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Dmitriy789 [7]
2 years ago
11

1. How many terms does the expression 5 + 9x · 7 + 2xº have? What are they?

Mathematics
1 answer:
mel-nik [20]2 years ago
6 0
This expression has four terms.

5, 9x, 7, and 2x


A term is a constant number, a variable, or a variable with a coefficient.
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charle [14.2K]

Answer: I believe it's 5 I am not sure

Step-by-step explanation:

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The formula for the area of a square is s2, where s is the side length of the square. What is the area of a square with a side l
jonny [76]

Answer:

36

step by step

given length=6

so area of square is given by s2 i.e 6^2

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8 0
3 years ago
If sin yº = 7/q and tan yº = 7/r , what is the value of cos yº? (6 points)
olya-2409 [2.1K]

Answer:

cos r/q is the answer,

Step-by-step explanation:

this can be seen when you elaborate sin=opposite/hypotenus and tan=opposite/adjacent by referring to the right angle triangle .

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4 0
3 years ago
There are three different cubes such that the first cube is 64 times the volume of the second, and the volume of the second cube
tankabanditka [31]

Answer:

4/3

Step-by-step explanation:

If the ratio between the volumes of the first and the second cube is 64, the ratio between the sides is the cubic root of the ratio between the volumes, so:

V1 / V2 = 64

s1 / s2 = \sqrt[3]{64}  = 4

Doing the same for the second and third cubes, we have:

V2 / V3 = 1/27

s2/ s3 = \sqrt[3]{1/27}  = 1/3

So the ratio of the first cube side and the third cube side is:

s1 / s3 = (s1/s2) * (s2/s3) = 4 * (1/3) = 4/3

5 0
3 years ago
consider the quadratic form q(x,y,z)=11x^2-16xy-y^2+8xz-4yz-4z^2. Find an orthogonal change of variable that eliminates the cros
Bezzdna [24]

Answer:

q(x,y,z)=16x^{2}-5y^{2}-5z^{2}

Step-by-step explanation:

The given quadratic form is of the form

q(x,y,z)=ax^2+by^2+dxy+exz+fyz.

Where a=11,b=-1,c=-4,d=-16,e=8,f=-4.Every quadratic form of this kind can be written as

q(x,y,z)={\bf x}^{T}A{\bf x}=ax^2+by^2+cz^2+dxy+exz+fyz=\left(\begin{array}{ccc}x&y&z\end{array}\right) \left(\begin{array}{ccc}a&\frac{1}{2} d&\frac{1}{2} e\\\frac{1}{2} d&b&\frac{1}{2} f\\\frac{1}{2} e&\frac{1}{2} f&c\end{array}\right) \left(\begin{array}{c}x&y&z\end{array}\right)

Observe that A is a symmetric matrix. So A is orthogonally diagonalizable, that is to say,  D=Q^{T}AQ where Q is an orthogonal matrix and D is a diagonal matrix.

In our case we have:

A=\left(\begin{array}{ccc}11&(\frac{1}{2})(-16) &(\frac{1}{2}) (8)\\(\frac{1}{2}) (-16)&(-1)&(\frac{1}{2}) (-4)\\(\frac{1}{2}) (8)&(\frac{1}{2}) (-4)&(-4)\end{array}\right)=\left(\begin{array}{ccc}11&-8 &4\\-8&-1&-2\\4&-2&-4\end{array}\right)

The eigenvalues of A are \lambda_{1}=16,\lambda_{2}=-5,\lambda_{3}=-5.

Every symmetric matriz is orthogonally diagonalizable. Applying the process of diagonalization by an orthogonal matrix we have that:

Q=\left(\begin{array}{ccc}\frac{4}{\sqrt{21}}&-\frac{1}{\sqrt{17}}&\frac{8}{\sqrt{357}}\\\frac{-2}{\sqrt{21}}&0&\sqrt{\frac{17}{21}}\\\frac{1}{\sqrt{21}}&\frac{4}{\sqrt{17}}&\frac{2}{\sqrt{357}}\end{array}\right)

D=\left(\begin{array}{ccc}16&0&0\\0&-5&0\\0&0&-5\end{array}\right)

Now, we have to do the change of variables {\bf x}=Q{\bf y} to obtain

q({\bf x})={\bf x}^{T}A{\bf x}=(Q{\bf y})^{T}AQ{\bf y}={\bf y}^{T}Q^{T}AQ{\bf y}={\bf y}^{T}D{\bf y}=\lambda_{1}y_{1}^{2}+\lambda_{2}y_{2}^{2}+\lambda_{3}y_{3}^{2}=16y_{1}^{2}-5y_{2}^{2}-5y_{3}^2

Which can be written as:

q(x,y,z)=16x^{2}-5y^{2}-5z^{2}

4 0
3 years ago
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