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3 years ago

Let A=3i-j-4k,B=-2i+4j-3k and C=i+2j-k compute 2A-B+3C

Mathematics

1 answer:

Paladinen [302]3 years ago

7 0

A = 3i - j - 4k

B = -2i + 4j - 3k

C = i + 2j - k

2A - B + 3C =

= 2(3i - j - 4k) - (-2i + 4j - 3k) + 3(i + 2j - k) =

= 6i - 2j - 8k + 2i - 4j + 3k + 3i + 6j - 3k =

= 6i + 2i + 3i - 2j - 4j + 6j - 8k + 3k - 3k =

= 11i - 8k

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Find the volume of the sphere. Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and round

bulgar [2K]

Answer:

Find the volume of the sphere.

Either enter an exact answer in terms of π or use 3.14 for π and round your final answer to the nearest hundredth.

The radius is 1

Volume = $\frac{4}{3} \pi$ or 4.19

Step-by-step explanation:

Given

Radius, r = 1

Required

Find the volume of sphere

Volume of a sphere is calculated using the following formula

$V = \frac{4}{3} \pi r^{3}$

Where V = Volume and r = radius

By Substitution,

$V = \frac{4}{3} \pi * 1^{3}\\\\V = \frac{4}{3} \pi * 1\\\\V = \frac{4}{3} \pi$

Solving further to get the numerical value of volume;

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V = 4.19 to the nearest hundredth

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3 years ago

There are many cylinders with radius 6 meters. Let h represent the height in meters and V represent the volume in cubic meters.

KiRa [710]

The equation that represents the volume of the cylinder is 36πhhh m³.

Explanation:

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3 years ago

Evaluate the expression when m=32 and n=6. m/4+n

babunello [35]

Answer:

Step-by-step explanation:

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3 years ago

A composite figure is shown.

VikaD [51]

The surface area of the pyramid is 60 square feet

The surface area of the square prism is 480 square feet

The surface area of the cube is 180 square feet

The total surface area is 720 square feet

<h3>Area of Composite figures</h3>

From the question, we are to calculate the surface area of each part of the composite figure

For the cube

Surface area of a cube is given by

$S = 6l^{2}$

Where $l$ is the length of a side

But only have 5 surfaces of the cube are part of the composite figure

∴ Surface area of the cubic part of the figure = $5l^{2}$

From the given information,

$l = 6 \ feet$

∴ Surface area of the cubic part of the figure = 5 × 6²

Surface area of the cubic part of the figure= 180 square feet

For the square prism

The surface area of a square prism is given by the formula,

$S = 2l^{2} + 4lh$

Where $l$ is the length of the sides and

$h$ is the height

But the square surfaces are not part of the surface of the figure

∴ Surface area of the square prism in the figure = $2l^{2} + 4lh - 2l^{2}$

Surface area of the square prism in the figure = $4lh$

From the given information,

$l = 6 \ feet$

$h = 20 \ feet$

Thus,

Surface area of the square prism part of the figure = 4×6×20

Surface area of the square prism part of the figure = 480 square feet

For the pyramid

The pyramid is a square pyramid

The surface area of a square pyramid is given by

$S = l^{2} + 2l\sqrt{\frac{l^{2} }{4}+h ^{2} }$

Where $l$ is the base length

and $h$ is the height of the prism

But the square base is not part of the surface of the figure

∴ Surface area of the pyramid part of the figure = $l^{2} + 2l\sqrt{\frac{l^{2} }{4}+h^{2} }\ - ( l^{2})$

Surface area of the pyramid part of the figure = $2l\sqrt{\frac{l^{2} }{4}+h^{2} }$

From the given information,

$l = 6 \ feet$

$h = 4 \ feet$

∴ Surface area of the pyramid part of the figure = $2(6)\sqrt{\frac{6^{2} }{4}+4^{2} }$

= $12\sqrt{\frac{36 }{4}+16}$

= $12\sqrt{9+16 }$

= $12\sqrt{25}$

= 12 × 5

= 60 square feet

Hence, the surface area of the pyramid is 60 square feet

Thus,

The total surface area = 180 square feet + 480 square feet + 60 square feet

The total surface area = 720 square feet

Hence, the total surface area is 720 square feet

Learn more on Calculating area of composite figures here: brainly.com/question/13175744

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2 years ago

Which of the following are solutions to the inequality, 16 < 15 x − 12 ? Select all that apply.

aalyn [17]

Answer:

25/7, 1.87, 3.25, and 22/7

Step-by-step explanation:

16 < 15x - 12

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+12. +12

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28 < 15x

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÷15 ÷15

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28/15 < x

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x > 28/15

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this is true for any number greater than 1 and 13/15 = 1.8666......

3 0

3 years ago

Read 2 more answers

Let A=3i-j-4k,B=-2i+4j-3k and C=i+2j-k compute 2A-B+3C​

Let A=3i-j-4k,B=-2i+4j-3k and C=i+2j-k compute 2A-B+3C