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Ludmilka [50]
3 years ago
12

What are two mixed numbers that have the sum of 3?

Mathematics
2 answers:
eimsori [14]3 years ago
6 0
1 and 1/2) + (1 and 1/2) = 3 
<span>(1 and 3/4) + (1 and 1/4) = 3 </span>
<span>(1 and 2/49) + (1 and 47/49) = 3</span>
Kisachek [45]3 years ago
5 0
1 1/2 + 1 1/2 or 1 2/3 + 1 1/3
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I think I got the period right, but I don’t know the rest. What is the equation?
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Solution

- The general form of a sinusoidal function is:

\begin{gathered} f(x)=A\sin B(x-h)+k \\ where, \\ |A|=\text{ Amplitude} \\ Period(T)=\frac{2\pi}{|B|} \\  \\ y=k\text{ \lparen The Midline\rparen} \end{gathered}

- First of all, let us find the value of B using the period formula given above.

\begin{gathered} \text{ We are told that the period is 6} \\ \therefore T=\frac{2\pi}{|B|} \\  \\ 6=\frac{2\pi}{|B|} \\ \text{ Make \mid B\mid the subject of the formula} \\  \\ \therefore|B|=\frac{2\pi}{6} \\  \\ |B|=\frac{\pi}{3} \\  \\ \text{ Thus,} \\ B=\pm\frac{\pi}{3} \\  \\ \text{ Since there is only the positive }\frac{\pi}{3}\text{ in the options,} \\  \\ B=\frac{\pi}{3} \end{gathered}

- Next, we should apply the condition given to us that f(2.5) = 5

\begin{gathered} f(x)=A\sin Bx+H \\ B=\frac{\pi}{3} \\  \\ f(x)=A\sin\frac{\pi}{3}x+H \\  \\ f(2.5)=5\text{ implies that }x=2.5,f(x)=5 \\  \\ 5=A\sin\frac{\pi}{3}(2.5)+H\text{  \lparen Equation 1\rparen} \end{gathered}

- We also know that the Amplitude and Valley are related to the midline as follows:

\begin{gathered} H-MinValue=A \\ MinValue=2 \\  \\ H-2=A \\ \therefore H-A=2\text{  \lparen Equation 2\rparen} \end{gathered}

Solving equations 1 and 2 simultaneously, we have

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