For what values of theta (0 less than or equal to theta less than or equal to 2pi) do maximum r values occur on the graph the polar equation r=4+3 sin3theta? Note that the maximum r-value occurs at a point that is the maximum distance from the pole.

Step-by-step explanation:

To find the values of the angle which makes maximum r you use the derivative of r

If you equals this derivative to zero you obtain the value of the angle:

However, the values of 5π/6 and 9π/6 are also available, because makes the sinusoidal function equal  to 1.

hence, the answer is:

answer b

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

1. 8

2. 9

3. 20

4. 3

5. 17

6. 2.2

7. 11.25

8. 1

9. 14

10. 2

step-by-step explanation:

thats the first half