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Andrews [41]
2 years ago
8

Estimate √53 between two numbers to the tenths place.

Mathematics
1 answer:
ZanzabumX [31]2 years ago
7 0

Answer:

  53 lies between 7.2² and 7.3²

Step-by-step explanation:

Estimating a root to the nearest tenth can be done a number of ways. The method shown here is to identify the tenths whose squares bracket the value of interest.

You have answered the questions of parts 1 to 3.

__

<h3>4.</h3>

You are given that ...

  7.2² = 51.84

  7.3² = 53.29

This means 53 lies between 7.2² and 7.3², so √53 lies between 7.2 and 7.3.

53 is closer to 7.3², so √53 will be closer to 7.3 than to 7.2.

7.3 is a good estimate of √53 to the tenths place.

_____

<em>Additional comment</em>

For an integer n that is the sum of a perfect square (s²) and a remainder (r), the square root is between ...

  s +r/(2s+1) < √n < s +r/(2s)

For n = 53 = 7² +4, this means ...

  7 +4/15 < √53 < 7 +4/14

  7.267 < √53 < 7.286

Either way, √53 ≈ 7.3.

__

The root is actually equal to the continued fraction ...

  \sqrt{n}=\sqrt{s^2+r}=s+\cfrac{r}{2s+\cfrac{r}{2s+\dots}}

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OlgaM077 [116]

Answer:

Step-by-step explanation:

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Then you want to make 4 1/3 into a improper fraction, which would be 13/3 you want to multiply this by 4 and you will get 52/12. You will then add 52/12 to 9/12 and get 61/12 or 5 1/12.

If you need any more help please let me know.

4 0
3 years ago
Jan is 2/3 of Karyn's age. Jan's age 8 years ago is 2/5 of Katyn's age 4 yeats from now. Jan is how many younger than Karyn?
Elden [556K]

Answer:

12 years younger.

Step-by-step explanation:

Let Jan's age be J and Karyn's age be K.

J= \frac{2}{3}  K

Jan's age 8 years ago is 2/5 of Karyn's age 4 yeaRs from now.

J-8 = \frac{2}{5} (K+4)

=> (\frac{2}{3} - \frac{2}{5} ) K = \frac{8}{5} + 8

=> 4K = 48 X 3

=> K= 36.

=> J= 24.

So Jan is 12 years younger.

8 0
3 years ago
Maria has a collection of 40 baseball cards, of which x cards are damaged. The value of each undamaged card is 5 dollars and the
hodyreva [135]

(40 - x) represents A. the number of undamaged cards

Step-by-step explanation:

Step 1; Maria has a total of 40 cards out of which x number of cards are damaged so 40 - x cards are undamaged. The value of an undamaged card is 5 dollars whereas every damaged card has a value of 3 dollars.

Step 2; We need to determine what each term in equation 5(40−x)+3x represents. The equation will give us how much total value Maria's card collection has.

The first term 5 (40 - x) signifies the total value of the undamaged cards in the deck where (40 - x) equals the total number of undamaged cards.

The second term represents the total value of the undamaged cards.

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7 0
3 years ago
Find the following integral
ololo11 [35]

There's nothing preventing us from computing one integral at a time:

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\displaystyle \int_0^{1-x}\int_0^{2-x}xyz\,\mathrm dz\,\mathrm dy = \frac12\int_0^{1-x}xy(2-x)^2\,\mathrm dy \\\\ = \frac14xy^2(2-x)^2\bigg|_{y=0}^{y=1-x} \\\\= \frac14x(1-x)^2(2-x)^2

\displaystyle\int_0^1\int_0^{1-x}\int_0^{2-x}xyz\,\mathrm dz\,\mathrm dy\,\mathrm dx = \frac14\int_0^1x(1-x)^2(2-x)^2\,\mathrm dx

Expand the integrand completely:

x(1-x)^2(2-x)^2 = x^5-6x^4+13x^3-12x^2+4x

Then

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4 0
2 years ago
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Feliz [49]

Answer:

x=11

Step-by-step explanation:

Simplifying X= 7+4

therefore x=11

8 0
3 years ago
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