a farmer sells his corn for $230 a metric ton with a small surcharge of $25. his neighbor sells her corn for $230 a metric ton and gives $15 rebate. write the cost model equations for both farmers and find the amount of corn that makes the costs equal.

Step-by-step explanation:

Step one:

The farmer sells his corn for $230 a metric ton

small surcharge = $25.

let the amount per metric ton be x

and let the total cost per x metric ton be y

the total cost function is

y=230x+251

The neighbor sells her corn for $230 a metric ton

he gives $15 rebateA rebate is a partial refund of the cost of an item

let the amount per metric ton be x

and let the total cost per x metric ton be y

the total cost function is

y=230x-152

Step two:

Equating the two equation above

230x+25=230x-15

230x-230x=25+15

0=40

The result shows that based on the cost function of both farmer, there will never be an amount of corn that would make them have the same cost

pla·gia·rism

/ˈplājəˌrizəm/

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noun

the practice of taking someone else's work or ideas and passing them off as one's own.

step-by-step explanation:

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