Write a linear function f with the values f(0)=-1 and f(2)=-5

What is the rectangular equivalence to the parametric equations?

Usimov [2.4K]

Answer:

$\left(\frac{x-2}{3} \right)^{2}+\left(\frac{y+1}{2} \right)^{2} = 1$ (An ellipse)

Step-by-step explanation:

Let consider the following trigonometric identity:

$\sin^{2}\theta + \cos^{2}\theta = 1$

Each trigonometric function is cleared respectively in given parametric equations:

$\cos \theta = \frac{x-2}{3}$ and $\sin \theta = \frac{y + 1}{2}$

The equivalent expression in rectangular form is:

$\left(\frac{x-2}{3} \right)^{2}+\left(\frac{y+1}{2} \right)^{2} = 1$

Which represents an ellipse.

6 0

3 years ago

A fish tank, in the shape of a rectangular prism with dimensions 51 cm by 39 cm by 28 cm, is 95% filled with water. A solid log

GenaCL600 [577]

Answer:

The end answer is 669.4

Step-by-step explanation:

So you take the volume of the fish tank: 51*39*28=55692, but the tank is only 95% full, so you take 55692 and divide it by 100 and multiply it by 95, you get 52907.4. Then you calculate the volume of the log: 3.14*5^2*44=3454.

Now that we know these values, we take the volume of the water which is 52907.4 and add the volume of the log 3454 which gets you 56361.4.

Now we know the combined volume of the water and the log, we can remove the volume of the tank, which will still be holding the water that hasn't exceeded the capacity of the tank: 56361.4-55692=669.4

So then we know what has exceeded the capacity of the tank, which is how much water has spilled

So the water spilled equals 669.4 cubic centimetres of water.

6 0

3 years ago

Marcus is comparing the costs of two cellular phone services.

kolbaska11 [484]

The true statements about Marcus graph are:

The initial cost of phone service 1 is greater than the initial cost of phone service 2
The unit rate of phone service 2 is greater than the unit rate of phone service 2

<h3>How to determine the true statement</h3>

From the complete question, we have the following parameters:

<u>Phone service 1</u>

Initial cost: $40
Rate: $8.50 per service

<u>Phone service 2</u>

Initial cost: $30
Rate: $10.50 per service

By comparing the above parameters:

The initial cost of phone service 1 is greater than the initial cost of phone service 2
The unit rate of phone service 2 is greater than the unit rate of phone service 2

The above statements represent the true statements about the Marcus' graph

Read more about graphs at:

brainly.com/question/14323743

7 0

2 years ago

In a random sample of 2500 sports fans, 61% prefer basketball over soccer.

timama [110]

The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The Margin of error in this survey is 1%.

<h3>What is the margin of error?</h3>

The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The wider the margin of error, the less confident one should be that a poll result reflects the outcome of a population-wide survey.

The random sample of 2500 sports fans, out of which 61% prefer basketball over soccer, therefore, we can write n=2500 and p=0.61. Thus, the margin of error can be written as,

$MOE=\sqrt{\dfrac{\hat p(1-\hat p)}{n}} = \sqrt{\dfrac{0.61(1-0.61)}{2500}} = 0.00975 = 0.975\% \approx 1\%$

Hence, the Margin of error in this survey is 1%.

Learn more about Margin of Error:

brainly.com/question/13990500

#SPJ1

7 0

2 years ago

Susan is buying uniform shirts that cost $12 each. She has $50 total to spend. She also has a coupon for $10 off her purchase. A

Makovka662 [10]

$50+$10 (The coupon)=$60 to spend
$60/12=5 uniform shirts.

4 0

4 years ago

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