Please help me thanks you so much

If the point A at (5, 3) is rotated clockwise about the origin through 90°, what

Lerok [7]

Answer:

(5,-3) in the 4th quadrant

Step-by-step explanation:

8 0

3 years 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

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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

Read 2 more answers

A rectangular field is 27 meters long and 18 meters wide. If fencing costs $12 per yard, how much will it cost to enclose the fi

Zina [86]

Answer:

1080 dollars

Step-by-step explanation:

Well you said yards and meters but imma ingore that.

So the perimeter is 27+27+18+18 = 90

90*12= 1080

7 0

3 years ago

Read 2 more answers

ਕind me When x = 4 and y = 3, find the value of: a) 2x + 7y - 10

Andre45 [30]

Answer:

19

Step-by-step explanation:

by replacing x and y with their given values ,

we get :-

=》2x + 7y - 10

=》(2 × 4) + (7 × 3) - 10

=》8 + 21 - 10

=》29 - 10

=》19

5 0

3 years ago

Help pls

konstantin123 [22]

Answer:

40 minutes

Step-by-step explanation:

We simply want to find the least common multiple (lcm) of the two times (5 and 8). Which is 40 minutes

For a more visual representation every 5 minutes Georgia will cross the starting line while it will take Susana 8 minutes to cross after starting at the same time.

So Georgia will cross at (5, 10, 15, 20, 25, 30, 35, 40) minutes

While Susana will cross at (8, 16, 24, 32, 40) minutes

4 0

3 years ago