Suppose an ant is sitting on the perimeter of the unit circle at the point (1,0). if the ant travels a distance of 2π3 in the counter-clockwise direction, then the coordinates of the point where the ant stops will be

The coordinates of the point where ant stopped will be (0,1)

Step-by-step explanation:

Given an ant is sitting on the perimeter of the unit circle at the point (1,0). If the ant travels a distance of in the counter-clockwise direction, we have to find the coordinates of point where ant stops.

The ant is sitting at point A.

The circumference of unit circle=2πr=2π(1)=2π units

Now given ant travel a distance of .

We have to find the circles completed to find the coordinates of the point.

In order to find circles we have to divide by 2π

      (First circle)

   (Second circle)

First circle is completely covered then first quadrant of second circle is completed.

Hence, the coordinates of the point where ant stopped will be (0,1)

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.