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leva [86]
3 years ago
5

On May 14, 1898, a severe hailstorm hit Kansas City. The largest hailstones were 9.5 inches in circumference. Find the radius of

one of the largest hailstones. The formula for the circumference of a circle is c =2nr.
Mathematics
1 answer:
tigry1 [53]3 years ago
6 0
C = \pir
9.5 = 2\pir
\pir = 4.75
r = 1.511971959 
The number above should be rounded to the nearest 2 decimal places, so the answer is 1.51.
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Find the value of k if the distance between (2,k) and (6,7) is 4√2 unit​
andreyandreev [35.5K]

Answer:

k = 3

Step-by-step explanation:

We have the distance formula: d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}. We can plug in 4\sqrt{2} = d, x2 = 6, x1=2, y2 = 7, y1 = k.

Then, we can solve the question using some algebra to find that k = 3.

Edit: Here is a step by step:

4\sqrt{2} = \sqrt{(6-2)^2 + (7-k)^2}\\

(4\sqrt{2})^2 = (6-2)^2 + (7-k)^2

32 = (4)^2 + (7-k)^2

32 = 16 + (7-k)^2

32 - 16 =  (7-k)^2

16 =  (7-k)^2

\sqrt{16} =  (7-k)

4 = 7-k

k = 3

4 0
3 years ago
Prove the divisibility of the following numbers:
Brut [27]

Answer:

Step-by-step explanation:

To prove divisibility, we need to factor the divident such that one of its factors matches the divisor.

(I use the notation x|y to denote that x divides y)

(A)

75^{30}|45^{45}\cdot15^{15}\\45^{45}\cdot15^{15}=3^{45}\cdot 15^{45}\cdot 15^{15}=\\=3^{45}\cdot 15^{60}=3^{45}\cdot 15^{30}\cdot 15^{30}=3^{45}\cdot (3\cdot5)^{30}\cdot 15^{30}=\\=3^{45}\cdot 3^{30}\cdot(5\cdot 15)^{30}=3^{45}\cdot 3^{30}\cdot(75)^{30}\\\implies\\75^{30}|3^{45}\cdot 3^{30}\cdot75^{30}

(B)

72^{63}|24^{54}\cdot 54^{24}\cdot2^{10}\\24^{54}\cdot 54^{24}\cdot2^{10}=(2^{162}\cdot 3^{54})\cdot(2^{24}\cdot 3^{72}) \cdot 2^{10}\\=2^{196}\cdot 3^{126}

In this case, it is easier to also factor the divisor to primes:

72^{63}=2^{189}\cdot 3^{126}

Both of these factor must be matched in the dividend in order to prove divisibility, and that indeed turns out to be true:

2^{189}\cdot 3^{126}|2^{196}\cdot 3^{126}\implies\\2^{189}|2^{196}\,\,\mbox{and}\,\,3^{126}|3^{126}

6 0
3 years ago
Look at the picture<br>​
butalik [34]

The interval where the function is increasing is (3, ∞)

<h3>Interval of a function</h3>

Given the rational function shown below

g(x) = ∛x-3

For the function to be a positive function, the value in the square root  must be positive such that;

x - 3 = 0

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x = 0 + 3

x = 3

Hence the interval where the function is increasing is (3, ∞)

Learn more on increasing function here: brainly.com/question/1503051

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8 0
2 years ago
A circle with radius 3 has a sector with a central angle of 1/9 pi radians
marissa [1.9K]

Complete question:

A circle with radius 3 has a sector with a central angle of 1/9 pi radians

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Answer:

The area of the sector = \frac{\pi}{2} square units

Step-by-step explanation:

To find the area of the sector of a circle, let's use the formula:

A = \frac{1}{2} r^2 \theta

Where, A = area

r = radius = 3

\theta = \frac{1}{9}\pi

Substituting values in the formula, we have:

A = \frac{1}{2}*3^2* \frac{1}{9}\pi

A = \frac{1}{2}*9* \frac{1}{9}\pi

A = 4.5 * \frac{1}{9}\pi

A = \frac{\pi}{2}

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8 0
3 years ago
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Korvikt [17]

Answer:

4

Step-by-step explanation:

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population or a probability distribution. For a data set, it may be thought of as the "middle" value. And the middle value in this problem is 4.

8 0
3 years ago
Read 2 more answers
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