MATHEMATICS HIGH SCHOOL

Express Fx and Fy in terms of the length of the vector F and the angle θ, with the components separated by a comma.

Answers

Answer 1

Answer:

Fx, Fy = F cos θ, F sin θ

Further explanation

This is a fundamental problem with vector components.

A vector quantity is some quantities that have the magnitude and a direction. For example, all forces or momentums are vectors.
Whereas, a scalar quantity only has magnitude. For example, all forms of energy are scalars.

The list below shows some recognized methods to represent a vector. i.e., a force.

$\boxed{ \ \textit{\textbf{F}}, \vec{F}, \bar{F} \ }$

It is possible to split one vector into two vectors. This process is called resolving and the vectors that we get are called the components of the original vector.

Vector problems can always be solved by using the mathematics of trigonometry, i.e., the functions of sine or cosine. This is particularly appropriate when resolving.

By using the cartesian coordinate system, see the attachment on how to calculate the values of either these components.

Horizontal component: $\boxed{ \ F_x = \textit{\textbf{F}}\ cos \ \theta \ }$
Vertical component: $\boxed{ \ F_y = \textit{\textbf{F}} \ sin \ \theta \ }$

Here, the angle between the vector F and the horizontal axis we call θ (theta).

As a reminder:

$\boxed{cos \ \theta = (adjacent)/(hypotenuse)} \rightarrow cos \ \theta = (F_x)/(F) \rightarrow \boxed{F_x = F cos \ \theta}$
$\boxed{sin \ \theta = (opposite)/(hypotenuse)} \rightarrow sin \ \theta = (F_y)/(F) \rightarrow \boxed{F_y = F sin \ \theta}$

Learn more

Finding the acceleration between two vectors brainly.com/question/6268248
A correct representation of 0.000025 in scientific notation brainly.com/question/2261308
The theoretical density of platinum which has the FCC crystal structure brainly.com/question/5048216

Keywords: express Fx and Fy, in terms of the length of the vector F, and the angle θ, with the components, separated by a comma, resolving, split, horizontal, vertical, angle, theta, sine, cosine, trigonometry, cartesian coordinate system

Answer 2

Answer:

The components of the vector F are $\fbox{\begin\nF\cos\theta\end{minispace}}$ and $\fbox{\begin\nF\sin\theta\end{minispace}}$ .

Further Explanation:

A physical quantity can be defined as the physical property that can be measured and have some value in numbers.

For example- mass, amount of substance, length, time, electric current, temperature, force, light intensity, density, velocity, speed etc.

A quantity is said as a vector if it has some magnitude and direction in order to give the details regarding the quantity.

For example- Force, velocity, current density, electric field, magnetic field, displacement, acceleration, momentum etc.

A quantity is said as a scalar if it has only the magnitude in order to give the details regarding the quantity.

For example- speed, distance, current, volume, density, mass, energy, time, temperature etc.

Given:

The resultant vector is $F$ .

The horizontal component is ${\vec F_x}$ .

The vertical component is ${\vec F_y}$ .

Concept:

Let a vector have some length $F$ and making an angle $\theta$ with horizontal axis.

The triangle rule of resultant vector state that when two vector is denoted by the two sides of the triangle and the magnitude and the direction is taken in the same direction then the third side of the triangle denoted by resultant vector with some magnitude and direction.

The diagram is drawn as shown in the Figure 1.

The vertical component is along y-axis and the vertical component of the vector $\vec F$ is expressed as:

${\vec F_y}=F\sin\theta$

The horizontal component is along x-axis and the horizontal component of the vector $\vec F$ is expressed as:

${\vec F_x}=F\cos\theta$

therefore, the components of the vector F are $\fbox{\begin\nF\cos\theta\end{minispace}}$ and $\fbox{\begin\nF\sin\theta\end{minispace}}$ .

Learn more:

1. Displacement vector https://brainly.in/question/3332823

2. Magnitude of the vector brainly.com/question/12501440

3. Magnitude of the vector brainly.com/question/11538030

Answer Details:

Grade: High school

Subject: Physics

Chapter: Kinematics

Keywords:

Express, Fx, Fy, vector, F, angle, theta, components, Fsin theta, Fcos theta.

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Answer:

Step-by-step explanation:

Given:x+2<-5. choose the solution set.

Answers

Step-by-step explanation:

x+2<−5

Step 1: Subtract 2 from both sides.

x+2−2<−5−2

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Answer:

x<−7

Help me please I will UPVOTWhen you square each side of an equation, is the resulting equation equivalent to the original?

Answers

When you square each side of an equation then the resulting equation is not equivalent to the original

Yes, that is true.

If x = y, x² = y².
If x = y, substitute x into where y is;

x² = y²
x² = (x)²
Thus, yes they will be.

Let (Ω,F,P) be a probability space. Recall the R.V. X is called simple, if there exist A₁, …., Aₙ ∈ F and b₁, …, bₙ ∈ R such that X = ᵢ₌ₗ∑ⁿ bᵢ 1{A ᵢ }. Note that A; need not be disjoint. ...) ... a) Show that if R.V. X,Y are simple, then so is the linear combination aX + bY. b) Is it true that if X₁, X₂ are all simple then so are X₁ + X₂, and X₁ ∧ X₂ = min X1, X₂? c) Is the representation of X (i.e. the sets A₁,.., Aₙ and the scalars b₁, ..., bₙ) unique? d) What if Aᵢ are known to be disjoint? How many values can X take then? e) Show that R.V. X is simple if and only it takes finitely many values. f) Show that E[X] is well defined for X simple R.V.. In other words, if X has two representations: X = ᵢ₌ₗ∑ⁿ bᵢ 1{Aᵢ } and X = ᵢ₌ₗ∑ᵐ Cᵢ 1{Bᵢ), such that B₁, ..., Bₘ ∈ F and C₁, ..., Cₘ ∈ R, then we must have ᵢ₌ₗ∑ⁿ Bᵢ P(Aᵢ) = ᵢ₌ₗ∑ᵐ cᵢP(Bᵢ).

Answers

Answer:

see below

Step-by-step explanation:

a) If random variables X and Y are simple, then their linear combination aX + bY is also simple.

b) If X₁ and X₂ are simple, then X₁ + X₂ and X₁ ∧ X₂ are also simple.

c) The representation of a simple random variable X is not unique. There can be different sets of {Aᵢ} and corresponding scalars {bᵢ} that represent the same X.

d) If the sets Aᵢ are known to be disjoint, then X can take as many unique values as there are disjoint sets {Aᵢ}.

e) A random variable X is simple if and only if it takes a finite number of values.

f) The expected value E[X] is well-defined for a simple random variable X, regardless of its representation. It can be calculated using the formula E[X] = ∑ᵢ bᵢ P(Aᵢ) or E[X] = ∑ᵢ cᵢ P(Bᵢ), where {Aᵢ} and {Bᵢ} are sets and {bᵢ} and {cᵢ} are scalars representing X.

PLS HELPPPPP SOS HELP !!!!!Shandra is on vacation and wants to
buy souvenirs for at least 8 friends.
A postcard book costs $2.50 and a magnet costs $4.00. She can spend up to $30 altogether. Let x represent the number of postcard books and y represent the number of magnets.
Part A

A. x + y <8
B. 2.5x +4y <30
C. x+y > 8
D. 2.5x + 4y >8
E. x>0
F. y>0
G. x + y>0

Plsss help the one in the picture is part 2