There are two (equivalent) formulas for the circumference of a circle:
C = 2 pi r, where r is the radius of the circle
C = pi d, where d is the diameter of the circle
In this particular problem, however, we're dealing with arc length. For the shown central angle "theta" = 160 degrees, the arc length is 42 cm.
Knowing this enables us to calculate the radius or diameter of the circle.
Arc length = s = (radius) (central angle, in radians, not degrees)
First, convert 160 degrees to radians: 160 deg pi rad
----------- * ------------ = (8/9) pi rad
1 180 deg
Then 42 cm = r *(8/9) pi rad
Solve for the radius (r): divide 42 cm by (8/9) pi rad
Then use the formula for circumference introduced earlier:
C= 2 pi r Substitute [42 cm / ( (8/9) pi rad )] for r.
Simplify your result, and you will then have the circumference, C, in cm.
Perpendicular lines have negative reciprocal slopes. All that means is " flip " the slope and change the sign.
slope = -2, or -2/1....so flip the slope...-1/2...and change the sign...1/2.
so the perpendicular slope would be 1/2.
Answer:
$2728
Step-by-step explanation:
Use compound interest formula:
P = 1700, r = 0.03, n = 1, t = 16
Plug in numbers:
Simplify:
Use calculator:
Answer: A sequence of similar transformations of dilation and translation could map △ABC onto △A'B'C'.
Step-by-step explanation:
Similar transformations: If one figure can be mapped onto the other figure using a dilation and a congruent rigid transformation or a rigid transformation followed by dilation then the two figures are said to be similar.
In the attachment △ABC mapped onto △A'B'C' by a sequence of dilation from origin and scalar factor k followed by translation.
