Find the surface area of the composite solid.

Option B is correct.

Step-by-step explanation:

Given:

A Solid Figure made up pf cuboid and a triangular based prism.

To find: Total Surface area of the figure.

Total Surface Area = Area of front + Area of top + Area of Back + 2 × Area of side + Area of bottom

Area of Front = Area of Square + Area of rectangle

                      = 10 × 10

                      = 100 in.²

Area of top = Area of Rectangle

                   = 13 × 10

                   = 130 in.²

Area of back =  Area of square in down + Area of rectangle in up

                      = 10 × 10 + 5 × 10

                      = 100 + 50

                      = 150 in.²

Area of the bottom = Area of the rectangle

                                = 12 × 10

                                = 120 in.²

Area of the side = Area of rectangle + Area of the triangle

                           = 12 × 10 + 1/2 × 5 × 12

                           = 120 + 5 × 6

                           = 120 + 30

                           = 150 in.²

Total Surface Area = 100 + 130 +150 + 120 + 2 × 150

                               = 500 + 300

                               = 800 in.²

Therefore, Option B is correct.

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}