Describe the graph represented by the equation r = 4 / 2 + 3 sin theta

Hyperbola, horizontal directricx at a distance 4/3 units above the pole

Step-by-step explanation:

* The polar equation for a conic i

- For a conic with a focus at the origin, if the directrix is

 x = ± p, where p is a positive real number, and the eccentricity

 is a positive real number e, the conic has a polar equation

 # r = ep/(1 ± e cosФ)

- For a conic with a focus at the origin, if the directrix is

  y = ± p, where p is a positive real number, and the eccentricity

  is a positive real number e, the conic has a polar equation

 # r = ep/(1 ± e sinФ)

- For a conic with eccentricity e,

 #  if 0 ≤ e < 1, the conic is an ellipse

 # if e = 1, the conic is a parabola

 # if e > 1, the conic is an hyperbola

* Lets solve the problem

∵ 4 = r/(2 + 3sinФ)

- From the rule above

∴ Directrix is y = ± p

- Divide up and down by 2 to make the 1st term in the

 bracket down = 1

∴ r = 2/(1 + (3/2)sinФ)

- Compare it with the rule

∴ e = 3/2 > 1

∴ The conic is hyperbola

∵ ep = 2

∴ p = 2 ÷ e = 2 ÷ 3/2 = 2 × 2/3 = 4/3

∴ Directrix is y = ± 4/3

* Now we can describe the graph

- Hyperbola, horizontal directricx at a distance 4/3 units above the pole

part a

in a city ice cream is mostly only bought when the temperature is very high as ice cream cools down our

so we can derive the conclusion that as the temperature increases the number of ice creams sold also increases

part b

y intercept is 5

slope is 2

happy to

pls mark as brainliest

by definition, an arc subtended by a central angle of some given measure has the same measure. so .