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3 years ago

Which function is negative for the interval [-1,1] ?

Mathematics

1 answer:

iris [78.8K]3 years ago

7 0

Answer:

Option (2)

Step-by-step explanation:

Option (1)

In the interval [-1, 1] Or -1 ≤ x ≤ 1, value of the function will be represented by the y-values.

Since, the graph is below x-axis in the interval -1 ≤ x ≤ 0.5, function will be negative.

And in the interval 0.5 ≤ x ≤ 1, graph is above the x-axis, function will be positive.

Option (2)

In this option, graph is below the x-axis in the interval [-1, 1].

Therefore, the given graph is negative in this interval.

Option (3)

In this graph, function is negative and positive both in the interval -1 ≤ x ≤ 1.

Option (4)

In this graph function is completely above the x-axis in the interval -1 ≤ x ≤ 1.

So this function is positive in the interval [-1, 1].

Therefore, Option (2) will be the answer.

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Two companies have sent representatives to an industry conference. The first company sent 12 representatives and the second comp

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Answer:

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Step-by-step explanation:

Given that two companies have sent representatives to an industry conference.

The first company sent 12 representatives and the second company sent 20 representatives

Selecting any 22 out of these 32 can be done in $32C22 ==\frac{32!}{(22!(32−22)!)} \\= 64512240$

Favourable outcomes = No of ways of selecting 10 from I and 12 from II

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Probability required = $\frac{8314020}{64512240} \\=0.1289$

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3 years ago

A circle with center c(4,-2) contains the point D( 8,1). What is the equation of the line perpendicular to the radius of the cir

Nady [450]

Answer:

4x +3y = 10

Step-by-step explanation:

The radius CD has slope Δy/Δx = (1-(-2))/(8-4) = 3/4.

The equation for the perpendicular line through point C(4, -2) can be written as ...

Δx(x -4) +Δy(y -(-2)) = 0

4(x -4) +3(y +2) = 0

4x +3y -10 = 0 . . . . . . general form equation for the line

4x +3y = 10 . . . . . . . . .standard form equation for the line

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3 years ago

Evaluate the following algebraic expression at x=4, y=−3 and simplify your answer. −x−5y−1]

kondaur [170]

-13 hope this answers tour question

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3 years ago

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.

<h3 />

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:

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2 years ago

A manufacture of skateboards offered a 5/2/1 chain discount too many customers. Bobs sporting goods ordered 20 skateboards for a

Thepotemich [5.8K]

A discount string 5/2/1 means the following:
1) Apply 5% discount to the original price.
2) Apply 2% discount to the result of step 1).
3) Apply 1% discount to the result of step 2).
We have then that the result will be given by:
625 * (0.95) * (0.98) * (0.99) = 576.05625 $
Then, the price of each skateboard is:
(576.05625) /20=28.8028125 $
Answer:
The net price of the skateboards was:
28.8028125 $

7 0

3 years ago