Apendulum swinging through a central angle of 67 degrees completes an arc of length 7.2 cm. what is the length of the pendulum?

6.2 cm

Step-by-step explanation:

We are given that

Central angle =67 degrees

Length of an arc=7.2 cm

We have to find the length of pendulum.

We know that

Radian measure=

By using this formula

67 degrees = rad

Arc length, s=

Where r=Radius of circle

=Central angle (in rad)

s=Length of arc

Using this formula then we get

Hence, the length of pendulum=6.2 cm

length of pendulum is 6.16 cm

Step-by-step explanation:

The pendulum swings through a central angle of 67 degrees. The length of the arc formed by the movement of the pendulum is 7.2 cm. Therefore, the length of the pendulum will be the radius of the circle formed. The formula for determining the length of arc is expressed as

Length of arc = #/360 × 2 × π × r

Where

r = radius

π = constant whose value is 3.14

# = central angle

Therefore

7.2 = 67/360 × 2 × 3.14 × r

7.2 = 1.1688r

r = 7.2/1.1688 = 6.16 cm

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

1.3

step-by-step explanation:

3x2=6   9x+6

bring down the 6 on both sides

6+6=12

12= 9x

divide by 9

12/9 =

1.3 =x