Answer:
[tex]Length =3[/tex] [tex]Height = 2[/tex] and [tex]Width = \frac{3}{2}[/tex]
Explanation:
Given
[tex]Volume = 9m^3[/tex]
Represent the height as h, the length as l and the width as w.
From the question:
[tex]Length = 2 * Width[/tex]
[tex]l = 2w[/tex]
Volume of a box is calculated as:
[tex]V = l*w*h[/tex]
This gives:
[tex]V = 2w *w*h[/tex]
[tex]V = 2w^2h[/tex]
Substitute 9 for V
[tex]9 = 2w^2h[/tex]
Make h the subject:
[tex]h = \frac{9}{2w^2}[/tex]
The surface area is calculated as:
[tex]A = 2(lw + lh + hw)[/tex]
Recall that: [tex]l = 2w[/tex]
[tex]A = 2(2w*w + 2w*h + hw)[/tex]
[tex]A = 2(2w^2 + 2wh + hw)[/tex]
[tex]A = 2(2w^2 + 3wh)[/tex]
[tex]A = 4w^2 + 6wh[/tex]
Recall that: [tex]h = \frac{9}{2w^2}[/tex]
So:
[tex]A = 4w^2 + 6w * \frac{9}{2w^2}[/tex]
[tex]A = 4w^2 + 6* \frac{9}{2w}[/tex]
[tex]A = 4w^2 + \frac{6* 9}{2w}[/tex]
[tex]A = 4w^2 + \frac{3* 9}{w}[/tex]
[tex]A = 4w^2 + \frac{27}{w}[/tex]
To minimize the surface area, we have to differentiate with respect to w
[tex]A' = 8w - 27w^{-2}[/tex]
Set A' to 0
[tex]0 = 8w - 27w^{-2}[/tex]
Add [tex]27w^{-2}[/tex] to both sides
[tex]27w^{-2} = 8w[/tex]
Multiply both sides by [tex]w^2[/tex]
[tex]27w^{-2}*w^2 = 8w*w^2[/tex]
[tex]27 = 8w^3[/tex]
Make [tex]w^3[/tex] the subject
[tex]w^3 = \frac{27}{8}[/tex]
Solve for w
[tex]w = \sqrt[3]{\frac{27}{8}}[/tex]
[tex]w = \frac{3}{2}[/tex]
Recall that : [tex]h = \frac{9}{2w^2}[/tex] and [tex]l = 2w[/tex]
[tex]h = \frac{9}{2 * \frac{3}{2}^2}[/tex]
[tex]h = \frac{9}{2 * \frac{9}{4}}[/tex]
[tex]h = \frac{9}{\frac{9}{2}}[/tex]
[tex]h = 9/\frac{9}{2}[/tex]
[tex]h = 9*\frac{2}{9}[/tex]
[tex]h= 2[/tex]
[tex]l = 2w[/tex]
[tex]l = 2 * \frac{3}{2}[/tex]
[tex]l = 3[/tex]
Hence, the dimension that minimizes the surface area is:
[tex]Length =3[/tex] [tex]Height = 2[/tex] and [tex]Width = \frac{3}{2}[/tex]
Determine the size of memory needed for CD recording of a piece of music, which lasts for 26 minutes, is done with a 20-bit Analog-to-Digital Converter (ADC) in stereo (2 channels), at the rate of 44.1 kSa/s, with the compression factor 6 (allow 10% error margin).
Answer: the size of memory needed for the CD recording is 28.7 MB
Explanation:
so in the case of stereo, the bitrate is;
⇒ 26 × 60 × 44.1 × 10³ × 2
= 137592 × 10³
for 10 bit
⇒ 137592 × 10³ × 10
= 1375920 × 10³ bits
now divide by 8 (convert to bytes)
⇒ (1375920 × 10³) / 8
= 171,990,000 BYTE
divide by 1000 (convert to kilobytes)
= 171,990,000 / 1000
= 171,990 KILOBYTES
now Given that, the compression ratio is 6
so
171,990 / 6
= 28665 KB
we know that. 1 MB = 1000 KB
x MB = 28665 KB
x MB = 28665 / 1000
⇒ 28.665 MB ≈ 28.7 MB
Therefore the size of memory needed for the CD recording is 28.7 MB
How many flip-flop values are complemented in an 8-bit binary ripple counter to reach the next count value after: 0110111 and 01010110?
Answer:
- Four (4) flip-flop values will complemented
- one (1) flip-flop value will complemented
Explanation:
To find how many flip flop number of bits complemented, we just need to figure out what the next count in the sequence is and find how many bits have changed.
taking a look at the a) 00110111
we need to just 1 to the value,
so
00110111 + 0000001 = 00111000
So here, only the first four bits are complemented.
Therefore Four (4) flip-flop values will complemented
Next
b) 01010110
we also add 1 to the value
01010110 + 00000001 = 01010111
only the first bit is complemented.
Therefore one (1) flip-flop value will complemented
An astronomer of 65 kg of mass hikes from the beach to the observatory atop the mountain in Mauna Kea, Hawaii (altitude of 4205 m). By how much (in newtons) does her weight change when she goes from sea level to the observatory?
Answer:
[tex]0.845\ \text{N}[/tex]
Explanation:
g = Acceleration due to gravity at sea level = [tex]9.81\ \text{m/s}^2[/tex]
R = Radius of Earth = 6371000 m
h = Altitude of observatory = 4205 m
Change in acceleration due to gravity due to change in altitude is given by
[tex]g_h=g(1+\dfrac{h}{R})^{-2}\\\Rightarrow g_h=9.81\times(1+\dfrac{4205}{6371000})^{-2}\\\Rightarrow g_h=9.797\ \text{m/s}^2[/tex]
Weight at sea level
[tex]W=mg\\\Rightarrow W=65\times 9.81\\\Rightarrow W=637.65\ \text{N}[/tex]
Weight at the given height
[tex]W_h=mg_h\\\Rightarrow W_h=65\times 9.797\\\Rightarrow W_h=636.805\ \text{N}[/tex]
Change in weight [tex]W_h-W=636.805-637.65=-0.845\ \text{N}[/tex]
Her weight reduces by [tex]0.845\ \text{N}[/tex].
Which of the following terms describes the path from an electrical source to a switch or plug?
transmitter
circuit breaker
raceway
breaker panel
Answer:
transmitter hope thus helped!
Explanation:
Raceway is the answer
"A raceway is an enclosed conduit that forms a physical pathway for electrical wiring."
Support with three reasons the decision to use a plastic material for the package in the following
scenario.
Situation: A client has hired Jose, a materials engineer, to develop a package for an item he has begun
to market. The object needs to be mailed to customers within three days of being ordered.
Answer:
its durable. it's cheap. its recyclable
Explanation:
Plastic is made of lots of recycled materials that make it very useful and cheap.