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rodikova [14]
3 years ago
13

5/9 divided by 8/= ?

Mathematics
1 answer:
Svetllana [295]3 years ago
3 0
The answer is 0.06944 or as a fraction 5/72
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Show that f(x) f(y) - f(x+y), where f(x)= [cos x - sin x o] [sin x cos x o] [o o 1]
Naddik [55]

Answer:

The answer is below

Step-by-step explanation:

Show that f(x) f(y) = f(x+y)

From trigonometric:

sin(x + y) = sinxcosy + cosxsiny

sin(x - y) = sinxcosy - cosxsiny

cos(x + y) = cosxcosy - sinxsiny

cos(x - y) = cosxcosy + sinxsiny

f(x)=\left[\begin{array}{ccc}cosx&-sinx&0\\sinx&cosx&0\\0&0&1\end{array}\right] ,f(y)=\left[\begin{array}{ccc}cosy&-siny&0\\siny&cosy&0\\0&0&1\end{array}\right] \\\\\\f(x)f(y)=\left[\begin{array}{ccc}cosxcosy-sinxsiny&-cosxsiny-sinxcosy&0\\sinxcosy+cosxsiny&-sinxsiny+cosxcosy&0\\0&0&1\end{array}\right] \\\\\\f(x)f(y)=\left[\begin{array}{ccc}cos(x+y)&-sin(x+y)&0\\sin(x+y)&cos(x+y)&0\\0&0&1\end{array}\right] \\\\\\

f(x+y)=\left[\begin{array}{ccc}cos(x+y)&-sin(x+y)&0\\sin(x+y)&cos(x+y)&0\\0&0&1\end{array}\right] \\\\\\Therefore\ f(x)f(y)=f(x+y)

4 0
3 years ago
What is the product of (-3s+2t(4s-t)
galben [10]
Use the FOLD method<span>
(a+b)(c+d)=ac+ad+bc+bd

</span><span>−12<span>s<span><span>​^2 </span><span>​​</span></span></span>+ 3st + 8ts − 2<span>t<span><span>​^2</span><span>​​

</span></span></span></span>Collect like terms
-12{s}^{2}+(3st+8st)-2{t}^{2}

Simplify
<span>-12{s}^{2}+11st-2{t}^{2}<span>−12<span>s<span><span>​2</span><span>​​</span></span></span>+11st−2<span>t<span>​<span>2

The answer is = -12s^2 + 11st - 2t^2</span></span></span></span></span>
5 0
3 years ago
Find slope of (2,2) and (4,b)
elena-14-01-66 [18.8K]

Answer: Use the slope formula to find the slope

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3 years ago
If you rolled two dice, what is the probability
Softa [21]

Answer:

2/36 or 1/18 simplified

Step-by-step explanation:

you have all the combinations listed which is good.

probability = number of successful events / number of total events

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there are

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3 years ago
A professor went to a website for rating professors and looked up the quality rating and also the "easiness" of the six full-tim
Marat540 [252]

We are asked to determine the correlation factor "r" of the given table. To do that we will first label the column for "Quality" as "x" and the column for "Easiness" as "y". Like this:

Now, we create another column with the product of "x" and "y". Like this:

Now, we will add another column with the squares of the values of "x". Like this:

Now, we add another column with the squares of the values of "y":

Now, we sum the values on each of the columns:

Now, to get the correlation factor we use the following formula:

r=\frac{n\Sigma xy-\Sigma x\Sigma y}{\sqrt{(n\Sigma x^2-(\Sigma x)^2)(n\Sigma y^2-(\Sigma y)^2)}}

Where:

\begin{gathered} \Sigma xy=\text{ sum of the column of xy} \\ \Sigma x=\text{ sum of the column x} \\ \Sigma y=\text{ sum of the column y} \\ \Sigma x^2=\text{ sum of the column x\textasciicircum2} \\ \Sigma y^2=\text{ sum of the column y\textasciicircum2} \\ n=\text{ number of rows} \end{gathered}

Now we substitute the values, we get:

r=\frac{\left(6)(70.56)-(25.2)(16.4\right)}{\sqrt{((6)(107.12)-(25.2)^2)((6)(47.82)-(16.4)^2)}}

Solving the operations:

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1 year ago
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