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3 years ago

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Mathematics

1 answer:

OLEGan [10]3 years ago

5 0

The radius of the cylinder would be 17.99544

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Fundamental theorem of calculus<br> <img src="https://tex.z-dn.net/?f=g%28s%29%3D%5Cint%5Climits%5Es_6%20%7B%28t-t%5E4%29%5E6%7D

mr_godi [17]

Answer:

$\displaystyle g'(s) = (s-s^4)^6$

Step-by-step explanation:

The Fundamental Theorem of Calculus states that:
$\displaystyle \frac{d}{dx}\left[ \int_a^x f(t)\, dt \right] = f(x)$

Where <em>a</em> is some constant.

We can let:
$\displaystyle g(t) = (t-t^4)^6$

By substitution:

$\displaystyle g(s) = \int_6^s g(t)\, dt$

Taking the derivative of both sides results in:
$\displaystyle g'(s) = \frac{d}{ds}\left[ \int_6^s g(t)\, dt\right]$

Hence, by the Fundamental Theorem:

$\displaystyle \begin{aligned} g'(s) & = g(s) \\ \\ & = (s-s^4)^6\end{aligned}$

3 0

2 years ago

a basketball team played five games . in those games , the team won by 7 points , lost by 3 , won by 4, lost by 2 , and won by 9

Paul [167]

Answer: 3

Step-by-step explanation:

7-3+4-2+9=15

15/5=3

6 0

3 years ago

. A study of one thousand teens found that the number of hours they spend on social networking sites each week is normally distr

Gnesinka [82]

We are given the following data:

Sample Size = n = 1000

Sample Mean = u = 15 hours

Population Standard Deviation = s = 2 hours

Since we know the population standard deviation, we can use z distribution to find the confidence interval about the mean. z value for 95% confidence interval is 1.96.

Formula for the confidence interval is:

$(u-z\frac{s}{\sqrt{n}} , u+z\frac{s}{\sqrt{n}})$

Using the values in the formula, we get:

$(15-1.96\cdot\frac{2}{\sqrt{1000}}, 15+1.96\cdot\frac{2}{\sqrt{1000}})\\ \\ (14.88,15.12)$

Therefore, the 95% confidence interval about the population mean is 14.88 hours to 15.12 hours. So B option is the correct answer.

4 0

3 years ago

Read 2 more answers

Cornelius has 25 nickels, 39 dimes, 22 quarters, and 12 fifty-cent pieces. How

Mars2501 [29]

Answer:

16.65$

Step-by-step explanation:

6 0

3 years ago

Find the volume of a pyramid with a square base, where the perimeter of the base is 8.2\text{ cm}8.2 cm and the height of the py

7nadin3 [17]

Answer:

$V=18.2cm^3$

Step-by-step explanation:

The volume of the pyramid is given by:

$V=\frac{A_{b}h}{3}$

where $A_{b}$ is the area of the base and $h$ is the height.

We know that the height is:

$h=13cm$

Thus we need to find the area of the square at the base.

The perimeter of the square is:

$p=8.2cm$

this means that the length of the sides of the square is :

$l=\frac{p}{4}\\ \\l=\frac{8.2cm}{4}\\ \\l=2.05cm$

Now we can find the area of the base which the area of the square:

$A_{b}=l^2\\A_b=(2.05cm)^2\\A_b=4.2025cm^2$

and finally we find the volume:

$V=\frac{A_{b}h}{3}$

$V=\frac{(4.2025cm^2)(13cm)}{3}\\ \\V=\frac{54.6325cm^3}{3}\\ \\V=18.2108cm^3$

Which rounded to the nearest tenth of a cubic centimeter is: $V=18.2cm^3$

3 0

3 years ago