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3 years ago

Please help!! Timed assignment

Mathematics

1 answer:

sveticcg [70]3 years ago

3 0

Answer:

see the list below

Step-by-step explanation:

did all the formulas for each and I believe the order is from (smallest to biggest)

1. The half sphere or hemisphere (3rd in the picture)

2.The pyramid

3.slanted cone

4.cone

5.slanted cylinder

6.and finally the cylinder

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Step-by-step explanation:

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cos³ ( $\frac{\pi }{2}$ ) = 0³ = 0

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Clare is painting some doors that are all the same size. She used 2 liters of paint to cover 1 3/5 doors. How many liters of pai

barxatty [35]

Answer:

$1\frac{1}{4}\ liters$

Step-by-step explanation:

step 1

Convert mixed number to an improper fraction

$1\frac{3}{5}=\frac{1*5+3}{5}=\frac{8}{5}$

step 2

Using proportion

$\frac{2}{(8/5)}\frac{liters}{doors} =\frac{x}{1}\frac{liters}{door}\\ \\x=2/(8/5)\\ \\x=10/8\ liters$

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4 years ago

A lighthouse is located on a small island 2 km away from the nearest point P on a straight shoreline and its light makes four re

ddd [48]

Answer:

62.8 km per min

Step-by-step explanation:

Let the diagram of this situation is shown below,

In which $\theta$ is the angle made by light to the straight line joining the lighthouse and P,

∵ Light makes 4 revolutions per minute.

Also, 1 revolution = $2\pi$ radians

So, the change in angle with respect to t ( time ),

$\frac{d\theta}{dt}=8\pi\text{ radians per min}$

Let x be the distance of beam from P,

$\implies \tan \theta = \frac{x}{2}$

Differentiating with respect to x,

$\sec^2 \theta \frac{d\theta}{dt}=\frac{1}{2}\frac{dx}{dt}$

$(1+\tan^2 \theta) (8\pi) = \frac{1}{2}\frac{dx}{dt}$

$(1+\frac{x^2}{2^2})(8\pi) = \frac{1}{2}\frac{dx}{dt}$

If x = 1 km,

$(1+\frac{1}{4})8\pi =\frac{1}{2}\frac{dx}{dt}$

$\frac{5}{4}8\pi = \frac{1}{2}\frac{dx}{dt}$

$\implies \frac{dx}{dt}=\frac{80\pi}{4}= 20\pi\approx 62.8\text{ km per min}$

Hence, the beam of light moving along the shoreline with the speed of 62.8 km per min

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4 years ago