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Triss [41]
3 years ago
11

Which of the following is a factor of 3x3 + 18x2 + 27x

Mathematics
1 answer:
Elina [12.6K]3 years ago
3 0

So firstly, we have to factor out the GCF, or greatest common factor, of these terms. To find the GCF, list the factors of each term and the greatest one they share is their GCF. In this case, the GCF is 3x:

3x(x^2+6x+9)

Next, what's inside the parentheses is considered a perfect square. Using this format of (a+b)^2=a^2+2ab+b^2 , we can factor it as such:

x^2+6x+9=(x+3)^2\\3x(x+3)^2\\3x(x+3)(x+3)

<u>The factors of this expression are 3x, x + 3, and x + 3.</u>

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x = c1 cos(t) + c2 sin(t) is a two-parameter family of solutions of the second-order DE x'' + x = 0. Find a solution of the seco
igomit [66]

Answer:

x=-cos(t)+2sin(t)

Step-by-step explanation:

The problem is very simple, since they give us the solution from the start. However I will show you how they came to that solution:

A differential equation of the form:

a_n y^n +a_n_-_1y^{n-1}+...+a_1y'+a_oy=0

Will have a characteristic equation of the form:

a_n r^n +a_n_-_1r^{n-1}+...+a_1r+a_o=0

Where solutions r_1,r_2...,r_n are the roots from which the general solution can be found.

For real roots the solution is given by:

y(t)=c_1e^{r_1t} +c_2e^{r_2t}

For real repeated roots the solution is given by:

y(t)=c_1e^{rt} +c_2te^{rt}

For complex roots the solution is given by:

y(t)=c_1e^{\lambda t} cos(\mu t)+c_2e^{\lambda t} sin(\mu t)

Where:

r_1_,_2=\lambda \pm \mu i

Let's find the solution for x''+x=0 using the previous information:

The characteristic equation is:

r^{2} +1=0

So, the roots are given by:

r_1_,_2=0\pm \sqrt{-1} =\pm i

Therefore, the solution is:

x(t)=c_1cos(t)+c_2sin(t)

As you can see, is the same solution provided by the problem.

Moving on, let's find the derivative of x(t) in order to find the constants c_1 and c_2:

x'(t)=-c_1sin(t)+c_2cos(t)

Evaluating the initial conditions:

x(0)=-1\\\\-1=c_1cos(0)+c_2sin(0)\\\\-1=c_1

And

x'(0)=2\\\\2=-c_1sin(0)+c_2cos(0)\\\\2=c_2

Now we have found the value of the constants, the solution of the second-order IVP is:

x=-cos(t)+2sin(t)

3 0
3 years ago
Consider the given density curve. A curve starts at (0, 0), curves up to maximum point (3, question mark), and then decreases do
stepladder [879]

Answer:

5

Step-by-step explanation:

because i did it its 5

4 0
3 years ago
water weighs about 8.34 pounds per gallon. About how many ounces per gallon is the weight of the water?
notka56 [123]
Use a conversion factor and turn pounds to ounces. 1 pound = 16 ounces so
\frac{8.34pounds}{gallon} \times \frac{16 ounces}{ 1 pound} =133.44 \frac{ounces}{gallon}
3 0
3 years ago
The first one will get the brianlist please help answer these two
Julli [10]

Answer:

<em>Hello bakugo here!</em>

Step-by-step explanation:

I don't see anything, is there supposed to be anything here? if not

<em>Thank you extra for FREE points! :D</em>

8 0
3 years ago
Read 2 more answers
A number decreased by 5 is 50
Vinil7 [7]

Answer:

55 decrease by 5 is 50, or 55 - 5 = 50.

Step-by-step explanation:

Let x represent the missing number.

When you hear the words decrease, minus, that tells you to subtract.

Before we subtract, if there is a variable, we must do the opposite of subtraction, we need to add.

50 + 5 = x

Which means x = 50 + 5.

50 + 5 = 55.

Therefore, x = 55.

4 0
3 years ago
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