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Mazyrski [523]
2 years ago
6

What is 5 to the fourth power

Mathematics
2 answers:
Ivahew [28]2 years ago
8 0

Answer:

5^4 is 625

Step-by-step explanation:

5×5=25

25×5=125

125×5=625

1. 2. 3. 4. =

5×5×5×5=625

Basile [38]2 years ago
4 0
5^4 is 625 hope I could help
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The area enclosed by the graphs of y = 1/x, y = 1, and x = 3 is rotated about the line y = -1. Find the volume and show steps.
Natalija [7]

Answer:

A=\pi\displaystyle\biggr[\frac{16}{3}-2\ln(|3|)\biggr]\approx9.8524

Step-by-step explanation:

Use the Washer Method A=\pi\displaystyle \int\limits_{a}^{b}{\bigr[R(x)^2-r(x)^2\bigr] \, dx where R(x) is the outer radius and r(x) is the inner radius.

If we sketch out the graph, we see that y=1 intersects points (1,1) and (3,1), which will be our bounds of integration.

Here, our outer radius will be R(x)=(-1-1)=-2 and our inner radius will be r(x)=-1-\frac{1}{x}.

Thus, we can compute the integral and find the volume:

A=\pi\displaystyle\int\limits^{3}_{1} {(-2)^2-\biggr(-1-\frac{1}{x}\biggr)^2 } \, dx\\ \\A=\pi\displaystyle\int\limits^{3}_{1} {4-\biggr(1+\frac{2}{x}+\frac{1}{x^2}  \biggr) } \, dx\\\\A=\pi\displaystyle\int\limits^{3}_{1} {4-1-\frac{2}{x}-\frac{1}{x^2}} \, dx\\\\A=\pi\displaystyle\int\limits^{3}_{1} {3-\frac{2}{x}-\frac{1}{x^2}} \, dx\\\\A=\pi\displaystyle\biggr[3x-2\ln(|x|)+\frac{1}{x}\biggr]\Biggr|_{1}^{3}\\

A=\pi\displaystyle\biggr[\biggr(3(3)-2\ln(|3|)+\frac{1}{3}\biggr)-\biggr(3(1)-2\ln(|1|)+\frac{1}{1}\biggr)\biggr]\\\\A=\pi\displaystyle\biggr[\biggr(9-2\ln(|3|)+\frac{1}{3}\biggr)-\biggr(3+1\biggr)\biggr]\\\\A=\pi\displaystyle\biggr[\biggr(\frac{28}{3}-2\ln(|3|)\biggr)-\biggr(4\biggr)\biggr]\\A=\pi\displaystyle\biggr[\frac{16}{3}-2\ln(|3|)\biggr]\\A\approx9.8524

In conclusion, the volume of the solid of revolution will be about 9.8524 cubic units. See the attached graph for a helpful visual!

3 0
2 years ago
The owner of a busy coffee shop wanted to see if it was worth keeping tea on the menu. She logged the number of cups of tea she
Nimfa-mama [501]

Answer:

mean = 7

median = 7

range = 9

mid range = 7.5

Step-by-step explanation:

3, 5, 6, 7, 7, 9, 12

Range is the difference between the highest and lowest values of a set of observations

Range = highest value - lowest value

12 - 3 = 9  

Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order

3, 5, 6, 7, 7, 9, 12

median = 7

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

(6 + 12 + 5 + 7+  7 + 3 + 9) / 7 = 7

Mid range = (highest value + lowest value) / 2

(12 + 3) / 2 = 7.5

8 0
2 years ago
What is 3 2/9 * -1 5/7
oksian1 [2.3K]

Answer:

-116/21  or -5 11/21

Step-by-step explanation:

7 0
3 years ago
Solve the given equation by completing the square.
Dmitriy789 [7]

Answer:

a = -4, b = 3 and c = 6 (OR)

a = -4, b = -3 and c = 6

Step-by-step explanation:

x^{2} +8x = 38

Add 16 to both sides.

x^{2} +8x+16 = 38 + 16

(x+4)^{2} =54

x + 4 = \sqrt{54} or x + 4 = -\sqrt{54}

x+4=3\sqrt{6} or x+4=-3\sqrt{6}

x=-4+3\sqrt{6} or x=-4-3\sqrt{6}

Therefore, a = -4, b = 3 and c = 6 (OR)

a = -4, b = -3 and c = 6

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3 years ago
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2 years ago
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