Find the measure of the angle formed between the base of the cone and a line segment that represents the slant height.

Step-by-step explanation:

tan Ф = opposite /  adjacent

Ф = arctan ( 2 / 6)

Ф = 18.4349°   ( this is the angle opposite of the one wanted, or ∠C)

then

180 = 90+ 18.4349° +∠A

71.565 = ∠A

a; x = 0.5

step-by-step explanation:

-10x = -5

x = 0.5

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.