Earthworm Rivals are building the set for

their new music video. There is a tower made

of 9 glowing bricks that stands 5. 4 meters tall. If each of the bricks is the same exact size,

how tall is each brick?

To find the derivative of the function y = sin²(x) tan^6(x) / (x² + 1)² using logarithmic differentiation and y' = 2sin(x)tan^5(x)cos(x) + 6tan^5(x)sec^2(x) - 4xsin²(x)tan^6(x) / (x² + 1)²

Step 1: Take the natural logarithm of both sides:

ln(y) = ln(sin²(x) tan^6(x) / (x² + 1)²)

Step 2: Apply the properties of logarithms to simplify the expression:

ln(y) = 2ln(sin(x)) + 6ln(tan(x)) - 2ln(x² + 1)

Step 3: Differentiate implicitly with respect to x:

(d/dx) ln(y) = (d/dx) [2ln(sin(x)) + 6ln(tan(x)) - 2ln(x² + 1)]

Using the chain rule and the deivative of natural logarithm, we have:

y'/y = 2(cos(x)/sin(x)) + 6(sec²(x)/tan(x)) - 2(2x/(x² + 1))

Step 4: Multiply both sides by y to solve for y':

y' = y * [2(cos(x)/sin(x)) + 6(sec²(x)/tan(x)) - 2(2x/(x² + 1))]

Step 5: Substitute the value of y from the original equation:

y' = [sin²(x) tan^6(x) / (x² + 1)²] * [2(cos(x)/sin(x)) + 6(sec²(x)/tan(x)) - 2(2x/(x² + 1))]

Simplifying further, we have:

y' = 2sin(x)tan^5(x)cos(x) + 6tan^5(x)sec^2(x) - 4xsin²(x)tan^6(x) / (x² + 1)²

Therefore, the derivative of y = sin²(x) tan^6(x) / (x² + 1)² is:

y' = 2sin(x)tan^5(x)cos(x) + 6tan^5(x)sec^2(x) - 4xsin²(x)tan^6(x) / (x² + 1)²

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Answer: the probability is 1/221

The following correctly refers to the last element in the array of integers called numbers:

numbers[length of numbers-1].

An array is a collection of items, which can be of the same type and stored in contiguous memory. Once an array is created, its size cannot be altered during program execution. The last element in an array of integers called numbers can be referred to using numbers[length of numbers-1]. This is because array indexing starts from zero and the length of an array is the number of elements it contains, but indexing ends at length-1. Therefore, the last element in an array is always at the index length-1.It is important to note that array indexing is an error-prone area of programming, and one should always ensure that indices do not go out of bounds. This can lead to memory access violations and undefined behavior. A good practice is to use loops that start from 0 and end at length-1 when iterating over an array, to ensure that all elements are processed. It is also advisable to use constants or symbolic names to represent array indices, to make the code more readable and easier to maintain.

In summary, an array is a collection of items that can be stored in contiguous memory and cannot be resized during program execution. The last element in an array of integers called numbers can be referred to using numbers[length of numbers-1]. Array indexing is an error-prone area of programming, and one should always ensure that indices do not go out of bounds.

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Answer:

rotation of 90 degrees

Step-by-step explanation:

i took the k12 math quiz

Answer:

30.6452% decrease.

Step-by-step explanation:

\(\frac{10.75}{15.50} =69.354\)%

100-69.354 ≈ 30.6452%

Answer:

x = 77 degrees

Step-by-step explanation:

To get the value of x, we use the angle arc relationship

Mathematically, we have this as follows;

x = (76 + 78)/2

x = 77

Using Poisson distribution, the probability mass function is approximately 4.2%

To solve the problem, we can use the Poisson distribution since we are interested in the probability of a certain number of events (in this case, cars with 4 occupants) occurring in a given time period (morning commute).

The Poisson probability mass function is given by:

P(X = k) = (e^(-λ) * λ^k) / k!

where X is the random variable (number of cars with 4 occupants), λ is the mean (average) number of occurrences in the given time period (morning commute), and k is the number of occurrences we are interested in (k = 4 in this case).

Since the average number of non-driver passengers per car is 0.52, we can assume that the average number of total occupants (including the driver) is 1.52. Therefore, the mean (average) number of cars with 4 occupants in a given time period can be calculated as:

λ = (1.52)^4 * e^(-1.52) / 4!

Using a calculator, we get λ ≈ 0.0331.

Now we can plug in the values of λ and k into the Poisson probability mass function:

P(X = 4) = (e^(-0.0331) * (0.0331)^4) / 4!

Using a calculator, we get P(X = 4) ≈ 0.042

Therefore, the probability that a randomly selected car passing through the toll booth during the morning commute has 4 occupants (the driver and 3 passengers) is approximately 0.042 or 4.2%.

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The following expression shows the main expression after the negative exponents have been eliminated: A. m⁷n³n/m.

In Mathematics, an exponent can be defined as a mathematical operation that is used in conjunction with an algebraic expression to raise a quantity to the power of another and it is generally written as bⁿ.

By applying the property of exponents based on the law of indices for the division of powers, we have the following:

b⁻ⁿ = 1/bⁿ

In this context, the exponent n⁻¹ in the given algebraic expression would be rewritten based on the law of indices for the division of powers as follows;

n⁻¹ = 1/n

Substituting the given parameters into the given algebraic expression, we have the following;

(m⁷n³)/mn⁻¹ = (m⁷n³)/m × n

(m⁷n³)/m × n = (m⁷n³n)/m

(m⁷n³)/mn⁻¹ = m⁷n³n/m

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Answer:

Step-by-step explanation:

its A

Each side of the square has a length of approximately 12.02.

Without additional information or a diagram, it is difficult to determine what values are missing. However, we can use the Pythagorean theorem to solve for the length of the sides of the square.

Let's assume that TR is a diagonal of the square, and let x be the length of each side. Then, by the Pythagorean theorem,

TR^2 = x^2 + x^2

17^2 = 2x^2

289 = 2x^2

x^2 = 144.5

x ≈ 12.02

We can also solve this as:

Assuming that PQRS is square and TR is a diagonal of the square, we can use the Pythagorean theorem to find the length of each side of the square. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

In this case, if we draw a diagonal TR in the square, it divides the square into two right triangles, each with sides of length x (the length of one side of the square) and TR/√2 (half the diagonal). Applying the Pythagorean theorem to one of these right triangles, we get:

(x)^2 + (TR/√2)^2 = TR^2

Simplifying and solving for x, we get:

x = √(TR^2 - (TR/√2)^2) = TR/√2 = TR * √2 / 2

Plugging in TR = 17, we get:

x = 17 * √2 / 2 ≈ 12.02

Therefore, each side of the square has a length of approximately 12.02. Without additional information or a diagram, we cannot determine any other missing values.

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The number of vegetable bearing plants are : 0.45x, where x is the total number of plants.

A fraction in mathematics represents a portion or element of the whole. It represents the appropriate parts of the totality. A fraction is made up of two parts: the numerator and the denominator. The number at the top is the numerator, and the number at the bottom is the denominator. The numerator indicates the number of equal parts that were actually taken, whereas the denominator shows the total number of equal parts in the whole.

Let x be the initial plant population.

Now that 1/10 of plants bear fruit, the quantity of fruit-bearing plants is equal to 0.1x.

Plants remaining then equal x - 0.1x = 0.9x.

Once more, because half of the remaining plants give flowers, the number of flower-bearing plants is equal to 0.5(0.9x) = 0.45x.

As a result, the number of plants left is equal to 0.9x - 0.45x = 0.45x.

Given that all remaining plants produce veggies, the number of plants that do so is equal to 0.45.

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Answer:

Yes

Step-by-step explanation:

Let's pick 2 bionomials for this proof.

(3x+4) and (2x-4)

If we subtract (2x-4) from (3x+4) we will be left with x to the first power, which is a monimal.

So yes, you can subtract a binomial from another binomial and get a monomial.

Hope this helps!

Answer: 3X2+4x=-2

Step-by-step explanation:because thats the mathematic equation for a average square

Answer:

The independent variable is the variable that is manipulated or changed during an experiment. In this case, the independent variable is represented by the x-values of the given points.

So, the answer would be option A: {-2, 3, 1, 5}

Step-by-step explanation:

brainliest Plsssss

Answer:

\(\mathrm{1.\:D.\:8.4\%}\\\mathrm{2.\:C.\: \$96.60}\\\mathrm{3.\:D.\: \$227.85}\\\mathrm{4.\:B.\:\$490}\)

Step-by-step explanation:

1. The car's initial price was $273. Since the sale price is $250, the car is on a \(273-250=\$23\) discount. The percent of discount is the discount price over the initial price:

\(\frac{23}{273}\approx \fbox{$8.4\%$}\).

2. Since the weight racks were initially priced $46, then marked up 210%, their mark-up is:

\(46\cdot2.1=\fbox{$\$96.60$}\)

*Worth noting that this is the mark-up (as the question is asking), not the total price after the mark-up.

3. The TV's initial price is $325.50. If it's on sale for 30%, it's final price will be \(100\%-30\%=70\%\) of the initial price:

\(\$325.50\cdot 0.7=\fbox{$\$227.85$}\)

4. The final retail price will be the initial price + the mark-up:

\(280+280(0.75)=\fbox{$\$490$}\).

Segment CP is tangent to circle C at point B.

How to prove that the line is tangent to a circle?

Draw circle C with center at point A and radius AD = CD = DE.

Draw point P outside the circle C.

Draw segment AP and extend it to intersect the circle at point B.

Draw segment BD.

Draw segment CP.

Note that triangle BCD is isosceles, since CD = BD. Therefore, angle BDC = angle CBD.

Since angle BDC is an inscribed angle that intercepts arc BC, and angle CBD is an angle that intercepts the same arc, then angle BDC = angle CBD = 1/2(arc BC).

Since CD = DE, then angle CED = angle CDE. Therefore, angle DCE = 1/2(arc BC).

Since angles BDC and DCE are equal, then angles BDC and CBD are also equal, and triangle BPC is isosceles. Therefore, segment BP = segment PC.

Since BP = PC, then segment CP is perpendicular to segment BD, by the Converse of the Perpendicular Bisector Theorem.

Therefore, segment CP is tangent to circle C at point B.

Hence, the proof is complete.

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Answer:

The third one I believe.

Step-by-step explanation:

Given:

The upper left coordinates (-6,0)

The upper right coordinates (-4,0)

The area of the rectangle = 12

Find-:

Draw the rectangle in the graph

Explanation-:

The area of a rectangle is

The area is 12 then,

The coordinates is

So, the width is 2 then the length is:

The lowe

So, the rectangle graph is

Answer:

2.

Step-by-step explanation:

You need to collect data from all students to get an answer .

The statistical question from the given options is:

"How many pens are inside each of my classmates' desks?"

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Thus, the statistical question from the given options is:

"How many pens are inside each of my classmates' desks?"

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Answer:

solution given :

<A=?

<B=50°

<C=50°

if it is a triangle:

<A+<B+<C=180°( sum of interior angle of a triangle is 180°)

<A=180-50-50

<A=80°

<A=80° is a required answer.

Its a isosceles triangle

So

<A:-

Answer:

n = -6/5

Step-by-step explanation:

16 + 90n = 35n - 50

90n - 35n = -50 - 16

55n = -66

n = -66/55

n = -6/5

Check:

16 + 90*-6/5 = 35*-6/5 - 50

16 - 108 = -42 - 50 = -92

Hi, there.

 _____

\(\boxed{\begin{minipage}{10cm} \boldsymbol{\it{Arrange \ the \ like \ terms.}}\\ \\ \sf{90n-35n=-50-16}\\\sf{55n=-66}\\\boldsymbol{\it{Divide \ both \ sides \ by \ 55}}\\\\\sf{n=-66/55, which \ reduced \ to \ n=-6/5}\end{minipage}}\)

Hope the answer - and explanation - made sense,

happy studying!!!

Answer:

The larger jar contains 220 marbles

Step-by-step explanation:

Here, we are told a larger jar contains 1 5/6 of the content of a regular

The regular content is 120 marbles

So the number of marble we have will be

1 5/6 * 120

= 11/6 * 120

= 11 * 20 = 220 marbles

Answer:

220

Step-by-step explanation:

120 x 2 = 240

1/6 - 240 = 220

Answer:

8. 24+36+12= 72 in cubed

And yes it would fit because 72 is greater than 64

9. 2+21= 23 ft cubed

We can set a = 1 and c = 1/2. With these values, the Lyapunov function V(x, y) = x^2 + (1/2)y^2 satisfies the conditions and shows that the critical point at the origin is asymptotically stable.

To construct a suitable Lyapunov function, let's consider a function of the form V(x, y) = ax^2 + cy^2, where a and c are to be determined. We will choose a and c such that V(x, y) is positive definite and its derivative along the trajectories of the system is negative definite or negative semi-definite.

To show that the critical point at the origin is asymptotically stable, we need to demonstrate that there exists a Lyapunov function V(x, y) with the following properties:

V(x, y) is positive definite, i.e., V(x, y) > 0 for all (x, y) ≠ (0, 0).

V(x, y) is radially unbounded, meaning that as (x, y) approaches infinity, V(x, y) approaches infinity.

The derivative of V(x, y) along the trajectories of the system, dV/dt, is negative definite or negative semi-definite.

To determine the values of a and c, we can calculate the derivative of V(x, y) along the trajectories of the system:

dV/dt = ∂V/∂x * dx/dt + ∂V/∂y * dy/dt

Substituting the given system of differential equations: dV/dt = (2ax - 3ax^3 - cy^2) * (-x^3 + xy^2) + (2cy - 2cy^3 - cy^3) * (-2x^2y - y^3)

To ensure that dV/dt is negative definite or negative semi-definite, we can choose a and c such that the coefficients of x^4, x^2y^2, and y^4 terms in dV/dt are positive or zero. This condition guarantees that the critical point at the origin is asymptotically stable.

By comparing the coefficients, we can set a = 1 and c = 1/2. With these values, the Lyapunov function V(x, y) = x^2 + (1/2)y^2 satisfies the conditions and shows that the critical point at the origin is asymptotically stable.

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The total weight is 18.5 kilograms

They have 400 bottles left to package to meet their goal.

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”

In the problem above, we are given that:

In order to find how many bottles do they have left to package to meet their goal, we will multiply the percentage by the bottles to figure out how much they got left.

So,

\(\rightarrow\text{x}=0.40\times1000\)

\(\rightarrow\bold{x=400 \ bottles}\)

Therefore, they have 400 bottles left to package to meet their goal.

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Answer:

  x = 15

Step-by-step explanation:

We assume you want to find the value of x.

Know (or prove) that in this geometry, all of the right triangles are similar. That means the ratios of corresponding sides are proportional.

  short side / hypotenuse = 9/x = x/25

  x^2 = (9)(25) . . . . . . . . . . multiply by 25x ("cross multiply")

  x = √((9)(25)) = (3)(5) . . . take the square root

  x = 15

Answer:

r=244745.8 (approximately)

Step-by-step explanation:

r=x²/y

ry-x²=0

r(59000)-(380000)²=0

r=380000²/59000

r=144400000/59

r=244745.8 (approximately)