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AleksAgata [21]
3 years ago
8

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.

Mathematics
1 answer:
N76 [4]3 years ago
3 0
There would be a group of 12 and a group of 41
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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 <br> 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

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

we want to find all possible values of α+β+γ when <u>tanα+tanβ+tanγ = tanαtanβtanγ</u><u> </u>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 <u>when</u><u> </u><u>k </u><u>is </u><u>1</u> 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  }

<u>when</u><u> </u><u>i</u><u>s</u><u> </u><u>0</u>:

\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
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
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