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3 years ago

What causes a solution to a rational equation to be an extraneous solution?

Mathematics

2 answers:

LenKa [72]3 years ago

6 0

its B just did the pre test

nika2105 [10]3 years ago

5 0

Answer: If a solution results in zero when subsitituted into the denominator of the equation, the solution is extraneous.

This is because you obtained the solution from a simplified version of the original equation, but you have to check if the solution obtained is a real solution of the original equation

In the case that when you substitute the solution in the original version the denominator becomes zero, this solution must be rejected, because the division by zero is not defined.

You might be interested in

What is the area of the blue shaded region in the figure?

Lapatulllka [165]

Answer:

136cm, B

Step-by-step explanation:

Since you are dealing with area…multiply 17 and 8. After you multiply those those numbers, you’d get 136. The unshaded area is 30. Add those and you would get 166. Now you have to subtract 30 and you’d get B, 136cm.

6 0

2 years ago

Find the general solution of the differential equation and check the result by differentiation. (Use C for the constant of integ

atroni [7]

Answer: $y=Ce^(^3^t^{^9}^)$

Step-by-step explanation:

Beginning with the first differential equation:

$\frac{dy}{dt} =27t^8y$

This differential equation is denoted as a separable differential equation due to us having the ability to separate the variables. Divide both sides by 'y' to get:

$\frac{1}{y} \frac{dy}{dt} =27t^8$

Multiply both sides by 'dt' to get:

$\frac{1}{y}dy =27t^8dt$

Integrate both sides. Both sides will produce an integration constant, but I will merge them together into a single integration constant on the right side:

$\int\limits {\frac{1}{y} } \, dy=\int\limits {27t^8} \, dt$

$ln(y)=27(\frac{1}{9} t^9)+C$

$ln(y)=3t^9+C$

We want to cancel the natural log in order to isolate our function 'y'. We can do this by using 'e' since it is the inverse of the natural log:

$e^l^n^(^y^)=e^(^3^t^{^9} ^+^C^)$

$y=e^(^3^t^{^9} ^+^C^)$

We can take out the 'C' of the exponential using a rule of exponents. Addition in an exponent can be broken up into a product of their bases:

$y=e^(^3^t^{^9}^)e^C$

The term e^C is just another constant, so with impunity, I can absorb everything into a single constant:

$y=Ce^(^3^t^{^9}^)$

To check the answer by differentiation, you require the chain rule. Differentiating an exponential gives back the exponential, but you must multiply by the derivative of the inside. We get:

$\frac{d}{dx} (y)=\frac{d}{dx}(Ce^(^3^t^{^9}^))$

$\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*\frac{d}{dx}(3t^9)$

$\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*27t^8$

Now check if the derivative equals the right side of the original differential equation:

$(Ce^(^3^t^{^9}^))*27t^8=27t^8*y(t)$

$Ce^(^3^t^{^9}^)*27t^8=27t^8*Ce^(^3^t^{^9}^)$

QED

I unfortunately do not have enough room for your second question. It is the exact same type of differential equation as the one solved above. The only difference is the fractional exponent, which would make the problem slightly more involved. If you ask your second question again on a different problem, I'd be glad to help you solve it.

7 0

2 years ago

Kevin’s bill at a restaurant was $26.51. He left a 15% tip. About how much tip did Kevin leave?

Natasha2012 [34]

The solution is 3.97, but the question says ABOUT so you should round up and

the answer should be $4.00.

3 0

3 years ago

A local little league has a total of 85 players, of whom 20% are right-handed how many right-handed players are there?

Nadusha1986 [10]

Twenty percent of eighty-five is seventeen.

5 0

3 years ago

The box plots show the high temperatures in January and March for Denmark in degrees Fahrenheit. Box plots titled Average Daily

bazaltina [42]

Answer:

The mean temperature for March is higher than January's mean.

Step-by-step explanation:

I took the test. trust me and you will be set free ;D

3 0

3 years ago