A cable 103.6 meters long is cut into two pieces so that one piece is 52.6 meters longer than the other. Find the length of each piece of cable. Type the product of the lengths of the two pieces, rounded to the nearest tenth.

Step-by-step explanation:

Let the smaller piece = x

Then the larger piece = x + 52.6

Now they must add to 103.6

x + x + 52.6 = 103.6          Combine like terms on the left

2x + 52.6 = 103.6              Subtract 52.6 from both sides

2x = 103.6 - 52.6

2x = 51                               Divide by 2

x = 51/2

x = 25.5

x + 52.6 = 25.5 + 52.6 = 78.1

The product is 78.1 * 25.5 = 1991.6

you could deduce the conclusion directly using the facts pertaining to the specific situation.

hope this .

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9