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2 years ago

What areC12, C31, and C22 of matrix C?

Mathematics

1 answer:

Liono4ka [1.6K]2 years ago

5 0

Compute the sum to simplify C :

$C = \begin{bmatrix}16-0.5 & 9+0 \\ -3+5 & 0 + 8 \\ 4-3 & -10+14\end{bmatrix} = \begin{bmatrix}15.5 & 9 \\ 2 & 8 \\ 1 & 4\end{bmatrix}$

Now, $c_{ij}$ is the entry of the matrix in row i and column j, so

$C = \begin{bmatrix}15.5 & \boxed{9} \\ 2 & 8 \\ 1 & 4\end{bmatrix} \implies c_{12} = 9$

$C = \begin{bmatrix}15.5 & 9 \\ 2 & 8 \\ \boxed{1} & 4\end{bmatrix} \implies c_{31} = 1$

$C = \begin{bmatrix}15.5 & 9 \\ 2 & \boxed{8} \\ 1 & 4\end{bmatrix} \implies c_{22} = 8$

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Given that (x+y+z)(xy+xz+yz)=18 and that x^2(y+z)+y^2(x+z)+z^2(x+y)=6 for real numbers x, y, and z, what is the value of xyz?

worty [1.4K]

Answer:

Step-by-step explanation:

$(x+y+z)(xy+xz+yz)=18$ Equation 1

$x^2(y+z)+y^2(x+z)+z^2(x+y)=6$ Equation 2

What is the value of $xyz$ where each variable represents a real number?

Let's expand equation 1:

$(x+y+z)(xy+xz+yz)=18$

$x(xy)+x(xz)+x(yz)+y(xy)+y(xz)+y(yz)+z(xy)+z(xz)+z(yz)=18$

Simplify each term if can:

$x^2y+x^2z+xyz+y^2x+xyz+y^2z+xyz+z^2x+z^2y=18$

See if we can factor a little to get some of the left hand side of equation 2:

The first two terms have $x^2$ and if I factored $x^2$ from first two terms I would have $x^2(y+z)$ which is the first term of left hand side of equation 2.

So let's see what happens if we gather the terms together that have the same variable squared together.

$x^2y+x^2z+y^2x+y^2z+z^2y+z^2x+xyz+xyz+xyz=18$

Factor the variable squared terms out of each binomial pairing:

$x^2(y+z)+y^2(x+z)+z^2(y+x)+xyz+xyz+xyz=18$

Replace the sum of those first three terms with what it equals which is 6 from the equation 2:

$6+xyz+xyz+xyz=18$

Combine like terms:

$6+3xyz=18$

Subtract 6 on both sides:

$3xyz=12$

Divide both sides by 3:

$xyz=4$

4 0

3 years ago

1/2 +2/3=?<br> What's the answer?

11111nata11111 [884]

1 $\frac{1}{6}$

7 0

3 years ago

Read 2 more answers

a recipe for lasagna calls for 3 pounds of tomatoes to serve 5 people. a caterer wants to make enough lasagna to serve 110 peopl

Roman55 [17]

To do this you want to divide 110 by 5 to get 22. Now you want to multiply 3 by 22. That means the caterer need 66 pounds of tomatoes.

5 0

3 years ago

A medical researcher needs 37 people to test the effectiveness of an experimental drug. If 101 people have volunteered for the t

Rashid [163]

Answer:

The number of ways to select 37 people from 101 is, 5,397,234,129,638,871,133,346,507,775.

Step-by-step explanation:

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

${n\choose k}=\frac{n!}{k!\cdot (n-k)!}$

Compute the number of ways to select 37 people from 101 as follows:

${101\choose 37}=\frac{101!}{37!\cdot (101-37)!}$

$=\frac{101!}{37!\times 64!}\\\\=\frac{101\times 100\times 99\times....64!}{37!\times 64!}\\\\=5397234129638871133346507775$

Thus, the number of ways to select 37 people from 101 is, 5,397,234,129,638,871,133,346,507,775.

5 0

3 years ago

A manufacturing company ships its product in two different sizes of truck trailers. Each shipment is made in a trailer with dime

kherson [118]

Answer:

Mean volume shipped per trailer load = 2960 ft³

Step-by-step explanation:

Since both trailers are always full,

Total volume in one 30 feet trailer shipment = 8 × 10 × 30 = 2400 ft³

Total volume in one 40 feet trailer shipment = 8 × 10 × 40 = 3200 ft³

Assuming a basis of 10 shipments, 3 shipments are done using the 2400 ft³ trailer and 7 shipments are done using the 3200 ft³ trailer.

Mean volume shipped per trailer load = total volume shipped/number of shipments

Total volume shipped = (3 × 2400) + (7 × 3200) = 7200 + 22400 = 29600 ft³

Number of shipment in the basis used = 10

Mean volume shipped per trailer load = 29600/10 = 2960 ft³

4 0

3 years ago