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Stels [109]
3 years ago
12

Find The art length of a sector with an area of 8 square units.

Mathematics
1 answer:
frez [133]3 years ago
6 0
\bf \textit{area of a sector of a circle}\\\\
A=\cfrac{\theta \pi r^2}{360}\quad 
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad degrees\\
------\\
A=8\\
r=4
\end{cases}\implies 8=\cfrac{\theta \pi 4^2}{360}\implies \cfrac{8\cdot 360}{4^2\pi }=\theta 
\\\\\\
\cfrac{2880}{16\pi }=\theta \implies \boxed{\cfrac{180}{\pi }=\theta }\\\\
-------------------------------\\\\

\bf \textit{arc's length}\\\\
s=\cfrac{\theta \pi r}{180}\quad 
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad degrees\\
------\\
\theta =\frac{180}{\pi }\\
r=4
\end{cases}\implies s=\cfrac{\frac{180}{\underline{\pi} }\underline{\pi} \cdot 4}{180}\implies s=\cfrac{\underline{180}\cdot 4}{\underline{180}}
\\\\\\
\boxed{s=4}

if you do a quick calculation on what that angle is, you'll notice that it is exactly 1 radian, and an angle of 1 radian, has an arc that is the same length as its radius.

that's pretty much what one-radian stands for, an angle, whose arc is the same length as its radius.
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kifflom [539]
The easiest way to solve a problem like this is to cross multiply and solve 

The problem gives us a ratio 
2 pounds of granola = 3 pounds of raisins 
which makes a ratio of \frac{2}{3}
The other ratio is 
? pounds of granola = 24 pounds of raisins
which makes a ratio of \frac{x}{24}

To solve, set them equal to each other ...
\frac{2}{3} =  \frac{x}{24}

Now we must cross multiply...
To cross multiply, we multiply 2 and 24 
and we multiply 3 and x 
Now we have an equation to solve!
3x = 48 
To solve and get your final answer, divide...
x = \frac{48}{3}

x = 16
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3 years ago
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slamgirl [31]
Multiplied: <span>3/5a
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4 0
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Anastaziya [24]
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3 0
3 years ago
A line passes through the point (0,2) and has a slope of -1/2 what is the equation of the line
emmasim [6.3K]

Answer:

y = -1/2x + 2

Step-by-step explanation:

A line in slope-intercept form in y = mx + b

"m" is the slope

"b" is the y-intercept

x and y represent points on the graph

To write an equation, you need "m" and "b".

We already know m = -1/2

The point (0, 2) is the y-intercept. The y-intercept occurs when x = 0.

Points are in the form (x , y), so x = 0 and y = 2.

Therefore b = 2.

Substitute m = -1/2 and b = 2 into the equation:

y = mx + b

y = -1/2x + 2

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3 years ago
The Ipad that Ms. Hopham would like to buy for research is $1,299. This week it is on sale for $990, and the sales tax is 6%. Ho
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6% = 0.06

Multiply.

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Add.

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Best of Luck!

4 0
3 years ago
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