Answer:
B. Inscribed equilateral triangle.
Step-by-step explanation:
An equilateral triangle is a type of triangle that has all sides to have the same length.
An inscribed figure or shape is one which has been constructed within the boundaries of another figure or shape.
In the given question, the markings is construction of an inscribed equilateral triangle. This procedure of the construction after completion, generate the triangle as shown in the construction attached to this answer.
Answer:
1. x = √(73)/2 - 9/2 or x = -9/2 - √(73)/2
2. x = (512 2^(1/3) + (18 i √(16303) + 16222)^(2/3))/(6 (9 i √(16303) + 8111)^(1/3)) + 16/3 or x = 16/3 + (256 (-1)^(2/3))/(3 (1/2 (9 i √(16303) + 8111))^(1/3)) - 1/3 ((-1)/2)^(1/3) (9 i √(16303) + 8111)^(1/3) or x = ((-2)^(2/3) (9 i √(16303) + 8111)^(2/3) - 512 (-2)^(1/3))/(6 (9 i √(16303) + 8111)^(1/3)) + 16/3 or x = 1/3 (10 - 3 √(11))^(-1/3) ((-1)^(1/3) (10 - 3 √(11))^(2/3) - (-1)^(2/3)) - 1/3 or x = 1/3 ((-10 - 3 √(11))^(1/3) - (-1)^(1/3) (3 √(11) - 10)^(1/3)) - 1/3 or x = 1/3 (10 - 3 √(11))^(-1/3) (-(10 - 3 √(11))^(2/3) - 1) - 1/3
3. x = 2/5 or x = (i √(3))/2 - 1/2 or x = -(i √(3))/2 - 1/2
4. x = 1/4 + (4 √(54714) + 441)^(1/3)/(4 3^(2/3)) - 61/(4 (12 √(54714) + 1323)^(1/3)) or x = (-(-3)^(1/3) (4 √(54714) + 441)^(2/3) - 61 (-3)^(2/3))/(12 (4 √(54714) + 441)^(1/3)) + 1/4 or x = (61 (-3/(441 + 4 √(54714)))^(1/3) + (-1)^(2/3) (441 + 4 √(54714))^(1/3))/(4 3^(2/3)) + 1/4
Step-by-step explanation:
Too long! I try to add to the comments!
has only one critical point at
. The function has Hessian
which is positive definite for all
, which means
attains a minimum at the critical point with a value of
.
To find the extrema (if any) along the boundary, parameterize it by
and
, with
. On the boundary, we have
Find the critical points along the boundary:
Respectively, plugging these values into
gives 11, 47, 43, and 47. We omit the first and third, as we can see the absolute extrema occur when
.
Now, solve for
for both cases:
so
has two absolute maxima at
with the same value of 47.
Answer:
2 kg
Step-by-step explanation:
5 - 3 = 2
Answer:
x = 11 ,
<APT = 6x + 1 ➡ 67°
<PTA = 9x - 24 ➡75°
<PAT = 5x - 17 ➡ 38°
Step-by-step explanation:
(5x - 17) + (9x - 24) + (6x + 1)=180°
20x - 40 = 180°
20x = 180° + 40°
20x = 220°
x = 11
