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3 years ago

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Tameron is driving 540 miles to college. If he drives at an average rate of 45 miles per hour, how many hours will it take him t

o get 3434 of the way there?

1 answer:

andreev551 [17]3 years ago

5 0

Given:
540 miles to college
average rate of 45 miles per hour

How many hours will it take him to get 3/4 of the way there?

540 miles * 3/4 = (540 * 3) / 4 = 1620/4 = 405 miles

405 miles / 45 mph = 9 hours.

It would take Tameron 9 hours to travel 3/4 of the way there.

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Find an explicit solution to the Bernoulli equation. y'-1/3 y = 1/3 xe^xln(x)y^-2

NNADVOKAT [17]

$y'-\dfrac13y=\dfrac13xe^x\ln x\,y^{-2}$

Divide both sides by $\dfrac13y^{-2}(x)$ :

$3y^2y'-y^3=xe^x\ln x$

Substitute $v(x)=y(x)^3$ , so that $v'(x)=3y(x)^2y'(x)$ .

$v'-v=xe^x\ln x$

Multiply both sides by $e^{-x}$ :

$e^{-x}v'-e^{-x}v=x\ln x$

The left side can be condensed into the derivative of a product.

$(e^{-x}v)'=x\ln x$

Integrate both sides to get

$e^{-x}v=\dfrac12x^2\ln x-\dfrac14x^2+C$

Solve for $v(x)$ :

$v=\dfrac12x^2e^x\ln x-\dfrac14x^2e^x+Ce^x$

Solve for $y(x)$ :

$y^3=\dfrac12x^2e^x\ln x-\dfrac14x^2e^x+Ce^x$

$\implies\boxed{y(x)=\sqrt[3]{\dfrac14x^2e^x(2\ln x-1)+Ce^x}}$

4 0

2 years ago

A simple random sample with n = 58 provided a sample mean of 24.5 and a sample standard deviation of 4.4. (Round your answers to

nasty-shy [4]

Answer: (23.53, 25.47)

Step-by-step explanation:

The confidence interval for population mean(when population standard deviation is unknown) is given by :-

$\overline{x} \pm\ t^*\dfrac{s}{\sqrt{n}}$

, where $\overline{x}$ = sample mean

n = sample size.

s = sample standard deviation.

t* = Critical value.

Given : $\overline{x}=24.5$

s= 4.4

Confidence level = 90% =0.090

Significance level = $\alpha=1-0.90=0.10$

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Degree of freedom : df= n-1= 57

Using t-distribution table , the critical value :

$t_{\alpha/2,\ df}= t_{0.05,\ 57}=1.6720$

Then, the confidence interval will be :-

$24.5 \pm\ (1.6720)\dfrac{4.4}{\sqrt{58}}$

$24.5 \pm\ (1.6720)\dfrac{4.4}{7.61577310586}$

$24.5 \pm\ 0.965995165263\approx24.5\pm0.97\\\\=(24.5-0.97,\ 24.5+0.97)\\\\=(23.53,\ 25.47)$

Hence, a 90% confidence interval for the population mean = (23.53, 25.47)

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3 years ago

The angles in a triangle are in the ratio 1 2 3 show that the triangle is a right angled triangle

adelina 88 [10]

Answer:

If in a 1:2:3 ratio, then

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Therefore, triangle must have angles of 30, 60, 90

Step-by-step explanation:

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2 years ago

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Tju [1.3M]

5x+25=85

Add 25 because he already saved that amount of money
5x because 5 is the amount of money he makes a week and x= number of weeks.
And =85 because that’s the total cost
To find the amount of weeks, just solve the equation
5x+25=85
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2 years ago

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Natasha2012 [34]

Answer:

yes

Step-by-step explanation:

that is correct unless your asking something else?

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2 years ago