What is the derivative of x(t)? X(t)= 1- CosCWnt)/Wn2 1- CosWn(t-1))/Wn2 1- CoscWilt-T2/Wn2

The matrix A must have the following form:
A = [ a11 a12 a13 a14 ]
   [ a21 a22 a23 a24 ]
   [ a31 a32 a33 a34 ]
   [ a41 a42 a43 a44 ]
   [ a51 a52 a53 a54 ]

In order for a matrix A to define a mapping from R4 into R5 by the rule T(x) = Ax, the matrix A must have 5 rows and 4 columns.

This is because the number of rows in the matrix determines the dimension of the output space, while the number of columns determines the dimension of the input space. In this case, the output space is R5 and the input space is R4, so the matrix must have 5 rows and 4 columns.

In general, if a matrix A is used to define a mapping from Rn into Rm by the rule T(x) = Ax, then the matrix A must have m rows and n columns.

So, the matrix A must have the following form:

A = [ a11 a12 a13 a14 ]
   [ a21 a22 a23 a24 ]
   [ a31 a32 a33 a34 ]
   [ a41 a42 a43 a44 ]
   [ a51 a52 a53 a54 ]

where each aij is a scalar.

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The simplification of the expression is  \(\frac{15\sqrt{2} }{4}\)

First, find the factors of the number that ahs square root

Given,

= \(\frac{5}{\sqrt{2} } + \frac{9}{\sqrt{6} } - \frac{2}{\sqrt{50} } + \sqrt{32}\)

Multiply the numerators by the surd of the denominators

= \(\frac{5 *\sqrt{2} }{\sqrt{2}*\sqrt{2 } } + \frac{9 *\sqrt{8} }{\sqrt{8}* \sqrt{8} } - \frac{2 *\sqrt{50} }{\sqrt{50 * \sqrt{50} } } + \sqrt{32}\)

Multiply through and find their square root

= \(\frac{5\sqrt{2} }{2} + \frac{18\sqrt{2} }{8 } - \frac{10\sqrt{2} }{50} + 16\sqrt{2}\)

To simply, we have

= \(\frac{5\sqrt{2} }{2}+ \frac{9\sqrt{2} }{4} + \frac{1\sqrt{2} }{5} + 16\sqrt{2}\)

Find the LCM

= \(\frac{10\sqrt{2} + 45\sqrt{2}+ 4\sqrt{2} + 16\sqrt{2} }{20}\)

Add through

= \(\frac{75\sqrt{2} }{20}\)

= \(\frac{15\sqrt{2} }{4}\)

Thus, the simplification of the expression is  \(\frac{15\sqrt{2} }{4}\)

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Answer:

7

Step-by-step explanation:

6² = 36 and 7² = 49

47 is between 36 and 49, but it is closer to 49. Therefore, the answer would be 7.

Answer: I don't know how to type the infinity symbol on my phone but..

(-infinity, -5)

Basically x can be anything less than -5.

Answer:

1

Step-by-step explanation:

Any number multiplied by its reciprocal is equal to 1.

\(-\frac{14}1 \times -\frac1{14} = 1\)

\(\frac{1}{2} (n+8) + \frac{3}{4} \)

\(\frac{1(n+8)}{2} + \frac{3}{4} \)

\(\frac{n+8}{2} + \frac{3}{4} \)

\(\frac{2(n+8)}{4} + \frac{3}{4} \)

\(\frac{2(n+8) + 3}{4} \)

\(\frac{2n + 16 +3}{4} \)

\( \frac{2n + 19}{4} \)

Explanation: To solve this question we just need to substitute the x and y values from each point into the equation, if the equality is true it means the point is on the graph but if the equality is wrong it means the point is not on the graph of the equation.

Step 1: Let's substitute the values for each of the points and calculate as follows

Final answer: So the points on the graph are (0,-2) and (8,2).

Answer:

-2

Step-by-step explanation:

Three times the sum of a number and ten is twenty-four.​

3 x (n + 10) = 24

24 / 3 = 8

n + 10 = 8

-2 + 10 = 8

3 x (-2 + 10) = 24

3 x 8 = 24

Answer:

\( - 2\)

Step-by-step explanation:

do the math

There are 30 of 1/10's in the number 3

From the question, we have the following parameters that can be used in our computation:

How many 1/10's are in 3?​

The above statement is a quotient expression that has the following features

Dividend = 3

Divisor = 1/10

So, we have

Quotient = Dividend /Divisor

Substitute the known values in the above equation, so, we have the following representation

Quotient = 3/(1/10)

Evaluate

Quotient = 30

Hence, there are 30 1/10's

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To solve for d:

1. Remove parenthesis:

2. Leave the terms with d in one side of the equation:

-Add 1.2 in both sides of the equation:

-Substract 0.3d and 0.1d in both sides of the equation:

3. Opperate similar terms:

4. Divide into (-0.2) both sides of the equation:

Using the SSA method, the maximum number of triangles that can be generate is 1.

In the given question,

In SSA case for an obtuse angle, we have to find the maximum number of triangles that can be generate with the given information.

As we know that,

There cannot be a second obtuse angle if the specified first angle is already obtuse since the triangle's angle total would be greater than 180°. As a result, there is only one way to construct the triangle, making SSA a valid congruence theorem when the supplied angle is acute.

So the maximum number of triangles that can be generate is 1.

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Answer:

5/12

Step-by-step explanation:

The required fraction form of the expression 3 / 4 - 1 / 3 is 5 / 12

The process in mathematics to operate and interpret the function to make the function simple or more understandable is called simplifying and the process is called simplification.

Fraction is defined as the number of compositions that constitute the Whole. Fraction Is represented as x = a / b where a is the numerator and b is the denominator.

Question asked to write the given expression3/4 - 1/3 in fraction form

Let the required fraction be x,
x = 3 / 4 - 1 / 3
x = ( 9 - 4 ) / 15
x = 5 / 12

Thus , The required fraction form of the expression 3 / 4 - 1 / 3 is 5 / 12.

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To find the unknown values in a right-angled triangle, such as the length of one side (a), we need additional information. Without specific measurements or relationships provided, the value of a cannot be determined.

In a right-angled triangle, the side lengths are typically denoted as a, b, and c, where a and b are the lengths of the two shorter sides (legs) and c is the length of the hypotenuse. To find the length of side a, we typically need either the lengths of the other sides (b and c), or additional information such as angles or ratios involving the sides.

The calculation of side lengths in a right-angled triangle often relies on trigonometric functions like sine, cosine, or tangent, or the Pythagorean theorem. These relationships allow us to solve for unknown side lengths when given certain measurements or angles.

Without specific values for side b or any additional relationships or measurements provided, it is not possible to determine the length of side a in the right-angled triangle. The determination of side lengths in a right-angled triangle requires further information or the application of relevant formulas or relationships associated with right triangles.

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Step-by-step explanation:

By 2 point form

y-y1= m(x-x1)

y-2 = -3(x-1)

y-2=-3x+3

3x+y=5... this is the required line

The average value of the function f(x) = \(9 - x^2\) over the interval [-3, 3] is 6.0000. The values of x in the interval for which the function equals its average value are x = -2.4495 and x = 2.4495.

To find the average value of a function over an interval, we need to calculate the definite integral of the function over the interval and divide it by the length of the interval. In this case, we have the function

f(x) = \(9 - x^2\) and the interval [-3, 3].

First, we calculate the definite integral of f(x) over the interval [-3, 3]:

\(\(\int_{-3}^{3} (9 - x^2) \, dx = \left[9x - \frac{x^3}{3}\right] \bigg|_{-3}^{3}\)\)

Evaluating the definite integral at the upper and lower limits gives us:

\(\((9(3) - \frac{{3^3}}{3}) - (9(-3) - \frac{{(-3)^3}}{3})\)\)

= (27 - 9) - (-27 + 9)

= 18 + 18

= 36

Next, we calculate the length of the interval:

Length = 3 - (-3) = 6

Finally, we divide the definite integral by the length of the interval to find the average value:

Average value = 36/6 = 6.0000

To find the values of x in the interval for which the function equals its average value, we set f(x) equal to the average value of 6 and solve for x:

\(9 - x^2 = 6\)

Rearranging the equation gives:

\(x^2 = 3\)

Taking the square root of both sides gives:

x = ±√3

Rounding to four decimal places, we get:

x ≈ -2.4495 and x ≈ 2.4495

Therefore, the values of x in the interval [-3, 3] for which the function equals its average value are approximately -2.4495 and 2.4495.

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To make a model of corresponding angles using toothpicks or straws, you can take two pieces of the material and place them next to each other at the same angle.

When two parallel lines are intersected by another line, corresponding angles are the angles that are created in matching corners or corresponding corners with the transversal.

To make a model of co-interior angles, you can place the two pieces of material on top of each other, with one inside the other at the same angle. To make a model of alternate angles, you can place the two pieces of material on opposite sides of a straight line, with one angle facing up and the other angle facing down.

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Complete question

make a model of corresponding angles using toothpicks or straws

Using simple mathematical operations, we know that 8% of sugar is used in 4 cups.

So, % of sugar used in 4 cups:

So, % of sugar Kim used:

Therefore, using simple mathematical operations, we know that 8% of sugar is used in 4 cups.

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Aya can make 14 mats of 1 foot long.

Division is one of the fundamental arithmetic operation, which is performed to get equal parts of any number given, or finding how many equal parts can be made. It is represented by the symbol "÷" or sometimes "/"

Given that, Aya has 14\(\frac{2}{5}\) feet of chain. She wants to make pieces foot long mat.

Let can make x mats out of the given chain, since each mat is 1 foot long, so,

1×x =  14\(\frac{2}{5}\)

x = 72/5

x = 14.4

x ≈ 14

Hence, She can make 14 mats out of the given chain.

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Answer: 122°

Step-by-step explanation:

Because angles on a straight line are supplementary (add up to 180°), then:

m∠2 = 180° - 58°

        = 122°

The plot of y(t) will show how the mass oscillates with time, starting from the equilibrium position and gradually coming to rest due to the damping effect of the friction.

The given equation represents the motion of a mass connected to a spring with viscous friction. To plot the displacement, y(t), we need to solve the differential equation. With initial conditions y(0) = 0, we can find the solution using the Laplace transform. After solving the equation, we can plot y(t) for t < 0 and t ≥ 0 separately. For t < 0, the applied force, f(t), is zero, so the mass will not experience any external force and will remain at rest. For t ≥ 0, the applied force is 10, and the mass will respond to this force and undergo oscillatory motion around the equilibrium position.

To solve the given differential equation, we can start by finding the characteristic equation by setting the coefficients of y, its derivative, and its second derivative to zero:

s^2 + 18s + 102 = 0.

Solving this quadratic equation gives us the roots s1 = -3 + 3i and s2 = -3 - 3i. These complex roots indicate that the mass will undergo damped oscillations.

Using the Laplace transform, we can solve the differential equation and obtain the expression for Y(s), the Laplace transform of y(t):

(s^2 + 18s + 102)Y(s) = F(s),

where F(s) is the Laplace transform of f(t). Since f(t) = 10 for t ≥ 0, its Laplace transform is F(s) = 10/s.

Solving for Y(s) gives us:

Y(s) = 10 / [(s^2 + 18s + 102)].

To find y(t), we need to inverse Laplace transform Y(s). Using partial fraction decomposition, we can express Y(s) as:

Y(s) = A / (s - s1) + B / (s - s2),

where A and B are constants to be determined. After finding A and B, we can inverse Laplace transform Y(s) to obtain y(t).

With the given initial condition y(0) = 0, we can solve for A and B by setting up equations using the initial value theorem:

A / (s1 - s1) + B / (s1 - s2) = 0,

A / (s2 - s1) + B / (s2 - s2) = 0.

Solving these equations will give us the values of A and B. Finally, we can substitute these values back into the inverse Laplace transform of Y(s) to obtain y(t).

For t < 0, since the applied force f(t) is zero, the mass will not experience any external force. Therefore, y(t) will remain at its initial position, y(0) = 0.

For t ≥ 0, the applied force f(t) is 10, and the mass will respond to this force and undergo oscillatory motion around the equilibrium position. The displacement, y(t), will depend on the properties of the mass, the spring, and the viscous friction. The plot of y(t) will show how the mass oscillates with time, starting from the equilibrium position and gradually coming to rest due to the damping effect of the friction.

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Answer:

look below

Step-by-step explanation:

a)

x ÷ 60 = num of days

b)

if we substitute x for 280,

280 ÷ 60 = 4.3333...

It will take 4.333 days (4 days 8 hr) to complete the novel.

Answer:

arc XY = 46°

Step-by-step explanation:

The inscribed angle XZY is half the measure of its intercepted arc , then

arc XY = 2 × 23° = 46°

Answer:is that 3i or what?

-

Step-by-step explanation

Answer:

It's answer is d) 9

.........

Answer:

7/12 chance

Step-by-step explanation:

(1 2 3 4 5 6)

(1 2 3 4 5 6)

All the possibilities:

(1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1)

(1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2)

(1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3)

(1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4)

(1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5)

(1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6)

There are 18 odd sums.

(1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1)

(1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2)

(1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3)

(1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4)

(1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5)

(1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6)

There are 3 possibilities whose sums add up to 10.

Since there are 36 total possibilities and 21 numbers that fit the rule of having an odd sum or a sum of 10. There is a 21/36 chance or simplified, 7/12 chance.