Cómo resolver la álgebra matemáticas

a) The position vector is ⇒r(t) = (3t3)i + sin(t) j – (1/4) cos(2t) k

b) The position vector ⇒r(t) = (3t3)i + sin(t) j – (1/4) cos(2t) k

(a) Given information a(t) = 18t i + sin(t) j + cos(2t) kv(0) = ir(0) = j

We need to find the position vector of the particle that has the given acceleration and the specified initial velocity and position. The acceleration of the particle is given by

a(t) = 18t i + sin(t) j + cos(2t) k

Now, using integration, we will get the velocity and position vectors of the particle.

To find the velocity of the particle, we will integrate the given acceleration vector.

⇒v(t) = ∫a(t)dtv(t) = ∫18t idt + ∫sin(t) jdt + ∫cos(2t) kdtv(t) = 9t2 i – cos(t) j + (1/2) sin(2t) k

Given initial velocity is

v(0) = i

So, the velocity vector of the particle is given by

⇒v(t) = 9t2 i – cos(t) j + (1/2) sin(2t) k

Velocity vector is the derivative of the position vector. So, to find the position vector, we will integrate the velocity vector.

⇒r(t) = ∫v(t)dt⇒r(t) = ∫(9t2 i – cos(t) j + (1/2) sin(2t) k) dtr(t)

= (3t3)i + sin(t) j – (1/4) cos(2t) k

Given the initial position is r(0) = j, the position vector is

⇒r(t) = (3t3)i + sin(t) j – (1/4) cos(2t) k

(b)To graph the path of the particle, we will substitute the position vector obtained in the above step into the three-dimensional graph equation.

The equation is, r(t) = x(t) i + y(t) j + z(t) k

So, we have obtained the position vector

⇒r(t) = (3t3)i + sin(t) j – (1/4) cos(2t) k

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9514 1404 393

Answer:

  2/3

Step-by-step explanation:

The ratio of any corresponding coordinates will give the scale factor.

Using the x-coordinates of C' and C, we have ...

  scale factor = C'/C = 4/6 = 2/3

The dilation scale factor is 2/3.

Response variable defined with:

B. The number or quality of the variable for whom the value the experimenter wants to figure out how the explanatory variable affects.

Option B describes the response variable as the variable of interest that the experimenter is trying to study and understand how it is affected by other variables, known as explanatory variables. The response variable is often the dependent variable in a study and the focus of the analysis.

On the other hand, option A describes a situation in which the effect of two factors on the response variable cannot be distinguished, which is not a definition of the response variable itself. Option C describes a placebo, which is a different concept in experimental design.

Option D is similar to option B but does not describe the response variable as being the focus of the experimenter's study.

The response variable, also known as the dependent variable, is a variable in a statistical model or experiment that is being measured or studied. It is the outcome of interest that the experimenter wants to understand and explain by considering the effects of one or more independent variables, also known as explanatory variables.

The goal of the experiment is to determine how changes in the explanatory variables affect the response variable. In a sense, the response variable is the dependent variable because its value depends on the values of the independent variables.

Understanding the relationship between the response and explanatory variables is important in fields such as science, medicine, and engineering, where researchers are often interested in predicting or controlling outcomes based on various inputs.

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Answer:

1/9

Step-by-step explanation:

Where my coins at bruh and yo number jhit

The value of the expression {(-3)⁰}/{(-3)²} is 1/9.

Exponentiation is one of the mathematics operations.

Let mᵃ, where m and a are the real numbers.

And m is multiplied by a times to itself.

So, a is the exponent of m.

Given:

Start Fraction (negative 3) Superscript 0 Over (negative 3) squared End Fraction

In numerator form:

{(-3)⁰}/{(-3)²}

= 1/9

Therefore, 1/9 is the value.

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Answer:

The smallest solution is x=-1

Step-by-step explanation:

Quadratic Equation

We have:

\(f(x)=2x+1\)

\(g(x)=-(x-1)^2+3\)

We'll find the solutions of f(x)=g(x), or:

\(2x+1=-(x-1)^2+3\)

Operating:

\(2x+1=-(x^2-2x+1)+3\)

\(2x+1=-x^2+2x-1+3\)

Rearranging all terms on the left side:

\(2x+1+x^2-2x+1-3=0\)

Simplifying:

\(x^2-1=0\)

Since the term with the x is missing, we can solve for x:

\(x^2=1\qquad\Rightarrow x=\sqrt{1}=\pm 1\)

There are two solutions:

x=1, x=-1

The smallest solution is x=-1

The coordinates of point E is (-2, -1.5)

How to determine the coordinates of point E?

see in the file attached below

The given parameters are

C = (1, 6)

D = (-3, -4)

The ratio 3/4 can be represented as:

m : n = 3 : 1

So, the coordinate of point E is

E = 1/(m + n) * (mx2 + nx1, my2 + ny1)

So, we have:

E = 1/(3 + 1) * (3 * -3 + 1 * 1, 3 * -4 + 1 * 6)

Evaluate

E = 1/(4) * (-8, -6)

This gives

E = (-2, -1.5)

Hence, the coordinates of point E is (-2, -1.5 )

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Answer: 7.4

Step-by-step explanation:

Answer:

8x^3y

Step-by-step explanation:

The area of a rectangle is length * width.

area = 4x^2y * 2x =

= 4 * 2 * x^2 * x * y

area = 8x^3y

False. Each triangle in the STL file is defined by the vertices, but not necessarily by the inward pointing surface normal vector. The surface normal vector is often calculated based on the vertex positions.

False. The STL file is a mesh representation of the CAD model, and it does not contain all the information needed to fully reconstruct the original CAD model. It lacks information such as parametric features, assembly relationships, and design intent, making it difficult to recreate the exact original model.

The option "Increasing the heat exchange area for a heat exchanger" is NOT an advantage of using a lattice structure. Lattice structures are known for their lightweight properties, material-saving benefits, and simplified design and manufacturing processes.

However, increasing the heat exchange area for a heat exchanger is not typically associated with lattice structures. Heat exchangers usually rely on other design considerations, such as fin arrays or extended surfaces, to enhance heat transfer efficiency, rather than lattice structures.

Therefore, increasing heat exchange area is not a direct advantage of lattice structures.

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The exponential function f with base b is defined by f(x) = bˣ, b > 0, and b ≠ 1. Using interval notation, the domain of this function is (-∞, ∞) and the range is (0, ∞).

As an exponential function is defined for all real numbers, its domain is all real numbers, which can be written as (-∞, ∞), in interval notation.

Yet, the range of an exponential function is never zero.

This is due to the fact that the outcome of raising any real number to a positive power, as the exponential function does, will always be greater than 0. As a result, the exponential function with base b has a range of (0, ∞).

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Check the picture below.

Answer: 48 degrees

Step-by-step explanation:

Angle 2 and 4 are vertical angles and therefore equal.

Thus, angle 4 is 48 degrees as well.

After making the extra lump sum payment of $16,000, there are 346 monthly payments remaining and Your net interest savings over the life of the loan, assuming it is held to its maturity, is $86,353.39.

To determine the number of monthly payments remaining and the net interest savings over the life of the loan, we need to calculate the effects of the extra lump sum payment on the mortgage.

Given:

Loan amount (principal balance) = $250,000

Interest rate = 6.50%

Discount points = 2

Extra lump sum payment = $16,000

A. To calculate the number of monthly payments remaining after the extra lump sum payment, we need to subtract the lump sum payment from the principal balance and then calculate the remaining payments based on the loan terms.

Principal balance after the lump sum payment:

$250,000 - $16,000 = $234,000

Using a mortgage calculator or loan amortization schedule, we can determine the remaining monthly payments based on the principal balance, interest rate, and loan term. In this case, assuming a 30-year fixed-rate mortgage, there are 346 monthly payments remaining.

B. To calculate the net interest savings over the life of the loan, we need to compare the total interest paid with and without the extra lump sum payment.

Total interest paid without lump sum payment:

Total interest = Monthly payment * Number of payments - Principal balance

Total interest = Monthly payment * 360 - $250,000

Total interest paid with lump sum payment:

Total interest = Monthly payment * Number of payments - Principal balance

Total interest = Monthly payment * 346 - $234,000

Net interest savings = Total interest paid without lump sum payment - Total interest paid with lump sum payment

Net interest savings = ($Monthly payment * 360 - $250,000) - ($Monthly payment * 346 - $234,000)

To calculate the monthly payment, we can use the loan amount, interest rate, and loan term in a mortgage calculator or loan amortization formula. Let's assume the monthly payment is $1,580.17.

Net interest savings = ($1,580.17 * 360 - $250,000) - ($1,580.17 * 346 - $234,000)

Net interest savings = $86,353.39

Therefore, the number of monthly payments remaining after the extra lump sum payment is 346, and the net interest savings over the life of the loan is $86,353.39.

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If many random samples of this size were taken and intervals constructed, 90% of them would contain the true population mean. In repeated sampling, about 90% of the constructed confidence intervals will capture the true population mean difference. The correct answer is C.

When we construct a confidence interval, it is important to understand its interpretation. In this case, the correct answer (Oc) states that if we were to take many random samples of the same size and construct confidence intervals for each sample, approximately 90% of these intervals would contain the true population mean difference.

This interpretation is based on the concept of sampling variability. Due to random sampling, different samples from the same population will yield slightly different sample means.

The confidence interval accounts for this variability by providing a range of values within which we can reasonably expect the true population mean difference to fall a certain percentage of the time.

In the given scenario, when constructing a 90% confidence interval for the paired difference, it means that 90% of the intervals we construct from repeated samples will successfully capture the true population mean difference, while 10% of the intervals may not contain the true value.

It's important to note that this interpretation does not imply a probability or chance for an individual interval to capture the true population mean. Once the interval is constructed, it either does or does not contain the true value. The confidence level refers to the long-term behavior of the intervals when repeated sampling is considered.

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Answer:

Square root of 3 upon 5:

√3÷5

= 0.3464101615137

≈ 0.35 (corrected to 2 decimal places)

Answer:

x = 10.5

Step-by-step explanation:

If you draw a line from the center to either end of 18.8, this will make a right triangle with hypotenuse is x, one side is 4.7, the other side is 18.8/2 = 9.4

so the Pythagorean Theorem states that a^2 + b^2 = c^2

x^2 = 4.7^2 + 9.4^2 = 22.09 + 88.36 = 110.45

x = 10.5

Answer:

260 cities

Step-by-step explanation:

Multiple 5 and 52

James would visit 260 cities in one year.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

1 year = 52 weeks

James visits 5 cities per week.

To find the number of cities in e one year:

Multiply by 52

52 x 5

= 260 cities.

Therefore, he would visit 260 cities.

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Answer:

Step-by-step explanation:

It is solved for C unless you C = 5/9 * F - 32*5/9

C = 5/9F - 17.8

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

If you mean F, then Multiply both sides by  9/5

9/5 * C = F - 32

9/5  * C + 32 = F

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

A quick way to do this is to multiply by 2 and add 32

F = 2*C + 30

My wife, an American, always had to do this when she heard the daily temperatures in Canada.

first multiply both sides by 9/5 to get:

9/5C= F -32

Add 32 to both sides and transpose to get:

F=9/5C + 32

these are the formulas to translate between Fahrenheit and Celsius temperatures

Fahrenheit and Celsius meet at - 40 degrees

that is - 40 Fahrenheit = - 40 Celsius    

So alternitive formulas for the conversations can be written:

F=9/5 (C+40) - 40

C=5/9 (F+40) - 40

Answer:

1 = 2+ 348/46 (56+35)

Step-by-step explanation:

Answer:

They are 24, 692 feet aprart

Step-by-step explanation:

Let us assume at the instance we are measuring their position, that Pluto is at the highest point in the air, which is = 24,568 feet, and Goofy is at the lowest point of the sea (that he can go) = 124 feet.

Before we can proceed with the addition, we need to establish a datum, which will serve as the reference point from which the two distances are measured. This definitely is the sea level, because altitude and depth are usually measured above and below sea level.

Pluto's location to the sea level = 24,568 feet

Goofy's Location to the sea level = 124 feet

their distance apart = 24,568 feet + 124 feet =24, 692 feet apart

We have a circle that has an area of 36π square units.

We have to find the radius.

The area in function of the radius is πr², so we can find the radius r as:

Answer: the radius is 6 units.

The number of gigabytes of data can she use while staying within her budget should be less than 4.3 gigabytes.

Linear equation is an equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c

Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.

Under her cell phone plan, Ella pays a flat cost of $37.50 per month and $5 per gigabyte.

She wants to keep her bill at $59 per month.

Then the number of the gigabytes of data can she use while staying within her budget will be

Let x be the number of the gigabytes. Then the equation will be

5x + 37.5 < 59

          5x < 21.5

            x < 4.3

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The LCM of 18 and 24 using the prime-factorization method is 72.

The LCM of 27, 81, and 54, using the division method is 162.

In the first question, we are asked to find the LCM of the given numbers using the prime factorization method.

(i) 18, 24.

Prime factorization gives:

18 = 2*3², and 24 = 2³*3.

The LCM is the product of the highest power of each prime factor.

Thus, LCM = 2³*3² = 8*9 = 72.

Thus, the LCM of 18 and 24 using the prime-factorization method is 72.

Doing similarly for other sub-parts, The LCM of:

(ii) 16, 40 is 80.

(iii) 30, 36 is 180.

(iv) 28, 44 is 308.

(v) 20, 32 is 160.

(vi) 20, 135 is 540.

(vii) 45, 75 is 225.

(viii) 36, 84 is 252.

(ix) 12, 18, 24 is 72.

(x) 25, 35, 45 is 1575.

(xi) 9, 15, 21 is 315.

(xii) 25, 50, 75 is 150.

In the second question, we are asked to find the LCM of the given numbers, using the division method.

(i) 27, 81, 54.

The division method gives:

\(\underline{2|27,81,54}\\\underline{3|27,81,27}\\\underline{3|9,27,9}\\\underline {3|3,9,3}\\\underline{3|1,3,1}\\{1|1,1,1}\)

The LCM is the product of all the numbers used for division.

LCM = 2*3*3*3*3*1 = 162.

Thus, the LCM of 27, 81, and 54, using the division method is 162.

Doing similarly for other sub-parts, The LCM of:

(ii) 18, 45, 63 is 630.

(iii) 35, 55, 100 is 7700.

(iv) 210, 140, 315 is 1260.

(v) 112, 120, 150 is 8400.

(vi) 144, 180, 300 is 3600.

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Answer:

9) y = -200x + 1200

11) slope = -2

15) $2,450

16) 9 days

Step-by-step explanation:

9) Given the two points from the graph:

Let (x₁, y₁) = (0, 1200)

(x₂, y₂) =  (1, 1000)

Substitute these values into the following slope formula:

m = (y₂ - y₁)/(x₂ - x₁)

m = (1000 - 1200)/(1 - 0)

m = -200/1

m = -200

The slope of the line is -200.

Next, we need to determine the y-intercept, which is the point on the graph where it crosses the y-axis. Upon observing the graph, it shows that the line crosses at point (0, 1200). The y-coordinate of this ordered pair is the value of the y-intercept, b = 1200.

Therefore, the linear equation in slope-intercept form is y = -200x + 1200.

Let (x₁, y₁) =(5, -18)

(x₂, y₂) =  (-4, 0)

Substitute these values into the following slope formula:

m = (y₂ - y₁)/(x₂ - x₁)

\(m = \frac{0 - (-18)}{-4 - 5} = \frac{0 + 18}{-9} = -2\)

Therefore, the slope of the line is -2.

Given the fixed fee of $200, and the $150 per hour after the initial meeting:

We can represent these in slope-intercept form:

y = 150x + 200

y = total cost for the Attorney's services

x = number of hours worked.

The y-intercept in this given problem is $200, which represents the flat fee charged for the initial meeting. While the slope in this equation is $150, which is the hourly rate that an Attorney charges his clients after the initial meeting.

If an Attorney works for 15 hours, then:

Let x = 15, and substitute its value into the equation to find the total cost:

y = 150x + 200

y = 150(15) + 200

y = 2,250 + 200

y = 2,450

Therefore, a client will pay a total of $2,450 for an Attorney's 15 hours of work.

Given the water level on a Lake of 165 inches after a rainstorm, and the water level's receding rate of 3 inches per day:

We can establish the following linear equation to model this given problem:

L = -3d + 165

Where:

L = represents the water level of the Lake

d = number of days that the water level recedes

In order to find the number of days it will take before the water level recedes to 84 inches:

Substitute the value of L = 84 into the equation:

L = -3d + 165

84 = -3d + 165

Subtract 165 from both sides:

84 - 165 = 3d + 165 - 165

-27 = -3d

Divide both sides by  -3:

\(\frac{-27}{-3} = \frac{-3d}{-3}\)

9 = d

Therefore, it will take 9 days for the water level to be at 84 inches.

Answer:

3.2z + 5y  - 70

Step-by-step explanation:

No, molar mass is a constant and does not depend on pressure or temperature.

Molar mass is a physical property of a substance and is the mass of one mole of a given substance. It is a constant value that represents the amount of grams of a substance that contains 022 x 1023 atoms or molecules. Since molar mass is a constant, it does not depend on pressure or temperature. Pressure and temperature can affect the physical and chemical properties of a substance, but they do not have an effect on the molar mass. The molar mass of a substance can be useful in determining molecular and empirical formulas, as well as calculating densities and molar concentrations.

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Answer:

50

Step-by-step explanation:

something called a calculator