Answer:
B = 45°
BC = 14 km
AB = 14√2 km ≈ 19.80 km
Step-by-step explanation:
If one acute angle (A) of a right triangle is 45°, then the other one is also:
... 180° -90° -45° = 45°
The sides opposite these congruent angles are the same length, 14 km in this case, and the hypotenuse is found from the Pythagorean theorem to be √2 times either leg length.
... AB² = AC² +BC²
... AB = √(AC² +BC²) = (14 km)√(1² +1²) = 14√2 km
The cost to produce a product is modeled by the function , where x is the number of products produced.
We have to determine the minimum cost of producing this product.
Since,
Now, consider the equation
Dividing the above equation by 5, we get
Now, considering the coefficient of 'x', dividing it by '2' and then adding and subtracting the square of the number which we got after dividing .
Since, coefficient of 'x' is 14, and half of 14 is '7'.
So, adding and subtracting from the above equation.
Now, we have to determine the minimum cost to produce the product.
Since,
Now, let f'(x)=0
Therefore, x=7
Now, consider which is greater than 0.
Therefore, x= 7 is the minimum cost.
The minimum cost to produce the product is $7.