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3 years ago

Y=sech(tan‐¹x) find the derivative

Mathematics

1 answer:

Klio2033 [76]3 years ago

8 0

Recall that

d/dx sech(x) = - sech(x) tanh(x)

d/dx tan⁻¹(x) = 1/(1 + x²)

Then by the chain rule,

dy/dx = - sech(x) tanh(x) / (1 + x²)

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The mean consumption of water per household in a city was 1425 cubic feet per month. Due to a water shortage because of a drough

liberstina [14]

Answer:

a) $t=\frac{1175-1425}{\frac{250}{\sqrt{100}}}=-10$

The degrees of freedom are given by:

$df=n-1=100-1=99$

The p value for this case would be given by:

$p_v =P(t_{99}$

Since the p value is significantly lower than he significance level given we have enough evidence to reject the null hypothesis and we can conclude that the true mean is lower than 1425

b) For this case we need to find a critical value in the t distribution with 99 degrees of freedom who accumulates 0.025 of the area in the right tail and we got:

$t_{\alpha/2}=1.984$

Since the calculated value is higher than the critical value we can reject the null hypothesis at the significance level provided and we can say that the true mean is higher than 1425

Step-by-step explanation:

Information given

$\bar X=1175$ represent the sample mean for the cubic feets of households

$\sigma=250$ represent the population standard deviation

$n=100$ sample size

$\mu_o =1425$ represent the value to verify

$\alpha=0.025$ represent the significance level

t would represent the statistic

$p_v$ represent the p value

Part a

We want to test that the mean consumption of water per household has decreased due to the campaign by the city council, the system of hypothesis would be:

Null hypothesis: $\mu \geq 1425$

Alternative hypothesis: $\mu < 1425$

Since we don't know the deviation the statistic is given by:

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

The statistic is given by:

$t=\frac{1175-1425}{\frac{250}{\sqrt{100}}}=-10$

The degrees of freedom are given by:

$df=n-1=100-1=99$

The p value for this case would be given by:

$p_v =P(t_{99}$

Since the p value is significantly lower than he significance level given we have enough evidence to reject the null hypothesis and we can conclude that the true mean is lower than 1425

Part b

For this case we need to find a critical value in the t distribution with 99 degrees of freedom who accumulates 0.025 of the area in the right tail and we got:

$t_{\alpha/2}=1.984$

Since the calculated value is higher than the critical value we can reject the null hypothesis at the significance level provided and we can say that the true mean is higher than 1425

6 0

3 years ago

if 6th term of an ap is -10 and 10 th term is -26 then find thr 15 term plzzzzzzzzzzzzzzzzzzzzzzz answer i will give whatever y

Rudik [331]

Answer:

-46

Step-by-step explanation:

We need to find the common difference of this arithmetic sequence:

$\frac{-26-(-10)}{10-6} =\frac{-16}{4} =-4$

So, the common difference d = -4. We can now write the equation:

$a_n=a_1+d(n-1)$

$a_{15}=a_6+d(15-6)=-10-4(9)=-10-36=-46$

So, the 15th term is -46.

Hope this helps!

5 0

3 years ago

Read 2 more answers

Enny White is shopping for CDs. She decides to purchase 3 movie soundtracks. The music store has 7 different movie soundtracks i

Gala2k [10]

Answer:

35 different selections of soundtracks are possible

Step-by-step explanation:

Total number of soundtracks available at the store = 7

Enny decides to purchase 3 movie soundtracks.

So, in this problem we have to find in how many ways can Enny chose 3 soundtracks out of 7. The order in which the soundtracks are chosen does not matter e.g soundtracks A,B and C are the same as soundtracks B,C and A.

In an arrangement when the order does not matter, we use combinations to find the total possible number of arrangements or selections.

So, for this problem choosing 3 soundtracks out of 7 means forming combinations from 7 objects taken 3 at a time. This can be represented mathematically as:

$^{7}C_{3}$

The general formula for combinations is:

$^{n}C_{r}=\frac{n!}{r!\times(n-r)!}$

Using the values, we get:

$^{7}C_{3}=\frac{7!}{3!\times(7-3)!} =35$

This means, Enny can make 35 different selections of soundtracks.

7 0

3 years ago

The area of the rectangular sandbox at Dave’s school is 108 square feet. The sand box has a width of 9 feet as shown in the diag

atroni [7]

What is the question?

7 0

3 years ago

Solve C = AB + D for B.

OLEGan [10]

Answer:

(C-D)/A = B

Step-by-step explanation:

C = AB + D

Subtract D from both side

C-D = AB + D-D

C-D = AB

Divide each side by A

(C-D)/A = AB/A

(C-D)/A = B

8 0

4 years ago

Y=sech(tan‐¹x) find the derivative ​

Y=sech(tan‐¹x) find the derivative