Answer:
Step-by-step explanation:
1.The prime factorization of 54 is: 2 x 3 x 3 x 3.
2.The prime factorization of 24 is: 2 x 2 x 2 x 3.
3.The prime factors and multiplicities 54 and 24 have in common are: 2 x 3.
4.2 x 3 is the GCF of 54 and 24.
Answer: GCF(54,24) = 6.
Answer:
Step-by-step explanation:
A <u>helix</u> is a curve for which the tangent makes a constant angle with a fixed line. The shortest path between two points on a cylinder (one not directly above the other) is a fractional turn of a helix, as can be seen by cutting the cylinder along one of its sides, flattening it out, and noting that a straight line connecting the points becomes helical upon re-wrapping (see attached diagram for helix).
The parametrization for the helix is
where 
is the radius of the helix, 
is the constant, and 
is the parameter
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If we set the vertex at (0,0) then the curve goes through (30,30)
<span>y = 1/30 x^2 </span>
<span>x^2 = 30y </span>
<span>Since the parabola x^2 = 4py has its focus at y=p, 4p=30 and the mic should be 15/2 inches up from the vertex.</span>
Answer:
z = 21 ; y= 16
Step-by-step explanation:
first of all we have to isolate a variable.
In second expression we can obtain:
3y = 2z+6
y = 2/3 z + 2
now we have to substitute this value in the first equation and solve it
8(2/3z+2)-5z = 23
16/3z + 16 -5z = 23
16z +48 - 15z = 69
z = 21
now we have to substitute z in the second equation:
y = 2/3 (21) +2
y = 14+ 2 = 16
y = 16
