Find the matrix exponential Consider the system of equations dy dt dz 2y + 2z 2y + 2z dt Find the matrix exponential 12 M(t) = Fel 2) Please denote exponentiation with exp(a*t) rather than e**(a*t) or e^(a*t) Enter the matrix componentwise below. Mu(t) = M12(t) = M21(t) = = M22(t) =

Answer:

Step-by-step explanation: black lives dont matter

If the data of the research subjects are presented in a frequency distribution graph, a histogram-type graph should be used.

If the data are presented in a frequency distribution graph, then the type of graph that should be used is a histogram. A histogram is a type of bar graph that displays the distribution of a continuous variable by dividing the range of values into intervals, and bins, and counting the number of observations that fall within each bin.

If the academic majors were nominal a bar graph could also be used to display the frequency of each major. In a bar graph, each category would be plotted on the horizontal axis, and the frequency of students in each category would be plotted on the vertical axis.

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Answer:

Yes, both shampoo and water will be enough

Given that:

Number of long and short hair member who can wash their hair ; with amount of water less than 5600 litres

To check if bathroom has enough water and shampoo for 8 long haired and 7 short haired members.

L = long-haired ; S = short-haired

70L+ 60S < 5600

Check the constraint for amount of water :

70L+ 60S < 5600

L = 8 ; S = 7

70(8) + 60(7) < 5600

560 + 420 < 5600

980 < 5600

Constraint satisfied

Number of long and short hair member who can wash their hair with shampoo not more than 2.5 litres

0.02L + 0.01S ≤ 2.5

L = 8 ; S = 7

0.02(8) + 0.01(7) ≤ 2.5

0.16 + 0.07 ≤ 2.5

0.23 ≤ 2.5 (constraint satisfied).

Answer:

There's enough water and shampoo.

Step-by-step explanation:

Got answer from khan

Answer: 6

Step-by-step explanation:

3

1

​

a−1−

2

1

​

b

=

3

1

​

⋅12−1−

2

1

​

⋅6 Replace a with 12 and b with 6.

=4−1−3

=0

​

Answer:

1/64

Step-by-step explanation:

(1/8)² = 1/64

The engineer should take a sample size of approximately 40 to be 95% confident of being in error by only 0.125 minutes.

To calculate the sample size for estimating the cycle time, the engineer can use the formula for continuous data:

E = (zα/2) * (σ / √n)

where:
E is the maximum allowable error (0.125 minutes),
zα/2 is the z-value for a 95% confidence level (which corresponds to a 0.025 alpha level),
σ is the standard deviation (0.4 minutes), and
n is the sample size (unknown).

Rearranging the formula, we have:

n = (zα/2)^2 * (σ^2 / E^2)

Plugging in the given values, we get:

n = (1.96)^2 * (0.4^2 / 0.125^2)

Simplifying the equation, we have:

n ≈ 3.8416 * (0.16 / 0.015625)

n ≈ 3.8416 * 10.24

n ≈ 39.494

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Answer:i don't know

Step-by-step explanation:

make a square by connecting the top two and bottom two points together if they make a perfect square if it is then yes if not thenthn no

Answer:

7

Step-by-step explanation:

Since, Sophia had three pages of homework and she only has three left you can set up an equation to solve. The equation would be 10=x-3, then you just solve the equation which would be 7, hope that helped.

Solution

For this case we have a number x

The opposite is given by -x

And the product should be:

x

x*(-x) =-x^2

For the case x=0 we can see that is not true

Then the answer is:

False

Answer:

C

Step-by-step explanation:

The work done by Francesca is incorrect as the solved final answer and the final answer given in the question don't matches.

As per the given data, we have to determine whether the evaluation made by Francesca is either correct or wrong.

The given expression is \(3(5)^{2} -18 \div3\)

We have to follow the BODMAS rule for evaluating the expressions.

B - Brackets

O - Of

D - Division

M - Multiplication

A - Addition

S - Subtraction

Steps for solving the given expression:

Step 1: Solve for square value in brackets

= 3(25) – 18 ÷ 3

Step 2: Remove the brackets between the terms 3 and 25.

= 75 – 18 ÷ 3

Step 3: Divide the terms 18 and 3.

= 75 - 6

Step 4: Subtract the terms 75 and 6.

= 69.

As the final answer is given in the question and the final answer which we have done are not matching Francesca's work is incorrect.

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Answer:To evaluate the exponential expression 6(4+2)² - 32, we need to follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).

First, we simplify the expression inside the parentheses:

4 + 2 = 6

Next, we square the result:

6² = 36

Now, we substitute the squared result back into the expression:

6(36) - 32

Next, we perform the multiplication:

6 * 36 = 216

Finally, we subtract 32:

216 - 32 = 184

Therefore, the value of the given exponential expression 6(4+2)² - 32 is 184.

To determine if the Mean Value Theorem (MVT) applies to the function f(x) = 4x^(1/7) on the interval [-128, 128), we need to check if the function satisfies the conditions of the MVT.

The Mean Value Theorem states that if a function f(x) is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one point c in (a, b) such that f'(c) = (f(b) - f(a))/(b - a).

In this case, the interval is [-128, 128), which is a closed interval. To check if the MVT applies, we need to ensure that the function is continuous on [-128, 128] and differentiable on (-128, 128).

Continuity: The function f(x) = \(4x^(1/7)\) is a power function and is continuous for all x values, including the interval [-128, 128]. Therefore, the function is continuous on the interval.

Differentiability: The function f(x) = \(4x^(1/7)\)is differentiable for all x values except at x = 0. Since the interval (-128, 128) does not include x = 0, the function is differentiable on the interval.

Therefore, both conditions for the MVT are satisfied, and we can conclude that the Mean Value Theorem applies to the function f(x) = \(4x^(1/7)\) on the interval [-128, 128).

Next, we can find or approximate the point(s) that are guaranteed to exist by the Mean Value Theorem.

The Mean Value Theorem guarantees the existence of at least one point c in (-128, 128) such that f'(c) = (f(128) - f(-128))/(128 - (-128)).

Let's calculate the values:

f(128) = \(4(128)^(1/7)\)≈ 4.5534

f(-128) = \(4(-128)^(1/7)\)≈ -4.5534

f'(c) = (4.5534 - (-4.5534))/(128 - (-128)) = 9.1068/256 ≈ 0.0356

Therefore, by the Mean Value Theorem, there exists at least one point c in the interval (-128, 128) such that f'(c) ≈ 0.0356.

Please note that the specific value of c cannot be determined without further analysis or calculations. The Mean Value Theorem guarantees its existence but does not provide an exact value.

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In chapter 6 of Lord of the Flies, Ralph is insistent on the need to search for the beast and maintain the fire as a means of survival and rescue.

However, Jack and the boys have other ideas. They want to spend their time playing and having fun instead of focusing on practical matters. Some of the suggestions made by Jack and the boys include staying up and telling ghost stories, going for a swim, going back to the beach, or playing at the fort. These activities may provide temporary enjoyment for the boys, but they do not address the pressing issues of survival and rescue. As the story unfolds, it becomes clear that Jack and Ralph have fundamentally different priorities, which ultimately leads to a clash between them and the formation of two rival factions on the island.

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Answer:

\(b. \: \: 32\)

Step-by-step explanation:

\(4(x - 2)\)

\(4(10 - 2)\)

\(4(8)\)

\(32\)

Answer:

A

Step-by-step explanation:

hi! this is modus ponens. modus ponens is a form of assumption, and modus tollens denies the initial statement. modus ponens is like saying if A, then B occurs as well. if A is proven to be true, B must also be true. this makes sense in this situation because it says if an animal is a dog, then it barks (if A, then B). the animal barks, so it is a dog (A is true, so B must also be true).

hope this helps!

A) x = 0

B) x = 1 or 0

Part A; (7²)ˣ = 1

From Laws of indices, we know that any number raised to the power of 0 equals 1.

Thus; 7⁰ = 1

We now have;

(7²)ˣ = 7⁰

Opening the bracket, 2 will multiply x to give;

= 7⁰

Both powers will be equal because their base numbers are equal.

Thus; 2x = 0

x = 0

Part B;

= 1

Like in Part A, 7⁰ = 1

Thus;

1ˣ = 1⁰

Equating both powers; x = 0

Again, x could also be gotten from;

1ˣ = 1¹

x = 1

This is because 1¹ is still equal to 1.

x = 1 or 0

Answer:

\(A) a^{2} +a\)

Step-by-step explanation:

\(a^{2} -1\\a+1\)
____

\(a^{2}+a\)

Hope this helps

Answer: 34/9

Step-by-step explanation:

5  2/3  /   3/2

= 17/3  /   3/2

=17/3 x 2/3        [reciprocal]

=34/9

Hope it helped u,

pls mark as the brainliest

^_^

Answer:

7  1/6

Step-by-step explanation:

just simple division, Hope this helps!

On using the implicit differentiation the equation of the tangent line the the curve "x² + 2xy - y² + x = 39" at the point (5,9) is 29x - 8y = 73  .

The equation of the curve is  x² + 2xy - y² + x = 39 ;

to find the equation of the tangent , we differentiate the curve with respect to "x" ,

On differentiation ,

We get ,

⇒ d/dx (x² + 2xy - y² + x) = 0 ,

⇒ 2x + 2y + 2x(dy/dx) - 2y(dy/dx) + 1 = 0 ,

⇒ dy/dx = (1 + 2x + 2y)/(2y - 2x) ....equation(1)

We know that the equation of tangent at the point (x₀,y₀) is given as : ⇒ y = y₀ + y'(x₀)(x - x₀) ...equation(2)

where x₀ = 5 and y₀= 9

So from equation(1) , y'(x₀) = (1 + 10 + 18)/(18 - 10) = 29/8 ,

Then equation(2) becomes , y = 9 + 29/8(x - 5) ,

⇒ y = (29/8)x - (73/8) ,

⇒ 29x - 8y = 73 .

Therefore , the equation of the tangent line is 29x - 8y = 73 .

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The given question is incomplete , the complete question is

How do you use implicit differentiation to find an equation of the tangent line to the curve x² + 2xy - y² + x = 39 at the given point (5,9)?

Answer:

His conjecture is not logical.

Step-by-step explanation:

If he sold a car to a couple above 30, how did he think only younger people bought cars? He is not logical.

The width of the round cake needs to be approximately 2 times the radius, or about 15.6 inches, to have the same volume as the rectangular prism cake.

A three-dimensional structure with six rectangular faces that are parallel and congruent together is called a rectangular prism. It has a length, width, and height. By multiplying the length, width, and height together, one may get the volume. Contrarily, a cylinder is a three-dimensional shape with two congruent and parallel circular bases. It has a height and a radius, and you can determine its volume by dividing the base's surface area by the object's height. A cylinder has curved edges and no corners while a rectangular prism has straight edges and corners.

The volume of the rectangular cake is given as:

V = length * width * height

Substituting the values we have:

16 * 12 * 3 = 576 cubic inches

Now, for the cylindrical cake to be of the same volume we have:

V = π * radius² * height

π * radius² * 3 = 576

(3.14) * radius² * 3 = 576

radius = 15.6 inches

Hence, the width of the round cake needs to be approximately 2 times the radius, or about 15.6 inches, to have the same volume as the rectangular prism cake.

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There are no like terms.

Answer:

=r−8s−5

This equation is a second degree equation that has a solution of 7.

To find a second degree equation with a solution of 7, we can use the fact that the solutions of a quadratic equation are given by the quadratic formula: x = (-b ± √(b^2 - 4ac))/(2a).
Since we want the solution to be 7, we can set x = 7 in the quadratic formula and solve for the other variables.
First, let's set x = 7 and simplify the equation: 7 = (-b ± √(b^2 - 4ac))/(2a).
Next, let's multiply both sides of the equation by 2a to eliminate the fraction: 14a = -b ± √(b^2 - 4ac).
Now, let's square both sides of the equation to get rid of the square root: (14a)^2 = (-b ± √(b^2 - 4ac))^2.
Expanding both sides of the equation gives: 196a^2 = b^2 ± 2b√(b^2 - 4ac) + (b^2 - 4ac).
Simplifying further, we have: 196a^2 = 2b^2 ± 2b√(b^2 - 4ac) - 4ac.
Now, we can rearrange the equation to have all terms on one side: 2b^2 ± 2b√(b^2 - 4ac) + 4ac - 196a^2 = 0.
In summary, the second degree equation that has a solution of 7 is 2b^2 ± 2b√(b^2 - 4ac) + 4ac - 196a^2 = 0.

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Answer:

Math Expert Answer

Step-by-step explanation:

So toms equation is y= 4x + 6 and addisons equation is y=10x so they will meet eachother in 1 hour. You can use a desmos calculator to input the equations for the answer

Answer:

1 hour

Step-by-step explanation:

Let's set up an equation for Tom's and Addison's distances: T(x) = 4x + 6, A(x) = 10x, where x is the amount of time since Addison started (in hours).

We solve for A(x) = T(x) and get:

10x = 4x + 6 → subtract 4x from both sides

6x = 6 → divide both sides by 6

x = 1

Therefore, it took Addison 1 hour to catch up with Tom

Answer:

Sarah has greatest percentage of heads

Answer:

Sarah.

Alice had 75 percent

Mary had 80 percent

Ellen had 60 percent

while Sarah got 85 percent

Step-by-step explanation:

Mary 8 out of 10 is technically 8/10 and fractions are division problems so 8/10 is 0.8 times 10 is 80 same goes for the rest of them, divide then multiply by 10

Answer:

The resultant velocity is 12.21 m/s.

Step-by-step explanation:

We are given that the water from a fire hose follows a path described by y equals 2.0 plus 0.9 x minus 0.10 x squared ​(units are in​ meters).

Also, v Subscript x is constant at 10.0 ​m/s.

The water from a fire hose follows a path described by the following equation below;

\(y=2.0 + 0.9x-0.10x^{2}\)

The velocity of the \(x\) component is constant at =  \(v_x=10.0 \text{ m/s}\)

and the point at which resultant velocity has to be calculated is (9.0,2.0).

Let the velocity of x and y component be represented as;

\(v_x=\frac{dx}{dt} \text{ and } v_y=\frac{dy}{dt}\)

Now, differentiating the above equation with respect to t, we get;

\(y=2.0 + 0.9x-0.10x^{2}\)

\(\frac{dy}{dt} =0 + 0.9\frac{dx}{dt} -(0.10\times 2)\frac{dx}{dt}\)

\(\frac{dy}{dt} = 0.9\frac{dx}{dt} -0.2\frac{dx}{dt}\)

\(v_y = 0.9v_x -0.2v_x\)

\(v_y = 0.7v_x\)

Now, putting \(v_x=10.0 \text{ m/s}\) in the above equation;

\(v_y = 0.7 \times 10.0\) = 7 m/s

Now, the resultant velocity is given by = \(v=\sqrt{v_x^{2}+v_y^{2} }\)

                            \(v=\sqrt{10^{2}+7^{2} }\)

                               = \(\sqrt{149}\) = 12.21 m/s

Answer:

4n^2

Step-by-step explanation:

n to the power of 2 (squared), multiplied by 4

\(4n^{2}\)

An algebraic expression is one that is constructed using integer constants, variables, and algebraic operations.

Any of the common arithmetic operations, such as addition, subtraction, multiplication, division, raising to a whole number power, and taking roots, is a basic algebraic operation.

Square of \(n=n^{2}\)

Four times the square of \(n^{2}\) is equal to \(4n^{2}\)

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(a) Mean = (9 + 15 + 18 + 11 + 12) / 5 = 65 / 5 = 13

(b) Mean of the sample = (9 + 15) / 2 = 24 / 2 = 12

(c) The means of the samples vary, but they tend to be close to the population mean of 13.

(d) Since the problem does not provide the values for the 25 x values, we cannot construct a density histogram or determine if most of the values are near the population mean.

(a) The mean of the population is calculated by summing all the values and dividing by the total number of values:

Mean = (9 + 15 + 18 + 11 + 12) / 5 = 65 / 5 = 13

(b) To calculate the mean for a random sample of size 2, we randomly select two values from the population and calculate their mean:

Random sample: 9, 15

Mean of the sample = (9 + 15) / 2 = 24 / 2 = 12

(c) Repeatedly selecting random samples of size 2 and calculating the mean for each sample:

Here are the means for 25 random samples of size 2 (selected without replacement):

Sample 1: 9, 18 -> Mean = (9 + 18) / 2 = 27 / 2 = 13.5

Sample 2: 11, 9 -> Mean = (11 + 9) / 2 = 20 / 2 = 10

Sample 3: 15, 12 -> Mean = (15 + 12) / 2 = 27 / 2 = 13.5

...

Sample 25: 12, 15 -> Mean = (12 + 15) / 2 = 27 / 2 = 13.5

The means of the samples vary, but they tend to be close to the population mean of 13.

(d) Constructing a density histogram using the 25 x values:

Since the problem does not provide the values for the 25 x values, we cannot construct a density histogram or determine if most of the values are near the population mean.

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