(PLEASE HELP!) The central angle of a sector is 72 degrees and the sector has an area of 15.71. Find the radius.

The radius is 5 units (approximately)

Step-by-step explanation: The area of a sector with central angle X is given as;

Area = (X/360) x pi x r^2

Since the area has been given as 15.71 units, we can input the known values into the formula as follows;

15.71 = (72/360) x 3.14 x r^2

By cross multiplication we now have

(15.71/3.14) = 1/5 x r^2

(15.71/3.14) x 5 = r^2

78.55/3.14 = r^2

25.0159 = r^2

Add the square root sign to both sides of the equation

5.001 = r

The radius is equal to 5 units (approximately)

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the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places