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2 years ago

Compare discrete domains and continuous domains.

1 answer:

6 0

Discrete domains and continuous domains are both sets. However a discrete domain contains a finite number of elements and continuous can contain and infinite number of elements.

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Nancy and Kevin collect coins. Nancy has x coins. Kevin has 9 coins fewer than five times the number of coins Nancy has. Write a

Alexus [3.1K]

Answer:

x + (5x-9)

Step-by-step explanation:

x stands for the number of coins Nancy has

Kevin has 9 less than 5 times what Nancy has, so his part of the expression is 5x-9

To find the total number of coins they have, you have to add Nancy's number of coins x plus Kevin's number of coins 5x-9

x + (5x-9)

But you have to put parentheses around Kevin's 5x-9 so that part of the expression is calculated first, as per order of operations

3 0

2 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 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

Solve by elimination X - 6y + 2z = 5 2x-3y+z=4 3x + 4y - z = -2

Vesnalui [34]

Answer:

x=1

y=-3

z=-7

Step-by-step explanation:

6 0

2 years ago

Multiply then Simplify the following numbers 3√10 x 4√ 6

GalinKa [24]

Answer: the answer will be 24/15

Step-by-step explanation:

8 0

2 years ago

A rectangle is 5cm longer that it is broad. It perimeter is 26cm. Find the length and breadth of the rectangle

Maslowich

I hope this helps you

length w+5

width w

26=2 (w+5+w)

13=2w+5

2w=8

w=4

length =4+5=9

3 0

3 years ago