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gavmur [86]
3 years ago
14

13 cm Diameter 6.4 cm Find the volume to the nearest hundredth using 3.14 instead of PI

Mathematics
1 answer:
AlekseyPX3 years ago
7 0

Answer:

418.00 cm³

Step-by-step explanation:

The volume of a cylinder is given by πr²h (r being the radius and h being the height)

The radius is half of the diameter: 6.4/2 is 3.2.

The height shown here is 13.

Instead of pi, the question says to use 3.14 instead of pi.

Putting these all together, you get 3.14×(3.2)²×13.

This can be expanded to 3.14×10.24×13.

From there, multiplying it all together gives you 417.9968 cm³.

The problem says to the nearest hundredth, so you want to round it to 2 decimal places. Since the 6 is above 5, it gets rounded up, leaving you with 418.00 cm³.

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Solving for matrices
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Answer:

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Step-by-step explanation:

The augmented matrix for the system of three equaitons is

\left(\begin{array}{ccccc} 3&-4&-5&|&-27\\5&2&-2&|&11\\5&-4&4&|&-7\end{array}\right)

Multiply the first row by 5, the second row by -3 and add these two rows:

\left(\begin{array}{ccccc} 3&-4&-5&|&-27\\0&-26&-19&|&-168\\5&-4&4&|&-7\end{array}\right)

Subtract the third row from the second:

\left(\begin{array}{ccccc} 3&-4&-5&|&-27\\0&-26&-19&|&-168\\0&6&-6&|&18\end{array}\right)

Divide the third row by 6:

\left(\begin{array}{ccccc} 3&-4&-5&|&-27\\0&-26&-19&|&-168\\0&1&-1&|&3\end{array}\right)

Now multiply  the third equation by 26 and add it to the second row:

\left(\begin{array}{ccccc} 3&-4&-5&|&-27\\0&-26&-19&|&-168\\0&0&-45&|&-90\end{array}\right)

You get the system of three equations:

\left\{\begin{array}{r}3x-4y-5z=-27\\-26y-19z=-168\\-45z=-90\end{array}\right.

From the third equation

z=\dfrac{90}{45}=2.

Substitute z=2 into the second equation:

-26y-19\cdot 2=-168\\ \\-26y-38=-168\\ \\-26y=-168+38=-130\\ \\y=\dfrac{130}{26}=5.

Now substitute z=2 and y=5 into the first equation:

3x-4\cdot 5-5\cdot 2=-27\\ \\3x-20-10=-27\\ \\3x-30=-27\\ \\3x=-27+30=3\\ \\x=1.

The solution is (1,5,2)

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3 years ago
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3 0
3 years ago
Read 2 more answers
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tldr; we can treat this like a box that we put something into (x) and we get something back from it (y).

We can then take this data we get and put it in a table.  This is useful for finding patterns.

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6 0
4 years ago
Please help and show working (please)
Alexxandr [17]

In mathematical notation, ∑ means summation. So wherever you see the symbol, you have to sum over all elements in the set. Let's solve the question.

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b. ∑f^{2} means to sum all elements in the set f as the square of the elements f = 5^{2} + 9^{2} + 10^{2} + 16^{2} = 25 + 81 + 100 + 256 = 462

c. ∑mf means to sum all elements as the product of the elements of m and f = (12×5) + (15×9) + (20(12^{2}(5)) + (15^{2}(9)) + (20^{2}(10)) + (30^{2}(16)) = 2114510) + (30×16) = 875

d. ∑m^{2}f means to sum all elements as the product of the square of m and f = ((12*12)(5)) + ((15*15)(9)) + ((20*20)(10)) + ((30*30)(16)) = 21145

4 0
3 years ago
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