In an upcoming cartoon, the hero is a gymnast. In one scene he swings around a high bar. Describe the rotation matices that would be needed so four frames of the movie would show the illustrated motion (below), one frame after the other.


a. What do you need to do first to describe the motion?

b. Can you use just one rotation matrix, or do you need three?

Answer:

.2 miles per minute or .2x

Step-by-step explanation:

it move one tenth in half a minute so it moves 2 tenths in a minute.

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

The slope of the tangent line to the graph of the function y = x^4 - 10x^2 + 9 at x = 1 can be found by taking the derivative of the function and evaluating it at x = 1. The equation of the tangent line can then be determined using the point-slope form.

Taking the derivative of the function y = x^4 - 10x^2 + 9 with respect to x, we get:

dy/dx = 4x^3 - 20x

To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative:

dy/dx (at x = 1) = 4(1)^3 - 20(1) = 4 - 20 = -16

Therefore, the slope of the tangent line is -16.

To find the equation of the tangent line, we use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Given that the point of tangency is (1, y(1)), we substitute x1 = 1 and y1 = y(1) into the equation:

y - y(1) = -16(x - 1)

Expanding the equation and simplifying, we have:

y - y(1) = -16x + 16

Rearranging the equation, we obtain the equation of the tangent line:

y = -16x + (y(1) + 16)

To find the slope of the tangent line, we first need to find the derivative of the given function. The derivative represents the rate of change of the function at any point on its graph. By evaluating the derivative at the specific value of x, we can determine the slope of the tangent line at that point.

In this case, the given function is y = x^4 - 10x^2 + 9. Taking its derivative with respect to x gives us dy/dx = 4x^3 - 20x. To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative equation, resulting in dy/dx = -16.

The slope of the tangent line is -16. This indicates that for every unit increase in x, the corresponding y-value decreases by 16 units.

To determine the equation of the tangent line, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1). We know the point of tangency is (1, y(1)), where x1 = 1 and y(1) is the value of the function at x = 1.

Substituting these values into the point-slope form, we get y - y(1) = -16(x - 1). Expanding the equation and rearranging it yields the equation of the tangent line, y = -16x + (y(1) + 16).

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

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The terms denοminatοr and numeratοr are nοt directly related tο a mοdel unless the mοdel invοlves a fractiοn οr a ratiο.

The denοminatοr and numeratοr are terms οften used in mathematics and fractiοns. In a fractiοn, the numeratοr is the tοp number, and the denοminatοr is the bοttοm number. The numeratοr represents the number οf parts being cοnsidered οr cοunted, while the denοminatοr represents the tοtal number οf parts in the whοle.

The terms denοminatοr and numeratοr are nοt directly related tο a mοdel unless the mοdel invοlves a fractiοn οr a ratiο.

Hοwever, in statistical mοdels, the dependent and independent variables can be thοught οf as the numeratοr and denοminatοr οf a ratiο οr a fractiοn. The dependent variable represents the numeratοr, the number οf events οr οbservatiοns οf interest, while the independent variable represents the denοminatοr, the tοtal number οf events οr οbservatiοns.

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Answer:

The distributive property here is to just multiply each value by tree number outside the parenthesis.

3 ( 4x - 2t)

12x - 6t

That would be your answer.

Answer:

Remember that a number divided by itself is 1. That means if the numerator and denominator are the same, the fraction is equal to 1. So all of the following are equal to 1: 2/2, 3/3, 4/4, and so on.

Step-by-step explanation:

Please Mark me as a brainest

The result of the expression 4.44 x 10⁷ ÷ 2.25 x 10⁵ is 1.973 x 10² in scientific notation.

What is meant by expression?

An expression is a combination of numbers, symbols, and operators that represents a mathematical quantity or relationship. It may contain variables, constants, and functions, and can be evaluated or simplified to obtain a numerical or symbolic value.

According to the given information

To divide two numbers in scientific notation, we need to divide their coefficients and subtract their exponents.

Using this formula, we can simplify the given expression as follows:

(4.44 x 10⁷) ÷ (2.25 x 10⁵) = (4.44 ÷ 2.25) x 10^(7-5) = 1.973 x 10²

Therefore, the result of the expression 4.44 x 10⁷ ÷ 2.25 x 10⁵ is 1.973 x 10² in scientific notation.

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The result of the calculation is approximately 197.33. Written in scientific notation, it is 1.97333 x 10².

What is an arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term. For example, the sequence 2, 5, 8, 11, 14, ... is an arithmetic sequence with a common difference of 3, since each term after the first is found by adding 3 to the preceding term.

The nth term of an arithmetic sequence can be found using the formula:

an = a1 + (n-1)d

To divide two numbers written in scientific notation, we divide their coefficients (the numbers before the "x 10^") and subtract their exponents. So, for this calculation, we have:

(4.44 x 10⁷) ÷ (2.25 x 10⁵) = (4.44 ÷ 2.25) x 10^(7-5) = 1.973333... x 10²

Therefore, the result of the calculation is approximately 197.33. Written in scientific notation, it is 1.97333 x 10².

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Answer:

Waves transfer energy, but not matter.

Waves transfer energy from one point to another without moving matter.

i hoped this helped

Answer:

Median Range IQR

Northside players. 37 33. 17

Southside players. 37. 43. 30

Answer:

−7x^2+4x+6

Step-by-step explanation:

HOPE THIS HELPS!!!!

Answer: =−7x2+4x+6

Step-by-step explanation: distribute the Negative Sign:

=−7x2+3+−1(−4x−3)

=−7x2+3+−1(−4x)+(−1)(−3)

=−7x2+3+4x+3

Combine Like Terms:

=−7x2+3+4x+3

=(−7x2)+(4x)+(3+3)

=−7x2+4x+6

Answer:

=−7x2+4x+6

The mathematical expression y(x,t) = Asin(kx)sin(wt) provides a way to describe the behavior of a standing wave in terms of its amplitude, frequency, and location along the string.

At time t=0,

the standing wave can be mathematically expressed as

y(x,0) = Asin(kx)sin(w*0) = Asin(kx)sin(0) = 0.

This means that the displacement of the string is zero at time t=0.

However, it is important to note that this does not mean that the string is not moving at all. Rather, it means that the string is in a state of equilibrium at time t=0, with the maximum transverse displacement being A.

As time progresses, the standing wave will oscillate between the maximum positive and negative transverse displacement values, creating a pattern of nodes (points of zero displacements) and antinodes (points of maximum displacement).

The wave number k and angular frequency w are both constants that are dependent on the physical properties of the string and the conditions under which the wave is being produced.

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If he arranges them into 6 equal rows, 4 posters will be in each row.

One of the fundamental arithmetic operations in mathematics is the division, which is the process of dividing a group of items into equal pieces. Every day, we might employ the division approach in various situations. Fraction division differs significantly from natural number division. We must change the division operator into a multiplication operator when dividing fractions. Therefore, the dividend should be multiplied by the inverted divisor.

Given,

Total posters = 24

Arranging them into 6 equal rows,

Dividing:

24÷ 6

Reciprocating,

24 × 1/6

4

If he arranges them into 6 equal rows, 4 posters will be in each row.

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Answer:

False.

6 miles is farther than 6 kilometers. One mile is equal to 1.60934 kilometers, so 6 miles is equal to 6 x 1.60934 = 9.65604 kilometers. Therefore, 6 miles is farther than 6 kilometers.

Step-by-step explanation:

The answer is:

Work/explanation:

We can't really compare two things if they have different units.

So we need to convert kilometers to miles first.

1 km is approximately equal to 0.621 miles.

So 6 km would be approximately 3.728 miles.

6 miles is further away than 3.728 miles.

6 km is not as far as 6 miles. And now we know why.

The rate of change is -1/2

Initial point is (-2,-1)

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

Consider any two pairs of points:

(-2,-1)  and (0,-2)

The slope is the same as the rate of change

Rate of change = change in y values/change in x values

                         = (-2 - (-1) ) / (0-(-2))

                         = ( -2 + 1) / (+2)  

Rate of change  = (-1/2)

The rate of change is -1/2

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Answer:

y = 5/4 x + 9

y = -5x+4

Step-by-step explanation:

a)The equation of the line in slope intercept form is expressed as y = mx+b

m is the slope

b is the intercept

Given

Slope m = 5/4

y-intercpet = 9

Substitute

y = mx+b

y = 5/4 x + 9

b) Given the coordinates (0,4) and (2, -6)

Slope m = -6-4/2-0

m = -10/2

m = -5

Since the y intercept of the line is (0, 4), hence b = 4

Get the equation

Recall

y = mx+b

y = -5x +4

This gives the required equation

The compound inequality for the given situation is $2.75x + $4.25y ≥ $65 and $2.75x + $4.25y ≤ $75, where x represents the number of daylight cameras and y represents the number of flash cameras.

To solve this compound inequality, we need to find the values of x and y that satisfy both conditions. The inequality $2.75x + $4.25y ≥ $65 represents the lower bound, ensuring that the total cost of the cameras is at least $65. The inequality $2.75x + $4.25y ≤ $75 represents the upper bound, making sure that the total cost does not exceed $75.

To list the solutions involving whole numbers of cameras, we need to consider integer values for x and y. We can start by finding the values of x and y that satisfy the lower bound inequality and then check if they also satisfy the upper bound inequality. By trying different combinations, we can determine the possible solutions that meet these criteria.

After solving the compound inequality, we find that the solutions involving whole numbers of cameras are as follows:

(x, y) = (10, 10), (11, 8), (12, 6), (13, 4), (14, 2), (15, 0), (16, 0), (17, 0), (18, 0), (19, 0), (20, 0).

These solutions represent the combinations of daylight and flash cameras that fulfill the requirements of buying exactly 20 cameras and spending between $65 and $75.

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Answer:

D

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

used graphing calculator

The given expression is 4(8x + 5). This is a product of a coefficient and a binomial expression. In mathematics, a binomial is a polynomial with two terms.

They are represented as ax + b or a + bx or (a + b) etc. Given expression is 4(8x + 5). We can simplify this by applying the distributive property. It is given as follows; The distributive property of multiplication states that a(b + c) = ab + ac To simplify the given expression, we need to multiply the coefficient 4 with each term in the parentheses.

It can be done as follows; 4(8x + 5) = 4*8x + 4*5 We multiply 4 with 8x and 4 with 5 to obtain; 32x + 20 This is the main answer. Therefore, the simplified form of 4(8x + 5) is 32x + 20. To simplify the given expression 4(8x + 5), we can use the distributive property. According to this property, the product of a number with the sum of two or more terms is equal to the sum of the products of that number with each term of the sum. In other words, a(b + c + …) = ab + ac + … In the given expression, 4 is multiplied with the binomial (8x + 5). Hence,

4(8x + 5) = 4*8x + 4*5

= 32x + 20

Hence, the simplified form of 4(8x + 5) is 32x + 20.

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A parameter can change for a set population when there is a change in the population distribution or when the population is no longer considered "set". A parameter is a fixed numerical characteristic of a population that is measured by a statistic.

When there is a change in the distribution of a population, the parameter that describes the population will change. For example, the mean of a population will change if there is a shift in the distribution of scores. Similarly, the standard deviation will change if there is a change in the variability of scores.

A parameter can also change if the population is no longer considered "set". For example, if a population is defined as all the residents of a particular city, the parameter will change if people move in or out of the city. In this case, the parameter can be thought of as a snapshot of the population at a particular point in time.

In conclusion, a parameter can change for a set population when there is a change in the population distribution or when the population is no longer considered "set".

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Answer:

Yes, it is representative because each type of book was represented in the approximate proportion that exists in the library.

Step-by-step explanation:

Given is a chart, showing the distribution of the number of books in a library.

Also given that Sahira chooses a random sample from the library and records the type of books in the chart below.

Sahira's sample can be said to be representative because given that books are taken at random.  So just because literacy books were more we cannot say it is not representative  II option is not right, because each book was not chosen uniquely, just random books were drawn

Lastly The Answer is C) Yes, it is representative because each type of book was represented in the approximate proportion that exists in the library is right, because each book selected represents the sample from population of full library books.

Answer:

it is c

Step-by-step explanation:

just did it

Answer: I believe he could wear 768 outfits

Step-by-step explanation: I had a similar question consisting of the same numbers.

Answer:

1

Step-by-step explanation:

Using the sum to product formulae and the exact values

sin x + sin y = 2sin(\(\frac{x+y}{2}\) )cos(\(\frac{x-y}{2}\) )

cos x + cos y = 2cos(\(\frac{x+y}{2}\) )cos(\(\frac{x-y}{2}\) )

sin45° = cos45° = \(\frac{1}{\sqrt{2} }\) , cos30° = \(\frac{\sqrt{3} }{2}\)

Given

\(\frac{sin75+sin15}{cos75+cos15}\)

= \(\frac{2sin(\frac{75+15}{2})cos(\frac{75-15}{2}) }{2cos(\frac{75+15}{2})cos(\frac{75-15}{2}) }\)

= \(\frac{2si45cos30}{2cos45cos30}\)

= (2 × \(\frac{1}{\sqrt{2} }\) × \(\frac{\sqrt{3} }{2}\) ) ÷ (2 × \(\frac{1}{\sqrt{2} }\) × \(\frac{\sqrt{3} }{2}\) )

= 1

Answer:  1

Step-by-step explanation:

sin 75 = sin(30 + 45) = sin30 · cos45  + cos30 · sin45

                                 \(=\dfrac{1}{2}\cdot \dfrac{\sqrt2}{2}+\dfrac{\sqrt3}{2}\cdot\dfrac{\sqrt2}{2}\qquad =\dfrac{\sqrt2+\sqrt6}{4}\)

sin 15 = sin(45 - 30) = sin45 · cos30  - cos45 · sin30

                                  \(=\dfrac{\sqrt2}{2}\cdot \dfrac{\sqrt3}{2}-\dfrac{\sqrt2}{2}\cdot\dfrac{1}{2}\qquad =\dfrac{\sqrt6+\sqrt2}{4}\)

cos 75 = cos(30 + 45) = cos30 · cos45  - sin30 · sin45

                                   \(=\dfrac{\sqrt3}{2}\cdot \dfrac{\sqrt2}{2}-\dfrac{1}{2}\cdot\dfrac{\sqrt2}{2}\qquad =\dfrac{\sqrt6-\sqrt2}{4}\)

cos 15 = cos(45 - 30) = cos45 · cos30  + sin45 · sin30

                                   \(=\dfrac{\sqrt2}{2}\cdot \dfrac{\sqrt3}{2}+\dfrac{\sqrt2}{2}\cdot\dfrac{1}{2}\qquad =\dfrac{\sqrt6+\sqrt2}{4}\)

       \(\dfrac{\sin 75+\sin 15}{\cos 75+\cos 15}\)

   \(=\dfrac{\frac{\sqrt2+\sqrt6}{4}+\frac{\sqrt6-\sqrt2}{4}}{\frac{\sqrt6-\sqrt2}{4}+\frac{\sqrt6+\sqrt2}{4}}\\\\\\=\dfrac{\frac{\sqrt6}{2}}{\frac{\sqrt6}{2}}\\\\\\=1\)

Any height below the ground level is usually considered to be negative while any one above the ground level is usually considered to be positive.

Depth of first level of parking garage = 21.4 ft

149.8/7 = 21.4 ft

Height of each floor = 21.4 ft

This will also be the same depth of the first floor.

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Answer:

21.4 ft

Step-by-step explanation:

its the answer no need to explain

The segment FG is reflected by the rule (x, y) → (-x, y). Hence, option C is the correct answer.

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century. In geometry, object transformations constitute the foundation for the majority of proofs. Transformations allow us to change any image in a coordinate plane. The rules of transformations can be utilised to better understand the images used in video games.

The transformation, or f: X X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation.

FG has points at F(-6, -3) and G(-3, 6), and F'(6, -3) and G'(3, 6).

It is reflected by the rule (x, y) → (-x, y).

Hence, option C is the correct answer.

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The formula for the interior angles is (3-2)180 which equals 180 degrees

It is important to note the properties of a polygon. They include;

A triangle is a two-dimensional shape and has three sides, thus, it is a polygon.

The formula for calculating the sum of the interior angles of any polygon is expressed as;

Sum of interior angles = (n-2)180

where, n is the number of sides

Substitute the number of sides as 3

Sum of interior angles = (3-2)180

expand the bracket

Sum of interior angles = 180 degrees

Hence, a triangle has a measure of 180 degrees

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The latest time for pickup, found by converting the 150 minutes maximum time provided by the school, from minutes to hours is about 5:45 pm

Minutes can be converted into hours by dividing the number of minutes by 60, which is the number of minutes in an hour.

The time that school ends = 3:15 pm

The latest time for pick up after school care = 150 minutes after school ends

Therefore, the latest time for pick up after school care = 3:15 pm + 150 minutes

60 minutes = 1 hour

150 minutes = (1/60) × 150 = 2.5

The latest for pick up = 3:15 pm + 2.5 hours = 5:45 pm

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There are 99 students who speak all three languages: Mandarin, Japanese, and Korean. The minimum number of students who speak all three languages is 99.

The method used to solve this problem is based on set theory, which is a branch of mathematics that deals with the study of sets, their properties, and their relationships with one another. Specifically, the principle of inclusion-exclusion, which is used in this problem, is a counting technique that is often used in combinatorics and probability theory, which are also branches of mathematics.

Let X be the number of students who speak all three languages.

Then we have:

Number of students who speak only Mandarin = 174 - 102 - 81 - X = -9 - X (since there cannot be a negative number of students)

Number of students who speak only Japanese = 139 - 102 - 71 - X = -34 - X (since there cannot be a negative number of students)

Number of students who speak only Korean = 112 - 81 - 71 - X = -40 - X (since there cannot be a negative number of students)

Number of students who speak only one language = -9 - X + (-34 - X) + (-40 - X) = -83 - 3X (since there cannot be a negative number of students)

Total number of students who speak at least one language = 268 - 37 = 231

Therefore, the number of students who speak all three languages is:

Total number of students who speak at least one language - Number of students who speak only one language - Number of students who do not speak any of the three languages

= 231 - (-83 - 3X) - 37

= 297 + 3X

Since the number of students who speak all three languages cannot be negative, we have:

297 + 3X ≥ 0

3X ≥ -297

X ≥ -99

Therefore, the minimum number of students who speak all three languages is 99.

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The second Taylor polynomial P₂(x) has a minimum error of 0 when x = 0.5. To find the actual error in using P₂(0.5) to approximate f(0.5), find the value of c and make necessary adjustments to the original equation.

The function f(x) = x³ is a second Taylor polynomial with a first derivative of f'(x) = 3x² and a second derivative of f''(x) = 6x. The second Taylor polynomial P₂(x) about x₀ = 0 is 3x². To find the actual error in using P₂(0.5) to approximate f(0.5), we can use Lagrange's form of the remainder term and Lagrange's form of the fourth derivative of f(x) = 24c. The fourth derivative of f(x) is fⁿ⁺¹(c) = 24c, and the fourth derivative of f(x) is fⁿ⁺¹(c) = 24c.

To find the actual error in using P₂(0.5) to approximate f(0.5), we need to find the value of c such that the actual error E = |R₂(0.5)| is minimum. Substituting x = 0.5 in the third derivative of f(x), we get f'''(0.5) = 6(0.5) = 3. Substituting this value of f'''(c) in the remainder term formula, we get |R₂(0.5)| = 2c/3, which is between 0 and 0.5. To make E minimum, we must make |R₂(0.5)| minimum, which occurs when c = 0. Substituting c = 0 in R₂(0.5) = -4c/3, we get R₂(0.5) = -4(0)/3, which is zero.

In conclusion, the second Taylor polynomial P₂(x) is a second Taylor polynomial with a minimum error of 0 when x = 0.5. To find the actual error in using P₂(0.5) to approximate f(0.5), we need to find the value of c and make the necessary adjustments to the original equation.

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Step 2: She did not simplify under the square root correctly

under the square root:

(-6)^2 =36

and -4(5)(-8) =160

therefore under the square root it needs to be square root of 36+160 which is square root of 196.

That answer is 14 when square rooted

Answer:

step 2

Step-by-step explanation:

(-6)^2 ≠ 36^2

(-6)^2 = 36

The calculated value of the total interest is 12479.04

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

25998 x .08 x 6

In the above equation, we have

Principal = 25998

Rate of interest = 0.08

Time = 6

using the above as a guide, we have the following:

Total interest = 25998 x .08 x 6

Evaluate

Total interest = 12479.04

Hence, the total interest is 12479.04

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