Answer:
Rotation about 180*
Translation about 7 units to the right and 8 down
Step-by-step explanation:
Circumference is found by evaluating C = 2 pi r, where r is the radius of the circle. Here, C = 2 pi (2.4 cm) = 4.8 pi.
Answer:
Yes, it is a solution
Step-by-step explanation:
9x+7y=-11
-2x-5y=30
substitute 5 for x and -8 for y and test:
9(5)+7(-8)=-11
45-56=-11 , this is true
-2(5)-5(-8)=30
-10+40=30 , this is true also
Answer:
Step-by-step explanation:
Hence, the result will be
you can put the scalar in to get
Answer:
r = 3.628 cm
h = 10.88 cm
cost = 11.16 cents
Step-by-step explanation:
we know the total volume = 450 cc
then pi * r ^ 2 * h = 450
solved for h:
h = 450 / (pi * r ^ 2)
h = 143.31 / r ^ 2
now the total cost of packing = 2 * 3.14 * r * h * 0.03 + 3.14 * r ^ 2 * 0.03 + 3.14 * r ^ 2 * 0.06
= 0.1884 * r * h + 0.0942 * r ^ 2 + 0.1884 * r ^ 2
= 0.1884 * r * h + 0.2826 * r ^ 2
putting the value of h in the previous equation we obtain
total cost = 27 / r + 0.2826 * r ^ 2
we have to minimize this to differentiate it and equate it with 0
:
-27 / r ^ 2 + 0.5652 * r = 0
r ^ 3 = 27 / 0.5652
r ^ 3 = 47.77
r = 3,628 cm
replacing:
we get h = 450 / (3.14 * 3,628 ^ 2) = 10.88 cm
the total cost can be calculated for the equation
we get the total cost = 27 / 3,628 + 0.2827 * 3,628 ^ 2 = 11.16 cents
