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3 years ago

PLEASE HELP!:

1 answer:

3 0

Equations are used more in every day life. We live in a capitalist society. We deal with money everyday and ambiguous costs are not acceptable. Whenever you buy or sell an item it's always for an calculated value never a range of values.

For literal equation example; How to calculate the price of an item, p after a discount rate d

x = p/(1-d)

p = x(1 - d)

Literal equations you solve for the formula, the new price of the item, p. So you have a general formula for finding the new price of an item on sale.

p = x(1 - d)

when you have the formula you can then put in the values, calculate the discount price of items see relationships between variables.

if the original cost x is 100$ and discount is 10% how much will the item cost?

p = 100(1 - 0.10)
p = 100(0.9)
p = $90

In a one or two step equation there are numbers and only one unknown value to solve for. These can be solved in one or two steps according to the name.. There are no values to substitute for variables.

One step equation: (unknown solved for in one step)
5x = 25
divide by 5
x = 5

Two Step equation: (unknown solved for in two steps)
2x - 8 = 10
add 8
2x = 18
divide by 2
x = 9

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(1 point) The matrix A=⎡⎣⎢−4−4−40−8−4084⎤⎦⎥A=[−400−4−88−4−44] has two real eigenvalues, one of multiplicity 11 and one of multip

serious [3.7K]

Answer:

We have the matrix $A=\left[\begin{array}{ccc}-4&-4&-4\\0&-8&-4\\0&8&4\end{array}\right]$

To find the eigenvalues of A we need find the zeros of the polynomial characteristic $p(\lambda)=det(A-\lambda I_3)$

Then

$p(\lambda)=det(\left[\begin{array}{ccc}-4-\lambda&-4&-4\\0&-8-\lambda&-4\\0&8&4-\lambda\end{array}\right] )\\=(-4-\lambda)det(\left[\begin{array}{cc}-8-\lambda&-4\\8&4-\lambda\end{array}\right] )\\=(-4-\lambda)((-8-\lambda)(4-\lambda)+32)\\=-\lambda^3-8\lambda^2-16\lambda$

Now, we fin the zeros of $p(\lambda)$ .

$p(\lambda)=-\lambda^3-8\lambda^2-16\lambda=0\\\lambda(-\lambda^2-8\lambda-16)=0\\\lambda_{1}=0\; o \; \lambda_{2,3}=\frac{8\pm\sqrt{8^2-4(-1)(-16)}}{-2}=\frac{8}{-2}=-4$

Then, the eigenvalues of A are $\lambda_{1}=0$ of multiplicity 1 and $\lambda{2}=-4$ of multiplicity 2.

Let's find the eigenspaces of A. For $\lambda_{1}=0$ : $E_0 = Null(A- 0I_3)=Null(A)$ .Then, we use row operations to find the echelon form of the matrix

$A=\left[\begin{array}{ccc}-4&-4&-4\\0&-8&-4\\0&8&4\end{array}\right]\rightarrow\left[\begin{array}{ccc}-4&-4&-4\\0&-8&-4\\0&0&0\end{array}\right]$

We use backward substitution and we obtain

$-8y-4z=0\\y=\frac{-1}{2}z$

$-4x-4y-4z=0\\-4x-4(\frac{-1}{2}z)-4z=0\\x=\frac{-1}{2}z$

Therefore,

$E_0=\{(x,y,z): (x,y,z)=(-\frac{1}{2}t,-\frac{1}{2}t,t)\}=gen((-\frac{1}{2},-\frac{1}{2},1))$

For $\lambda_{2}=-4$ : $E_{-4} = Null(A- (-4)I_3)=Null(A+4I_3)$ .Then, we use row operations to find the echelon form of the matrix

$A+4I_3=\left[\begin{array}{ccc}0&-4&-4\\0&-4&-4\\0&8&8\end{array}\right] \rightarrow\left[\begin{array}{ccc}0&-4&-4\\0&0&0\\0&0&0\end{array}\right]$

We use backward substitution and we obtain

$-4y-4z=0\\y=-z$

Then,

$E_{-4}=\{(x,y,z): (x,y,z)=(x,z,z)\}=gen((1,0,0),(0,1,1))$

8 0

3 years ago

A, b, c, and d please

DIA [1.3K]

<h2>Answers / Step-by-step explanation:</h2><h3>a. What is the length of one side of the square.</h3>

Looking at the image, the radius (r) of the circle appears to cover half of the length of a side of the square. Hence, the side of the square has a length of 2r.

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<h3>b. The formula A= πr² is used to find the area of a circle. The formula A=4r² can be used to find the area of the square. Write the ratio of the area of the circle to the area of the square in the simplest form.</h3>

$Ratio=\frac{\pi r^{2} }{4r^2} =\frac{\pi}{4}$ .

Notice that the value "r²" disappears from the expression because is being multiplied and divided by it at the same time.

$Ratio=\frac{4\pi }{16} =0.7854.$

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c. Complete the table.

To complete each cell of the table, simply take the equation of the asked parameter and substitute the value of r by the number indicated in the title of the column. For example, column 3 should be filled out like this:

Area of Circle (units²): π(3)²or 9π.

Length of 1 Side of the Square: 2r= 2(3)= 6.

Area of Square (units²)= 4r²= 4(3)²= 36.

Ratio: $\frac{\pi}{4}$ .

Do the same for all the other columns.

The answers to the table are presented on the attached image.

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d. What can you conclude about the relationship between the area of the circle and the square?

They will always have the same value, π/4, regardless of the size of the square and circle. As long as the circle borders meet the square's at the middle of each side of the square, the relationship will be the same.

4 0

2 years ago

What is the value of v?

melamori03 [73]

Answer:

70 degrees.

Step-by-step explanation:

They are vertical angles, and vertical angles are always congruent.

6 0

2 years ago

How do you solve an inequality that has a fraction (with a variable as the nemurator/demoninator

vichka [17]

Answer:

Solving with an equality is just simply the same as solving any algebra equations. If you were given a fraction, then just multiply both sides.

Example:

4 + $\frac{x}{2}$ > 14

Subtract 4 on both sides:

4 - 4 + $\frac{x}{2}$ > 14 - 4

$\frac{x}{2}$ > 10

Now multiply both sides by 2:

$\frac{x}{2}$ × 2 > 10 × 2

x > 20

3 0

3 years ago

What are solutions to the quadratic equation 2x^2+6x-10=x^2+6

Alex

Answer:

Step-by-step explanation:

$2x^2+6x-10=x^2+6\qquad\text{subtract}\ x^2\ \text{and 6 from both sides}\\\\x^2+6x-16=0\\\\x^2+2x-8x-16=0\\\\x(x+2)-8(x+2)=0\\\\(x+2)(x-8)=0\iff x+2=0\ \vee\ x-8=0\\\\x+2=0\qquad\text{subtract 2 from both sides}\\x=-2\\\\x-8=0\qquad\text{add 8 to both sides}\\x=8$

4 0

3 years ago

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