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2 years ago

Find the equation of the tangent at ( 0 , 2) to the circle with equation

Mathematics

1 answer:

Leto [7]2 years ago

7 0

Https://www.cymath.com/answer?q=(x%20%2B%202)%20%5E%202%20%2B%20(y%20%2B%201)%20%5E%202%20%3D%2013
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A population of fish in a lake is 14000 in 2010. The population decreases 6% annually. What is the population in 2019

kodGreya [7K]

Answer:

8022.

Step-by-step explanation:

Let x be the number of years after 2010.

We have been given a population of fish in a lake is 14000 in 2010. The population decreases 6% annually.

We can see that population of fish is the lake is decreasing exponentially as it is decreasing 6% annually.

Since we know that an exponential function is in form: $y=a*b^x$ , where,

a = Initial value,

b = For decrease or decay b is in form (1-r) where r represents decay rate in decimal form.

Let us convert our given decay rate in decimal form.

$6\5=\frac{6}{100}=0.06$

Upon substituting our given values in exponential form of function we will get the population of fish in the lake after x years as:

$y=14,000*(1-0.06)^x$

$y=14,000*(0.94)^x$

Let us find x by subtracting 2010 from 2019.

$x=2019-2010=9$

Upon substituting x=9 in our function we will get,

$y=14,000*(0.94)^9$

$y=14,000*0.5729948022286167$

$y=8021.927\approx 8022$

Therefore, the population of fish in 2019 will be 8022.

6 0

3 years ago

Write the standard equation of the circle shown.

zysi [14]

Answer:

Step-by-step explanation:

The equation of a circle centred at the origin is

x² + y² = r² ← r is the radius

The circle shown is centred at the origin and has a radius of 5, thus

x² + y² = 5² ⇒ x² + y² = 25 → b

4 0

3 years ago

Translate these points

zmey [24]

3,-4 is the correct anwser

3 0

3 years ago

A study was done by an online retail store to determine the rate at which users used its website. A graph of the data that was c

mariarad [96]

Answer:

The correct answer is C.

Step-by-step explanation:

First, we can eliminate A and D since it is obviously only 36 months.

Note that the question asks what can be interpreted from the <em>range</em> of the graph.

The range is the number of users in thousands (per month) (as can be seen from the side title).

While B is technically correct, it wrongly interprets the range. C is the best choice.

The correct answer is C.

3 0

3 years ago

you measure the period of a mass oscillating on a vertical spring ten times as follows: period (s): 1.06, 1.31, 1.28, 0.99, 1.48

lidiya [134]

The mean and (sample) standard deviation σ = 0.2098.

<h3>What exactly would the standard deviation indicate?</h3>

The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.

<h3>According to given information:</h3>

The mean is the product of the dataset's total and the sample size. Mathematically.

$\bar{x}=\frac{\sum X_i}{N}$

The individual periods are Xi.

The sample size is N.

$\sum X i$ = 1.06 + 1.31 + 1.28 + 0.99,+ 1.48 + 1.37+ 0.98 + 1.31 + 1.59 + 1.55

$\sum X i$ = 12.92

N = 10

While substituting the value we get:

x = 12.96/10

x = 1.292

The samples' average is 1.292.

The standard deviation:

$\sigma=\sqrt{\frac{\sum(x-\bar{x})^2}{N}}$

$\sum(x-\bar{x})^2$ = (1.48-1.292)^2+(1.37-1.292)^2+(0.98-1.292)^2+(1.31-1.292)^2+(1.59-1.292)^2+(1.55-1.292)^2.

$\sum(x-\bar{x})^2$ = 0.43996

Putting into the formula we get:

$\sigma=\sqrt{\frac{0.43996}{10}}$

σ = √(0.043996)

σ = 0.2098

The mean and (sample) standard deviation σ = 0.2098.

To know more about standard deviation visit:

brainly.com/question/18521100

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I understand that the question you are looking for is:

You measure the period of a mass oscillating on a vertical spring ten times as follows:

Period (s): 1.06, 1.31, 1.28, 0.99, 1.48, 1.37, 0.98, 1.31, 1.59, 1.55

Required:

What are the mean and (sample) standard deviation?

a. Mean: 1.228, Standard Deviation: 0.2135

b. Mean: 1.325, Standard Deviation: 0.1674

c. Mean: 1.292. Standard Deviation: 0.2211

d. Mean: 1.228, Standard Deviation: 0.2098

e. Mean: 1.292, Standard Deviation: 0.2135

7 0

1 year ago