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sweet-ann [11.9K]
3 years ago
10

Simplify this radical. the square root of 84

Mathematics
2 answers:
Mkey [24]3 years ago
3 0

Answer:

The square root of 84 is 9.1651...etc, so in a shorter form, <em>9</em>.



Lelu [443]3 years ago
3 0

Answer: \sqrt[2]{21}

Explanation: Work is provided in the image attached.

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An icicle with a diameter of 15.5 centimeters at the top, tapers down in the shape of a cone with a length of
Helga [31]

Answer:

Step-by-step explanation:

Note: I will leave the answers as fraction and in terms of pi unless the question states rounding conditions to ensure maximum precision.

From the question, we can tell it is a inversed-cone (upside down)

Volume of Cone = \pi r^{2} \frac{h}{3}

a) Given Diameter , d = 15.5cm and Length , h = 350cm,

we first find the radius.

r = \frac{d}{2} \\=\frac{15.5}{2} \\=7.75cm

We will now find the volume of the cone.

Volume of cone  \pi (7.75)^{2} \frac{350}{3} \\= \frac{168175\pi }{24}

We know the density of ice is 0.93 grams per 1cm^{3}

1cm^{3} =0.93g\\\frac{168175\pi }{24}  cm^{3} =0.93(\frac{168175\pi }{24} )\\= 20473 g(Nearest Gram)

b) After 1 hour, we know that the new radius = 7.75cm - 0.35cm = 7.4cm

and the new length, h = 350cm - 15cm = 335cm

Now we will find the volume of this newly-shaped cone.

Volume of cone = \pi (7.4)^{2} \frac{335}{3} \\= \frac{91723\pi }{15} cm^{3}

Volume of cone being melted = New Volume - Original volume

= \frac{168175\pi }{24} -\frac{91723\pi }{15} \\= \frac{35697\pi }{40} cm^{3}

c) Lets take the bucket as a round cylinder.

Given radius of bucket, r = 12.5cm (Half of Diameter) and h , height = 30cm.

Volume of cylinder = \pi r^{2} h\\=\pi (12.5)^{2} (30)\\=\frac{9375\pi }{2} cm^{3}

To overflow the bucket, the volume of ice melted must be more than the bucket volume.

Volume of ice melted after 5 hours = 5(\frac{35697\pi }{40} )\\=\frac{35697\pi }{8} cm^{3}

See, from here of course you are unable to tell whether the bucket will overflow as all are in fractions, but fret not, we can just find the difference.

Volume of bucket - Volume of ice melted after 5 hours

= \frac{9375\pi }{2} -\frac{35697\pi }{8 } \\=\frac{1803\pi }{8}cm^{3}

from we can see the bucket can still hold more melted ice even after 5 hours therefore it will not overflow.

4 0
2 years ago
The lengths in feet of three pieces of timber are
Sonbull [250]

The equal length of the logs will be 200 feets each.

Since the lengths in feet of three pieces of timber are 144, 216, 240 and the operator wants to cut them into 3 equal sizea, this will go thus:

= (144 + 216 + 240) / 3

= 600/3

= 200 feets each

Therefore, there'll be an equal length of 200 feets each.

Read related link on:

brainly.com/question/24664848

7 0
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The prefix octa-means what?
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The prefix means 8.How to remember this is a octagon which has 8 sides.Therefore Octa means eight.I hope this helped.
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Answer:

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Step-by-step explanation:

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