Answer:
28.07° ; 70.53° ; 53.13° ; 36.87°
Step-by-step explanation:
Using PYTHAGORAS RULE :
IMAGE 1:
value of cos α equals :
cos α = Adjacent / Hypotenus
cos α = 15 / 17
cos α = 0.88235
α = cos^-1 (0.88235)
α = 28.07°
IMAGE 2:
sin β = Opposite / Hypotenus
sin β = 14√2 / 21
sin β = 0.9428
β = sin^-1(0.9428)
β = 70.53°
IMAGE 3:
From trigonometry :
cot = 1 / tan
Tan = Opposite / Adjacent
Therefore, Cot = Adjacent / Opposite
cot γ = 3/4
cot γ = 0.75
γ = cot^-1 (0.75)
γ = 53.13°
IMAGE 4:
tan α = Opposite / Adjacent
tan α = 15 / 20
tan α = 0.75
α = tan^-1 (0.75)
α = 36.87°
Answer:
The Area of the sector is: A = 95.4 cm²
Step-by-step explanation:
Given
Central angle Ф = 135°
radius r = 9 cm
To determine
Area of the sector = ?
The Area of the sector can be calculated using the formula
A = Ф/360 × πr²
substitute Ф = 135°, r = 9 and π = 3.14
A = 135/360 × (3.14) (9)²
A = 95.4 cm²
Therefore, the Area of the sector is: A = 95.4 cm²
Answer:
- 40 packages from Fred Motors
- 20 packages from Admiral Motors
- 40 packages from Chrysalis
Step-by-step explanation:
I would formulate the problem like this. Let f, a, c represent the numbers of packages bought from Fred Motors, Admiral Motors, and Chrysalis, respectively. Then the function to minimize (in thousands) is …
objective = 500f +400a +300c
The constraints on the numbers of cars purchased are …
5f +5a +10c >= 700
5f +10a +5c >= 600
10f +5a +5c >= 700
Along with the usual f >=0, a>=0, c>=0. Of course, we want all these variables to be integers.
Any number of solvers are available in the Internet for systems like this. Shown in the attachments are the input and output of one of them.
The optimal purchase appears to be …
- 40 packages from Fred Motors
- 20 packages from Admiral Motors
- 40 packages from Chrysalis
The total cost of these is $40 million.
Almost; she's just missing 1, since 1*88 = 88.