1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Evgesh-ka [11]
3 years ago
5

I need some help with this calculus 1 implicit diffrention problem?

Mathematics
1 answer:
katen-ka-za [31]3 years ago
7 0

Answer:

y" = -24 / y³

Step-by-step explanation:

6x² + y² = 4

Take the derivative of both sides with respect to x.

12x + 2y y' = 0

Again, take the derivative of both sides with respect to x.

12 + 2y y" + y' (2y') = 0

12 + 2y y" + 2(y')² = 0

Solve for y' in the first equation.

2y y' = -12x

y' = -6x/y

Substitute and solve for y":

12 + 2y y" + 2(-6x/y)² = 0

12 + 2y y" + 2(36x²/y²) = 0

12 + 2y y" + 72x²/y² = 0

6y² + y³ y" + 36x² = 0

y³ y" = -36x² − 6y²

y" = (-36x² − 6y²) / y³

Solve for y² in the original equation and substitute:

y² = 4 − 6x²

y" = (-36x² − 6(4 − 6x²)) / y³

y" = (-36x² − 24 + 36x²) / y³

y" = -24 / y³

You might be interested in
Solve k(h-j)+h with h=5 ,j= -4, k=5
kifflom [539]
They gave you an eqution with variables and then they gave you numbers that all you have to do is put in
k(h-j)+h
5(5-4)+5
5(1)+5
5+5
10
5 0
4 years ago
How can I simplify/rewrite the 1st(top) equation into the 2nd(Botton),please show a step by step solution.​
Vaselesa [24]

Answer:

see below

Step-by-step explanation:

-2(4 - \frac{x}{2} )^{5} + C

Think of the above as:

  -\frac{2}{1} * (\frac{8}{2} - \frac{x}{2} )^{5} + C

= -\frac{2}{1} * \frac{(8 - x)^{5}}{2^{5}}  + C

= -\frac{2}{1} * \frac{(8 - x)^{5}}{32}  + C

= -\frac{1}{1} * \frac{(8 - x)^{5}}{16}  + C

=   \frac{-1(8 - x)^{5}}{16}  + C

=   \frac{(-8 + x)^{5}}{16}  + C

Can flip it around to be...

\frac{(x - 8)^{5}}{16}  + C

4 0
3 years ago
Haya la integral de xarcsenx/((1-x^2)^1/2). Utiliza la sustitución de t= arcsenx
ikadub [295]

Answer:

<em>Explicación más abajo</em>

Step-by-step explanation:

Integración Indefinida

La integral

I=\int \dfrac{x .arcsen\left(x\right)}{\sqrt{1-x^2}}

Se resuelve con el cambio de variables:

t=arcsen(x)

Una vez hechos los cambios, la integral se resuelve en función de t:

I=sen(t)-t.cos(t)+C

Hay que devolver los cambios para mostrarla en función de x.

El cambio de variables también se puede escribir:

x=sen(t)

Recordando que

cos(t)=\sqrt{1-sen^2(t)}

Entonces:

cos(t)=\sqrt{1-x^2}

Devolviendo los cambios:

I=sen(t)-t.cos(t)+C=x-arcsen(x)\sqrt{1-x^2}+C

Es la respuesta correcta

7 0
3 years ago
The function ƒ(x) = 6x is vertically shrunk by a factor of ½ and translated 9 units in the negative y- direction. Select the cor
vlada-n [284]

Answer:

A

Step-by-step explanation:

3 0
3 years ago
A forester studying diameter growth of red pine believes that the mean diameter growth will be different from the known mean gro
-Dominant- [34]

Answer:

t=\frac{1.6-1.35}{\frac{0.46}{\sqrt{32}}}=3.07  

The degrees of freedom are given by:

df =n-1= 32-1=31

Since is a two-sided test the p value would be:  

p_v =2*P(t_{31}>3.07)=0.0044  

Since the p value is a very low value we have enough evidence to conclude that true mean is significantly different from 1.35 in/year at any significance level commonly used for example (\alpha=0.01,0.05, 0.1, 0.15).

Step-by-step explanation:

Data given and notation  

\bar X=1.6 represent the sample mean

s=0.46 represent the sample deviation

n=32 sample size  

\mu_o =1.35 represent the value that we want to test  

\alpha represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is different from 1.35 in/year, the system of hypothesis would be:  

Null hypothesis:\mu =1.35  

Alternative hypothesis:\mu \neq 1.35  

The statistic is given by:

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}} (1)  

Calculate the statistic  

We can replace in formula (1) the info given like this:  

t=\frac{1.6-1.35}{\frac{0.46}{\sqrt{32}}}=3.07  

P-value  

The degrees of freedom are given by:

df =n-1= 32-1=31

Since is a two-sided test the p value would be:  

p_v =2*P(t_{31}>3.07)=0.0044  

Since the p value is a very low value we have enough evidence to conclude that true mean is significantly different from 1.35 in/year at any significance level commonly used for example (\alpha=0.01,0.05, 0.1, 0.15).

5 0
3 years ago
Other questions:
  • Your grandma lives 300 miles away. To go to her house, your average is 60 miles per hour(60mph). On the way home, you travel a b
    8·1 answer
  • Which line is perpendicular to the line whose equation is 5y + 6 = -3x?
    11·1 answer
  • An equation of the horizontal line that passes through the point (-2,5)
    8·1 answer
  • A sphere has a diameter of 8 feet.What is its surface area in square inches?Round your answer to the nearest hundredth.Use 3.14
    11·1 answer
  • Help me please please ‼️‼️
    15·1 answer
  • 5c+10=40.................
    9·2 answers
  • 10 The table shows the cost of blueberries at a local farmer's
    12·1 answer
  • Find (a) the range and (b) the standard deviation of the data set 40,35.45,55,60. Round to the nearest hundredth if necessary.
    11·1 answer
  • You are x year old. Write an expression to describe your uncle’s age
    9·1 answer
  • There are 5 red, 7 orange and 8 blue tickets in a bowl.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!