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Solve the rational equation $f=\frac{m^2v}{r}$

Step-by-step Solution

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Solution

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Final Answer

$m=\frac{\sqrt{f}\sqrt{r}}{\sqrt{v}},\:m=\frac{-\sqrt{f}\sqrt{r}}{\sqrt{v}}$
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Step-by-step Solution

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Multiply both sides of the equation by $r$

$m^2v=fr$

Learn how to solve integrals of exponential functions problems step by step online.

$m^2v=fr$

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Learn how to solve integrals of exponential functions problems step by step online. Solve the rational equation f=(m^2v)/r. Multiply both sides of the equation by r. Divide both sides of the equation by v. Simplifying the quotients. Removing the variable's exponent.

Final Answer

$m=\frac{\sqrt{f}\sqrt{r}}{\sqrt{v}},\:m=\frac{-\sqrt{f}\sqrt{r}}{\sqrt{v}}$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve for fSolve for mSolve for vSolve for rFind the discriminantSimplifyFactorFactor by completing the squareFind the integralFind the derivativeFind f=m^2v/r using the definitionSolve by quadratic formula (general formula)Find the rootsFind break even pointsFind the discriminant

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Function Plot

Plotting: $f+\frac{-m^2v}{r}$

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5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

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Main Topic: Integrals of Exponential Functions

Those are integrals that involve exponential functions. Recall that an exponential function is a function of the form f(x)=a^x.

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