Find the value of each variable. For the circle, the dot represents the center.

Solve the following system of linear equations: 3x1+6x2+6x3 = -9 -2x1–3x2-3x3 = 3 If the system has infinitely many solutions, y

choli [55]

Answer:

The set of solutions is $\{\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}12\\-7-r\\r\end{array}\right]: \text{r is a real number} \}$

Step-by-step explanation:

The augmented matrix of the system is $\left[\begin{array}{ccccc}3&6&6&-9\\-2&-3&-3&3\end{array}\right]$ .

We will use rows operations for find the echelon form of the matrix.

In row 2 we subtract $\frac{2}{3}$ from row 1. (R2- 2/3R1) and we obtain the matrix $\left[\begin{array}{cccc}3&6&6&-9\\0&1&1&-7\end{array}\right]$
We multiply the row 1 by $\frac{1}{3}$ .

Now we solve for the unknown variables:

$x_2+x_3=-7$ , $x_2=-7-x_3$
$x_1+2x_2+2x_3=-2$ , $x_1+2(-7-x_3)+2x_3=-2$ then $x_1=12$

The system has a free variable, the the system has infinite solutions and the set of solutions is $\{\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}12\\-7-r\\r\end{array}\right]: \text{r is a real number} \}$

6 0

3 years ago

PLEASE HELPP!

zheka24 [161]

Answer:

5^2 = 100

100 x 3.14 = 314

Now we multiply by 20 since it's the height.

314 x 20 = 6,280 cm^3 is your answer.

Formula of cylinder:

H x πr^2

Height x pi(3.14 or 22/7 depending what they tell you to use for pi) x radius being squared (your radius is half of your diameter or given radius).

7 0

3 years ago

A certain star is 2.4 x 102 light years from the Earth. One light year is about 5.9 x 1012 miles. How far

Studentka2010 [4]

Answer:

2.5 x $10^{15}$ miles

Step-by-step explanation:

We are given that 1 light year ≈ 5.9 x $10^{12}$ miles so:

4.3 x 10² light year · 5.9 x $10^{12}$ miles
1 light year

Multiply 4.3 an 5.9 and round to 2 significant digits then add the exponents:

≈25 x $10^{14}$

This is not the scientific notation since the number is not between 0 and 10 so we move the decimal point by 1 place to the left. We then add 1 to the exponent to obtain the final answer:

≈ 2.5 x $10^{15}$ miles

6 0

2 years ago

a) Estimate the volume of the solid that lies below the surface z = 7x + 5y2 and above the rectangle R = [0, 2]⨯[0, 4]. Use a Ri

SSSSS [86.1K]

In the $x$ direction we consider the $m=2$ subintervals [0, 1] and [1, 2] (each with length 1), while in the $y$ direction we consider the $n=2$ subintervals [0, 2] and [2, 4] (with length 2). Then the lower right corners of the cells in the partition of $R$ are (1, 0), (2, 0), (1, 2), (2, 2).

Let $f(x,y)=7x+5y^2$ . The volume of the solid is approximately

$\displaystyle\iint_Rf(x,y)\,\mathrm dx\,\mathrm dy\approx f(1,0)\cdot1\cdot2+f(2,0)\cdot1\cdot2+f(1,2)\cdot1\cdot2+f(2,2)\cdot1\cdot2=\boxed{164}$

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More generally, the lower-right-corner Riemann sum over $m=\mu$ and $n=\nu$ subintervals would be

$\displaystyle\sum_{m=1}^\mu\sum_{n=1}^\nu\left(7\frac{2m}\mu+5\left(\frac{4n-4}\nu\right)^2\right)\frac{2-0}\mu\frac{4-0}\nu=\frac83\left(101+\frac{21}\mu+\frac{40}{\nu^2}-\frac{120}\nu\right)$

Then taking the limits as $\mu\to\infty$ and $\nu\to\infty$ leaves us with an exact volume of $\dfrac{808}3$ .

7 0

3 years ago

Write an integer for each situation. 22°F below zero a. -22 b. 22 c. 2 d. -2

Sergeeva-Olga [200]

The answer is A because it is 22 below zero.

6 0

2 years ago