Answer:
Step-by-step explanation:
If the profit realized by the company is modelled by the equation
P (x) = −0.5x² + 120x + 2000, marginal profit occurs at dP/dx = 0
dP/dx = -x+120
P'(x) = -x+120
Company's marginal profit at the $100,000 advertising level will be expressed as;
P '(100) = -100+120
P'(100) = 20
Marginal profit at the $100,000 advertising level is $20,000
Company's marginal profit at the $140,000 advertising level will be expressed as;
P '(140) = -140+120
P'(140) = -20
Marginal profit at the $140,000 advertising level is $-20,000
<u>Based on the marginal profit at both advertising level, I will recommend the advertising expenditure when profit between $0 and $119 is made. At any marginal profit from $120 and above, it is not advisable for the company to advertise because they will fall into a negative marginal profit which is invariably a loss.</u>
Answer:
The rule of the arithmetic sequence is 13 - 2n
The 30th term is -47
Step-by-step explanation:
∵ f(n) = 11 and g(n) = -2(n - 1) = -2n + 2
∴ f(n) + g(n) = 11 + -2n + 2 = 13 - 2n
Use n = 1 , 2 , 3 , 4 to check the type of the sequence
∵ n = 1 ⇒ 13 - 2(1) = 11
∵ n = 2 ⇒ 13 - 2(2) = 13 - 4 = 9
∵ n = 3 ⇒ 13 - 2(3) = 13 - 6 = 7
∵ n = 4 ⇒ 13 - 2(4) = 13 - 8 = 5
∵ 11 , 9 , 7 , 5 is an arithmetic sequence with difference -2
∴ The rule of the arithmetic sequence is 13 - 2n
∴ The 30th term = 13 - 2(30) = -47
Quadrant one
Hope this helped
Answer:
21. ΔUYZ <u>Obtuse</u>
22. ΔBCD <u>Right or Rectangle</u>
23. ΔADB <u>Acute</u>
24. ΔUXZ <u>Acute</u>
25. ΔUWZ <u>Right or Rectangle</u>
26. ΔUXY <u>Equiangular and acute</u>
Step-by-step explanation:
We need to classify each triangle by its angles.
Acute: They have 3 acute angles (less than 90 degrees).
Rectangle: The inner angle A is straight (90 degrees) and the other 2 angles are sharp. The sides that form the right angle are called legs (c and b), the other side hypotenuse.
Obtuse: The inner angle A is obtuse (more than 90 degrees). The other 2 angles are acute.
ΔUYZ Obtuse The inner angle Y is obtuse (more than 90°).
ΔBCD Right or Rectangle The inner angle C is straight (90°).
ΔADB Acute It has 3 acute angles (less than 90°).
ΔUXZ Acute It has 3 acute angles (less than 90°).
ΔUWZ Right or Rectangle The inner angle W is straight (90°).
ΔUXY Equiangular and acute Which means all the inner angles are equal (60°).
