solve similar triangles (advanced)

a) Ross's vertical VO2 is 6.42 ml/min/kg.

b) Ross's total relative VO2 is 9.13 ml/min/kg.

To determine Ross's vertical VO2 and total relative VO2, we need to consider the speed and grade of the treadmill.

Given:

Speed = 55 m/min

Grade = 5%

a) Vertical VO2:

Vertical VO2 is the energy expenditure specifically related to vertical displacement.

To calculate it, we need to determine the vertical component of the speed.

Vertical Component of Speed = Speed * Grade/100

Vertical Component of Speed = 55 * 5/100

Vertical Component of Speed = 2.75 m/min

Vertical VO2 = Vertical Component of Speed * 1.8 ml/min/kg

Vertical VO2 = 2.75 * 1.8

Vertical VO2 = 4.95 ml/min/kg (rounded to two decimal places)

b) Total Relative VO2:

Total Relative VO2 includes both the vertical and horizontal components of the energy expenditure. To calculate it, we need to consider the total speed.

\(Total Speed =\sqrt{ (Speed^2 + Vertical Component of Speed^2)}\)

\(Total Speed = \sqrt{(55^2 + 2.75^2)} \\Total Speed = \sqrt{(3025 + 7.5625)} \\Total Speed = \sqrt{(3032.5625)}\)

Total Speed = 55.0726 m/min

Total Relative VO2 = Total Speed * 0.2 ml/min/kg

Total Relative VO2 = 55.0726 * 0.2

Total Relative VO2 = 11.0145 ml/min/kg (rounded to two decimal places)

Therefore, Ross's vertical VO2 is approximately 4.95 ml/min/kg, and his total relative VO2 is approximately 11.01 ml/min/kg.

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Answer:

Existen 6 formas posibles de cambiar un billete de 5000 por monedas de 200 y 500.

Step-by-step explanation:

En primer lugar, se determina el mínimo común múltiplo de 500 y 200. Si se multiplica a 500 por 2 y a 200 por 5, se encuentra que el mínimo común múltiplo es 1000. Entonces, se encuentra las siguientes dos conclusiones:

1) Se requiere dos monedas de 500 para obtener 1000.

2) Se requiere cinco monedas de 200 para obtener 1000.

Para determinar todas las formas posibles sin considerar el orden de las monedas, se requiere estudiar tres escenarios:

(i) Todas las monedas son de 200.

(ii) Todas las monedas son de 500.

(iii) Hay monedas de 200 y 500.

Caso 1 - Todas las monedas son de 200:

Es evidente que solo existe una forma.

Caso 2 - Todas las monedas son de 500:

Es evidente que solo existe una forma.

Caso 3 - Hay monedas de 200 y 500:

Existen las siguientes formas:

- 1000 en monedas de 200, 4000 en monedas de 500.

- 2000 en monedas de 200, 3000 en monedas de 500.

- 3000 en monedas de 200, 2000 en monedas de 500.

- 4000 en monedas de 200, 1000 en monedas de 500.

En resumen, existen 4 escenarios.

Finalmente, existen 6 formas posibles de cambiar un billete de 5000 por monedas de 200 y 500.

Answer:

132

Step-by-step explanation:

so all the angles of a triangles add up to equal 180 so to find the missing angle of the triangles we do 180-86-46 which equals 48. x is supplementary to the angles that equals 48 meaning that they will add up to equal 180. 180-48 = 132 so x =132

Options A and B are the best choices for showing the graphs of f(x) = x^2 and g(x) = (1/3)x^2. These options allow us to clearly see the differences between the two functions, with f(x) increasing more rapidly than g(x) as we move away from the vertex.

To answer your question, we need to graph both functions f(x) = x^2 and g(x) = (1/3)x^2.
First, let's consider the graph of f(x) = x^2. This is a quadratic function that opens upward (since the coefficient of x^2 is positive). The vertex of the parabola is at (0, 0), and the shape of the graph is symmetric about the y-axis. As we move away from the vertex in either direction, the function increases rapidly at first and then more slowly.
Now let's look at g(x) = (1/3)x^2. This function is also a quadratic with a positive coefficient of x^2, so it also opens upward. However, because the coefficient is smaller than 1, the function increases more slowly than f(x) as we move away from the vertex. The vertex of the parabola is also at (0, 0), and the shape is symmetric about the y-axis.
To visualize these graphs, we can use a graphing calculator or graph paper. Here are some options that could show the graphs of f(x) and g(x):

Option A:
This option shows f(x) in red and g(x) in blue. The graphs are clearly distinguishable, with f(x) increasing more rapidly than g(x) as we move away from the vertex.
Option B:
This option shows f(x) in blue and g(x) in red. The graphs are still distinguishable, but the colors are reversed.
Option C:
This option shows f(x) and g(x) in the same color (red). The graphs overlap quite a bit, making it difficult to see the differences between them.
Option D:
This option shows f(x) and g(x) in different shades of the same color (light blue and dark blue). The graphs are distinguishable, but the contrast between them is not as strong as in options A and B.

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Answers: x = 4 and y = 3

============================================================

Explanation:

Triangle UBD is congruent to triangle RAN

Note the order of the lettering as it's important.

BD and AN are the last two letters of UBD and RAN in that order. Therefore, these sides correspond and BD = AN. From that, we know,

BD = AN

2y+5 = 3y+2

5-2 = 3y-2y

3 = 1y

y = 3

-----------

Using similar logic, UD and RN are the first and last letters of UBD and RAN respectively. So,

UD = RN

15 = 2x+7

2x+7 = 15

2x = 15-7

2x = 8

x = 8/2

x = 4

the rate of change of height at h = 15cm, 0. 0159 cm/s

What is Rate?

A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.

When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.

Beads are dropped to create a conical pile such that the ratio of its radius to the height of the pile is constant at 2:3.

Volume is increasing at a rate of 5 cm3/s.

The volume of a Cone: 1/3 pi r^2 h

given r/h =2/3

V =0. 0159 cm/s

Hence the rate of change of height at h = 15cm, 0. 0159 cm/s

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Answer:

15

Step-by-step explanation:

Answer:

25% of 60 is 15

Step-by-step explanation:

let me know if it's correct

Answer:

24x - 6

Step-by-step explanation:

Perimeter = 2(8x - 3) + 2(4x)

Perimeter = 16x - 6 + 8x

Perimeter = 24x - 6

-Chetan K

Answer:

  inside

Step-by-step explanation:

All of the points on the circle are at distance 25 units from the center. If the questionable point is closer to the center than that, it is inside the circle.

The distance formula can be used.

  d = √((x2 -x1)^2 +(y2 -y1)^2)

  d = √((5 -(-5))^2 +(-24 -(-8))^2) = √(10^2 +(-16)^2) = √(100 +256) = √356

  d ≈ 18.9

The point (5, -24) is inside the circle centered at (-5, -8) with radius 25.

__

The equation of the circle is equivalent to d=25 using (x1, y1) as the center. It is usually written without the radical:

  (x -(-5))^2 +(y -(-8))^2 = 25^2

  (x +5)^2 +(y +8)^2 = 625

Answer:

The answer is inside.

Step-by-step explanation:

Took the test and got it right! Good luck! God Bless you!

Step-by-step explanation:

The letters for XYZ are in the wrong order.

The correct statement should be \(\triangle TUV \cong \triangle ZYX\)

============================================

Further Explanation:

The order of the letters matters when writing congruence statements.

The claim is that \(\triangle TUV \cong \triangle XYZ\)

The first two letters of each are "TU" and "XY" in that order.

But notice how TU has a single tickmark, while XY has a double tickmark. The two sides are clearly different.

--------

Instead, the statement should be: \(\triangle TUV \cong \triangle ZYX\) because of the following three facts:

Notice that:

Answer:

a^3b + 2a^2b^2 + ab^3

Step-by-step explanation:

(a+b)^2

= a^2 + 2ab + b^2

ab(a^2 + 2ab + b^2)

= a^3b + 2a^2b^2 + ab^3

Answer:

Please see the attached images

Step-by-step explanation:

The figure is a regular pentagon, so all its internal angles are equal. So the first step is to find the value of the internal angle, that will also be the minimum rotation angle to have a new figure in the same orientation.

The formula to find the internal angle of a regular polygon is:

Using n = 5, we have:

The internal angle is 108°.

A rotation of 108° would make all vertices move one position (to the position of the next vertix).

We can see that point A moved two positions (from the left vertix to the right vertix), so the rotation angle is 2 times the internal angle:

So the correct option is B.

Answer:

y11_maths_foundation_mock_apr18_paper1_answers.pdf

Step-by-step explanation:

use it to get answer

In this case, the distance from point y to the plane in ℝ_3 covered by \(u_{1}\) and \(u_{2}\) is 113/13.

The given vectors are

\(y =  \left[\begin{array}{ccc}4\\-9\\3\end{array}\right] ; u_{1}  =  \left[\begin{array}{ccc}-3\\-4\\1\end{array}\right] ; u_{2}  =  \left[\begin{array}{ccc}-1\\2\\5\end{array}\right]\)

We are to find the distance of y from the plane in ℝ_3 spanned by \(u_{1}\)and \(u_{2}\).

Now we'll get the plane's standard vector, which is supplied by the cross product of the two vectors \(u_{1}\) and \(u_{2}\), as follows:

\(u_{1} * u_{2} = \left[\begin{array}{ccc}-3\\-4\\1\end{array}\right]*\left[\begin{array}{ccc}-1\\2\\5\end{array}\right]\)

\(= det( i j k; -3 -4 1; -1 2 5 )\\ = 3 i -16 j -10 k\)

The equation of the plane is given by an

\((x - x_{0}) + b(y - y_{0}) + c(z - z_{0}) = 0\)

where a, b, and c are the coefficients of the equation and

\((x_{0}, y_{0}, z_{0})\) is a point on the plane.

Now, let's take a point on the plane, say

\(P(u_{1}) = \left[\begin{array}{ccc}-3\\-4\\1\end{array}\right]\)

Then, the equation of the plane is 3(x + 3) - 16(y + 4) - 10(z - 1) = 0 which can be simplified as 3x - 16y - 10z - 5 = 0

Now we know the equation of the plane in ℝ_3 spanned by \(u_{1}\) and \(u_{2}\).

So we can now use the formula for the distance of a point from a plane as shown below:

Distance of point y from the plane = |ax + by + cz + d| √(a² + b² + c²) where, a = 3, b = -16, c = -10 and d = -5

So, substituting the values we get,

Distance of point y from the plane = |3(4) -16(-9) -10(3) -5| √(3² + (-16)² + (-10)²)= |-113| √(269)= 113 / 13

∴ The distance between point y and the plane in ℝ_3 covered by \(u_1\) and \(u_{2}\) is 113/13.

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Answer:

48.25 minutes

Step-by-step explanation:

Divide 1544/32 to find the time per student

To find dy/dx, we differentiate both sides of the given equation with respect to x using the rules of differentiation. Applying the chain rule and the power rule, we have: -231x^6 + 297x^32y + 2yy' = 0

Next, we can solve this equation for dy/dx by isolating the derivative term. Rearranging the equation, we get:

dy/dx = (231x^6 - 2yy') / (297x^32)

Now, to find the equation of the tangent line at the point (1, 1), we substitute the coordinates (x, y) = (1, 1) into the derivative expression dy/dx.

Substituting x = 1 and y = 1 into the equation, we get:

dy/dx = (231(1)^6 - 2(1)(y')) / (297(1)^32)

      = (231 - 2y') / 297

Since the point (1, 1) lies on the tangent line, we can substitute x = 1 and y = 1 into the original equation to find y'. We have:

-33(1)^7 + 9(1)^33(1) + (1)^2 = -23

-33 + 9 + 1 = -23

-23 = -23

Thus, y' at (1, 1) is indeterminate. Therefore, we cannot determine the equation of the tangent line in the form y = mx + b without knowing the value of y'

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The probability that at least one of the lights is defective is 0.2661 .

in the question ,

it is given that

the total number of bulbs in the pack of new light bulbs is (n) = 5

percent of bulb that did not work is  = 6%

probability that lights did not work is (p) = 0.06

probability that lights work is (q) = 1 - 0.06 = 0.94

let x be the number of defective lights

So ,the probability that at least one of your lights is​ defective

is P(x ≥ 1) = 1 - P(x<1)

= 1 - P(x = 0)

By Binomial Probability

= 1 - ⁿCₓ*(p)ˣ*(q)ⁿ⁻ˣ

= 1 - ⁵C₀*(0.06)⁰*(0.94)⁵⁻⁰

= 1 - 1*1*(0.94)⁵         ...because ⁵C₀ = 1

= 1 - (0.94)⁵

= 1 - 0.7339

= 0.2661

Therefore , The probability that at least one of the lights is defective is 0.2661 .

The given question is incomplete , the complete question is

You purchased a​ five-pack of new light bulbs that were recalled because ​6% of the lights did not work. What is the probability that at least one of your lights is​ defective ?

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The quadratic function f(x)= 3x2 - 2x + 5 has an average rate of change from x = -2 to x = 0 of - 14.

Qualities and their permutations, theorems and surrounding structures, morphologies and their placements, and locations where they can be encountered are all included in the study of mathematics. The association between a group of inputs, of which each has a related output, is referred to as a "function." A function is a relationship between inputs and outputs where each input produces a single, unique result. Every function has a domain and a requires great, often known as a scope. F is typically used to denote functions (x). An x is the input. Based on the following criteria, there are four primary categories of functions that are available: on procedures, one-to-one functions, several more functions, within functions, and on functions.

given

The slope formula, (y2-y1)/, states that the average rate of change is the ratio of the change in y to the change in x.

(x2-x1) We have f(x), which is equivalent to byt but instead of y.

f(-2) - f (0)  /   -2

= f(14+4 + 5 ) + 5 / -2

28 / - 2

= -14

The quadratic function f(x)= 3x2 - 2x + 5 has an average rate of change from x = -2 to x = 0 of - 14.

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The critical value for a 99 confidence interval for a z interval is 2.576.

A confidence interval (CI) would be a range of values that, with a specific degree of certainty, are likely to encompass a population value. It is frequently stated as a percentage when a population mean falls between a higher and lower interval.

Some key features regarding the confidence interval are-

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Cyber safety is the use of information and communication technologies in a responsible and safe manner. It involves protecting information and keeping it secure, but it also entails handling information responsibly, showing consideration for others online, and following proper internet etiquette.

The Essential Eight are a collection of eight mitigation techniques: application control, application patching, configuring Microsoft Office macro settings, user application hardening, limiting administrative rights, operating system patching, multi-factor authentication, and regular backups.

Best Cybersecurity Advice for 2023:

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Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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The area of the composite figure that is composed of trapezoid rectangle and triangle is solved to be 55.3 square meters

The composite figure is made up of

The area is calculated by solving each area and adding them up

= area of trapezoid + area of rectangle +  area of triangle

= 1/2 x (2 + 4) x 2.1 + 10 x 4 + 1/2 x 4.5 x 4

= 1/2 x 6 x 2.1 + 10 x 4 + 1/2 x 4.5 x 4

= 6.3 + 40 + 9

= 55.3 square meters (to the nearest tenth)

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Answer:

(x - 3) (x - 8)

Step-by-step explanation:

To find IUF and EF in different situations, you need to determine the values of "m", "px", and "py" for the given function. Then, plug those values into the respective formulas. The IUF represents the importance of the function, while the EF represents the expected value.

In order to find EF and IUF in different situations, you need to understand the formulas and when to apply them.

1. Formula for IUF (Importance-Utility Factor):
  - In the first example, where u(x,y)=X^(1/2)*Y^(1/2), the formula for IUF is v=m/√(4pxpy).
  - Here, "m" represents the value of the function (32), and "px" and "py" represent the partial derivatives of "u" with respect to "x" and "y" (both equal to 1).
  - So, in this case, you can calculate IUF as v=32/√(4*1*1)=32/2=16.

2. Formula for EF (Expected Factor):
  - Continuing with the first example, the formula for EF is m=v√(4pxpy).
  - Plugging in the values, EF=32*√(4*1*1)=32*2=64.

3. Formula for IUF and EF in the second example:
  - In the second example, where u(x,y)=Min(x,2y), the formula for IUF is v=2m/√(2px+2py), and the formula for EF is m=v(2px+2py)/2.
  - Here, "m" represents the value of the function (15), and "px" and "py" represent the partial derivatives of "u" with respect to "x" and "y" (both equal to 1).
  - Plugging in the values, IUF=2*15/√(2*1+2*1)=30/√4=30/2=15, and EF=15*(2*1+2*1)/2=15*4/2=30.

In summary, to find IUF and EF in different situations, you need to determine the values of "m", "px", and "py" for the given function. Then, plug those values into the respective formulas. The IUF represents the importance of the function, while the EF represents the expected value. Make sure to use the correct formulas based on the given function.

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