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3 years ago

Find an equation of the circle that has center (-1, 3) and passes through (1. 1)

Mathematics

2 answers:

pshichka [43]3 years ago

3 0

Answer:

(x + 1)² + (y - 3)² = 8

Step-by-step explanation:

radius (r): √(1 - (-1))² + (1 - 3)² = √8 = 2√2

Formula for circle with center (h,k): (x – h)² + (y – k)² = r²

(x + 1)² + (y - 3)² = 8

Dovator [93]3 years ago

3 0

Answer:

( x + 1)^2 + (y - 3)^2 = 8

Step-by-step explanation:

The equation of a circle with a center and a point

( x - a) ^2 + ( y - b) ^2 = r^2

( a , b) - center of the circle

( x, y) - any point on the circle

r^2 - radius of the circle

We are provided with a center and a point

( -1 , 3) - ( a, b) - center

a = -1

b = 3

( 1 , 1) - ( x, y) - point

x = 1

y = 1

Step1: substitute the center of the circle into the equation

( x - (-1)^2 + ( y - 3)^2 = r^2

(x + 1)^2 + (y - 3)^2 = r^2

Step 2: sub the point into the equation

( x + 1)^2 + (y - 3)^2 = r^2

x - 1

y - 1

( 1 + 1)^2 + ( 1 - 3)^2 = r^2

( 2)^2 + ( -2)^2 = r^2

4 + 4 = r^2

8 = r^2

Step 3 : sub the radius into the equation

( x + 1)^2 + ( y - 3)^2 = r^2

( x + 1)^2 + (y - 3 )^2 = 8

Therefore, the equation of the circle is

( x + 1)^2 + ( y - 3)^2 = 8

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A particular algebra text has a total of 1382 pages which is broken into two parts the second part of the book has 64 more pages

AlladinOne [14]

Answer:

the first part of the book has 659 pages and the second part has 723 pages

Step-by-step explanation:

First we have to raise 2 equations, one that shows us the relationship between one part of the book and the other, and another equation that shows us that together they give us the total of pages

x = second part

y = first part

x = y + 64

x + y = 1382

As the first equation tells us that x = y + 64 we will replace x in the second equation with (y + 64)

x + y = 1382

(y + 64) + y = 1382

y + y = 1382 - 64

2y = 1318

y = 1318/2

y = 659

now we replace in the first equation to y by its value

x = y + 64

x = 659 + 64

x = 723

so the first part of the book has 659 pages and the second part has 723

7 0

3 years ago

a book of books weighs 21 pounds, half the books are taking out now the box weighs 14.5. whats the remaining weight of the box

pantera1 [17]

6.5 pounds left. i think

5 0

3 years ago

Read 2 more answers

The number of bacteria in a petri dish is 50,000 (on day 0) if the amount is doubling each day by when will the number of bacter

Drupady [299]

Answer:

f(x) = 50000*2^x
3 days

Step-by-step explanation:

Given:

Initial amount of bacteria = 50000
Growth rate = 2 times a day

Required equation:

f(x) = 50000*2^x

Solve for x:

400000 = 50000*2^x
2^x = 400000/50000
2^x = 8
2^x = 2^3
x = 3

After 3 days bacteria numbers will reach 400000

5 0

2 years ago

Can someone help me ASAP please. I'll give extra points if right fr

9966 [12]

Answer:

y = -1/4x + -6

Step-by-step explanation:

6 0

2 years ago

Both the La Plata river dolphin (Pontoporia blainvillei) and

Citrus2011 [14]

Answer:

1. A sperm whale is 3 orders of magnitude heavier than a La Plata river dolphin; 2. The radius of the larger ball is one (1) order of magnitude bigger than the radius of the smaller ball; 3. The volume of the larger ball is 3 orders of magnitude bigger than the volume of the smaller ball.

Step-by-step explanation:

If we expressed a number as:

$\\ N = a * 10^{b}$ (1)

Where

$\\ \frac{1}{\sqrt{10}} \leq a < \sqrt{10}$ (2)

$\\ 1 \leq a < 10$ (3)

Then, b represents the order of magnitude of such a number (Order of magnitude (2020), in Wikipedia).

The order of magnitude can be defined as "...the smallest power of ten needed to represent a quantity" (Weisstein, Eric W. "Order of Magnitude". From MathWorld--A Wolfram Web Resource).

Having gathered all this information, we can proceed as follows:

<h3>First case</h3>

The La Plata river dolphin weighs between 30 and 50kg and the sperm whale weighs between 35,000 and 40,000kg.

Then, considering (1) and (3) to express the dolphin and whale's weight (since in this way the order of magnitude is the same as the exponent part in the scientific notation):

$\\ 30kg \leq Dolphin_{weight} \leq 50kg$

$\\ 3*10^{1}kg \leq Dolphin_{weight} \leq 5*10^{1}kg$

$\\ 35000kg \leq Whale_{weight} \leq 40000kg$

$\\ 3.5*10^{4}kg \leq Whale_{weight} \leq 4.0*10^{4}kg$

Since the range for the weights are in the same order of magnitude for both dolphin and whale (considering the definition above):

$\\ Dolphin_{weight} = 10^{1}\;(order\;of\;magnitude=1)$

$\\ Whale_{weight} = 10^{4}\;(order\;of\;magnitude=4)$

Then

$\\ \frac{Whale_{weight} = 10^{4}}{Dolphin_{weight} = 10^{1}}$

$\\ \frac{Whale_{weight}}{Dolphin_{weight}} = \frac{10^{4}}{10^{1}}$

$\\ \frac{Whale_{weight}}{Dolphin_{weight}} = 10^{4-1}$

$\\ \frac{Whale_{weight}}{Dolphin_{weight}} = 10^{3}$

Thus

A sperm whale is 3 orders of magnitude heavier than a La Plata river dolphin.

<h3>Second case</h3>

Following the same reasoning, we can conclude that the radius of the larger ball is one (1) order of magnitude bigger than the radius of the smaller ball:

$\\ \frac{Larger\;ball_{radius}}{Smaller\;ball_{radius}} = \frac{10^{1}}{10^{0}}$