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Vesnalui [34]
2 years ago
13

Solve the Antiderivative.​

Mathematics
1 answer:
Black_prince [1.1K]2 years ago
3 0
1
∫ -------------------- dx
x² + 6x + 10


1
∫ -------------------- dx
(x+3)² + 1

Let t = x + 3
dt = dx

1
∫ -------------------- dt
t²+1

1/1 arctan(t/1)

1/1 arctan (x+3 / 1)


=arctan(x+3) + C
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jok3333 [9.3K]

Answer:

d

Step-by-step explanation:

the graph increases then goes horizontal

5 0
2 years ago
Read 2 more answers
Let the sample size of leg strengths to be 7 and the sample mean and sample standard deviation be 630 watts and 32 watts, respec
Colt1911 [192]

Answer:

a. There is_<u><em>sufficient</em></u> evidence that the leg

C. 0.010 < P-value < 0.025

b. Power of test = 1- β=0.2066

c. So the sample size is 88

Step-by-step explanation:

We formulate the null and alternative hypotheses as

H0 : u1= u2 against Ha : u1 > u2 This is a right tailed test

Here n= 7 and significance level ∝= 0.005

Critical value for a right tailed test with 6 df is 1.9432

Sample Standard deviation = s= 32

Sample size= n= 7

Sample Mean =x`= 630

Degrees of freedom = df = n-1= 7-1= 6

The test statistic used here is

Z = x- x`/ s/√n

Z= 630-600 / 32 / √7

Z= 2.4797= 2.48

P- value = 0.0023890 > ∝ reject the null hypothesis.

so it lies between 0.010 < P-value < 0.025

b) Power of test if true strength is 610 watts.

For  a right tailed test value of z is = ± 1.645

P (type II error) β= P (Z< Z∝-x- x`/ s/√n)

Z = x- x`/ s/√n

Z= 610-630 / 32 / √7

Z=0.826

P (type II error) β= P (Z< 1.645-0.826)

= P (Z> 0.818)

= 0.7933

Power of test = 1- β=0.2066

(c)

true mean = 610

hypothesis mean = 600

standard deviation= 32

power = β=0.9

Z∝= 1.645

Zβ= 1.282

Sample size needed

n=( (Z∝ +Zβ )*s/ SE)²

n=  ((1.645+1.282) 32/ 10)²

Putting the values  and solving we get 87.69

So the sample size is 88

5 0
3 years ago
Nuclear Power is a perfect example of exponential relations. Canada produces over half of its electricity using nuclear reactors
mario62 [17]

Solution :

Nuclear fission is exponential. With uranium atoms arranged properly it is possible to have the fission effect and cause more and more uranium nuclei to fission. This is known as chain reaction and a number of uranium atoms are fission together to increase exponentially.

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A). The long term nuclear waste are stored in deep excavations and covered with rocks and mud so that the harmful radioactive materials does not escape from them. They are also stored in some high density and thick cylinders and remained isolated in the dump yard from the people and nature.

B). Canada has a high source of renewable sources of energy. This is a clean source of energy and Canada can make best use of it. Most of the energy requirement of Canada can be taken care off by using wind energy. Canada is planning to set up wind energy mills in most of its part and generate electricity from it.

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3 years ago
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Answer:

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Step-by-step explanation:

Let the amount of time, in minutes, be x.

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For Container B, we can write:

500 - 6x [since it has 500 and is being drained with 6 per minute]

To find, we equate them and solve for x:

200+6x=500-6x\\6x+6x=500-200\\12x=300\\x=\frac{300}{12}\\x=25

<em>So, in 25 minutes (m), the two containers will have same amount of water</em>

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