Which of the following are dimensionally consistent? (Choose all that apply.)(a) a=v / t+xv2 / 2(b) x=3vt(c) xa2=x2v / t4(d) x=vt+vt2 / 2(e) v=x2 / at3(f) a3=x2v / t5(g) x=t(h) v=5at
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
A
is dimensionally consistent
B
is not dimensionally consistent
C
is dimensionally consistent
D
is not dimensionally consistent
E
is not dimensionally consistent
F
is dimensionally consistent
G
is dimensionally consistent
H
is not dimensionally consistent
Step-by-step explanation:
From the question we are told that
The equation are
[tex]A) \ \ a^3 = \frac{x^2 v}{t^5}[/tex]
[tex]B) \ \ x = t [/tex]
[tex]C \ \ \ v = \frac{x^2}{at^3}[/tex]
[tex]D \ \ \ xa^2 = \frac{x^2v}{t^4}[/tex]
[tex]E \ \ \ x = vt+ \frac{vt^2}{2}[/tex]
[tex]F \ \ \ x = 3vt[/tex]
[tex]G \ \ \ v = 5at[/tex]
[tex]H \ \ \ a = \frac{v}{t} + \frac{xv^2}{2}[/tex]
Generally in dimension
x - length is represented as L
t - time is represented as T
m = mass is represented as M
Considering A
[tex]a^3 = (\frac{L}{T^2} )^3 = L^3\cdot T^{-6}[/tex]
and [tex]\frac{x^2v}{t^5 } = \frac{L^2 L T^{-1}}{T^5} = L^3 \cdot T^{-6}[/tex]
Hence
[tex]a^3 = \frac{x^2 v}{t^5}[/tex] is dimensionally consistent
Considering B
[tex]x = L[/tex]
and
[tex]t = T[/tex]
Hence
[tex]x = t[/tex] is not dimensionally consistent
Considering C
[tex]v = LT^{-1}[/tex]
and
[tex]\frac{x^2 }{at^3} = \frac{L^2}{LT^{-2} T^{3}} = LT^{-1}[/tex]
Hence
[tex]v = \frac{x^2}{at^3}[/tex] is dimensionally consistent
Considering D
[tex]xa^2 = L(LT^{-2})^2 = L^3T^{-4}[/tex]
and
[tex]\frac{x^2v}{t^4} = \frac{L^2(LT^{-1})}{ T^5} = L^3 T^{-5}[/tex]
Hence
[tex] xa^2 = \frac{x^2v}{t^4}[/tex] is not dimensionally consistent
Considering E
[tex]x = L[/tex]
;
[tex]vt = LT^{-1} T = L[/tex]
and
[tex]\frac{vt^2}{2} = LT^{-1}T^{2} = LT[/tex]
Hence
[tex]E \ \ \ x = vt+ \frac{vt^2}{2}[/tex] is not dimensionally consistent
Considering F
[tex]x = L[/tex]
and
[tex]3vt = LT^{-1}T = L[/tex] Note in dimensional analysis numbers are
not considered
Hence
[tex]F \ \ \ x = 3vt[/tex] is dimensionally consistent
Considering G
[tex]v = LT^{-1}[/tex]
and
[tex]at = LT^{-2}T = LT^{-1}[/tex]
Hence
[tex]G \ \ \ v = 5at[/tex] is dimensionally consistent
Considering H
[tex]a = LT^{-2}[/tex]
,
[tex]\frac{v}{t} = \frac{LT^{-1}}{T} = LT^{-2}[/tex]
and
[tex]\frac{xv^2}{2} = L(LT^{-1})^2 = L^3T^{-2}[/tex]
Hence
[tex]H \ \ \ a = \frac{v}{t} + \frac{xv^2}{2}[/tex] is not dimensionally consistent
We want to see which ones of the given expressions are dimensionally consistent. We will see that the correct options are:
a) x = 3*v*th) v = 5*a*tWhat means to be dimensionally consistent?
This means that we have the same units in the left and in the right side of the equation.
The units are:
a = [m/s^2]x = [m]v = [m/s]t = [s]Now we can analyze the expressions to see the units in each one, I will show you how to do it:
a) a = v/t + x*v^2
Replacing the units we have:
[m/s^2] = [m/s]/[s] + [m]*[m^2/s^2]
[m/s^2] = [m/s^2] + [m^3/s^2]
You can see that we have an m^3 in the right side, so these are not equivalent.
b) x = 3*v*t
Replacing the units we have:
[m] = 3*[m/s]*[s] = 3*[m]
So yes, the units are the same in both sides, so this is dimensionally consistent.
With the same procedure we can see that:
c) [m^3/s^2] = [m^3/s] not consistentd) [m] = [m] + [m*s] not consistente) [m/s] = [m^2] not consistentf) [m^3/s^6] = [m^3/s] not consistentg) [m] = [s] not consistenth) [m/s] = 5*[m/s] consistentSo the correct options are b and h.
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Related Questions
The circle graph shows the most important problems for the
14,158,428 high school teenagers in a country. Without using a
calculator, estimate the number of high school teenagers for whom
drugs is the most important problem.
Drugs is the most important problem for approximately how many of the high school teenagers?
A 11.200.000
B. 1.400.000
C. 2.800.000
D. 8,400,000
Answers
Answer:
Option (C)
Step-by-step explanation:
From the circle graph attached,
14158428 students have been divided into the sectors of a circle which represent the most important problems for the high school teenagers.
Each sector corresponds the percent of different problem.
Red sector (22% of the total students) represents the most important problem of drugs.
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22% ≈ 20%
Now 20% of 14000000 high school students = 14000000×[tex]\frac{20}{100}[/tex]
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Answers
Answer:
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Answers
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Step-by-step explanation:
CR 3
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Answer:
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
Step 1:
2x + x = 180°
Step 2:
3x = 180°
Step 3:
x = 60°
Step 4:
60° times 2 = 120°
Answer:
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Answers
Answer:
248*a=391
Step-by-step explanation:
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Answers
Answer:
2&3
Step-by-step explanation:
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If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
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WE can have that as;
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or
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Also we can continue on but we would need to use one and these are the two that are greater than 1 but make up 5.
Therefore, the values of x for which the result of 5 x be greater than 1 would be 2 and 3.
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Miss Lawrence buys 8 ounces of smoked salmon at $17.98 per pound. How much money
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Answers
Answer:
1 pound = 16 ounces
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Step-by-step explanation:
Answer: 8.99
Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
for example :
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Answers
Answer:
Each pair of socks cost around $1.11 excluding taxes.
Step-by-step explanation:
To find how much it costs for one pair of socks, divide the cost with how many pairs there are.
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The heat in the house is set to keep the minimum and maximum temperatures (in degrees Fahrenheit) according to the equation |x – 72.5| = 4. What are the minimum and maximum temperatures in the house? 72.5°F and 76.5°F 68.5°F and 76.5°F 70.5°F and 74.5°F 72.5°F and 74.5°F
Answers
Answer:
The minimum and maximum temperatures in the house are 68.5°F and 76.5°.
To keep the house in heat, the minimum and maximum temperature is set to option 68.5°F and 76.5°F.
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For the given situation,
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The minimum and maximum temperatures can be found by substituting +4 and -4 in x.
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Answers
Answer:
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Step-by-step explanation:
A can factory requires 2 sheets of metal to make 36 cans and 10 sheets of metal to make 180 cans. The proportionality constant between the number of cans made and the number of sheets of metal used is 36 18 288 5
Answers
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Assuming linear relationship of the two, we can use either data point as follows:
y = kx
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Therefore, the proportionality constant is 1/18.
Step-by-step explanation:
solve the given triangle by finding the missing angle and other side lengths.
Answers
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Step-by-step explanation:
a triangle in general is 180 degrees. You take the angles given
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Subtract A and C from each side and end up with B = 22 degrees.
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Answer:
1.3
Step-by-step explanation:
divide the 20 cupcakes and the 15 students
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Fill in the blanks to complete the equation that describes the diagram.
Answers
Answer:
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Step-by-step explanation:
That’s the answer.
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Answers
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Step-by-step explanation:
Well substitute 3 for x into the equation and solve for to see if they equal each other.
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12 = 15 - 3
12 = 12
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Answers
Answer:
Step-by-step explanation:
y + 2 = -1/2(x - 4)
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Answers
Answer:
i think it would be a.
Step-by-step explanation:
Answer:Gena and her friends each estimated the quotient of –137.56 divided by –6.12 using compatible numbers. Which shows the best estimate using compatible numbers?
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Step-by-step explanation: The answer is A because it is showing the right way to do the step
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Answers
...............
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Now, the circumference of the cross-section of the pencil is
[tex]= 2[/tex](π)r units
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Therefore, the length of the paper is
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
1/2(-1/3)=-1/6
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Answer:
1/2 multiplied by (-1/3)=-1/6 or 0.166666667
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you just multiply.
The traditional way of writing a number.
Answers
Step-by-step explanation:
In legal prose it is traditional to write every number twice, first in words, followed by the same number written in digits enclosed in brackets: That sentence contained twenty-five (25) words. Easy as one (1), two (2), three (3).
7.08x10^-4 in standard notation
Answers
Answer:
It's supposed to be 7.0800.
Step-by-step explanation:
Since it's 10 to the power minus 4 you'll have to count 4 places after the decimal point, so it'll be 7.0800
Answer:
0.000708
Step-by-step explanation:
you move the decimal 4 times to the left since the notation is negative. If the notation was positive, you would move it to the right.
Can i have the brainliest, please?
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Answers
Answer:
30 minuetes because their brain can take so many
Step-by-step explanation:
if f(x)= {2 for x>0, 0 for x=0, , then what is the value of -2 for x<0, f(7)-f(-4)?
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Are you sure you've written the problem right...it says x can not equal 0 or 1
Answer:
C -2,1 or 3 0nly
Step-by-step explanation:
Just did it mark it brainliest
Kelly works 8 hours less than three times as much as Marcy works for the week. Which expression represent
the number of hours Kelly works in relation to Marcy.
Answers
Answer:
X= 3y-8
Where
X represent hours worked by Kelly
Y represent hours worked by Marcy
Step-by-step explanation:
Kelly works 8 hours less than three times as much as Marcy works for the week.
Let the number of hours worked by Kelly= x
Let the number of hours worked by Marcy= y
X= 3y-8
What is 2.5 × 15.625
Answers
Answer:
39.0625
Step-by-step explanation:
Answer:
39.0625
Step-by-step explanation:
2.) 4 – бу = 28
Solve for the variable
Answers
Answer:
y = -4
Step-by-step explanation:
4 - 6y = 28
Group like terms
-6y = 28 - 4
-6y = 24
divide through by -6
-6y/-6 = 24/-6
y = -4