The energy, E, of a body of mass m moving with speed v is given by the formula below. The speed is nonnegative and less than the speed of light, c which is constant. Use lower case letters here. E = mc^2 (1/Squareroot1 - v^2/c^2 - 1)
(a) Find E/m = c^2Squareroot1 - v^2/c^2 - c^2/1 - v^2/c^2 what is the sign of this partial? Positive negative
(b) Find E/v =?
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
[tex]\frac{\delta E}{\delta m}= c^2 [\frac{1}{\sqrt{1 - \frac{v^2}{c^2} } } -1 ][/tex]
b
[tex]\frac{\delta E}{\delta V} = \frac{mc^3 v}{(c^2 - v^2 )^{\frac{3}{2} }}[/tex]
Step-by-step explanation:
From the question we are given
[tex]E = mc^2 [\frac{1}{\sqrt{1 - \frac{v^2}{c^2} } }- 1 ][/tex]
So we are asked to find [tex]\frac{\delta E}{\delta m}[/tex]
Now this is mathematically evaluated as
[tex]\frac{\delta E}{\delta m} = \frac{\delta }{\delta m} [mc^2 ( \frac{1}{\sqrt{1 - \frac{v^2}{c^2} } } -1 )][/tex]
[tex]= c^2 [\frac{1}{\sqrt{1 - \frac{v^2}{c^2 } } } -1 ] \frac{\delta m}{\delta m}[/tex]
[tex]= c^2 [\frac{1}{\sqrt{1 - \frac{v^2}{c^2} } } -1 ][/tex]
Also we are asked to find [tex]\frac{\delta E}{\delta V}[/tex]
Now this is mathematically evaluated as
[tex]\frac{\delta E}{\delta V} = \frac{\delta }{\delta v } [mc^2 ( \frac{1}{\sqrt{1 - \frac{v^2}{c^2} } } - 1 )][/tex]
[tex]\frac{\delta E}{\delta V} = mc^2 [\frac{\delta }{\delta v} (\frac{c}{\sqrt{c^2 -v^2} } - 1 )][/tex]
[tex]= mc^2 [c* [\frac{\delta }{\delta v} (c^2 - v^2 )^{-\frac{1}{2} }] - 0][/tex]
[tex]= mc^3 [- \frac{1}{2} (c^2 - v^2 )^{-\frac{3}{2} } * (-2v)][/tex]
[tex]= \frac{mc^3 v}{(c^2 - v^2 )^{\frac{3}{2} }}[/tex]
Related Questions
Find all zeros of f(x)=x^3−17x^2+49x−833
Answers
Answer:
x = 17 or x = ±7i
Step-by-step explanation:
x³ − 17x² + 49x − 833 = 0
x² (x − 17) + 49 (x − 17) = 0
(x² + 49) (x − 17) = 0
x = 17 or ±7i
What’s the correct explanation for this question?
Answers
Step-by-step explanation:
=> The volume of a triangular pyramid can be found using the formula V = 1/3AH where A = area of the triangle base, and H = height of the pyramid
=> The volume of a cone can be found by V = 1/3(Ab)(H) where Ab is base area and H is the height of the cone
The difference between both is that is it's base. A cone has a polygonal base while a pyramid has a tetragonal base
Colgate claims that 90% of dentists recommend Colgate toothpaste. Suppose you randomly choose 10 dentists and ask whether they recommend Colgate toothpaste. What is the probability that exactly 8 dentists in your sample recommend Colgate toothpaste
Answers
Answer:
the probability that exactly 8 dentists in 10 samples recommend Colgate toothpaste is;
P(X) = 0.0043
P(X) = 0.43%
Step-by-step explanation:
The probability that a dentist recommend Colgate is;
P = 90% = 0.9
The probability that a dentist doesn't recommend Colgate is;
P' = 1 - P = 1 -0.9 = 0.1
Of 10 sample dentists, the probability that exactly 8 dentists recommend Colgate toothpaste is;
8 will recommend and two will not recommend it.
P(X) = P^8 × P'^2
P(X) = (0.9)^8 × (0.1)^2
P(X) = 0.0043
P(X) = 0.43%
The Probability of exactly 8 dentists in sample recommend Colgate toothpaste is 0.0043.
Since, Colgate claims that 90% of dentists recommend Colgate toothpaste.
Probability of dentist, who recommend Colgate toothpaste = 0.9
Probability of dentist, who does not recommend Colgate toothpaste,
= 1 - 0.9 = 0.1
When 10 dentist randomly choose , out of which 8 dentists recommend Colgate toothpaste. It means that 8 recommend Colgate toothpaste and 2 recommend other tooth paste.
Thus, The Probability of exactly 8 dentists in sample recommend Colgate ,
[tex]=(0.9)^{8}*(0.1)^{2} =0.0043[/tex]
Learn more:
https://brainly.com/question/20046335
Write down the 1st term in the sequence given by: T(n) = n² + 3
Answers
Answer:
4
Step-by-step explanation:
T(n) = n² + 3
T(1) = 1² + 3 = 1 + 3 = 4
Let uequalsleft angle 4 comma negative 3 right angle, vequalsleft angle negative 2 comma 5 right angle, and wequalsleft angle 0 comma negative 6 right angle. Express 7 Bold u minus 5 Bold v plus Bold w in the form left angle a comma b right angle.
Answers
Answer:
[tex]<38,52>[/tex]
Step-by-step explanation:
[tex]u=<4,-3>\\v=<-2,5>\\w=<0,-6>[/tex]
We are required to express 7u-5v+w in the form <a,b>.
[tex]7u-5v+w =7<4,-3>-5<-2,5>+<0,-6>\\=<28,-21>-<-10,25>+<0,-6>\\=<28-(-10)+0, -21-25-6>\\=<38,52>\\$Therefore:$\\7u-5v+w=<38,52>[/tex]
which is the equation of a circle with center (-3, -5) and radius of 4
Answers
Answer: -8
Step-by-step explanation:
Find the number of possible outcomes if the numbers 1 through 7 are written on different pieces of paper and placed in a hat. Two of these numbered pieces of paper are selected without replacement, and a 2-digit number is formed using the first number drawn in the tens place and the second number drawn used in the ones place.
Answers
Answer:
The number of the possible outcomes are:
12,13,14,15,16,17
21,23,24,25,26,27
31,32,34,35,36,37
41,42,43,45,46,47
51,52,53,54,56,57
61,62,63,64,65,67
71,72,73,74,75,76
The total number of possible outcomes = 42
Step-by-step explanation:
Given that :
the numbers 1 through 7 are written on different pieces of paper; &
Two of these numbered pieces of paper are selected without replacement;
Also,
a 2-digit number is formed using the first number drawn in the tens place and the second number drawn used in the ones place.
Then:
if the first number drawn is 1 , then the possible outcomes will be :
12,13,14,15,16,17
If the first number drawn is 2; then the possible outcomes will be:
21,23,24,25,26,27
If the first number drawn is 3; then the possible outcomes will be:
31,32,34,35,36,37
If the first number drawn is 4; then the possible outcomes will be:
41,42,43,45,46,47
If the first number drawn is 5; then the possible outcomes will be:
51,52,53,54,56,57
If the first number drawn is 6; then the possible outcomes will be:
61,62,63,64,65,67
If the first number drawn is 7; then the possible outcomes will be:
71,72,73,74,75,76
The number of the possible outcomes are:
12,13,14,15,16,17
21,23,24,25,26,27
31,32,34,35,36,37
41,42,43,45,46,47
51,52,53,54,56,57
61,62,63,64,65,67
71,72,73,74,75,76
The total number of possible outcomes = 7 × 6 = 42
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 9 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 1.25 minutes.
Answers
Answer:
P(greater than 1.25 minutes) = 0.8611 (Approx)
Step-by-step explanation:
Given:
Waiting time = 0 - 9 minutes
Find:
Probability that selected passenger has a waiting time greater than 1.25 minutes.
Computation:
⇒ The probability that a randomly selected passenger has a waiting time greater than 1.25 minutes =
⇒ P(greater than 1.25 minutes) = [9-1.25] / 9
⇒ P(greater than 1.25 minutes) = [7.75] / 9
⇒ P(greater than 1.25 minutes) = 0.8611 (Approx)
if you start with (2,6) and move 2 units right and 3 units down what will you end up with?
Answers
For (2,6) the 2 is the x value which is the left/right position and 6 is the y value which is the up/down position.
Moving 2 units to the right, you would add 2 to the x value. Moving 3 units down you would subtract 3 from the y value.
The answer would be (4,3)
sarah can complete a project in 90 minutes and her sister betty can complete it in 120 minutes if they both work on the project at the same time how long will it take them to complete the project
Answers
Answer:
It will take them approximately 51.43 minutes to complete the project together
Step-by-step explanation:
This is what is called a "shared job" problem.
The best way to work on them is to start by finding the "portion" of the job done by each of the people in the unit of time.
So, for example, Sarah completes the project in 90 minutes, so in the unit of time (that is 1 minute) she completed 1/90 of the total project
Betty completes the project in 120 minutes, so in the unit of time (1 minute) she completes 1/120 of the total project.
We don't know how long it would take for them to complete the project when working together, so we call that time "x" (our unknown).
Now, when they work together completing the entire job in x minutes, in the unit of time they would have done 1/x of the total project.
In the unite of time, the fraction of the job done together (1/x) should equal the fraction of the job done by Sarah (1/90) plus the fraction of the job done by Betty. This in mathematical form becomes:
[tex]\frac{1}{x} =\frac{1}{90} +\frac{1}{120}\\\frac{1}{x} =\frac{4}{360} +\frac{3}{360}\\\frac{1}{x} =\frac{7}{360} \\x=\frac{360}{7} \\x=51.43\,\,min[/tex]
So it will take them approximately 51.43 minutes to complete the project together.
Please answer this correctly
Answers
Answer:
pic wont load
Step-by-step explanation:
Answer:
The quarter circle's area is 38.47 yard²
Step-by-step explanation:
The area of a full circle is pi * r ²
The area of a quarter circle is 1/4 * pi * r ²
Given:
Use 3.14 for pi
Round to the nearest hundredths.
Perimeter of quarter circle is 24.99 yards
For r you must leave it as 'r' because we do not know it for now...
1. Circumference of a full circle = 2* pi * r
2. 1/4 * ( 2 * pi * r )
1/4 * ( 2 * 3.14 * r )
1/2 * 3.14 * r
1.57 * r
3 Since r = 'r'
We have to 2 sides running from the centre of the 'pie' to the left and right of the quarter circle which both have a length of exactly 'r'. So you just add 2 * r.
4. The outcome of step 2 + step 3 is the perimeter of quarter circle, which was given as 24.99 inch
1.57 * r + 2 * r = 24.99
( 1.57 + 2 ) * r = 24.99
3.57 * r = 24.99
Divide left and right of the = sign by 3.57
3.57 / 3.57 * r = 24.99 / 3.57
1 * r = 24.99 / 3.57
r = 7
The area of a quarter circle is 1/4 * pi * r ²
1/4 * pi * 7²
1/4 * 49 * pi
49/4 * pi
49/4 * 3.14
38.465
Round to the nearest hundredths gives 38.47 yard²
The quarter circle's area is 38.47 yard²
A swimming pool is to be drained. The pool is shaped like a Rectangular prism with length 12m , with 10 m, and depth 3m. Suppose water is pumped out of the pool at a rate of 18 m3 per hour.if the pool starts completely full , how many hours does it take to empty the pool ?
Answers
Answer:
20 hours
Step-by-step explanation:
first calculate volume:
12x10x3=360
then divide by 18
360/18=20
So 20 hours in total
2(x+b)= ax + c
In the equation above, a, b, and c are constants. If
the equation has infinitely many solutions, which of
the following must be equal to c?
Α) α
B) 6
C) 2a
D) 26
Answers
NEED ASAP!!!!
Which equation represents the grafted function
Answers
Answer:
sorry i meant c
Step-by-step explanation:
find the area of the triangle. ? square units
Answers
Answer:
54 square units
Step-by-step explanation:
The formula for the area of a triangle is:
[tex]\frac{1}{2}[/tex] x base x height
The base is 12
The height is 9
So 1/2 x 12 x 9 = 54 square units
A commuter train travels 65 kilometers in 27 minutes. What is it’s speed in kilometers per hour?
Answers
Answer:
Per hour: 2.40740740741
Step-by-step explanation:
you have to divided 65 and 27 so
65/27
which is 2.40740740741
A triangular plate with base 3 m and height 5 m is submerged vertically in water so that the tip is even with the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m3.)
Answers
Answer:
The hydro-static force [tex]F=245000N[/tex]
Step-by-step explanation:
given data
base = 3 m
height = 5 m
density of water = 1000 kg/m3
Acceleration due to gravity = 9.8
The area if the strip needs to be calculated using similar triangular formula as well as the hydrostatic force
CHECK THE ATTACHMENT BELOW FOR DETAILED EXPLANATION
A 500.0 g piece of aluminum at 100° C is placed in 300ml of water. While in the water, the
aluminum then cools to 30°C. Calculate the amount of heat lost by the aluminum. The
specific heat of water is 4.18 J/g °C and the specific heat of aluminum is 0.90 J/g °C
Answers
Answer:
The amount of heat lost by the aluminum is 31,500 J
Step-by-step explanation:
Given;
mass of aluminum, m = 500 g
initial temperature of the aluminum, θ₁ = 100° C
final temperature of the aluminum, θ₂ = 30°C
specific heat capacity of water, C = 4.18 J/g °C
specific heat capacity of aluminum , C = 0.90 J/g
Heat lost by the aluminum is equal to heat gained by the water.
The amount of heat lost by the aluminum, is calculated as;
Q = MCΔθ
Q = 500 x 0.9 (100 - 30)
Q = 500 x 0.9 x 70
Q = 31,500 J
Therefore, the amount of heat lost by the aluminum is 31,500 J
Find the equations for a conical helix that has a radius of 8, a height of 12 and does exactly two complete revolutions (starting at the xy-plane). Include a plot of your conical helix.
Answers
Answer:
The equation are
[tex]x =\frac{ 12-z }{h} 8 cos (2 z)[/tex]
[tex]y = \frac{12-z }{12} 8sin (2z)[/tex]
z = z
Step-by-step explanation:
From the question we are told that
The radius of the conical helix is [tex]r= 8[/tex]
The height of the conical helix is [tex]h = 12[/tex]
The angular frequency is [tex]w = 2[/tex]
The plot of the conical helix is shown on the first uploaded image
Generally the parametric equation of a conical helix is mathematically represented as
for x -axis
[tex]x =\frac{ h-z }{h} r cos (wz)[/tex]
substituting values
[tex]x =\frac{ 12-z }{h} 8 cos (2 z)[/tex]
for y-axis
[tex]y = \frac{h-z }{h} rsin (wz)[/tex]
substituting values
[tex]y = \frac{12-z }{12} 8sin (2z)[/tex]
for z-axis
z = z
Use the substitution and to rewrite the equations in the system in terms of the variables and . Solve the system in terms of u and v . Then back substitute to determine the solution set to the original system in terms of x and y.
-3/x+4/y=11
1/x-2/y=-5
Answers
Answer:
x = -1 and y = 1/2
Step-by-step explanation:
Let u = 1/x, and v = 1/y
Then the pair of equations
-3/x + 4/y = 11
1/x - 2/y = -5
Can be written as
-3u + 4v = 11 .................................(1)
u - 2v = -5......................................(2)
From (2)
u = 2v - 5 .......................................(3)
Substituting (3) into (1)
-3(2v - 5) + 4v = 11
-6v + 15 + 4v = 11
-6v + 4v = 11 - 15
-2v = -4
v = 4/2 = 2
Substituting this value of v in (3)
u = 2v - 5
u = 2(2) - 5
= 4 - 5
= -1
That is
u = -1, v = 2
Since u = 1/x, and v = 1/y, we have
1/x = -1
=> x = -1
And
1/y = 2
=> y = 1/2
Therefore
x = -1 and y = 1/2
Find the area of the triangle
Answers
Answer:
54
Step-by-step explanation:
A = (9*12)/2
A = 9*6
A = 54
Answer:54
Step-by-step explanation:
multiply 9 and 12 then divide by 2 because a triangle is half of a square
When estimating a job to bid, a contractor’s estimator first determines the actual cost of labor using the function L(h) = 28.75h, where h is the number of estimated hours it will take to complete the job. Next, the estimator adds the labor burden, which accounts for taxes and insurance, using the function B(L) = 1.78L. Finally, the estimator calculates the selling price, including the markup for overhead and profit, using the function M(B) = 1.43B. Which composite function can be used to find the selling price for the labor portion of a bid based on the estimated number of hours?
Answers
Answer:
M(h) = 73.18025h
Step-by-step explanation:
The composite function is ...
M(B(L(h))) = M(B(28.75h)) = M(1.78(28.75h)) = M(51.175h)
= 1.43(51.175h) = 73.18025h
The composite function is ...
M(h) = M(B(L(h))) = 73.18025h
Answer:
a
Step-by-step explanation:
The radius of a circle is 10.7 m. Find the circumference
to the nearest tenth.
Answers
Answer:
2 x [tex]\pi[/tex] x 10.7 = 67.2
Step-by-step explanation:
Step-by-step explanation:
c=2πr
c=2×π×10.7m
c=67.2m
so about 67
sider F and C below. F(x, y, z) = yz i + xz j + (xy + 4z) k C is the line segment from (1, 0, −2) to (6, 4, 1) (a) Find a function f such that F = ∇f. f(x, y, z) = xyz+2z2+c (b) Use part (a) to evaluate C ∇f · dr along the given curve C.
Answers
Answer:
a) The function is [tex]f(x,y,z) = xyz+2z^2[/tex]
b) The value of the integral is 18
Step-by-step explanation:
a) We are given that [tex] F(x,y,z) (yz,xz,xy+4z)[/tex]. We want to find a function f such that the gradient of f is F. That is [tex]\nablda f = F[/tex] . Suppose that such f does exist, if that is the case, then by definition of the gradient, we have that
[tex] F(x,y,z) = (\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z})[/tex]
From here, we have that
[tex] yz = \frac{\partial f}{\partial x}[/tex]
if we integrate both sides with respect to x, we get that
[tex] f(x,y,z) = xyz+ g(y,z)[/tex]
where g is a function that depens on y and z only. Now, we differentiate this equation with respect to y and make it equal to the 2nd component of F. That is
[tex] xz + \frac{\partial g}\partial{y} = xz[/tex]
This implies that [tex]\frac{\partial g}{\partial y} =0[/tex]. This means that g actually depends only on z. Until now, f is of the form
[tex] f(x,y,z) = xyz+g(z)[/tex]
If we repeat the previous step, by differentiating with respect to z and making it equall to the third component of F we get
[tex] xy + \frac{\partial g}{\partial z} = xy + 4z[/tex]
This implies that [tex] \frac{\partial g}{\partial z} = 4z[/tex] . If we integrate both sides with respect to z, we get that [tex] g(z) = 2z^2[/tex]
So f is of the form [tex] f(x,y,z) = xyz+2z^2[/tex]
b) To calculate the integral over the given segment, we can use the function f. Since the path is from (1,0,-2) to (6,4,1), then the value of the integral is given by evaluatin f at the end point and the substracting the value of f at the start point, that is
[tex] \int_C F \cdot dr = f(6,4,1) -f(1,0,-2) = 24+2(1)^2- (0+2(-2)^2)) = 18[/tex]
YOU KNOW THE DRILL 2.0
Answers
Answer:
#1
Step-by-step explanation:
The four yellow boxes represent x so together they are 4 * x or 4x. The blue boxes seem to represent -1 and since there are three of them together they are -1 * 3 = -3. 4x + (-3) = 4x - 3.
Please help. I’ll mark you as brainliest if correct!
These are 2 math problems .
Answers
Answer:
-4 503/12 ≈ 41.91667Step-by-step explanation:
To find the average rate of change, find the change in function value, and divide that by the length of the interval.
1. ((g(1) -g(-1))/(1 -(-1)) = ((-4·1³ +4) -(-4(-1)³ +4)/(2) = (-8)/2 = -4
The average rate of change of g(x) on [-1, 1] is -4.
__
2. ((g(3) -g(-2))/(3 -(-2)) = ((6·3³ +3/3²) -(6·(-2)³ +3/(-2)²))/5
= (6·27 +1/3 -6·(-8) -3/4)/5 = (2515/12)/5
= 503/12 = 41 11/12
The average rate of change of g(x) on [-2, 3] is 41 11/12.
The volume of the box shown in the diagram is 40π3 cubic units. Find the length of ‘x’.
Answers
Answer:
4: 4[tex]\pi^2[/tex]
Step-by-step explanation:
2[tex]\pi[/tex] x 5 x [tex]x[/tex] = 10[tex]\pi x[/tex]
10[tex]\pi x[/tex] = 40[tex]\pi ^3}[/tex]
x = 4[tex]\pi^2[/tex]
Answer:
4π units
Step-by-step explanation:
v=lwh
40π^3=2π×5×h
40π^3=10π^2×h
h=40π^3/10π^2
h=4π units
mark brianliest if my answer suit your question please.
find the square root of 12 to the nearest hundredth
Answers
Answer:
\sqrt(12) hope this helped.
Write an expression without exponent that is equivalent to 2 to 3rd power nd 4 to the 3rd power
Answers
Answer:
8 and 64
Step-by-step explanation:
[tex]2^3[/tex] and [tex]4^3[/tex]
[tex]2^3=8[/tex]
[tex]4^3=64[/tex]
A diagonal of a cube measures 30 inches. The diagonal of a face measures StartRoot 600 EndRoot inches.
In inches, what is the length of an edge of the cube? Round the answer to the nearest tenth.
Answers
Answer:
17.3 Inches
Step-by-step explanation:
Given that the diagonal of a cube = 30 inches
For a cube of side length s, Length of its diagonal [tex]=s\sqrt{3}[/tex]
Therefore:
[tex]s\sqrt{3}=30\\$Divide both sides by \sqrt{3}\\s=30 \div \sqrt{3}\\s=17.3$ inches (to the nearest tenth.)[/tex]
Side Length of the cube is 17.3 Inches.
Answer:
17.3
Step-by-step explanation:
Edge 2020
