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What is the radius of a circle given by equation x^2 + y^2 - 2x + 8y - 47 = 0

Lera25 [3.4K]

X^2 + y^2 - 2x + 8y - 47 = 0
x^2 + y^2 - 2x + 8y = 47
(x^2 - 2x) + (y^2 + 8y) = 47
(x^2 - 2(1)x) + (y^2 + 2(4)y) = 47
(x^2 - 2(1)x + 1^2) + (y^2 + 2(4)y + 4^2) = 47 + 1^2 + 4^2
(x - 1)^2 + (y + 4)^2 = 64 = 8^2
r=8

7 0

2 years ago

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A box of candy is shaped like a triangular pyramid the volume of the candy box measures 120 in squared 3 the area of the base of

Zolol [24]

Answeh:

Height

A: Base Area

Volume = Ah/3

base=18

volume area of the box =120

=720

Step-by-step explanation:

8 0

3 years ago

Porter is visiting India and would like to purchase some local spices. He finds some spices that cost 401.39 rupees. If the curr

Murljashka [212]

The cost of spices in US dollars is $5.45

The cost of spices in Indian rupees = 401.39 rupees

The exchange rate is

1 dollar:73.6500 rupees

So we have to exchange the Indian rupees to the US dollars

The cost of spices in Indian rupees = 401.39 rupees

The cost of spices in US dollars = The cost of spices in Indian rupees / 73.6500

Substitute the values in the equation and fins the cost of spices in US dollars

The cost of spices in US dollars = 401.39 / 73.6500

Divide the numbers

= $5.45

Hence, the cost of spices in US dollars is $5.45

Learn more about exchange rate here

brainly.com/question/6358327

#SPJ1

6 0

1 year ago

Find all possible values of α+

const2013 [10]

Answer:

$\rm\displaystyle 0,\pm\pi$

Step-by-step explanation:

please note that to find but α+β+γ in other words the sum of α,β and γ not α,β and γ individually so it's not an equation

===========================

we want to find all possible values of α+β+γ when tanα+tanβ+tanγ = tanαtanβtanγ to do so we can use algebra and trigonometric skills first

cancel tanγ from both sides which yields:

$\rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \alpha ) \tan( \beta ) \tan( \gamma ) - \tan( \gamma )$

factor out tanγ:

$\rm\displaystyle \tan( \alpha ) + \tan( \beta ) = \tan( \gamma ) (\tan( \alpha ) \tan( \beta ) - 1)$

divide both sides by tanαtanβ-1 and that yields:

$\rm\displaystyle \tan( \gamma ) = \frac{ \tan( \alpha ) + \tan( \beta ) }{ \tan( \alpha ) \tan( \beta ) - 1}$

multiply both numerator and denominator by-1 which yields:

$\rm\displaystyle \tan( \gamma ) = - \bigg(\frac{ \tan( \alpha ) + \tan( \beta ) }{ 1 - \tan( \alpha ) \tan( \beta ) } \bigg)$

recall angle sum indentity of tan:

$\rm\displaystyle \tan( \gamma ) = - \tan( \alpha + \beta )$

let α+β be t and transform:

$\rm\displaystyle \tan( \gamma ) = - \tan( t)$

remember that tan(t)=tan(t±kπ) so

$\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm k\pi )$

therefore when k is 1 we obtain:

$\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta\pm \pi )$

remember Opposite Angle identity of tan function i.e -tan(x)=tan(-x) thus

$\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm \pi )$

recall that if we have common trigonometric function in both sides then the angle must equal which yields:

$\rm\displaystyle \gamma = - \alpha - \beta \pm \pi$

isolate -α-β to left hand side and change its sign:

$\rm\displaystyle \alpha + \beta + \gamma = \boxed{ \pm \pi }$

when is 0:

$\rm\displaystyle \tan( \gamma ) = -\tan( \alpha +\beta \pm 0 )$

likewise by Opposite Angle Identity we obtain:

$\rm\displaystyle \tan( \gamma ) = \tan( -\alpha -\beta\pm 0 )$

recall that if we have common trigonometric function in both sides then the angle must equal therefore:

$\rm\displaystyle \gamma = - \alpha - \beta \pm 0$

isolate -α-β to left hand side and change its sign:

$\rm\displaystyle \alpha + \beta + \gamma = \boxed{ 0 }$

and we're done!

8 0

3 years ago

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A horse-drawn carriage tour company has found that the number of people that take their tour depends on the price charged per cu

Mars2501 [29]

Answer:

The horse-drawn carriage tour company can expect to take in $6960 when the charge per customer is $60.

Step-by-step explanation:

p(2) = 120 -2·2 = 116 . . . . . expected number of customers per day

c(2) = 50 +5·2 = 60 . . . . . . charge per customer

Then ...

(p·c)(2) = p(2)·c(2) = 116·60 = 6960 . . . . revenue for the day

6 0

2 years ago

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