Answer:
[B] 0, 19.5, 160.5, 180, 360
Step-by-step explanation:
3 sin²θ = sin θ
3 sin²θ − sin θ = 0
sin θ (3 sin θ − 1) = 0
sin θ = 0 or sin θ = ⅓
If sin θ = 0, θ = 0°, 180°, 360°.
If sin θ = ⅓, θ = 19.5°, 160.5°.
Answer:
number of units for cost to be minimum=150
Step-by-step explanation:
y=2x^2-600 x+49000
dy/dx=4x-600
dy/dx=0 gives 4x-600=0
4x=600
x=150
d^2y/dx^2=4x
at x=150,d^2y/dx^2=4*150=600>0
so y is minimum at x=150
So, we know that:
We also know that 
. We will use that fact to find 
in terms of 
and 
.
Therefore:
Answer:
36
Step-by-step explanation:
24^2 = (12)(12+x)
576 = 144 + 12x
432 = 12x
36 = x
Answer:
24.5 unit²
Step-by-step explanation:
Area of ∆
= ½ | x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) |
= ½ | (-1)(3 -(-4)) + 6(-4 -3) + (-1)(3 - 3) |
= ½ | -7 - 42 |
= ½ | - 49 |
= ½ (49)
= 24.5 unit²
<u>Method 2:</u>
Let the vertices are A, B and C. Using distance formula:
AB = √(-1-6)² + (3-3)² = 7
BC = √(-6-1)² + (-4-3)² = 7√2
AC = √(-1-(-1))² + (4-(-3))² = 7
Semi-perimeter = (7+7+7√2)/2
= (14+7√2)/2
Using herons formula:
Area = √s(s - a)(s - b)(s - c)
here,
s = semi-perimeter = (14 + 7√2)/2
s - a = S - AB = (14+7√2)/2 - 7 = (7 + √2)/2
s - b = (14+7√2)/2 - 7√2 = (14 - 7√2)/2
s - c = (14+7√2)/2 - 7 = (7 + √2)/2
Hence, on solving for area using herons formula, area = 49/2 = 24.5 unit²
