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2 years ago

How many cubes with side lengths of

Mathematics

1 answer:

Bad White [126]2 years ago

5 0

question:

How many cubes with side lengths of \dfrac12 \text{ cm} 2 1 cmstart fraction, 1, divided by, 2, end fraction, start text, space, c, m, end text does it take to fill the prism?

Step-by-step explanation:

81 cubes are needed to fill the prism

Step-by-step explanation:

Volume of prism = 3 cubic units

Side lengths of cube = 1/3

Therefore the volume of the cube is,

V = a³ (a = side of the cube)

V = 1/3 × 1/3 × 1/3

= ( 1/3 )³

= 1/27 cubic units

To find the number of cubes needed to fill the prism, we need to divide the volume of cube by volume of the prism.

Number of cubes to fill the prism= Volume of prism / Volume of cube

= 3÷1/27

=3×27/1

= 81

Therefore, 81 cubes are needed to fill the prism

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Step-by-step explanation:

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In triangle ABC, mZA = (5x – 10), mZB = (12x)", and the exterior

Inessa [10]

Answer:

measure of exterior angle at C = 160°

Step-by-step explanation:

An exterior angle of a triangle equals the sum of the two remote interior angles

A and B are the remote interior angles. So,

m∠A + m∠B = measure of exterior angle at C

5x - 10 + 12x = 16x

17x - 10 = 16x

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2 years ago

When a product fails to perform as warranted, this is called a) contractual liability. O b) product malfunction. c) malicious ma

balu736 [363]

Answer:

d breach of warranty

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2 years ago

Choose all the functions that give the sequence:

TEA [102]

Hence, the functions that produce given sequence are:

f(n) = 2n + 1

f(n) = 2(n − 1) + 3

Further explanation:

We will put n=1,2,3,4,5 to find which functions give the given sequence

f(n) = 2n − 1

Putting values of n

$f(1)=2(1)-1=2-1=1\\f(2)=2(2)-1=4-1=3\\f(3)=2(3)-1=6-1=5$

This function doesn't generate the given sequence

f(n) = 2n + 1

Putting values of n

$f(1)=2(1)+1=2+1=3\\f(2)=2(2)+1=4+1=5\\f(3)=2(3)+1=6+1=7\\f(4)=2(4)+1=8+1=9\\f(5)=2(5)+1=10+1=11$

This function generates the given sequence.

f(n) = 2(n − 1) − 3

Putting values of n

$f(1) = 2(1 -1) -3=2(0)-3=0-3=-3\\f(2) = 2(2 -1) -3=2(1)-3=2-3=-1\\f(3) = 2(3-1) -3=2(2)-3=4-3=1$

This function doesn't generate the given sequence

f(n) = 2(n − 1) + 3

Putting values of n

$f(1) = 2(1 - 1) + 3=2(0)+3=0+3=3\\f(2) = 2(2 - 1) + 3=2(1)+3=2+3=5\\f(3) = 2(3 - 1) + 3=2(2)+3=4+3=7\\f(4) = 2(4 - 1) + 3=2(3)+3=6+3=9$

Hence, the functions that produce given sequence are:

f(n) = 2n + 1

f(n) = 2(n − 1) + 3

Keywords: Functions, Sequence

Learn more about functions at:

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8 0

3 years ago