Find the angle of arc BC

Mathematics

1 answer:

amid [387]3 years ago

6 0

Answer:

96°

Step-by-step explanation:

The measure of arc EC is twice the measure of ∠DEC, so is ...

arc EC = 2×68° = 136°

The measure of arc BC is found from the sum of arcs around a circle.

BC +CE +EB = 360° = BC +136° +128°

BC = 96° . . . . . subtract 264°

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A rectangular solid with a square base has a volume of 4096 cubic inches - determine the dimensions that yield the minimum surfa

Bumek [7]

Answer:

side of base, a = 10.1 inches, height, h = 40.1 inches

Step-by-step explanation:

Volume of rectangular solid, V = 4096 cubic inches

Let the side of base is a and the height is h.

$V = a^2h\\\\4096 = a^2 h ..... (1)$

surface area of the solid

$S = 2a^2 + 4 ah \\\\S = 2a^2 + 4 \times a \times \frac{4096}{a^2} from (1)\\\S = 2a^2 + \frac{4096}{a}\\\\\frac{dS}{da}= 4 a - \frac{4096}{a^2}\\\\4 a - \frac{4096}{a^2} = 0 \\\\a^3 = 1024\\\\a =10.1 inches$