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2 years ago

Determine the complement and/or supplement of each angle. If it is not possible, explain.

Mathematics

1 answer:

Alecsey [184]2 years ago

3 0

Answer:

complement: 32.8°
supplement: 122.8°

Step-by-step explanation:

The sum of an angle A and its complement C is 90°:

A + C = 90°

C = 90° -A . . . . . subtract A from both sides.

That is, the complement of an angle is found by subtracting the angle from 90°.

The sum of an angle and its supplement is 180°. This means the supplement of an angle is found by subtracting the angle from 180°. You may notice the supplement is 90° more than the complement.

A + S = 180°

S = 180° -A = 90° +(90° -A)

For the given angle, the complement is ...

C = 90° -57.2° = 32.8°

And the supplement is ...

S = 180° -57.2° = 122.8°

_____

<em>Additional comment</em>

We generally like angle measures to be positive (as with all measures in geometry). Hence, we might say that the complement of an angle greater than 90° does not exist. YMMV

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Answer:

correct option is 2187

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lateral surface area is 640.56 square inches

Step-by-step explanation:

Given

radius of cylinder = 12 inches

height of cylinder = 17 inches

we will us value of pi as 3.14

surface area for cylinder consist of two part

1. lateral surface area which is gven by $2\pi rl$

where r is radius of cylinder and l is height of cylinder

Thus, lateral surface area for given cylinder is

$2\pi rl\\ =>2* 3.14*12*17\\=> 1281.12$

Thus, lateral surface area for given cylinder is 1281.12 square inches.

_________________________________

second part of surface area is area of two base (upper and lower) of cylinder.

area of base is given by area of circle $\pi r^2$

$area \ of \base = \pi r^2 = 3.14*12^2\\=>area \ of \base = 3.14*144 = 452.16$

This, area of base is for one base of cylinder

since there are 2 base

area of both base will be = 2* area of one base

= 2*452.16 = 904.32.

Thus, area of base is 904.32 sq. in.

_______________________________________

Total surface area of cylinder = area of two base+ lateral surface area of cylinder = 1281.12 square inches + 904.32 square inches

= 2,185.44 square inches.

Thus, total surface area is 2,185.44 square inches.

lateral surface area is 640.56 square inches

but option which is closest to calculated value is 2187.

Thus, correct option is 2187

___________________________________________

Note: this problem can be directly solved using formula

total surface area for cylinder = $2\pi r^2 + 2\pi rl$

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