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3 years ago

12

A rectangular prism with a volume of 5 cubic units is filled with cubes with side lengths of 1/3

1 answer:

kogti [31]3 years ago

7 0

Answer:

135 cubes

Step-by-step explanation:

step 1

Find the volume of one cube

we know that

The volume of the cube is equal to

$V=b^3$

where

b is the length side of the cube

we have

$b=\frac{1}{3}\ units$

substitute

$V=(\frac{1}{3})^3$

$V=\frac{1}{27}\ units^3$

step 2

Find out how many 1/3 unit cubes does it take to fill the prism

Divide the volume of the prism by the volume of one cube

so

$5:\frac{1}{27}=5(27)= 135\ cubes$

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Describe the transformation that maps the pre-image A to the image A.

jolli1 [7]

Answer:

C) translated 1 unit to the left and then rotated 180° counterclockwise about the origin

Step-by-step explanation:

by inspection, shape A has been translated 1 unit to the left and then rotated 180° counterclockwise about the origin

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3 years ago

Given the sequence 1/2 ; 4 ; 1/4 ; 7 ; 1/8 ; 10;.. calculate the sum of 50 terms

miv72 [106K]

<u>Hint </u><u>:</u><u>-</u>

Break the given sequence into two parts .
Notice the terms at gap of one term beginning from the first term .They are like $\dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8}$ . Next term is obtained by multiplying half to the previous term .
Notice the terms beginning from 2nd term , $4,7,10,13$ . Next term is obtained by adding 3 to the previous term .

<u>Solution</u><u> </u><u>:</u><u>-</u><u> </u>

We need to find out the sum of 50 terms of the given sequence . After splitting the given sequence ,

$\implies S_1 = \dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8}$ .

We can see that this is in <u>Geometric</u><u> </u><u>Progression </u> where 1/2 is the common ratio . Calculating the sum of 25 terms , we have ,

$\implies S_1 = a\dfrac{1-r^n}{1-r} \\\\\implies S_1 = \dfrac{1}{2}\left[ \dfrac{1-\bigg(\dfrac{1}{2}\bigg)^{25}}{1-\dfrac{1}{2}}\right]$

Notice the term $\dfrac{1}{2^{25}}$ will be too small , so we can neglect it and take its approximation as 0 .

$\implies S_1\approx \cancel{ \dfrac{1}{2} } \left[ \dfrac{1-0}{\cancel{\dfrac{1}{2} }}\right]$

$\\\implies \boxed{ S_1 \approx 1 }$

$\rule{200}2$

Now the second sequence is in Arithmetic Progression , with common difference = 3 .

$\implies S_2=\dfrac{n}{2}[2a + (n-1)d]$

Substitute ,

$\implies S_2=\dfrac{25}{2}[2(4) + (25-1)3] =\boxed{ 908}$

Hence sum = 908 + 1 = 909

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3 years ago

After years of maintaining steady population of 32,000 the population of town begins to grow exponentially. After 1 year and an

GuDViN [60]

Answer: y = 32,000(1.08)^c

Step-by-step explanation:

Given that the initial population

P = 32000

t = 1 year

R = 8%

Y = 34,560

To predict y the number of people living in town after x years

t = x

Y = P(1 + 8%)^t

Y = 32000( 1.08)^x

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3 years ago

Arte-miy333 [17]

Answer:

Step-by-step explanation:

hypotenuse=2*AB

where AB is the smallest side.

Take AB as the base .

Draw a perpendicular at B.

A as the center and cut an arc AC=2 AB

Join AC.

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3 years ago

Which expression gives the volume of a sphere with radius 4

alisha [4.7K]

Area = 4*pi*r^2

Step-by-step explanation:

You can use this step to find the answer

<em>hope </em><em>it</em><em> helps</em><em> you</em><em>.</em><em>.</em><em>.</em><em> </em><em>pls </em><em>mark</em><em> brainliest</em>

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2 years ago

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