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3 years ago

What is the solution set of 6 x 2 - 24 = 0?

Mathematics

1 answer:

Aleks [24]3 years ago

4 0

Brainliest please?

Answer: no solution

there is no solution set

Step-by-step explanation:

6 x 2 = 12

12 - 24 = -12

-12 is not equal to 0

there are no solutions

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Consider the differential equation:

Wewaii [24]

(a) Take the Laplace transform of both sides:

$2y''(t)+ty'(t)-2y(t)=14$

$\implies 2(s^2Y(s)-sy(0)-y'(0))-(Y(s)+sY'(s))-2Y(s)=\dfrac{14}s$

where the transform of $ty'(t)$ comes from

$L[ty'(t)]=-(L[y'(t)])'=-(sY(s)-y(0))'=-Y(s)-sY'(s)$

This yields the linear ODE,

$-sY'(s)+(2s^2-3)Y(s)=\dfrac{14}s$

Divides both sides by $-s$ :

$Y'(s)+\dfrac{3-2s^2}sY(s)=-\dfrac{14}{s^2}$

Find the integrating factor:

$\displaystyle\int\frac{3-2s^2}s\,\mathrm ds=3\ln|s|-s^2+C$

Multiply both sides of the ODE by $e^{3\ln|s|-s^2}=s^3e^{-s^2}$ :

$s^3e^{-s^2}Y'(s)+(3s^2-2s^4)e^{-s^2}Y(s)=-14se^{-s^2}$

The left side condenses into the derivative of a product:

$\left(s^3e^{-s^2}Y(s)\right)'=-14se^{-s^2}$

Integrate both sides and solve for $Y(s)$ :

$s^3e^{-s^2}Y(s)=7e^{-s^2}+C$

$Y(s)=\dfrac{7+Ce^{s^2}}{s^3}$

(b) Taking the inverse transform of both sides gives

$y(t)=\dfrac{7t^2}2+C\,L^{-1}\left[\dfrac{e^{s^2}}{s^3}\right]$

I don't know whether the remaining inverse transform can be resolved, but using the principle of superposition, we know that $\frac{7t^2}2$ is one solution to the original ODE.

$y(t)=\dfrac{7t^2}2\implies y'(t)=7t\implies y''(t)=7$

Substitute these into the ODE to see everything checks out:

$2\cdot7+t\cdot7t-2\cdot\dfrac{7t^2}2=14$

5 0

3 years ago

SOMEONE PLSS HELPPPPPPPP

garri49 [273]

Probability is 0/12 since there are no blue lollipops in the bag.

7 0

3 years ago

Read 2 more answers

a movie ticket used to cost $4.25 back in 1990. inflation exist because products increase in value over time. the inflation rate

Andrews [41]

In the year 1998, movie tickets will be greater than $5.50 as determined by solving the equation y=4.25[(1.035)^x].

What is an equation?

Math can be used to analyze an equation or a set of equations.
An equation is a sentence that maintains the equivalence of two expressions. Most of the time, it is easy to solve the arithmetic equations given in an exact manner.
While perfect solutions can occasionally be found, it is more typical to find approaches that are just as accurate. It speaks to the particular guidelines for quadratic mathematical equations.

A movie ticket cost $4.25 in 1990.

The inflation rate is about 3.5%

Rate increased ,r=100%+3.5%=103.5%=1.035

equation generated is,

y=4.25[(1.035)^x]

Solving the equation for each year, we get the following data:

Tabulating the data

Year cost

1990 4.25

1991 ....

.... ....

1998 5.5964~ 5.6

In the year 1998, the will be greater than $5.50.

To learn more about equations visit:

brainly.com/question/17145398

#SPJ1

6 0

1 year ago

Clayton says that 2 1/2 + 3 3/5 will be more than 5 but less than 6 since 2 + 3 is 5. Is Clayton’s reasoning correct? Prove him

antoniya [11.8K]

He is wrong...

2 1/2 + 3 3/5 = 97/20

Simplified, I believe the answer is 4 17/20

7 0

4 years ago

Work out 1% of 200 litres need explination

Varvara68 [4.7K]

ANSWER

To find 1% of something (1/100 of something), divide by 100.

1% of 200 is 2.

6 0

3 years ago