Answer:
already put answer lol i just want points
Step-by-step explanation:
Answer: x = 38/3
Step-by-step explanation:
Answer:
B) BC'= 8, m A'= 28°
Step-by-step explanation:
When dilating a figure, it increases its size or decreases. In this case, as it is dilating by a factor of 1/2, you can assume it decreases.
To find the value of the new figure, A'B'C', you have to multiply the factor times the lengths of the triangle, or, the only one they are asking for in this case, the length BC':
- BC' = BC×1/2
- BC' = 16×1/2
- BC' = 8
The angles, otherwise, do not change. When figures are dilated, they are similar. The properties of similar figures are that they have congruent angles, therefore, the same angles. They do not have any effect caused by the factor, so m A' stays at 28°.
Let the lengths of the bottom of the box be x and y, and let the length of the squares being cu be z, then
V = xyz . . . (1)
2z + x = 16 => x = 16 - 2z . . . (2)
2z + y = 30 => y = 30 - 2z . . . (3)
Putting (2) and (3) into (1) gives:
V = (16 - 2z)(30 - 2z)z = z(480 - 32z - 60z + 4z^2) = z(480 - 92z + 4z^2) = 480z - 92z^2 + 4z^3
For maximum volume, dV/dz = 0
dV/dz = 480 - 184z + 12z^2 = 0
3z^2 - 46z + 120 = 0
z = 3 1/3 inches
Therefore, for maximum volume, a square of length 3 1/3 (3.33) inches should be cut out from each corner of the cardboard.
The maximum volume is 725 25/27 (725.9) cubic inches.
Answer:d
Step-by-step explanation: