Marcus and three of his friends are guessing the radius of a circular pond. they read that the circumference is 157 ft, so they can use the equation 3.14*2r=157 to determine which of these guesses which form the replacement set {20,25,30,35} is correct? . what is the radius of the pond? a. 20ft b. 25ft c. 30ft d. 35ft

Option B. 25 ft

Step-by-step explanation:

we know that

The circumference of a circle is equal to

we have

assume

substitute in the formula

Solve for r

Divide by 2(3.14) both sides

answer is 67%

step-by-step explanation:

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