Answer:
15,000cm^3
Step-by-step explanation:
Dividing the solid into 2;
Volume = Volume of A + Volume of B
Volume of Top prism (A) =25cm * 20cm * 10cm
Volume of Top prism (A) = 5000cm^3
Volume of bottom prism B = 20cm * 50 * 10
Volume of bottom prism B = = 10000cm^3
Volume of the figure = 5000 + 10000
Volume of the figure = 15,000cm^3
The value of <em>x</em> where by exterior angles theorem, ∠DCO equals 2·x, 69° equals the sum of ∠DCO and x° is <em>x </em>= 23°
<h3>What is the exterior angles theorem?</h3>
The exterior angles theorem states that the exterior angle of a triangle is equal to the sum of the opposite interior angles.
The given parameters are;
Points on the circle are; ABCD
Straight lines = AOBE and DCE
Segment CO = Segment CE
∠AOD = 69°
∠CEO = x°
∠OCD = ∠ODC base angles of isosceles triangle
69° = ∠x° + ∠ODC exterior angle of a triangle
∠DOC = 180 - 2×∠ODC (Angle sum property of a triangle)
180 - 2×∠ODC + x° + 69° = 180° (Sum of angles on a straight line are supplementary)
x° + 69° - 2×∠ODC = 0
∠ODC = 2·x° (exterior angle of a triangle is equal to the sum of the opposite interior angles)
69° = x° + ∠ODC = x° + 2·x° = 3·x° (substitution property of equality)
69° = 3·x°
x = 69° ÷ 3 = 23°
Learn more about angles in a triangle here:
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Answer:
The factor form of given expression is (x-4)(x-2i)(x+2i).
Step-by-step explanation:
The given expression is
It can be written as
According to the rational root theorem, all possible rational roots are in the form of
Where, a₀ is constant term and 
is leading coefficient.
Since the value of f(x) is 0 at x=4, therefore 4 is a root of the function and (x-4) is a factor of given expression.
Use synthetic method to find the remaining factors.
Therefore the factor form of given expression is (x-4)(x-2i)(x+2i).
Answer: x = 5
Step-by-step explanation:
Answer:
32.738ft³
32.7ft³
Step-by-step explanation:
This is half a sphere therefore volume=4/3πr³×1/2
4/3×22/7×2.5³×1/2
=32.738ft³
