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NARA [144]
3 years ago
15

The diameter of a iron sphere is 8 cm. It is beaten and drawn into a wire with a diameter of 2 mm. Find the length of the wire.

Mathematics
1 answer:
djyliett [7]3 years ago
6 0

Answer : The length of the wire is, 8533 cm

Step-by-step explanation :

As the iron sphere is beaten and drawn into a wire. That means, their volume will be equal.

Volume of iron sphere = Volume of cylindrical wire

The formula will be:

\frac{4}{3}\pi r_1^3=\pi r_2^2h

where,

r_1 = radius of sphere = \frac{Diamtere}{2}=\frac{8cm}{2}=4cm

r_2 = radius of cylindrical wire = \frac{Diamtere}{2}=\frac{2mm}{2}=1mm=0.1cm

h = height of cylindrical wire or length of wire

Now put all the given values in the above formula, we get:

\frac{4}{3}\pi r_1^3=\pi r_2^2h

\frac{4}{3}\times r_1^3=r_2^2h

\frac{4}{3}\times (4)^3=(0.1)^2h

h=8533.33cm\approx 8533cm

Therefore, the length of the wire is, 8533 cm

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Sever21 [200]

Answer:

width = 1.8 in

length =   3.6 in

height =8-3w =8-3(1.8)= 2.6 in

Step-by-step explanation:

A designer is making a rectangular prism box with maximum volume, with the sum of its length, width, and height 8 in

Let l , w and h are the length , width and height

l +w+h=8\\l=2w

Plug it in the first equation

2w+w+h=8\\3w+h=8\\h=8-3w

volume the box is length times width times height

volume = (2w)(w)(8-3w)\\16w^2-6w^3

To get maximum volume we take derivatived

v'=32w-18w^2

set the derivative =0 and solve for w

0=32w-18w^2\\0=-2w(9w-16)\\w=0 , w= \frac{16}{9}

width = 1.8 in

length = 2w= 3.6 in

height =8-3w =8-3(1.8)= 2.6 in

6 0
3 years ago
Find the measures of the interior angles.<br><br><br><br><br><br><br> what is angle A, B, and C
lina2011 [118]

Answer:

75 degrees.

Step-by-step explanation:

All interior angles of a triangle add up to 180.

So we can set up an equation: 65+40+x=180

105+x=180

x=180-105

x=75

4 0
2 years ago
Read 2 more answers
The weight of people in a small town in missouri is known to be normally distributed with a mean of 154 pounds and a standard de
ad-work [718]
If a random sample of 20 persons weighed 3,460, the sample mean x-bar would be 3460/20 = 173 pounds.
The z-score for 173 pounds is given by:
z=\frac{173-154}{29}=0.655
Referring to a standard normal distribution table, and using z = 0.66, we find:
P(\bar x\ \textless \ 173)=0.7454
Therefore
P(\bar x\ \textgreater \ 173)=1-0.7454=0.2546
The answer is: 0.2546

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3 years ago
What is the common difference of 80,60,45,33.75
GenaCL600 [577]

Answer:

The common difference (or common ratio) = 0.75

Step-by-step explanation:

i) let the first term be a_{1} = 80

ii) let the second term be a_{2}  = a_{1} . r = 80 × r = 60      ∴  r = \frac{60}{80} = 0.75

iii) let the third term be     a_{3}  = a_{2} . r = 60 × r = 45      ∴  r = \frac{45}{60} = 0.75

iv) let the fourth term be   a_{4} = a_{3} . r = 45 × r = 33.75   ∴ r = \frac{33.75}{45} = 0.75

Therefore we can see that the series of numbers are part of a geometric progression and the first term is 80 and the common ratio = 0.75.

4 0
3 years ago
Solve for x Round to the nearest tenth one place after the decimal !
aniked [119]

Answer:

x = 14.4

Step-by-step explanation:

x is sin(angle 24/30)×24

how do we get the angle at 24/30 ?

by using the extended Pythagoras for baselines opposite other than 90 degrees.

c² = a² + b² - 2ab×cos(angle opposite of c)

in our example the angle 24/30 is opposite of the side 18.

so,

18² = 24² + 30² - 2×24×30×cos(angle 24/30)

324 = 576 + 900 - 1440×cos(angle 24/30)

324 = 1476 - 1440×cos(angle 24/30)

1440×cos(angle 24/30) = 1152

cos(angle 24/30) = 1152/1440 = 576/720 = 288/360 = 144/180 = 72/90 = 36/45 = 12/15 = 4/5

angle 24/30 = 36.9 degrees

x = sin(36.9) × 24 = 14.4

4 0
3 years ago
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