50 points Simplify the expression. sin^2 theta/csctheta tan^2theta a. sin^2 theta b. sin cos^2 theta c. sec^2 theta d. csc theta

B. sin(theta) cos^2(theta)

Step-by-step explanation:

sin^2(theta) / csctheta tan^2(theta)

To solve, we convert to sine and cosine and then simplify.

means by the priority of operators (* and / from left to right)

(sin^2(theta) / csctheta) * tan^2(theta)

= sin^2(theta) / (1/sin(theta) * (sin(theta)/cos(theta)^2

= sin^2(theta) * sin(theta) * sin^2(theta) / cos^2(theta)

= sin^5(theta) / cos^2(theta)

which obviously does not correspond to any of the answers.

IF the expression were missing parentheses in the denominator, then it becomes:

sin^2(theta) / (csctheta tan^2(theta))

= sin^2(theta) / (1/sin(theta) * sin^2(theta) /cos^2(theta))

= sin^2(theta) / (sin(theta)/cos^2(theta)

= sin(theta) cos^2(theta)

which corresponds to answer B.

Step-by-step explanation:

Simplify the expression.

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

25.2

step-by-step explanation:

2+4x6-8/10= 25.2