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1 year ago

Two submersibles, one red and one blue, started rising toward the surface at the same time. They each rose at a constant speed.

Mathematics

1 answer:

Mrrafil [7]1 year ago

4 0

Answer: The red submersible started from a higher altitude and the red submersible rose faster.

Step-by-step explanation:

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Jacob solves the system of equations by forming a matrix equation.

Lyrx [107]

Simultaneous equations can be solved using inverse matrix operation.

The complete steps of Jacob's solution are:

$\left[\begin{array}{cc}4&1\\-2&3\end{array}\right]^{-1} \cdot \left[\begin{array}{cc}4&1\\-2&3\end{array}\right]\left[\begin{array}{c}x&y\end{array}\right] = \frac{1}{14}\left[\begin{array}{cc}3&-1\\2&4\end{array}\right] \cdot \left[\begin{array}{c}2&-22\end{array}\right]$

$\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{cc}4&1\\-2&3\end{array}\right] \cdot \left[\begin{array}{c}2&-22\end{array}\right]$

$\left[\begin{array}{c}x&y\end{array}\right] = \frac{1}{14} \left[\begin{array}{c}28&-84\end{array}\right]$

$\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}2&-6\end{array}\right]$

We have:

$4x + y = 2$

$-2x + 4y = -22$

Calculate the determinant of $\left[\begin{array}{cc}4&1\\-2&3\end{array}\right]$

$|A| = 4 \times 3 -1 \times -2$

$|A| = 12 +2$

$|A| = 14$

So, the inverse matrix becomes

$A = \frac{1}{14}\left[\begin{array}{cc}4&1\\-2&3\end{array}\right]$

Replace the first column with $\left[\begin{array}{c}2&-22\end{array}\right]$ to calculate the value of x

$x = \frac{1}{14}\left[\begin{array}{cc}2&1\\-22&3\end{array}\right]$

So, we have:

$x = \frac{1}{14}(2 \times 3 - 1 \times -22)$

$x = \frac{1}{14}(6 +22)$

$x = \frac{1}{14}(28)$

$x = 2$

Replace the second column with $\left[\begin{array}{c}2&-22\end{array}\right]$ to calculate the value of y

$y = \frac{1}{14}\left[\begin{array}{cc}4&2\\-2&-22\end{array}\right]$

So, we have:

$y = \frac{1}{14}(4 \times -22 - 2 \times -2)$

$y = \frac{1}{14}(-88 +4)$

$y = \frac{1}{14}(-84)$

$y = -6$

Hence, the complete process is:

$\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{cc}4&1\\-2&3\end{array}\right] \cdot \left[\begin{array}{c}2&-22\end{array}\right]$

$\left[\begin{array}{c}x&y\end{array}\right] = \frac{1}{14} \left[\begin{array}{c}28&-84\end{array}\right]$

$\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}2&-6\end{array}\right]$

Read more about matrices at:

brainly.com/question/11367104

6 0

1 year ago

What is the length of the altitude of the equilateral triangle below?

Mazyrski [523]

ANSWER

The length of the altitude is $3\sqrt{3}$ units

<u>EXPLANATION</u>

The altitude of a triangle is the vertical height of the triangle.

From the diagram the altitude is $a$

Method 1: We can use Pythagoras theorem to find $a$

$6^2=a^2+3^2$

$6^2-3^2=a^2$

$36-9=a^2$

$27=a^2$

We take the square root of both sides,

$\sqrt{27}=a$

$\sqrt{9\times3}=a$

$\sqrt{9} \times \sqrt{3}=a$

$3\sqrt{3}=a$

Method 2 Using Trigonometry

$sin(60\degree)=\frac{a}{6}$

$6sin(60\degree)=a$

$a=6\times \frac{\sqrt{3}} {2}$

$a=3\sqrt{3}$

6 0

2 years ago

Read 2 more answers

Jeff has 8 red marbles, 6 blue marbles, and 4 green marbles that are the same size and

Arada [10]

Answer:
1/3

Explanation:

5 0

1 year ago

Read 2 more answers

Delia went to a market to buy 4.5 pounds of sliced fruit in a container she paid with a $20 bill and a $5 bill and received $4.6

andreyandreev [35.5K]

20+5=25 then 25-4.67=20.33 so then you do 20.33/4.5=4.5 so the cost for one pound of fruit is $4.57. Hope this helps :)

4 0

2 years ago

Boden is making a prize wheel for the school fair. The ratio of winning spaces to losing spaces is shown in the diagram. The tab

IceJOKER [234]

The correct answers are Losing 12; Winning 15

Explanation:

The ratio of winning to losing is 5: 6 or 5/6. This means for every 5 winning spaces in the wheel there are 6 losing spaces. This ration should be used to complete the values of the table.

1. The first row shows there are 10 winning and you need to calculate the number of losing spaces. The process is shown below.

$\frac{5}{6} = \frac{10}{x}$ - Express the ratios using fractions; use x to show the missing value