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pantera1 [17]
3 years ago
10

The volume of a cylindrical soup can is represented by the expression πr3 + 7πr2, where r is the radius of the cylinder. Which s

tatement best interprets the factor (r + 7) in this context
Mathematics
1 answer:
Ganezh [65]3 years ago
5 0

Answer:

Step-by-step explanation:

Given the volume of the cylindrical soup expressed as V = πr³+ 7πr²

From V = πr³ + 7πr²;

factor out the common variable

V = πr³ + 7πr²

V = πr²(r+7) ... 1

The original volume of a cylinder V =  πr²h .... 2 where;

r is the radius of the cylinder

h is the height of the cylinder

Equating equation 1 and 2, we will have;

πr²(r+7)  =  πr²h

Divide both sides by  πr²

πr²(r+7)/ πr² = πr²h/ πr²

r+7 = h

h = r+7

<em>Hence the factor in the context given is equivalent to the height of the cylinder written as a function of its radius r</em>.<em> The statement means that the height of the cylindrical soup is 7 more than its radius.</em>

<em></em>

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Answer:

Question 1:

The angles are presented here using Autocad desktop application

The two column proof is given as follows;

Statement                   {}                             Reason

S1. Line m is parallel to line n       {}            R1. Given

S2. ∠1 ≅ ∠2                   {}                            R2. Vertically opposite angles

S3. m∠1 ≅ m∠2                    {}                     R3. Definition of congruency

S4. ∠2 and ∠3 form a linear pear      {}      R4. Definition of a linear pair

S5. ∠2 is supplementary to ∠3 {}      R5. Linear pair angles are supplementary

S6. m∠2 + m∠3 = 180°              {}                Definition of supplementary angles

S7. m∠1 + m∠3 = 180°              {}                 Substitution Property of Equality  

S8. ∠1 is supplementary to ∠3           {}      Definition of supplementary angles

Question 2:

(a) The property of a square that is also a property of a rectangle is that all the interior angles of both a square and a rectangle equal

(b) The property of a square that is not necessarily a property of all rectangles is that the sides of a square are all equal, while only the length of the opposite sides of a rectangle are equal

(c) The property of a rhombi that is also a property of a square is that all the sides of a rhombi are equal

(d) A property of a rhombi that is not necessarily a property of all parallelogram is that the diagonals of a rhombi are perpendicular

(e) A property that applies to all parallelogram is that the opposite sides of all parallelogram are equal

Step-by-step explanation:

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