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Find the Pythagorean triplet in which one number is 32

Answers

Answer 1

Answer:

Answer:

What is the Pythagorean triplet of 32?

But 32/2 = 16 which is even so:

But 32/4 = 8 which is even so:

But 32/8 = 4 which is even so:

Answer 2

Answer:

Answer:

Answer in explanation below.

Step-by-step explanation:

32² => 1024 => 1024/4 => 256 => 256 + 1 = 257, 256 - 1 = 255: 32, 255, 257

16² => 256 => 256/4 => 64 => 64 + 1 = 65, 64 - 1 = 63: 2 x ( 16, 63, 65) = 32, 126, 130

8² => 64 => 64/4 => 16 => 16 + 1 = 17, 16 - 1 = 15: 4 x ( 8, 15, 17) = 32, 60, 68

4² => 16 => 16/4 => 4 => 4 + 1 = 5, 4 - 1 = 3: 8 x ( 4, 3, 5) = 32, 24, 40

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Whitley park is a rectangular park with a perimeter of 70 yards. One side of Whitley park is 18 feet long. What is the area of Whitley park?

Answers

If Whitley park is a rectangular park with a perimeter of 70 yards. One side of Whitley park is 18 feet long then 174 yards is the area.

What is Area of Rectangle?

Area of rectangle is length times of breadth.

We know that 18 feet=6 yards.

It is given that One side of Whitley park is 18 feet long, so one side of length is 6 yards.

2(Lenght+breadth)=70

2(L+6)=70

2l+12=70

2l=70-12

2l=58

l=29 yards

Now

Area =Length×breadth

=29×6

= 174 square yards

Hence 174 square yards is the area of Whitley park.

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Answer:

174 yards squared

Step-by-step explanation:

I didn’t study and it’s 2 am pls help

Answers

Answer:

7. g(3) = 42

8. f(6) = - 124

9. g(15) = 3

10. h(-3) = 1/8

Step-by-step explanation:

7. g(x) = 4x² + 6

g(3) = 4×3² + 6

= 4×9 + 6

= 36 + 6

= 42

8. f(x) = - 3x² - 4x + 8

f(6) = - 3×6² - 4×6 + 8

= - 3×36 - 24 + 8

= - 108 -16

= - 124

9. g(x) = √(x - 6)

g(15) = √(15 - 6)

= √9

= 3

10. h(x) = 2ˣ

h(-3) = 2⁻³

= 1/2³

= 1/8

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 cross product in q(x,y,z) and express q in the new variables.

Answers

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

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

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:

$A=\left(\begin{array}{ccc}11&((1)/(2))(-16) &((1)/(2)) (8)\n((1)/(2)) (-16)&(-1)&((1)/(2)) (-4)\n((1)/(2)) (8)&((1)/(2)) (-4)&(-4)\end{array}\right)=\left(\begin{array}{ccc}11&-8 &4\n-8&-1&-2\n4&-2&-4\end{array}\right)$

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:

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

$D=\left(\begin{array}{ccc}16&0&0\n0&-5&0\n0&0&-5\end{array}\right)$

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:

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

Skyler solved an equation incorrectly, as shown below:Step 1: 12 + x = 36
Step 2: x = 36 + 12
Step 3: x = 24

Which statement best explains why Step 2 is incorrect in Skyler's solution?

Answers

Answer:

Step 2 is incorrect.

Step-by-step explanation:

It's incorrect because I'm pretty you need to do inverse operation. To get 24 you must subtract, not add.

Wai recorded the length of each string needed for a knitting project. What is the total length of the string needed?

Answers

Answer:

The answer is "14.625 ft"

Step-by-step explanation:

In the given question some information is missing that is attachment of file which can be described as follows:

Add products:

$\rightarrow \ ((1)/(8))* 1+((1)/(4))* 1+((1)/(2))* 3+((3)/(4))*8+(1)*4+1 (3)/(8)* (2)1 (3)/(8) \n\n \rightarrow 11/8\n\n$

$\rightarrow (1)/(8)* 1+((1)/(4))*1+((1)/(2))*3+((3)/(4))*8+(1)*4+(11)/(8)*(2)\n\n$

$\rightarrow ((1)/(8))+((1)/(4))+((3)/(2))+(6)+(4)+(11)/(4)\n\n\rightarrow ((1+2+12+48+32+22)/(8)) \n\n\rightarrow (117)/(8) \n\n \rightarrow 14.625 \ ft \n$

Suppose that det(a) = a b c d e f g h i = 2 and find the determinant of the given matrix. a b c −4d −4e −4f a + g b + h c + i

Answers

I'll go out on a limb and suppose you're given the matrix

$\mathbf A=\begin{bmatrix}a&b&c\nd&e&f\ng&h&i\end{bmatrix}$

and you're asked to find the determinant of $\mathbf B$ , where

$\mathbf B=\begin{bmatrix}a&b&c\n-4d&-4e&-4f\na+g&b+h&c+i\end{bmatrix}$

and given that $\det\mathbf A=2$ .

There are two properties of the determinant that come into play here:

(1) Whenever a single row/column is scaled by a constant $k$ , then the determinant of the matrix is scaled by that same constant;

(2) Adding/subtracting rows does not change the value of the determinant.

Taken together, we have that

$\det\mathbf B=-4\det\mathbf A=-8$

Final answer:

Due to insufficient information, we cannot calculate the determinant of the given matrix. The determinant calculation varies based on the matrix's size and the specifics of its elements.

Explanation:

The question asked was to find the determinant of a given matrix when the det(a) = 2. However, the information provided is insufficient to determine the actual matrix determinant due to numerical errors and unrelatable data. The determinant of a matrix is calculated differently depending on the type of matrix. For a 2x2 matrix, if the matrix is [a b; c d], the determinant would be 'ad - bc'. For a 3x3 matrix, the determinant process involves more steps including finding minors and cofactors of matrix elements. However, without the actual specifics of the matrix, the determinant cannot be calculated.

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