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3 years ago

If Sophia sees clowns perform, then she smiles

Mathematics

2 answers:

kap26 [50]3 years ago

6 0

Answer:

yep

Step-by-step explanation:

GREYUIT [131]3 years ago

4 0

Answer: Yeah- I

..................................I

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A) The equilibrium prices P1 and P2 for two goods satisfy the equations:

Allisa [31]

The value of P1 and P2 using the inverse matrix is 5 and 6 respectively.

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The equilibrium prices of the three independent commodities using the inverse matrix are P1 = 4, P2 = 7, P3 = 8 respectively.

<h3>What is a matrix?</h3>

A matrix can be defined as a collection of integers(numbers that are either positive or negative) that are organized in rows and columns to construct a rectangular array. The numbers in this matrix system are referred to as elements.

To determine the values of P1 and P2 for the system of equations given by using an inverse matrix, we have:

9P1 + P2 = 51

3P1 +4P2 = 39

Representing the above data in matrix form, we have:

$\left[\begin{array}{cc}9&1\\3&4\\ \end{array}\right] \left[\begin{array}{c} \mathbf{P_1} \\ \mathbf{P_2}\\ \end{array}\right] = \left[\begin{array}{c} \mathbf{51} \\ \mathbf{39} \\ \end{array}\right]$ which is in the form AX = B

In order for us to determine the values of P1 and P2, Let take the inverse of A⁻¹ on both sides of the AX= B, we have:

$\mathbf{{A^{-1} AX} = A^{-1} B}$

X = A⁻¹ B

Let's start by finding A⁻¹;

$\mathbf{A = \left[\begin{array}{cc}9&1\\3&4\end{array}\right] }$

$\mathbf{A^{-1} = \dfrac{1}{36-3}\left[\begin{array}{cc}4&-1\\3&9\end{array}\right] }$

$\mathbf{A^{-1} = \dfrac{1}{33}\left[\begin{array}{cc}4&-1\\3&9\end{array}\right] }$

Now, Let's Find A⁻¹B;

$\mathbf{A^{-1}B = \dfrac{1}{33}\left[\begin{array}{cc}4&-1\\3&9\end{array}\right] \left[\begin{array}{c}51\\39\\ \end{array}\right] }$

$\mathbf{\implies \dfrac{1}{33}\left[\begin{array}{cc}204&-39\\-153&+351\end{array}\right] }$

$\mathbf{\implies \left[\begin{array}{c}\dfrac{165}{33}\\ \\ \dfrac{198}{33}\end{array}\right] }$

$\mathbf{\implies \left[\begin{array}{c}5\\ \\ 6\end{array}\right] }$

$\left[\begin{array}{c}\mathbf{P_1}\\ \mathbf{P_2}\end{array}\right]= \left[\begin{array}{c}5\\ 6 \end{array}\right] }$

Therefore, we can conclude that the value of P1 and P2 using the inverse matrix is 5 and 6 respectively.

To determine the equilibrium prices of the three independent commodities using the inverse matrix, we have:

P₁ + 2P₂ + 3P₃ = 42

2P₁ + P₂ + 4P₃ = 47

P₁ + 3P₂ + 4P₃ = 57

The matrix in AX = B form is computed as:

$\implies\left[ \begin{array}{ccc}1&2&3\\2&1&4\\1&3&4\end{array}\right] \left[\begin{array}{c}P_1\\P_2\\P_3 \end{array}\right] = \left[\begin{array}{c}42\\47\\ 57\end{array}\right]$

$\mathbf{A^{-1} = \dfrac{1}{|A|} \ (adj \ A)}$

$\mathbf{A^{-1} = \dfrac{1}{1(4-12) -2(8-4) +3(6-1)} \left[\begin{array}{ccc}-8&4&5\\1&1&-1\\5&2&-3\end{array}\right] }^1$

$\mathbf{A^{-1}B = -1 \left[\begin{array}{ccc}-8&1&5\\-4&1&2\\5&2&-3\end{array}\right] }\left[\begin{array}{c}42\\47\\57\end{array}\right]$

$\mathbf{A^{-1}B = -\left[\begin{array}{ccc}-336&+47&+285\\-168&+47&+114\\210&-47&-171\end{array}\right] }$

$\mathbf{A^{-1}B = -\left[\begin{array}{c}-4\\-7\\-8\end{array}\right] }$

$\mathbf{A^{-1}B = \left[\begin{array}{c}4\\7\\8\end{array}\right] }$

Therefore, we can conclude that the values of P1 = 4, P2 = 7, P3 = 8 respectively.

Learn more about matrix here:

brainly.com/question/1821869

3 0

2 years ago

What is 3,125 divided by 200 as a decimal?

natulia [17]

Answer:

15.625

Step-by-step explanation:

3,125/200 = 15.625

8 0

3 years ago

Read 2 more answers

Graph: f(x) = -3sin (x/2 - π/4)

charle [14.2K]

This sine function has the form y = f(x) = a sin (bx + c), where |a| is the amplitude, b is the frequency, and c determines the phase shift.

The period of this sine curve is 2 pi/b, or (in this problem) 2 pi/(1/2).

The phase shift of this curve is -c/b, or -(pi/4)/(1/2). Simplify this.

The amplitude is |-3|, or just 3.

Draw a set of coordinate axes. Draw light horizontal lines through y=3 and y=-3. These are the max and min. values of this sine function.

Plot the phase shift on your x-axis.

Your sine function will begin at (phase shift value, 0) and continue for one period. Add the period to the phase shift value. Draw a sine curve beginning and ending at these two x-values.

I encourage you to share your calculations and to sketch the graph described here. Then I could give you more specific feedback on your work. Good luck!

3 0

3 years ago

NEED HELP!!!

AnnyKZ [126]

Answer:

see explanation

Step-by-step explanation:

(1)

$\frac{6}{2}$ = $\frac{4}{p}$ ( cross- multiply )