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3 years ago

Does 2^8 equal (3sqrt{16})^6

Mathematics

1 answer:

ale4655 [162]3 years ago

4 0

Answer:

Does 2⁸ = (3√16)⁶? No.

Step-by-step explanation:

2⁸ = (3√16)⁶

Evaluate 2⁸. This can simply be written out as:

2 * 2 * 2 * 2 * 2 * 2 * 2 * 2

4 * 2 * 2 * 2 * 2 * 2 * 2

8 * 2 * 2 * 2 * 2 * 2

16 * 2 * 2 * 2 * 2

32 * 2 * 2 * 2

64 * 2 * 2

128 * 2

256.

256 = (3√16)⁶

Evaluate √16.

256 = (3*4)⁶

Multiply 3 and 4.

256 = 12⁶

Evaluate 12⁶. This can be rewritten as:

12 * 12 * 12 * 12 * 12 * 12

144 * 12 * 12 * 12 * 12

1728 * 12 * 12 * 12

20736 * 12 * 12

248832 * 12

2985984.

Since 256 ≠ 2985984, the answer to this question is no.

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Working alone, Henry takes 3 hours less than Mary to clean the carpets in the entire office. Working together, they can clean th

Sati [7]

Answer:

It would take Henry 3 hours to clean the office carpets if Mary were not there to help

Step-by-step explanation:

Assume that it takes Henry t hours to clean the carpets

∵ Henry takes 3 hours less than Mary to clean the carpets

∵ Henry takes t hours

- That means add 3 to t to find Mary time

∴ Mary takes t + 3 hours

∵ The rate of Henry is $\frac{1}{t}$

∵ The rate of Mary is $\frac{1}{t+3}$

∵ Working together, they can clean the carpets in 2 hours

- Add the two rates and equate the answer by $\frac{1}{2}$ (their rate together)

∴ $\frac{1}{t}+\frac{1}{t+3}=\frac{1}{2}$

Multiply the two denominators and multiply each numerator by the other denominator to add the two fractions of the left hand side

∵ $\frac{(1)(t+3)}{t(t+3)}+\frac{(1)t}{t(t+3)}=\frac{1}{2}$

∴ $\frac{(t+3)}{t(t+3)}+\frac{t}{t(t+3)}=\frac{1}{2}$

- Add the two fractions in the left hand side

∴ $\frac{t+3+t}{t(t+3)}=\frac{1}{2}$

∴ $\frac{2t+3}{t^{2}+3t}=\frac{1}{2}$

Use the cross multiplication

∵ (t² + 3t)(1) = 2(2t + 3)

∴ t² + 3t = 4t + 6

- Subtract 4t from both sides

∴ t² - t = 6

- Subtract 6 from both sides

∴ t² - t - 6 = 0

- Factorize it into two factors

∴ (t - 3)(t + 2) = 0

Equate each factor by 0 to find t

∵ t - 3 = 0

- Add 3 to both sides

∴ t = 3

∵ t + 2 = 0

- Subtract 2 from both sides

∴ t = -2 ⇒ reject this answer because there is no - ve time

∴ t = 3

∴ Henry would take 3 hours to clean the carpets alone

It would take Henry 3 hours to clean the office carpets if Mary were not there to help

8 0

3 years ago

Samiya bought a tree 3 inches long. Each year, the tree expected to grow 5 inches. How long (How many years) it takes the tree t

Ghella [55]

Answer: 19 years to reach 98 inches

Step-by-step explanation:

Its already 3 inches tall, if it grows 5 inches every year or expected to it would take : 3 + 5 = 8

8 + 5 = 13

13 + 5 = 18

18 + 5 = 23

23 + 5 = 28

28 + 5 = 33

33 + 5 = 38

38 + 5 = 43

43 + 5 = 48

48 + 5 = 53

And it goes on until 98 inches. Leaving your answer : 19 years.

4 0

3 years ago

Can someone help me with 9 and 10 please

AfilCa [17]

It would cross the y-axis at 2 and it would cross the x-axis at -2

Explanation- x is the horizontal line and the y is the vertical line. Basically whichever number the line crosses on the x-axis line or the y-axis line would be your answer.

Hope this helps(:

3 0

3 years ago

A student has gotten the following grades on his tests. What is the minimum grade he must get on the last test in order to have

Schach [20]

Where are the following grades ? how am i supposed to answer without all parts of the question .

6 0

3 years ago

13y-2x=3<br> slope intercept

Fiesta28 [93]

Answer:

World shown below!

Step-by-step explanation:

Slope-intercept form: y = mx + b

13y - 2x = 3

Add 2x to both sides;

13y = 2x + 3

Divide both sides by 13;

$y = \frac{2}{13}x+\frac{3}{13}$

8 0

3 years ago