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3 years ago

Sin(5x+15)=cos(4x−6)

Mathematics

1 answer:

Thepotemich [5.8K]3 years ago

8 0

Answer:

Step-by-step explanation:

you know ; for all reals a ; cos(π/2 - a) = sin(a)

so : sin(5x+15) = cos(π/2-(5x+15) ) = cos(π/2-5x-15)

sin(5x+15)=cos(4x−6) eqivaut : cos(π/2-5x-15) = cos(4x−6)

note : cos(a)=cos(b) : a= b +2kπ or a= - b +2kπ ....k in Z

π/2-5x-15 = 4x−6 + 2kπ or π/2-5x-15 = - (4x−6) + 2kπ....k in Z

continue calculate : x .......

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2 years ago

Express the function graphed on the axes below as a piecewise function.

adoni [48]

Answer:

f(x) = {x-3 for x ≤ -1; -3x+14 for x > 5}

Step-by-step explanation:

To write the piecewise function, we can consider the pieces one at a time. For each, we need to define the domain, and the functional relation.

<h3>Left Piece</h3>

The domain is the horizontal extent. It is shown as -∞ to -1, with -1 included.

The relation has a slope (rise/run) of +1, and would intersect the y-axis at -3 if it were extended.

The first piece can be written ...

f(x) = x-3 for x ≤ -1

<h3>Right Piece</h3>

The domain is shown as 5 to ∞, with 5<em> not included</em>.

The relation is shown as having a slope (rise/run) of (-3)/(1) = -3. If extended, it would intersect the point (5, -1), so we can write the point-slope equation as ...

y -(-1) = -3(x -5)

y = -3x +15 -1 = -3x +14

The second piece can be written ...

f(x) = -3x +14 for x > 5

<h3>Whole function</h3>

Putting these pieces together, we have ...

$\boxed{f(x)=\begin{cases}x-3&\text{for }x\le-1\\-3x+14&\text{for }5 < x\end{cases}}$

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<em>Additional comment</em>

Sometimes it is convenient to write inequalities in number-line order (using < or ≤ symbols). This gives a visual indication of where the variable stands in relation to the limit(s). Perhaps a more conventional way to write the domain for the second piece is, <em>x > 5</em>.

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3 years ago

in an election a candidate go 82 votes.He won the election beating his rival candidate by 576 votes.How many votes were pull?

Tanya [424]

Answer:

if you like please mark me brainlaist

Step-by-step explanation:

thanks

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3 years ago