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1 year ago

The circle below is centered at the point (-3/4) and has a radius of length 3 what is its equation??

2 answers:

6 0

{x-(-3/4)}^2=3^2
(x+3/4)^2=9
{(4x+3)/4}^2=9
(4x+3)^2/16=9
(4x+3)^2=9*16
16x^2+2*4x*3+3^2=144
16x^2+24x+9=144
16x^2+24x+9-144=0
16x^2+24x-135=0

Juli2301 [7.4K]1 year ago

4 0

Answer:

$(x+3)^2+(y-4)^2=9$

Step-by-step explanation:

We are given a circle which is centered at the point (-3,4) and has a radius of length 3.

We have to find the equation of the circle.

The equation of circle centered at (a,b) and radius r is:

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

Here a=-3 , b=4 and r=3

Hence, equation of circle is:

$(x+3)^2+(y-4)^2=3^2$

$(x+3)^2+(y-4)^2=9$

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The general form of the equation of a circle is x2 + y2 + 42x + 38y − 47 = 0. The equation of this circle in standard form is .

Readme [11.4K]

Answer:

(-21,-19)

$\sqrt{849}$

Standard form

Step-by-step explanation:

We are given the equation of circle

$x^2+y^2+42x+38y-47=0$

General equation of circle:

$x^2+y^2+2gx+2fy+c=0$

Centre: (-g,-f)

Radius: $\sqrt{g^2+f^2-c}$

Compare the equation to find f, g and c from the equation

$g\rightarrow 21$

$f\rightarrow 19$

$c\rightarrow -47$

Centre: (-21,-19)

Radius (r) $=\sqrt{21^2+19^2+47}=\sqrt{849}$

Standard form of circle:

$(x+21)^2+(y+19)^2=849$

The centre of circle at the point (-21,-19) and its radius is $\sqrt{849}$ .

The general form of the equation of a circle that has the same radius as the above circle is standard form.

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2 years ago

Read 2 more answers

A) The sum of −3x+5 and 7−4x is subtracted from 5x+17.

AlekseyPX

A. -3x+5+7-4x
-3x-4x+5+7
-7x+12

-7x+12-5x+17
-7x-5x+12+17
-12x+29

B. -5*(x+2)= -5x-10
-6x-1+ (-5x-10)= -6x-5x-1-10=
-11x-11

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1 year ago

On a certain route, an airline carries 7000 passengers per month, each paying $30. A market survey indicates that for each $

KengaRu [80]

Answer:

The ticket price that maximizes revenue is $50.

The maximum monthly revenue is $250,000.

Step-by-step explanation:

We have to write a function that describes the revenue of the airline.

We know one point of this function: when the price is $30, the amount of passengers is 7000.

We also know that for an increase of $1 in the ticket price, the amount of passengers will decrease by 100.

Then, we can write the revenue as the multiplication of price and passengers:

$R=p\cdot N=(30+x)(7000-x)$

where x is the variation in the price of the ticket.

Then, if we derive R in function of x, and equal to 0, we will have the value of x that maximizes the revenue.

$R(x)=(30+x)(7000-100x)=30\cdot7000-30\cdot100x+7000x-100x^2\\\\R(x)=-100x^2+(7000-3000)x+210000\\\\R(x)=-100x^2+4000x+210000\\\\\\\dfrac{dR}{dx}=100(-2x)+4000=0\\\\\\200x=4000\\\\x=4000/200=20$

We know that the increment in price (from the $30 level) that maximizes the revenue is $20, so the price should be:

$p=30+x=30+20=50$

The maximum monthly revenue is:

$R(x)=(30+x)(7000-100x)\\\\R(20)=(30+20)(7000-100\cdot20)\\\\R(20)=50\cdot5000\\\\R(20)=250000$

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2 years ago

The expression 4\cdot3^t4⋅3 t 4, dot, 3, start superscript, t, end superscript gives the number of ducks living in Anoop's pond

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Answer:

There were 4 ducks living in Anoop's pond when he first built it.

Step-by-step explanation:

y e s

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1 year ago

Read 2 more answers

The orbit of the planet Venus is nearly circular. An astronomer develops a model for the orbit in which the sun has coordinates

klio [65]

Since the Venus orbits round the sun, the sun is the center of the circular path of the revolution of the planet, Venus.

Thus, the distance of the planet, Venus fron the sun is given by the distance between the points (0, 0) and (41, 53).

Recall that the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Thus, the distance between the points (0, 0) and (41, 53) is given by:

$d= \sqrt{(41-0)^2+(53-0)^2} \\ \\ = \sqrt{41^2+53^2} = \sqrt{1,681+2,809} \\ \\ = \sqrt{4,490} =67 \ units$

Given that each unit of the plane represents 1 million miles, therefore, the distance from the sun to the Venus is 67 million miles.

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1 year ago