For questions related to conversion of units.

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2answers
86 views

How do you take the inner product of a vector whose components have different units?

How do you take the inner product of a vector whose components have different units? For example, what is the inner product of $\langle1m, 1s\rangle$ and $\langle2m, 3s\rangle$?
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0answers
3k views

How to find out the depth of a cuboid

A water tank in the form of a cuboid is 15m long,10m wide. What will be depth of this tank, if it contains a maximum of ...
0
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1answer
24 views

english to metric conversion with cubes

How do you convert $ft^3$ to $cm^3$? I can find an exact relationship online, but what if I just knew how many $m$ are in a $lb$ or something like that?
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votes
1answer
33 views

How do you figure out the formula to convert between units?

I know that to, for example, convert from Fahrenheit to Celsius you subtract 32 and then divide by 1.8. I'm interested in how this type of formula can be developed. So, given two different sets of ...
0
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1answer
12 views

Distance/measurement question! Help!

There is a question in a book that I am trying to solve. "A man usually rides his bike 1 kilometers per hour, yet the wind slows him to 6.76 kilometers for 26 minutes and 5.55 kilometers for 10. How ...
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0answers
13 views

Nondimensionalisation - does it always reduce the number of parameters?

I've just made my ODE system of 8 equations dimensionless, but I've come out with exactly the same number of dimensionless parameters as I had in the system with units. Can nondimensionalisation ...
4
votes
5answers
606 views

Is there a basic “unit” of measurement in math

I am wondering if there is a basic unit in math. $$3\ cm \times 2\ cm = 6\ cm^2$$ The $cm$ is a unit of measurement, but what about: $$3\ cm \times 2 = 6\ cm$$ Should the $2$ have a unit of ...
0
votes
1answer
17 views

What is the measurement of side KL in a scalene triangle

Given: $\triangle FGH\cong \triangle JKL$ What is the measure of side 2 on triangle 2? Here is what I have. Triangle 1: Side 1: Unknown Side 2: Unknown Side 3: 12 Triangle 2: Side 1: Unknown ...
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1answer
42 views

How strong can an earthquake be in measurement by the Richter scale in comparison to a weaker earthquake?

I've seen that the Richter scale measures the strength of any earthquake from 1 to 10 and I've also learned that a 2 is 32 (not 2) times as strong as a 1. What other comparisons of these numbers can ...
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votes
1answer
44 views

How am I supposed to convert between a teaspoon and a tablespoon?

I've sometimes been having trouble figuring out the conversion between a teaspoon (tsp.) and a tablespoon (tbsp.). How will I know when to multiply or divide by three to do these conversions? I ...
4
votes
4answers
10k views

Units of a log of a physical quantity

So I have never actually found a good answer or even a good resource which discusses this so I appeal to experts here at stack exchange because this problem came up again today. What happens to the ...
2
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1answer
155 views

Radian, an arbitrary unit too?

Why is the radian defined as the angle subtended at the centre of a circle when the arc length equals the radius? Why not the angle subtended when the arc length is twice as long as the radius , or ...
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0answers
75 views

Square Inches vs Inches Squared

I was just asked the question, is there a difference between 12 square inches and 12 inches squared. At first I assumed that 12 inches squared mean a square with sides of 12 inches. In this case the ...
1
vote
1answer
42 views

convert unit of measure mpg->lp100km

So, I have the problem to convert mpg to lp100km. I have tried to calculate them by hand, given that 1 mile = 1.60934 km and 1 gallon = 3.78541 litres, and it yields me like: 1 mpg = 235.133 lp100km ...
0
votes
0answers
143 views

Answer Conversion Problem Numerically in Kilometers Per Hour

A sprinter set a high school record in track and field, running 200.0 m in 22.0s . What is the average speed of the sprinter in kilometers per hour? Express the answer numerically in kilometers per ...
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1answer
27 views

Double unit conversion metric to…US? [closed]

I had 5.52g/cm^3. I knew how to get it to 5.522x10^3 Kg/m^3. But now I not sure how to get it to lb/ft^3 correctly.
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2answers
48 views

Conversion of dosage based on body weight

Infant ibuprofen containes 100mg/5.0mL suspension. The recommended dose is 10mg/kg body to weight. How many mL of this suspension should be given to an infant weighing 18 lb? That's not a serious ...
0
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2answers
126 views

Converting squared or cubed units

At the moment I am going from square meters to square yards. One meter is $1.0936$ yards. So I figure $1\text{m}^2 = 1.0936 \text{yards}^2$ I know it isn't but I want to learn a good systematic ...
0
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2answers
75 views

How many inches are in 7.94 feet?

Question: the height on my land is 7.94 feet noted by a surveyor on a Certificate of Elevation form. In layman's terms, that is 7 feet and how many inches? or how much of an inch is it short of 8 ...
0
votes
1answer
53 views

If the cost per minute is $\$0.032$, is the cost per hour $\$1.92$ or $1.92$¢?

I hope someone can help me with this problem. The cost per minute to make a phone call is $0.032, I'm that multiplying this by 60 will get total cost per hour. ...
1
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1answer
25 views

How to normalise equations of the form $dy/dx=B$ and $d^2y/dx^2=A$?

So I am trying to normalise equations of the form, $$dy/dx=B \mbox{ and } d^{2}y/dx^{2}=A$$ If I define $y^{*}$ as; $$y^{*}=By \Rightarrow dy^{*}/dy=B $$ Is it also then true that, $$d(dy^{*})/dy = B ...
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votes
2answers
1k views

Difference between “sq km” and “km sq”

If I have a square with side $2\ \text{km}$, what is its area: $2\ \text{sq km}$ or $4\ \text{km}^2$?
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2answers
144 views

Convert angles from the sexagecimal system to centesimal one

How do you convert angles from the sexagecimal system to centesimal one? For example 63 degrees 14 minutes 51 seconds reduced to centesimal ?? Here's how it's done but I don't understand the ...
0
votes
1answer
22 views

Find total yards with LXWXH?

I have a box I need to cover all 6 sides with a single layer fiberglass fabric. The fabric comes in 50" or 28" widths. The dimensions of the box are 34" long; 15" wide; 12" High. How do I determine ...
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2answers
39 views

How can I Express It In DMS FORM? [closed]

This (below) 35.24 degree 160.11 degree -381.87 degree 280.99 degree -525.66 degree 85.372 degree
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1answer
50 views

sub-nanoseconds resolution

I found following statement in a higher engineering mathematics reference book, But couldn't understand how it has been determined ? I have two values as follows: nanoseconds - could be any 30 ...
2
votes
1answer
21 views

Division of Compound Units

Why are compound units of speed,density etc. expressed in terms of a numerator and a denominator? For example, m/s, kg/m3 etc. I've always understood division as either the inverse of multiplication, ...
1
vote
1answer
45 views

Taylor's series and the function argument dimension

I've stumbled over an interesting question. In $\cos(x)$, $x$ is measured in, say, radians. When I expand cosine in Taylor's series, I have the terms with $x^3$, $x^5$ etc. so I am summing up ...
0
votes
1answer
11 views

How to determine a deficit of base 10 exponent from a minimum unit

I'm trying to determine if a number includes a portion in deficit of a base 10 exponent from a minimum unit. For example, given a minimum unit of $0.01$, $1$ would pass the test, but $1.001$ would ...
1
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1answer
134 views

What are the units of Singular Value Decomposition components?

I have a symmetric variance/covariance matrix $A$ which is of size (27 x 27). I know that it's rank deficient (rank = 21). I also know that the units of $A$ are $m^2$. I am trying to use Singular ...
0
votes
1answer
30 views

I have trouble understanding simple equality passage

I don't know why I always have trouble with these things, there is something that must do 'click' in my head. Knowing that 1000000 cm³ = 1 m³, how do you get that ...
3
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3answers
106 views

Why radian is dimensionless?

Can't understand why we say that radians are dimensionless. Actually, I understand why this is happening: theta = arc len / r ...
16
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8answers
4k views

Why do we require radians in calculus?

I think this is just something I've grown used to but can't remember any proof. When differentiating and integrating with trigonometric functions, we require angles to be taken in radians. Why does ...
0
votes
3answers
41 views

Significance of squared in meters per second squared [closed]

What exactly is the difference between $3 \mathrm m/\mathrm s^2$ and $3 \mathrm m/\mathrm s$? According to Wikipedia... An object experiences a constant acceleration of one metre per second ...
0
votes
1answer
26 views

How many gallons are used in the U.S. each day and if this gasoline were used to fill a cubical tank how big would one side be?

The question I am trying to solve is: Part I) How many gallons of gasoline are used in the U.S. in one day assuming there are $2$ cars for every $3$ people and each car is driven $10,000$ miles a ...
-2
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1answer
63 views

Why is the cos, sin definition of the unit circle true?

So imagine we have a unit circle and there a point $M$ on it. Then the $x$ coordinate of $M$ is $\cos(\theta) $ ($\theta$ is the angle ${IOM}$ as you know) and its $y$ coordinate is $\sin(\theta)$. ...
0
votes
2answers
83 views

Two dimensional integral gives a volume, but what if I don't deal with distances and volumes?

I have I believe a simple question which relates to two-dimensional integral. I have been reading enough (and watch video tutorials) on the technique to hopefully understand it well. Every tutorial ...
3
votes
7answers
176 views

Software for unit aware calculations?

When doing engineering calculations it is great convenience to do have software that keeps track of units. Example when calculate something trivial as stress: $\sigma = \frac FA$ And be able to ...
1
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1answer
28 views

cross-products versus units of measure

If I draw 2 perpendicular line segments on the ground, 3 meters and 4 meters, how far into the sky does their cross-product extend? What if instead the line lengths are 300 cm and 400 cm? Can ...
1
vote
1answer
78 views

Angular speed to linear speed: Arbitrarily discarding Radians units?

I asked this question long ago, but wanted to see if I can get some new perspectives this time. Why is the radians implicitly cancelled? Somehow, the feet just trumps the numerator unit. For all ...
1
vote
2answers
94 views

Square Root Yields Different Result After Unit Conversion [duplicate]

This is boggling my mind. The square root of 100 seconds is 10 seconds The square root of ...
0
votes
2answers
47 views

How to change to same units

Could anyone help me change it into same units/ values? I need to have them all in "years" Demand(D): Every month there is 5000 food: Therefore, $D= 5000 * 12 = 60000$ food per year Production(P): ...
0
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1answer
36 views

D=P/gv^3 what units is the D

(Sorry for my bad english) I got a task to do: In the research, scientists noticed that the necessary power P is obtained from P=Dgv^3, where D is constant, g is the earth's standard acceleration ...
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2answers
22 views

What is the length of the bar needed to represent 75 kilometers( in centimeters)?

In a bar graph, 1 centimeter represents 30 kilometers. What is the length of the bar needed to represent 75 kilometers( in centimeters)?
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1answer
30 views

Conversion Question

A heavy rain fell on a city for 26 minutes, at a rate of 3.9mm/hr. If the area of the city is 244km^2, how many gallons of water fell on the city that day?
0
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1answer
67 views

Rates of Change Question with Mixed Units

I have come across the following question in a past exam paper of a module that I will be teaching this semester. The volume $V$ of m$^3$ of earth removed from a pit after $t$ hours is given by ...
1
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1answer
903 views

Units in definite integral

I've been given a problem in my electrical engineering class which is confusing me. I'm given $i(t) = 5\sin(6 \pi t/\mathrm s)\, \mathrm{mA}$ (mA is mC/s) and I need to find the total charge ...
7
votes
4answers
238 views

Is there an established notation, either modern or historical, for any unit of measure which is then further subdivided into 360 degrees or parts?

This question about notation is simple as dirt, but would be useful for me regardless, because of some work that I'm doing in music theory. Basically, while there's a notation for subdividing the ...
0
votes
1answer
64 views

convert from one time scale to another

i would like to exactly to convert given scale of time into years and month,suppose we have time $T = 2.35$ years clearly it is more then $2$ year,but what about $0.35$?in which scale it is given? ...
5
votes
2answers
755 views

Arbitrarily discarding/cancelling Radians units when plugging angular speed into linear speed formula?

Why is the radians implicitly cancelled? Somehow, the feet just trumps the numerator unit. For all other cases, you need to introduce the unit conversion fraction, and cancel explicitly. Is it ...