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3 years ago

Find the number whose cube are 4913

Mathematics

2 answers:

mario62 [17]3 years ago

6 0

Step-by-step explanation:

4913 is said to be a perfect cube because 17 x 17 x 17 is equal to 4913.

Alja [10]3 years ago

5 0

Answer:

${17}^{3 } = 4913$

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) Use the Laplace transform to solve the following initial value problem: y′′−6y′+9y=0y(0)=4,y′(0)=2 Using Y for the Laplace tra

artcher [175]

Answer:

$y(t)=2e^{3t}(2-5t)$

Step-by-step explanation:

Let Y(s) be the Laplace transform Y=L{y(t)} of y(t)

Applying the Laplace transform to both sides of the differential equation and using the linearity of the transform, we get

L{y'' - 6y' + 9y} = L{0} = 0

(*) L{y''} - 6L{y'} + 9L{y} = 0 ; y(0)=4, y′(0)=2

Using the theorem of the Laplace transform for derivatives, we know that:

$\large\bf L\left\{y''\right\}=s^2Y(s)-sy(0)-y'(0)\\\\L\left\{y'\right\}=sY(s)-y(0)$

Replacing the initial values y(0)=4, y′(0)=2 we obtain

$\large\bf L\left\{y''\right\}=s^2Y(s)-4s-2\\\\L\left\{y'\right\}=sY(s)-4$

and our differential equation (*) gets transformed in the algebraic equation

$\large\bf s^2Y(s)-4s-2-6(sY(s)-4)+9Y(s)=0$

Solving for Y(s) we get

$\large\bf s^2Y(s)-4s-2-6(sY(s)-4)+9Y(s)=0\Rightarrow (s^2-6s+9)Y(s)-4s+22=0\Rightarrow\\\\\Rightarrow Y(s)=\frac{4s-22}{s^2-6s+9}$

Now, we brake down the rational expression of Y(s) into partial fractions

$\large\bf \frac{4s-22}{s^2-6s+9}=\frac{4s-22}{(s-3)^2}=\frac{A}{s-3}+\frac{B}{(s-3)^2}$

The numerator of the addition at the right must be equal to 4s-22, so

A(s - 3) + B = 4s - 22

As - 3A + B = 4s - 22

we deduct from here

A = 4 and -3A + B = -22, so

A = 4 and B = -22 + 12 = -10

It means that

$\large\bf \frac{4s-22}{s^2-6s+9}=\frac{4}{s-3}-\frac{10}{(s-3)^2}$

and

$\large\bf Y(s)=\frac{4}{s-3}-\frac{10}{(s-3)^2}$

By taking the inverse Laplace transform on both sides and using the linearity of the inverse:

$\large\bf y(t)=L^{-1}\left\{Y(s)\right\}=4L^{-1}\left\{\frac{1}{s-3}\right\}-10L^{-1}\left\{\frac{1}{(s-3)^2}\right\}$

we know that

$\large\bf L^{-1}\left\{\frac{1}{s-3}\right\}=e^{3t}$

and for the first translation property of the inverse Laplace transform

$\large\bf L^{-1}\left\{\frac{1}{(s-3)^2}\right\}=e^{3t}L^{-1}\left\{\frac{1}{s^2}\right\}=e^{3t}t=te^{3t}$

and the solution of our differential equation is

$\large\bf y(t)=L^{-1}\left\{Y(s)\right\}=4L^{-1}\left\{\frac{1}{s-3}\right\}-10L^{-1}\left\{\frac{1}{(s-3)^2}\right\}=\\\\4e^{3t}-10te^{3t}=2e^{3t}(2-5t)\\\\\boxed{y(t)=2e^{3t}(2-5t)}$

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3 years ago

The Knicks and Nets have a total 30 players.

Blababa [14]

Answer:

Step-by-step explanation:

From the problem statement, we can set up the following two equations:

$K + N = 30$

$20K + 10N = 500$

where $K$ is the number of Knicks players, and $N$ is the number of Nets players.

We can substitute the first equation into the second and solve for $K$

$K + N = 30$

$N = 30 - K$

$20K + 10N = 500$

$20K + 10(30 - K) = 500$

$20K + 300 - 10K = 500$

$10K + 300 = 500$

$10K = 200$

$K = 20$

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3 years ago

What is the greatest common factor of 28x²y-7xy^5?

Alchen [17]

The greatest common factor of this can be solved by looking at the individual parts and splitting it up.

First, we have 28 and 7. Well, thats an easy one. 7 goes into 28 4 times so we are now left with 4 and 1.

We can also write the rest of this like this 4(x*x*y) - 1(x*y*y*y*y*y)

Now, what values are in both equations. We have one x and one y that can be taken out of both.

We end up with 7xy(4x-7y^4)

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3 years ago

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Find the minimum product of two numbers whose difference is 17. <br> what are the numbers?

Marysya12 [62]

A number is an arithmetic value that is used to represent a quantity and calculate it. The two numbers will be 17 and 0, so the product of the two is minimal.

<h3>What are Numbers?</h3>

A number is an arithmetic value that is used to represent a quantity and calculate it. Numericals are written symbols that represent numbers, such as "3."

Given the difference between the two numbers is 17. Let the first number be zero, then the second number will be 17. Thus, the product of the two numbers will be 0, which is the minimum.

If the first number is further increased such as 1, then the other number will be 18, and the product of the two will be 18, which is greater than zero.

Hence, the two numbers will be 17 and 0, so the product of the two is minimal.

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Im not sure how to do it because you don't have a plus or minus sign. add that and then i will show you.

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