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3 years ago

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Mathematics

1 answer:

attashe74 [19]3 years ago

6 0

Answer:

r=2.9cm

Step-by-step explanation:

we know the formula, mass= density*volume

as a result we can figure out the volume = mass/density

=485/8 cm^3

=60.625cm^3

here comes another formula of volume of cone = $\frac{1}{3}$ $\pi$ $r^{2}$ $h^{}$

we will use this to find the radius,

$\frac{1}{3}$ $\pi$ $r^{2}$ $h^{}$ =60.625

$\pi$ $r^{2}$ $h^{}$ =181.875

h is 70mm which we will turn to 7cm

$\pi$ $r^{2}$ *7=181.875

$r^{2}$ =8.27

r=2.875825cm

r=2.9cm

nice question. hope this helps

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timurjin [86]

Answer:

Proved

Step-by-step explanation:

$cos^4\alpha +sin^4\alpha =\frac{1}{4}(3+cos4\alpha )\\\\$

Take the Left Hand Side:

$cos^4\alpha +sin^4\alpha\\\\(cos^2\alpha )^2+(sin^2\alpha )^2\\\\(\frac{1+cos2\alpha }{2})^2+(\frac{1-cos2\alpha }{2})^2 \\\\\frac{1+2cos2\alpha +cos^22\alpha }{4}+\frac{1-2cos2\alpha +cos^22\alpha }{4} \\\\$

$\frac{1+2cos2\alpha +cos^22\alpha +1-2cos2\alpha +cos^22\alpha }{4} \\\\\frac{2+2cos^22\alpha }{4} \\\\\frac{1+cos^22\alpha }{2} \\\\\frac{1}{2}(1+cos^22\alpha )\\\\$

$\frac{1}{2}(1+\frac{1+cos4\alpha }{2})$

$\frac{1}{2}(\frac{2+1+cos4\alpha }{2})\\\\\frac{1}{4}(3+cos4\alpha )\\\\$

Hence Proved!

The following identities were used are attached in an image

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3 years ago

Layla drew a quadrilateral with 4 right angles and 2 pairs of opposite sides sides that are parallel.What quadrilateral best des

marishachu [46]

The answer is Rectangle

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3 years ago

There are a total of 96 children in Years 4, 5 and 6

BaLLatris [955]

Answer: 20 children

Step-by-step explanation:

Given

Year 4: 11 cannot swim

Year 5: 21 can swim

Year 6: 18 of 30 can swim

Total 96 children

Total 37 cannot swim

First Step: find the number of people from year 5 who cannot swim

There are 30-18=12 people who cannot swim in year 6
There are 11 who cannot swim in year 4
Thus, we use the total number [37]-[year 4+year 6]=37-23=14 people who cannot swim in the year 5

Second Step: find the number of children in year 5

There are 21 children who can swim
There are 14 children who cannot swim
21+14=35 children

Third Step: find the number of children in year 4 who can swim

There are 30 children in year 6
There are 35 children in year 5
There are 11 children in year 4 who cannot swim
There are in total 96 children
96-30-35-11=20 children in year 4 who can swim

Hope this helps!! :)

Please let me know if you have any questions

7 0

3 years ago

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marin [14]

Answer:

7.8

Step-by-step explanation:

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3 years ago

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