Calculate The Arc Length Of The Indicated Portion Of The Curver(t) = (1 - 9t)i (5 + 2t)j (6t - 5)k, -10 ≤ t ≤ 6

Answer:

tạo độ của anh ấy dừng là:

Step-by-step explanat ion(:-2,2.5)

The price of one pound of banana = b

As one pound of oranges costs $0.75 more than one pound of bananas, so, the price of one pound of orange = b+0.75.

The price of 3 pounds of banana = 3b,

and the price of 2 pounds of oranges = 2(b+0.75).

Now, as she pays $4.50 for 3 pounds of bananas and 2 pounds of oranges.

So, for this situation the required equation is

3b + 2(b+0.75) =4.5

On solving this equation, we have

\(\Rightarrow 3b+2b+2\times0.75=4.5\)

\(\Rightarrow 5b +1.5=4.5\)

\(\Rightarrow 5b =4.5-1.5=3\)

\(\Rightarrow b =\frac 3 5=0.6\)

Hence, the price of one pound of banana = $ 0.60

and the price of one pound of orange

=b+0.75= 0.60+0.75=$1.35.

Answer:

Side-Angle-Side

Step-by-step explanation:

See attachment for figures

Given

Midpoint L

Lines KN and MP

Required

Which method proves the congruency of the triangles

Since L is the midpoint, then the following relationship exists:

This implies that two sides of both triangles are equal

Also, because KN is a transversal of MP and vice versa, then angles KLM and PLN are equal

Conclusively, 2 corresponding sides and 1 corresponding angle have been proven to be equal.

Hence, the method that prove that the triangles are equal is Side-Angle-Side (SAS)

The value of \(\(\sin(t)\tan(t)\)\) is \(If \(\tan(t) = \sin(t) = \frac{144}{145}\) and \(\cos(t) < 0\)\), then \(\(\tan(t) = \frac{144}{145}\) and \(\cos(t) = -\frac{1}{145}\).\)

(a) To find the value of\(\(\sin(t)\tan(t)\)\), we can use the identity \(\(\tan(t) = \frac{\sin(t)}{\cos(t)}\)\). Substituting this into the expression, we have \(\(\sin(t)\tan(t) = \sin(t)\left(\frac{\sin(t)}{\cos(t)}\right)\)\). Simplifying, we get \(\(\sin(t)\tan(t) = \frac{\sin^2(t)}{\cos(t)}\)\). Since the Pythagorean identity states that \(\(\sin^2(t) + \cos^2(t) = 1\)\), we have \(\(\sin^2(t) = 1 - \cos^2(t)\).\) Substituting this into the expression, we get \(\(\sin(t)\tan(t) = \frac{1 - \cos^2(t)}{\cos(t)}\)\). Using the identity \(\(\tan(t) = \frac{\sin(t)}{\cos(t)}\)\), we can rewrite the expression as \(\(\sin(t)\tan(t) = \frac{1}{\cos(t)}\)\). Since \(\(\sec(t) = \frac{1}{\cos(t)}\)\), we have \(\(\sin(t)\tan(t) = \sec(t)\)\). Therefore, the value of\(\(\sin(t)\tan(t)\) is \(1\)\).

(b) Given \(\(\tan(t) = \sin(t) = \frac{144}{145}\)\) and \(\(\cos(t) < 0\)\), we know that \(\(\cos(t)\)\)is negative. Using the Pythagorean identity \(\(\sin^2(t) + \cos^2(t) = 1\)\), we can substitute\(\(\sin(t) = \frac{144}{145}\)\) to find \(\(\cos^2(t) = 1 - \left(\frac{144}{145}\right)^2\)\). Simplifying, we get \(\(\cos^2(t) = \frac{1}{145^2}\)\). Since \(\(\cos(t)\)\) is negative, we have \(\(\cos(t) = -\frac{1}{145}\)\). Similarly, since \(\(\tan(t) = \sin(t)\)\), we have \(\(\tan(t) = \frac{144}{145}\)\). Therefore, \(\(\tan(t) = \frac{144}{145}\) and \(\cos(t) = -\frac{1}{145}\)\).

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The relative minimum points are (-1/2, 1, -19/4) and no saddle points of the function f(x,y) = 7x² - 8y² + 7x + 16y + 8. The only critical point is (-1/2, 1).

To find the critical points of the function f(x,y) = 7x² - 8y² + 7x + 16y + 8, we need to solve the system of partial derivatives equal to zero:

f x = 14x + 7 = 0

f y = -16y + 16 = 0

Solving for x and y, we get:

x = -1/2

y = 1

So the only critical point is (-1/2, 1).

To classify the critical point, we need to calculate the second-order partial derivatives:

f xx = 14

f xy = 0

f yx = 0

f yy = -16

Using the Hessian matrix at the critical point is:

D = f xx f yy - f xy f yx = (14)(-16) - (0)(0) = -224

Since D < 0 and f xx > 0, we have a relative minimum at (-1/2, 1).

Since there is only one critical point, there are no saddle points.

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Answer:

- x= 10-6y+y²

Step-by-step explanation:

|x-1|=3-y

(|x-1|)²=(3-y)²

x-2x+1=9-6y+y²

-x=9-6y+y²+1

Each employee makes 35 x 7.60 = 266 per week.

105 employees x 266 = 27,930 per week total pay.

27930 x 10 % = 27930 x 0.10 = 2,793 more per week.

The graph of this function opens up and all the y-values range from -3 to infinity, so therefore the range is all x≥-3

The range of the function f(x) = |x| – 3 is {f(x) ∈ ℝ | f(x) ≥ –3}. The correct option is A.

The range of a function in mathematics can refer to one of two closely related ideas: The function's codomain a representation of the action A binary relation f between two sets X and Y is a function if there is exactly one y in Y such that f connects x to y for every x in X.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

The graph of this function opens up and all the y-values range from -3 to infinity, therefore, the range is all x≥-3. The graph is attached with the answer below.

Therefore, the range of the function f(x) = |x| – 3 is {f(x) ∈ ℝ | f(x) ≥ –3}. The correct option is A.

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Answer:the answer is B

Step-by-step explanation:Bisect each of the angles with vertices at their houses

To find a meeting place that is equidistant from Jo, Boris, and Carrie's houses, the friends should draw perpendicular bisectors from each side of the triangle.

Perpendicular lines are those that are parallel to one another and result in a 90° angle at their intersection.

Here are the steps to follow:

Draw a rough sketch of the triangle using the given information, labeling each vertex and the length of each side.

Locate the midpoint of each side of the triangle by measuring the length of each side and finding the point that is equidistant from the endpoints of that side. Label each midpoint.

Draw a line perpendicular to each side of the triangle at its midpoint, using a straightedge or ruler to ensure that the lines are straight and meet at a point inside the triangle.

The point where the three perpendicular bisectors meet is the circumcenter of the triangle. This point is equidistant from each of the three vertices of the triangle and is the meeting place that the friends are looking for.

So the answer is (D) Draw perpendicular line segments from each vertex to the opposite side.

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one real eigenvalue. find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace.

What is eigenvalue?

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that, when the linear transformation is applied to it, changes at most by a scalar factor. The factor by which the eigenvector is scaled is known as the associated eigenvalue, frequently denoted by lambda.

a) -4

b) 1

c) 1

Step-by-step explanation:

a) The matrix A is given by:

\(A=\left[\begin{array}{ccc}-3 & 0 & 1 \\2 & -4 & 2 \\-3 & -2 & 1\end{array}\right]\\\)

where lambda are the eigenvalues and I is the identity matrix. By replacing you obtain:

\(A-\lambda I=\left[\begin{array}{ccc}-3-\lambda & 0 & 1 \\2 & -4-\lambda & 2 \\-3 & -2 & 1-\lambda\end{array}\right]\)

and by taking the determinant:\(\begin{aligned}& {[(-3-\lambda)(-4-\lambda)(1-\lambda)+(0)(2)(-3)+(2)(-2)(1)]-[(1)(-4-\lambda)(-3)+(0)(2)(1-} \\& \lambda)+(2)(-2)(-3-\lambda)]=0 \\& -\lambda^3-6 \lambda^2-12 \lambda-16=0\end{aligned}\)

and the roots of this polynomial is:

\(\begin{aligned}& \lambda_1=-4 \\& \lambda_2=-1+i \sqrt{3} \\& \lambda_3=-1-i \sqrt{3}\end{aligned}\)

hence, the real eigenvalue of the matrix A is -4.

b) The multiplicity of the eigenvalue is 1.

c) The dimension of the eigenspace is 1 (because the multiplicity determines the dimension of the eigenspace)

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Complete Quetion

The matrix A= (−3 0 1, 2 −4 2, −3 −2 1) has one real eigenvalue. Find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace. The eigen value = has multiplicity = and the dimension of the corresponding eigenspace is:_______.

Answer:

Step-by-step explanation:

Step 1 : Write +2x as a difference

= x^2-4x+6x-24

Step 2: Factorize out common terms

= x(x-4)+6(x-4)

Factorize out (x-4)

(x-4)(x+6)

\(x^{2} +2x-24\\Write+2x -as-a-difference\\x^{2} -4x+6x-24\\Factor out common terms\\x(x-4)+6(x-4)\\Factor out (x+4)\\(x-4)(x+6)\)

Answer: D ON EDGE

Step-by-step explanation:

Answer:

\(3 \times \frac{1}{3 } + \frac{1}{2} \times - 12( \frac{1}{3} ) = \frac{1}{3} \)

Using the Central Limit Theorem, the given statements are true or false in following

a) True

b) True

c) True

d)True

e) True

a) From the definition of central limit theorem, by law of large number to sample average converge almost slowly to the population average.

So, based on CLT the sample mean be used a3 gond estimator of the population mean assuing that the sample size. sufficiently large i.e ., True.

b) Same reason as (a) , based on CLT the usually considers that sample 51Z6 30 is sufficiently large is true

c) If we generate 1000 samples of Binomial (10;0.3)distribution are plot a histogram then it looks like normal distribution.

So, the Central Limit Theorem be applied to both discrete and continols Fandom variables is true.

d) Whatever be the parent distribution , if sample size ,n is large then sample mean means

converges in probability to the population mean.

So, the given option (d) is true .

e) If population size is normally distributed then sample mean is also normally distributed for all sample size.

So, option(e) is also true.

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Complete question:

Problem Central Limit Theorem) _ Are the following statements true or false?

a)Easy. Based the Central Limit Theorem_ the sample mean be used a3 gond estimator of the population mean assuing that the sample size. sufficiently large.

b)Easy. Then applying the Central Limit Theorem. l usually conziders that sample 51Z6 30 is sufficiently large.

c)Easy. the Central Limit Theorem be applied to both discrete and continols Fandom variables .

d): Assuming that the sample size is sufficiently large the Central Limit Theorem permits draw conclusions about the population based strictly sample data. and without having aIV knowledge about the distribution of the underlying population:

(e) Moderate_ Assuming that the population is normally distributed_ the sampling distribution of the sample mean is normally distributed for samples of all sizes_

The structure known as the Burj Khalifa is taller than a stack of the money it took to construct it.

The Burj Khalifa is an iconic skyscraper in Dubai, United Arab Emirates. With a height of 828 meters (2,716 ft), it is now the highest structure in the world.

The Burj Khalifa's construction began in 2004 and was finished in 2009. The skyscraper was constructed by the architectural firm Skidmore, Owings & Merrill and was mostly funded by the government of Dubai.

The Burj Khalifa stands 828 meters (2,716 ft) tall. According to sources, the overall cost of constructing the Burj Khalifa was around $1.5 billion USD. A stack of $1.5 billion USD would be roughly 165 metres (541 feet) tall if the typical US $100 bill has a thickness of 0.11 millimeters.

Therefore, the structure known as the Burj Khalifa is taller than a stack of the money it took to construct it.

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\( \frac{1}{(5 \times 10^{2} ) + (2 \times {10}^{3}) } \\ \\ \frac{1}{(5 \times 100) + (2 \times 1000)} \\ \\ \frac{1}{(500) + (2000)} \\ \\ \frac{1}{2500} \)

The probability of exactly two dice having a face value of 6 when rolling three fair six-sided dice is 5/72.

To find the probability of exactly two dice having a face value of 6 when three fair six-sided dice are rolled, we can use the concept of combinations.

The total number of possible outcomes when rolling three dice is 6^3 = 216, as each die has 6 possible outcomes.

Now, let's determine the number of favorable outcomes where exactly two dice have a face value of 6.

We have three scenarios where exactly two dice show a 6:

The first die shows a 6, the second die shows a 6, and the third die does not show a 6.

The first die does not show a 6, the second die shows a 6, and the third die shows a 6.

The first die shows a 6, the second die does not show a 6, and the third die shows a 6.

In each scenario, the probability of rolling a 6 on one die is 1/6, and the probability of not rolling a 6 is 5/6.

Scenario 1:

Probability = (1/6) * (1/6) * (5/6) = 5/216

Scenario 2:

Probability = (5/6) * (1/6) * (1/6) = 5/216

Scenario 3:

Probability = (1/6) * (5/6) * (1/6) = 5/216

Adding up the probabilities from each scenario:

Total Probability = (5/216) + (5/216) + (5/216) = 15/216 = 5/72

Therefore, the probability of exactly two dice having a face value of 6 when rolling three fair six-sided dice is 5/72.

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Answer:

-5/6

Step-by-step explanation:

Using the slope formula we can easily find the slope

m=(y2-y1)/(x2-x1)

m=(-1-4)/(10-4)

m=-5/6

The perimeter of triangle is 66.24 units.

What is triangle?

In Euclidean geometry, any 3 points, once non-collinear, verify a unique triangle and at the same time, a unique plane

Main body:

according to question :

c = 28

let the vertices be A,B,C

∠A= 30°

by using trigonometric ratios,

BC/ AB = sin30°

AB = C = 28

BC/28 = sin30°

BC = 28*sin30°

BC= 28*(1/2)

BC = 14

similarly

AB /CA = cos 30°

28/CA = √3/2

CA = 28*√3/2

CA = 14/√3

CA = 24.24

Hence , perimeter = AB +BC +CA = 28+14+24.24

                              =66.24 units

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The equivalent expression for 1.5 cubed over 1.3 raised to the fourth power all raised to the power of negative six is 1.5 to the eighteenth power over 1.3 to the twenty-fourth power.

Here are the steps to simplify the expression:

Apply the negative power rule: (1.5 cubed over 1.3 raised to the fourth power) raised to the power of negative six is equal to (1.3 raised to the fourth power over 1.5 cubed) raised to the power of six.

Apply the power of a quotient rule: (1.3 raised to the fourth power over 1.5 cubed) raised to the power of six is equal to (1.3 raised to the fourth power)⁶ / (1.5 cubed)⁶.

Apply the power of a power rule: (1.3 raised to the fourth power)⁶ is equal to 1.3(⁴*⁶) = 1.3²⁴.

Apply the power of a power rule: (1.5 cubed)⁶ is equal to 1.5(³*⁶) = 1.5¹⁸.

Therefore, the equivalent expression is 1.5¹⁸ / 1.3²⁴.

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Answer:

A is the answer

Step-by-step explanation:

The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers. To calculate the t-value, the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.

Given, M₁ = 35

M₂ = 45

SM1-M2 = 6.00

The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers.

To calculate the t-value,

the formula we need to use here is:

t = (M₁ - M₂) / SM1-M2

Substituting the given values into the formula:

t = (35 - 45) / 6.00

t = -10 / 6.00

t = -1.67

Therefore, we can conclude that the value of t is -1.67 for the samples given.

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The APR for the loan is 300%

APR stands for annual percentage rate. It is a standardized way of measuring the cost of borrowing money. It takes into account not only the interest rate on a loan but also any fees that are charged as part of the loan.

Given: Cheatem loans will lend you $400 and you will repay them $500 in one month

interest = 500-400 = $100

duration = 1 month

1 year = 12 months

APR = (interest/amount borrowed) / (duration/duration in a year)

APR = (100/400)  /  (1/12)

APR = 300%

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Answer:

the answer would be b

Step-by-step explanation:

hoped that helped:P

Answer:

b=2/3

Step-by-step explanation:

Let's solve the equation step by step

( b ) = 2/3

Remove bracket

b=2/3

The sum of the internal angles in a quadrilateral is equal to 360, therefore:

The graph of y = x(x² - 2)(x² + x + 1) intersects the x-axis in three different points.

The answer is (C) Three.To determine the number of points where the graph of the equation y = x(x² - 2)(x² + x + 1) intersects the x-axis, we need to find the x-values that make the equation equal to zero.

Setting y = 0, we have:

0 = x(x² - 2)(x² + x + 1)

Since the product of three factors is zero, at least one of the factors must be zero.

1. Setting x = 0:

0 = 0(x² - 2)(x² + x + 1)

This gives us one solution: x = 0.

2. Setting x² - 2 = 0:

x² = 2

Taking the square root of both sides:

x = ±√2

This gives us two additional solutions: x = √2 and x = -√2.

3. Setting x² + x + 1 = 0:

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 1, b = 1, and c = 1. Substituting these values into the quadratic formula:

x = (-1 ± √(1² - 4(1)(1))) / (2(1))

Simplifying:

x = (-1 ± √(-3)) / 2

Since the discriminant is negative, there are no real solutions for this quadratic equation.

In summary, we have found three different x-values where the equation intersects the x-axis: x = 0, x = √2, and x = -√2.

Therefore, the graph of y = x(x² - 2)(x² + x + 1) intersects the x-axis in three different points. The answer is (C) Three.

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Answer:

25.25

Step-by-step explanation:

hope it helps and have a nice day ! :)

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