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3 years ago

15

What is the fraction

t=" \frac{60}{64} " align="absmiddle" class="latex-formula"> in its lowest term

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

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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

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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

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