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2 years ago

the two triangles below are similar use what you know about similar triangles to find the missing side. show your work

Mathematics

1 answer:

lara31 [8.8K]2 years ago

7 0

If both triangles are similar the ratio of sides will be same

$\\ \sf\longmapsto \frac{x}{24} = \frac{6}{12} \\ \\ \sf\longmapsto 12x = 6 \times 24 \\ \\ \sf\longmapsto 12x = 144 \\ \\ \sf\longmapsto x = \frac{144}{12} \\ \\ \sf\longmapsto x = 12$

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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.

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1 year ago

Suppose a teacher gives 10 points for putting your name on a 100 point test. The minimum score on that test is 10 and the maximu

Varvara68 [4.7K]

I think it is x+10=>100

8 0

3 years ago

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Serga [27]

Answer:

15m+80 would be the correct equation

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3 years ago

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The table shown below gives the approximate number of pieces of mail handled by the United States Postal Service for different y

netineya [11]

Answer:

Step-by-step explanation:

Answer:

1.08×10^11

Step-by-step explanation:

1.08 times 10 to the power of 11

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2 years ago

Tim spends about 1/3 of each weekday sleeping and about 7/24 of each weekday in school. What fraction of the weekday does Tim sp

White raven [17]

We have been given that Tim spends about 1/3 of each weekday sleeping and about 7/24 of each weekday in school. And we need to find what fraction of the weekday does Tim spend either sleeping or in school.

This means that we need to find the time he spends in sleeping when he is in the school.

Therefore, we have to add the time he spends in sleeping and the time he spends in school.

Therefore, required fraction is given by

$\frac{1}{3} +\frac{7}{24}$

Now in order to add the fractions, we have to make the denominator same.

Multiply the numerator and denominator of first fraction by 8 to make the same denominator.

$\frac{8}{24} +\frac{7}{24}$

Now, we have the same denominator hence, we can add the numerator

$\frac{8+7}{24}$

$\frac{15}{24}$

Therefore, Tim spends 15/24 hours each weekday sleeping in the school.

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2 years ago

the two triangles below are similar use what you know about similar triangles to find the missing side. show your work​

the two triangles below are similar use what you know about similar triangles to find the missing side. show your work