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4 years ago

If xh=10 feet and mxy =100 degrees then determine the arc length of xy

Mathematics

1 answer:

schepotkina [342]4 years ago

7 0

Answer:

The arc length XY is equal to $\frac{50}{9}\pi\ ft$ or $17.4\ ft$

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Find the circumference of the circle H

The circumference is given by the formula

$C=2 \pi r$

we have

$r=xh=10\ ft$

substitute

$C=2 \pi (10)\\C=20\pi\ ft$

step 2

we know that

The circumference of a circle subtends a central angle of 360 degrees

using proportion

Find out the length of the arc xy if the central angle is equal to 100 degrees

Remember that

$m\angle XHY=arc\ XY=100^o$ ---> by central angle

$\frac{20\pi}{360^o}=\frac{x}{100^o}\\\\x=20\pi(100)/360\\\\x=\frac{2,000}{360}\pi\ ft$

Simplify

$x=\frac{50}{9}\pi\ ft$ ----> exact value

To find out the approximate value

assume

$\pi=3.14$

substitute

$x=\frac{50}{9}(3.14)=17.4\ ft$ ----> approximate value

therefore

The arc length XY is equal to $\frac{50}{9}\pi\ ft$ or $17.4\ ft$

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butalik [34]

Write the equations in matrix,

$\left[\begin{array}{ccc}5&-1&1\\1&2&-1\\2&3&-3\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}4\\5\\5\end{array}\right]$

Using row transformation,
R₂ <---> R₃

$\left[\begin{array}{ccc}5&-1&1\\2&3&-3\\1&2&-1\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}4\\5\\5\end{array}\right]$

Using,
R₂ ---> R₂ - 2R₃

$\left[\begin{array}{ccc}5&-1&1\\0&-1&-1\\1&2&-1\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}4\\-5\\5\end{array}\right]$

Using,
R₂ --- > (-1)R₂

$\left[\begin{array}{ccc}5&-1&1\\0&1&1\\1&2&-1\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}4\\5\\5\end{array}\right]$

Using row transformation,
R₂ <----> R₃
$\left[\begin{array}{ccc}5&-1&1\\1&2&-1\\0&1&1\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}4\\5\\5\end{array}\right]$

Using,
R₂ ---> R₂ - R₁/5

$\left[\begin{array}{ccc}5&-1&1\\0&11/5&-6/5\\0&1&1\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}4\\21/5\\5\end{array}\right]$

Using,
R₃ ---> R₃ - 5R₂/11

$\left[\begin{array}{ccc}5&-1&1\\0&11/5&-6/5\\0&0&17/11\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}4\\21/5\\34/11\end{array}\right]$

∴ 5x-y+z = 4 ====(i)
11y-6z = 21 === (ii)
17z=34 === (iii)

from iii,
z=2.
Plug z=2 in ii to get y,
∴y=3.
Plug y and z values in i to get x,
∴x=1

Therefore the solution to the system of equations is (1,3,2)

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4 years ago

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1. Draw the graph of f(x) = cos x for 0 I know how to construct the graph but I don’t know how to get the figures. Please help

KengaRu [80]

Answer:

Please refer to the attached figure.

Step-by-step explanation:

Given the function:

$f(x) =cosx \ where\ \{0^\circ\leq x\leq 360^\circ\}$

OR, the given function can also be written as:

$y = f(x) = cosx$

We know that graph of cosine is a wave.

and the range of cosine function is [-1, 1]

First of all, let us have a table of values at major values of x.

$x = 0, f(x) = 1\\x = 90, f(x) = 0\\x = 180, f(x) = -1\\x = 270, f(x) = 0\\x = 360, f(x) = 1$

So, the table of values for f(x) is:

$\begin{center}\begin{tabular}{ c c }x & cosx \\0 & 1 \\90 & 0\\180 & -1\\270 & 0\\360 & 1\\\end{tabular}\end{center}$

Let us mark these points on the xy coordinate axis where x axis represents value of<em> x </em>and y axis represents value of $f(x) = cosx$ and then join the points using a wave.