Separate 53 people into two groups so that the first group has 7 fewer than 4 times the number of people in the second group.

It takes 7 hours for 12 people to

Alborosie

Answer: You would need 5 men to paint a room in 3 hours

YWW :)

6 0

3 years ago

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4.82 write as a fraction or mixed number in simplest form

Dima020 [189]

I'm pretty sure 4.82 as a simplified fraction is 241/50.

6 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

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8. A triangle has sides with lengths of 6, 8, and 10 units, and a square has a

svet-max [94.6K]

Difference between the area of the triangle and square is 25

Step-by-step explanation:

Step 1: Find the area of the triangle given its 3 sides using the Heron's formula.

Area of the triangle = $\sqrt{s (s-a)(s-b)(s-c)}$ where s = $\frac{a + b + c}{2}$

⇒ s = (6 + 8 + 10)/2 = 24/2 = 12

$\sqrt{s(s-a)(s-b)(s-c)}$ = $\sqrt{12(12-6)(12-8)(12-10)}$

= $\sqrt{12(6)(4)(2)}$ = $\sqrt{576}$ = 24 sq. units

Step 2: Find the area of the square with perimeter = 28 units.

Perimeter of the square = 4 × side = 28

⇒ Side of the square = 28/4 = 7 units

⇒ Area of the square = (side)² = 7² = 49 sq. units

Step 3: Find the difference between the area of the square and triangle.

Difference = 49 - 24 = 25

8 0

3 years ago

How do you solve this problem?

yaroslaw [1]

Hope this helped! I decided to write it out for you so it would be easier to explain.

8 0

3 years ago