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marissa [1.9K]
3 years ago
15

What is the fraction

t=" \frac{60}{64} " align="absmiddle" class="latex-formula"> in its lowest term
Mathematics
1 answer:
Verdich [7]3 years ago
4 0
15 would be the lowest term

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An arc 28 cm is cut from a circle of radius 15 cm. Find the angle of the sector formed by this arc.
Nutka1998 [239]

Answer:

\displaystyle \frac{28}{15}\; \text{radians}, which is approximately 107^{\circ}.

Step-by-step explanation:

In a given circle, the angle of a sector is proportional to the length of the corresponding arc:

\displaystyle \frac{\text{angle of sector $1$}}{\text{angle of sector $2$}} = \frac{\text{length of arc of sector $1$}}{\text{length of arc of sector $2$}}.

For the circle in this question, r = 15\; \rm cm, and the circumference would be:

2\, \pi \, r = 30\, \pi\; \rm cm.

The full circle itself is like a sector with an angle of 2\, \pi, with the arc length equal to the circumference of the circle.

\displaystyle \frac{\text{angle of sector}}{\text{angle of full circle}} = \frac{\text{length of arc of sector}}{\text{circumference of circle}}.

\displaystyle \frac{\text{angle of sector}}{2\,\pi\; \rm rad} = \frac{28\; \rm cm}{30\, \pi\; \rm cm}.

Rearrange the equation to find the angle of the sector:

\begin{aligned} & \text{angle of sector} \\ =\; & (2\,\pi\; \rm rad) \cdot \frac{28\; \rm cm}{30\, \pi\; \rm cm} \\ =\; & \frac{28}{15}\; \rm rad\end{aligned}.

In other words, the angle of this sector would be \displaystyle \frac{28}{15}\; \rm rad. Multiply that measure in radians by \displaystyle \frac{360^{\circ}}{2\,\pi\; \rm rad} to find the value of the angle measured in degrees:

\begin{aligned} & \frac{28}{15}\; \rm rad \times \frac{360^{\circ}}{2\,\pi\; \rm rad} \approx 107^{\circ}\end{aligned}.

7 0
3 years ago
What is the value of x in the equation
Nastasia [14]

Answer:

54

Step-by-step explanation:

\frac{1}{3x}  -  \frac{1}{2}  = 18 \frac{1}{2}  \\  \\  \frac{1}{3x}  -  \frac{1}{2}  =  \frac{37}{2}   \\  \\  \frac{1}{3x}  =  \frac{37}{2}  -  \frac{1}{2}  \\  \\  \frac{1}{3x}  =  \frac{37 - 1}{2}  \\  \\  \frac{1}{3x}  =  \frac{36}{2}  \\  \\  \frac{1}{3x}  = 18 \\  \\ 1 = 54x

8 0
3 years ago
Misty surveyed 200 students and asked their favorite type of music. The results
NemiM [27]

Answer:

The answer is 9%

Step-by-step explanation:

18

200

x 100% = 9%

I turned 200 into 100% and if you divide 18 by 2 you can get 9

Hope this helped if you need more info let me know!!

8 0
2 years ago
Read 2 more answers
Nita wants to buy a new keyboard for her computer. She will buy the keyboard when it is on sale for under $50 Write an inequalit
Olin [163]
K>$50
hope that helps
5 0
4 years ago
Read 2 more answers
One angle of a right triangle measures 60°. The side opposite this angle measures 15 inches.
Delicious77 [7]

Step-by-step explanation:

To solve this question I would use the sin rule.

The sin rule states that

\frac{a}{ \sin(a) }  =  \frac{b}{ \sin(b)  }

Therefore if you substitute in your numbers you get:

\frac{a}{ \sin(90) }  =  \frac{15}{ \sin(60) }

If you rearrange that you get:

a =  \frac{15}{ \sin(60) }  \times  \sin(90)

Therefore a = 17.3 Inches (to 3 sf)

This can also be done with basic trigonometry where you would get

\sin(60)  =  \frac{15}{h}

Rearranging to

h =  \frac{15}{ \sin(60) }

meaning the answer is 13.7 inches

6 0
4 years ago
Read 2 more answers
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