All categories

2 years ago

If the diameter of a circle is 6 inches, how long is the arc subtended by an angle measuring 70°?

1 answer:

6 0

Since the diameter of the circle is 6 inches, then the radius will be half that, or 3 inches,

$\bf \textit{arc's length}\\\\
s=\cfrac{r\pi \theta }{180} \quad 
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad degrees\\
------\\
r=3\\
\theta =70
\end{cases}\implies s=\cfrac{3\cdot \pi \cdot 70}{180}\implies s=\cfrac{7\pi }{6}$

You might be interested in

Find an equation of the circle that satisfies the given conditions.

hodyreva [135]

The equation of a circle:
$(x-h)^2+(y-k)^2=r^2$
(h,k) - the coordinates of the centre
r - the radius

The midpoint of the diameter is the centre of a circle.
The coordinates of the midpoint:
$(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$
(x₁,y₁), (x₂,y₂) - the coordinates of endpoints

$P(-1,1) \\
x_1=-1 \\ y_1=1 \\ \\ Q(5,9) \\ x_2=5 \\ y_2=9 \\ \\
\frac{x_1+x_2}{2}=\frac{-1+5}{2}=\frac{4}{2}=2 \\ \frac{y_1+y_2}{2}=\frac{1+9}{2}=\frac{10}{2}=5$

The centre of the circle is (2,5).

The radius is the distance between an endpoint of the diameter and the centre.
The formula for distance:
$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$(-1,1) \\ x_1=-1 \\ y_1=1 \\ \\ (2,5) \\ x_2=2 \\ y_2=5 \\ \\ d=\sqrt{(2-(-1))^2+(5-1)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5$

The radius is 5.

$(x-2)^2+(y-5)^2=5^2 \\
\boxed{(x-2)^2+(y-5)^2=25}$

4 0

2 years ago

In the diagram, PQ¯¯¯¯¯¯¯¯ is tangent to the circle at point Q, and secant PS¯¯¯¯¯¯¯ intersects the circle at points R and S. Th

dimaraw [331]

The tangent secant theorem says

PR × PS = PQ²

4 × (4+5) = PQ²

36 = PQ²

PQ=6

Answer: 6

3 0

2 years ago

The height of a tree was 12 feet. after a year, the tree's height increased 25%. what is the height of the tree after a year

g100num [7]

15ft because 12x.25=3 so 3ft is 25% of the 12ft, add the 3+12=15

6 0

2 years ago

the head of a nail is circular , as shown the head of this nail has a diameter of 6 millimeters what measurment is closet to the

Nikitich [7]

Answer:

Area of nail's head = 28.26 millimeter² (Approx.)

Step-by-step explanation:

Given:

Head of nail is circular

Diameter of nail's head = 6 millimeter

Find:

Area of nail's head

Computation:

Radius of nail's head = Diameter / 2

Radius of nail's head = 6 / 2

Radius of nail's head = 3 millimeter

Area of circle = πr²

Area of nail's head = πr²

Area of nail's head = (22/7)(3)²

Area of nail's head = (22/7)(9)

Area of nail's head = (3.14)(9)

Area of nail's head = 28.26 millimeter² (Approx.)

5 0

2 years ago

PLEASE HELP!!

Musya8 [376]

Answer:

x = - 33

Step-by-step explanation:

Given

$\frac{2}{3}$ (x + 6) = - 18

Multiply both sides by 3 to clear the fraction

2(x + 6) = - 54 ( divide both sides by 2 )

x + 6 = - 27 ( subtract 6 from both sides )

x = - 33

6 0

2 years ago

Read 2 more answers