sure to include the values for the rates of change in your answer . Ex

arsen [322]

<h2>Answer:</h2>

A rate of change tells us how one quantity changes in relation to another quantity. In a mathematical language, we can write this as follows:

$Rate \ of \ Change=\frac{Change \ in \ y}{Change \ in \ x}$

For linear functions. the rate of change is the slope of the line. Thus:

FOR THE TABLE:

By taking two points we can get the rate of change, so let's take $(1,5) \ and \ (2,7)$ :

$ROC=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ ROC=\frac{7-5}{2-1} \\ \\ ROC=\frac{2}{1} \\ \\ \boxed{ROC=2}$

FOR THE GRAPH:

Let's take $(1,1) \ and \ (2,4)$ :

$ROC=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ ROC=\frac{4-1}{2-1} \\ \\ ROC=\frac{3}{1} \\ \\ \boxed{ROC=3}$

As you can see, $3>2$ so <em>the ROC of the function given by the graph is greater than the ROC of the function given by the table.</em>

3 0

3 years ago