95141 1404 393
Answer:
- arc BC: 8.55 cm
- chord BC: 8.03 cm
Step-by-step explanation:
The length of an arc that subtends central angle α will be ...
s = rα . . . . where α is in radians
The central angle BOC is twice the measure of angle QBC, so is 70°, or 7π/18 radians. So, the length of arc BC is ...
s = (7 cm)(7π/18) ≈ 8.55 cm . . . arc BC
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For central angle α and radius r, the chord subtending the arc is ...
c = 2r·sin(α/2)
c = 2(7 cm)sin(35°) ≈ 8.03 cm . . . . chord AB
4b + 22 = 5 (b + 4) - 1 (remove the parantheses)
4b + 22 = 5b + 20 - 1 (calculate)
4b + 22 = 5b + 19 (move the terms)
4b - 5b = 19 - 22 (collect like terms and calculate)
-b = -3 (change the signs)
<em>b = 3</em>
Answer:
Part 1: 31x+25=180
part 2: x=5
Step-by-step explanation:
there are 180° on a straight line, which is the base/ bottom line of the traingle (indicated by the arrow on the end).
so, 180-151= 29
29° is the third angle on the traingle.
now, there are 180° in a triangle, therefore to find an equation for x:
29+20x-3+11x-1= 180 (adding up all the angles and making it equal to 180°)
now simplify this equation to get:
31x+25=180 (PART 1)
to find x simply solve the equation:
31x=180-25
31x= 155
x= 155/31
x=5 (PART 2)
Answer:
The height of the prism is 2m
Step-by-step explanation:
Given;
The volume of pentagonal prism, V = 4.8 m^3
Area of the prism, A = 2.4 m^2
To determine the height of the prism, we consider the following;
Volume of any prism = Area of the prism x height of the prism
Height of the prism = volume of the prism / Area of the prism
Height of the prism = 4.8 / 2.4
Height of the prism = 2 m
Therefore, the height of the prism is 2m
Triangular inequality: Length of third side must be less than the sum of the lengths of the other 2 sides.
x < 18 + 29
x < 47
so Maximum length of third side is 46 units.
Also 29 < 18 + x
x > 11 so minimum length = 12
Difference = 46-11 = 35
