A ship drops its anchor into the water and creates a circular ripple. The radius of the ripple increases ata rate of 50 cm/s. If the origin is used as the location where the anchor was dropped into the water.

Find the equation for the circle 12 seconds after the anchor is dropped

Please write all the steps it’s for my summer school test and I need it done quick as possible thanks.

Answers

Answer 1

Answer:

The equation for the circle 12 seconds after the anchor is dropped is x^2 + y^2 = 360,000

Step-by-step explanation:

To find the equation for the circle 12 seconds when the radius of the ripple increases at a rate of 50 cm/s, the circle radius will be;

50 * 12 = 600 cm

Then place the equation inform of Pythagoras equation which is;

x^2 + y^2 = r^2

Where r is the radius

x^2 + y^2 = 600^2

x^2 + y^2 = 360,000

Then, the equation for the circle 12 seconds after the anchor is dropped is x^2 + y^2 = 360,000

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Write a real world situation that would representby the system y=3x +20 and y=5x + 10

Answers

there are 2 car rental companies
the first one charges 3 dollars per day you drive plus a 20 dollar insurance fee

the second one charges 5 dollars per day and a 10 dollar insurance fee
y=cost
x=days

What is the common ratio of the geometric sequence whose second and fourth terms are 6 and 54, respectively?

Answers

Hi there! T4=T2×r²,6r²=54. Therefore, the answer would be 3.

a₂ = 6 a₄ = 54

$a_(n) = q^(n-1) * a_(1)$

$\left \{ {{ a_(2) = q^(2-1) * a_(1) } \atop { a_(4) = q^(4-1)* a_(1) }} \right. \n \n \left \{ {{6 = q * a_(1) } \atop {54 = q^(3) * a_(1) }} \right. \n \n \left \{ {{ a_(1) = (6)/(q) } \atop {54 = q^(3) * (6)/(q) }} \right. \n \n \left \{ {{ a_(1) = (6)/(q) } \atop {54 = q^(2) * 6 }} \right.$

$\left \{ {{ a_(1) = (6)/(q) } \atop { q^(2) =9}} \right. \n \n \left \{ {{ a_(1) = (6)/(q) } \atop {q= √(9) }} \right.$
q = 3 q = -3

a₁ = 6/3 = 2 a₁ = 6/-3 = -2

Determine the solution to f(x) = g(x) using the following system of equations:f(x) = 5.5x − 13
g(x) = −5x + 18.5

x = 1
x = 2
x = 3
x = 4

Answers

f(x) = g(x)

f(x) = 5.5x - 13
g(x) = -5x + 18.5

5.5x - 13 = -5x + 18.5
5.5x + 5x = 18.5 + 13
10.5x = 31.5
x = 31.5/10.5
x = 3

f(3) = 5.5(3) - 13 = 16.5 - 13 = 3.5
g(3) = -5(3) + 18.5 = -15 + 18.5 = 3.5

Answer:

The solution of the equation f(x) = 5.5x − 13 and g(x) = −5x + 18.5 is 3 .

Step-by-step explanation:

As given

f(x) = g(x)

Here

f(x) = 5.5x − 13

g(x) = −5x + 18.5

Put in the above equation

5.5x − 13 = −5x + 18.5

5.5x + 5x = 18.5 + 13

10.5x = 31.5

$x = (31.5)/(10.5)$

x = 3

Therefore the value of x is 3 .

Tell which measure of central tendency best describes the data. Time spent on Internet (min/day): 75 38 43 120 65 48 52 A. Mean B. Median C. Mode

Answers

Answer:

B. Median

Step-by-step explanation:

We have been given data about time spent on Internet (min/day). We are asked to determine the best measure of central tendency for the given data.

Data: 75, 38, 43, 120, 65, 48, 52,

We can see that our given data has a very large value outlier (120), so it will increase the mean.

There is no mode for the given data set as no value repeats.

We know that median is best measure for data set with large valued outliers because median is not affected by outliers.

Therefore, option B is the correct choice.

The measure of central tendency that best describes the data is B. Median.

Which measure of central tendency best describes the data on time spent on the Internet?

Mean:

= (75 + 38 + 43 + 120 + 65 + 48 + 52) / 7

= 69.86

Median:

We arrange data in ascending order: 38, 43, 48, 52, 65, 75, 120. Since there are seven values, the median is the middle value: 52

Mode: There is no value that appears more than once in the data set.

Therefore, the measure of central tendency that best describes the data is B. Median.

Answers

The largest possible map that can fit on the page is 8 in. by 12 in.

What is Ratio?

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

We can begin by finding the scale factor by which the map needs to be reduced.

Since the map dimensions are 24 in. by 36 in., and we want to fit it onto a page that is 8 in. by 10 in.

We need to reduce each dimension by the same factor.

Let x be the scale factor:

24/x = 8

36/x = 10

Solving for x, we get:

x = 24/8 = 3

Therefore, we need to reduce the map by a scale factor of 3.

To find the dimensions of the largest possible map that can fit on the page, we divide the original map dimensions by 3:

24/3 = 8

36/3 = 12

Hence, the largest possible map that can fit on the page is 8 in. by 12 in.

To learn more on Ratios click:

brainly.com/question/1504221

#SPJ2

Since 10 in will be the longer side, to find the shorter did
x/10 = 24/36
x/10 = 2/3
x = 10•(2/3)
x = 6 2/3
So the dimensions are
6 2/3 in by 10 in

A rope is 66 feet long. It is cut into two pieces such that one piece is half the length of the other. What is the length of the longer piece of rope?a.22 feet
b.26 feet
c.33 feet
d.44 feet

Answers

So if one bit of the length, is half the size of the other bit then we can make the following equation, for x being the length of rope:

x + 2x = 66
3x = 66
x = 22

That is the length, of the smaller one (half the big one), so 2x = 44. Hence d) is your answer.

Hope I helped!

let's say the two piece's lengths are x and y

so x+y=66

then we are told that "one piece is half the length of the other"
so x = (1/2)y

we plug this into the first equation and get
(1/2)y + y = 66
or
1.5 y = 66

divide both sides by 1.5 to get y alone
y = 66 / 1.5 = 44

we can check to see if y is the longer one by finding x
x = 66 - y = 66 - 44 = 22

44 is bigger than 22
therefore 44 is the length of the longer piece

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