Find the measure of a central angle that intercepts an arc of 27 inches in a circle whose radius is 10 inches.

154.7°

Step-by-step explanation:

Formula for calculating length of an arc = theta/360× 2πr

Where r is the radius

theta is the angle subtended by the arc

Given length of an arc = 27in

Radius of the circle = 10in

Substituting this values in the formula to get theta

27 = theta/360 × 2π(10)

27 = theta/360×20π

20π × theta = 360×27

62.832 × theta = 9720

theta = 9720/62.832

theta = 154.7°

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."