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3 years ago

Write the equation of a circle for which the endpoints of a diameter are (-2,-2) and (4,-10)

Mathematics

1 answer:

Maurinko [17]3 years ago

6 0

Answer:

Therefore the required Equation of Circle

$x^{2}+y^{2}-2x+12y+12=0$

Step-by-step explanation:

Given:

End point of Diameter be

point A( x₁ , y₁) ≡ ( -2 ,-2 )

point B( x₂ , y₂) ≡ ( 4 , -10 )

To Find:

Equation of a circle =?

Solution:

When end points of the Diameter are A( x₁ , y₁) , B( x₂ , y₂). then the Equation of Circle is given as

$(x-x_{1})(x-x_{2})+(y-y_{1})(y-y_{2})=0$

Substituting the end point are

$(x-(-2))(x-4)+(y-(-2))(y-(-10))=0\\(x+2))(x-4)+(y+2))(y+10))=0\\$

Applying Distributive Property we get

$x^{2} -2x-8+y^{2}+12y+20 =0\\\\x^{2}+y^{2}-2x+12y+12=0$

Therefore the required Equation of Circle

$x^{2}+y^{2}-2x+12y+12=0$

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Graph the system of equations.<br> 2x - y=4<br> 1 x - y = -2

dybincka [34]

PPLMway will help

Step-by-step explanation:

4 0

3 years ago

A stereo store is offering a special price on a complete set ofcomponents (receiver, compact disc player, speakers, cassette dec

Korvikt [17]

Answer:

Step-by-step explanation:

(a)

The number of receivers is 5.

The number of CD players is 4.

The number of speakers is 3.

The number of cassettes is 4.

Select one receiver out of 5 receivers in $5C_1$ ways.

Select one CD player out of 4 CD players in $4C_1$ ways.

Select one speaker out of 3 speakers in $3C_1$ ways.

Select one cassette out of 4 cassettes in $4C_1$ ways.

Find the number of ways can one component of each type be selected.

By the multiplication rule, the number of possible ways can one component of each type be selected is,

The number of ways can one component of each type be selected is

$=5C_1*4C_1*3C_1*4C_1\\\\=5*4*3*4\\\\=240$

Part a

Therefore, the number of possible ways can one component of each type be selected is 240.

(b)

The number of Sony receivers is 1.

The number of Sony CD players is 1.

The number of speakers is 3.

The number of cassettes is 4.

Select one Sony receiver out of 1 Sony receivers in ways.

Select one Sony CD player out of 1 Sony CD players in ways.

Select one speaker out of 3 speakers in ways.

Select one cassette out of 4 cassettes in $4C_1$ ways.

Find the number of ways can components be selected if both the receiver and the CD player are to be Sony.

By the multiplication rule, the number of possible ways can components be selected if both the receiver and the CD player are to be Sony is,

Number of ways can one components of each type be selected

$=1C_1*1C_1*3C_1*4C_1\\\\=1*1*3*4\\\\=12$

Therefore, the number of possible ways can components be selected if both the receiver and the CD player are to be Sony is 12.

(c)

The number of receivers without Sony is 4.

The number of CD players without Sony is 3.

The number of speakers without Sony is 3.

The number of cassettes without Sony is 3.

Select one receiver out of 4 receivers in 4C_1 ways.

Select one CD player out of 3 CD players in 3C_1 ways.

Select one speaker out of 3 speakers in 3C_1 ways.

Select one cassette out of 3 cassettes in 3C_1 ways.

Find the number of ways can components be selected if none is to be Sony.

By the multiplication rule, the number of ways can components be selected if none is to be Sony is,

$=4C_1*3C_1*3C_1*3C_1\\\\=108$

[excluding sony from each of the component]

Therefore, the number of ways can components be selected if none is to be Sony is 108.

(d)

The number of ways can a selection be made if at least one Sony component is to be included is,

= Total possible selections -Total possible selections without Sony

= 240-108

= 132

Therefore, the number of ways can a selection be made if at least one Sony component is to be included is 132.

(e)

If someone flips the switches on the selection in a completely random fashion, the probability that the system selected contains at least one Sony component is,

$= \text {Total possible selections with at least one Sony} /\text {Total possible selections}$

= 132 / 240

= 0.55

The probability that the system selected contains exactly one Sony component is,

$= \text {Total possible selections with exactly one Sony} /\text {Total possible selections}$ $\frac{1C_1*3C_1*3C_1*3C_1+4C_11C_13C_13C_1+4C_13C_13C_13C_1}{240} \\\\=\frac{99}{240} \\\\=0.4125$

Therefore, if someone flips the switches on the selection in a completely random fashion, then is the probability that the system selected contains at least one Sony component is 0.55.

If someone flips the switches on the selection in a completely random fashion, then is the probability that the system selected contains exactly one Sony component is 0.4125.

6 0

3 years ago

A box is in the shape of an equilateral triangular prism. if the box is to be covered with paper on its lateral sides, how many

Zarrin [17]

The total surface area of the triangular prism that has a height of h and the side length of a is given below.

$\rm a(\dfrac{\sqrt3}{2} \ a + 3h)$

<h3>What is a triangular prism?</h3>

A triangular prism is a closed solid that has two parallel triangular bases connected by a rectangle surface.

A box is in the shape of an equilateral triangular prism.

If the box is to be covered with paper on its lateral sides.

Let a be the side length of the equilateral triangle and h be the height of the prism.

Then the surface area of the triangular prism will be

Surface area = 2 × area of triangle + 3 × area of the rectangle

The area of the triangle will be

$\rm Area\ of\ triangle = \dfrac{\sqrt{3}a^2}{4}$

The area of the rectangle will be

$\rm Area \ of \ rectangle = a \ h$

Then the total surface area will be

$\rm Surface\ area = 2 \times \dfrac{\sqrt3 a^2 }{4} + 3 ah\\\\\\Surface\ area = a(\dfrac{\sqrt3}{2} \ a + 3h)$

More about the triangular prism link is given below.

brainly.com/question/21308574

7 0

2 years ago

a 2014 mustang originally costs $25000.00 and depreciates at a rate of 8% per year. What is the cost of the car after 7 years?

frutty [35]

$11,000 will bet the cost in 7 years

Given:

Original cost: $25,000

Depreciation rate: 8%

Term: 7 years

Formula for Depreciation:

A = C ( 1 - ( r ) (t) )

A = Future Value

C = Original Cost

r = rate

t = term

Solution:

Substitute the given values to the formula for depreciation.

A = $25,000( 1 - ( 0.08)(7))

A = $25,000( 1 - .56 )

A = $25,000(0.44 )

A = $11,000

8 0

2 years ago

Population a current census shows that the population of a city is 3.5 million using the formula p= aert find the expected popul

Yuki888 [10]

Answer: the expected population of the city in 30 years is 5470781

Step-by-step explanation:

The population growth is exponential. The growth rate is exponential. We would apply the formula for exponential growth which is expressed as

A = P(1 + r)^t

Where

A represents the population after t years.

t represents the number of years.

P represents the initial population.

r represents rate of growth.

From the information given,

P = 3.5 × 10^6

r = 1.5% = 1.5/100 = 0.015

t = 30 years

Therefore,

A = 3.5 × 10^6(1 + 0.015)^30

A = 3.5 × 10^6(1.015)^30

A = 5470781

6 0

3 years ago