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Aneli [31]
3 years ago
9

Y=sin(x-3pie/2) is the graph of the y=sin(x)shifted in which direction?​

Mathematics
1 answer:
Gre4nikov [31]3 years ago
8 0

\bf ~~~~~~~~~~~~\textit{function transformations} \\\\\\ f(x)=Asin(Bx+C)+D \qquad \qquad f(x)=Acos(Bx+C)+D \\\\ f(x)=Atan(Bx+C)+D \qquad \qquad f(x)=Asec(Bx+C)+D \\\\[-0.35em] ~\dotfill\\\\ \bullet \textit{ stretches or shrinks}\\ ~~~~~~\textit{horizontally by amplitude } A\cdot B\\\\ \bullet \textit{ flips it upside-down if }A\textit{ is negative}\\ ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }B\textit{ is negative}\\

\bf ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{C}{B}\\ ~~~~~~if\ \frac{C}{B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{C}{B}\textit{ is positive, to the left}\\\\ \bullet \textit{vertical shift by }D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}

\bf \bullet \textit{function period}\\ ~~~~~~\frac{2\pi }{B}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\ ~~~~~~\frac{\pi }{B}\ for\ tan(\theta),\ cot(\theta)

now, with that template in mind

\bf y = sin\left( x - \frac{3\pi }{2} \right)\implies y = \stackrel{A}{1}sin\left( \stackrel{B}{1}x \stackrel{C}{- \frac{3\pi }{2}} \right)+\stackrel{D}{0} \\\\\\ C = -\cfrac{3\pi }{2}\qquad \qquad \textit{\underline{horizontal shift} to the right of }\stackrel{3\pi }{2}\textit{ units}

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There are two numbers whose sum is 64. The larger number subtracted from 4 times the smaller number gives 31. Find the numbers.
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There are two numbers whose sum is 64. The larger number subtracted from 4 times the smaller number gives 31. Then the numbers are 45 and 19

<h3><u>Solution:</u></h3>

Given that, There are two numbers whose sum is 64.  

Let the number be a and b in which a is bigger.

Then, a + b = 64 ------ eqn (1)

The larger number subtracted from 4 times the smaller number gives 31.  

4 x b – a = 31  

4b – a = 31 ----- eqn (2)

We have to find the numbers.

So, from eqn (2)

a = 4b – 31

Subatitute a in (1)

4b – 31 + b = 64

On solving we get

5b  = 64 + 31  

5b = 95

b = 19

So, b = 19, then eqn 1

a + 19 = 64

On simplification,

a = 64 – 19

a = 45  

Hence, the two numbers are 45 and 19

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Step-by-step explanation:

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Could someone please help me with this question? 15 points.
polet [3.4K]
1a) f(x) = I x+2 I. This is a piece-wise graph ( V form)
      x = 0 →f(x) =2 (intercept y-axis)
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      x = -4→f(x) = 2 (don't forget this is in absolute numbers)
Now you can graph the V graph

1b) Translation: x to shift (-3) units and y remains the same, then
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zhannawk [14.2K]
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