An object is moving in the plane according to these parametric equations:

x(t) = πt + cos(4πt + π/2)
y(t) = sin(4πt + π/2)

the slope of the tangent line to the path at time t is

4πcos(4πt + π/2) divided by (π-4πsin(4πt+π/2))

the first time the tangent line is vertical will be t = ?

the second time the tangent line is vertical will be t = ?

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