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2 years ago

What is the minimum number of angles required to determine the Cartesian components of a 3D vector and why?

Mathematics

1 answer:

Reika [66]2 years ago

4 0

Answer: 3

Step-by-step explanation:

The 3D vector consists of 3 axes, let's say x, y and z.

Now, a vector P lies in all of them.

So, the angle it makes with x axis is α

The angle it makes with y axis is β

The angle it makes with z axis is γ

So, to determine the Cartesian components or to resolve the vector into it's Cartesian components we need 3 angles with each axis.

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If the measure of angle ABC is 57 degrees, what is the measure of arc AB

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a cereal box is 18 inches by 3 inches by 12 inches. After breakfast, the box is one-third full. How many cubic inches of cereal

Nadusha1986 [10]

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3 years ago

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What is the ratio of the radius of a circle to its circumference 12π 1πr 1π 2π

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3 years ago

An orange juice company sells a can of frozen orange juice that measures 9.4 centimeters in height and 5.2 centimeters in diamet

drek231 [11]

<h2>Hello!</h2>

The answer is:

The third option:

2.7 times as much.

To calculate how many more juice will the new can hold, we need to calculate the old can volume to the new can volume.

So, calculating we have:

Old can:

Since the cans have a right cylinder shape, we can calculate their volume using the following formula:

$Volume_{RightCylinder}=Volume_{Can}=\pi r^{2} h$

Where,

$r=radius=\frac{diameter}{2}\\h=height$

We are given the old can dimensions:

$radius=\frac{5.2cm}{2}=2.6cm\\\\height=9.4cm$

So, calculating the volume, we have:

$Volume_{Can}=\pi *2.6cm^{2} *9.4cm=199.7cm^{3}$

We have that the volume of the old can is:

$Volume_{Can}=199.7cm^{2}$

New can:

We are given the new can dimensions, the diameter is increased but the height is the same, so:

$radius=\frac{8.5cm}{2}=4.25cm\\\\height=9.4cm$

Calculating we have:

$Volume_{Can}=\pi *4.25cm^{2} *9.4cm=533.40cm^{3}$

Now, dividing the volume of the new can by the old can volume to know how many times more juice will the new can hold, we have:

$\frac{533.4cm^{3} }{199.7cm^{3}}=2.67=2.7$

Hence, we have that the new can hold 2.7 more juice than the old can, so, the answer is the third option:

2.7 times as much.

Have a nice day!

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2 years ago