Find the x- and y-components of the vector d⃗ = (9.0 km , 35 ∘ left of +y-axis).

Answers

Answer 1

Final answer:

The x- and y-components of the given vector are calculated using trigonometric functions, resulting in -5.16 km along the x-axis and 7.37 km along the y-axis, considering the direction of the vector relative to the axes.

Explanation:

The question asks to find the x- and y-components of the vector d⟷ = (9.0 km, 35° left of +y-axis). To solve this, we use trigonometric functions, specifically sine and cosine, because the vector makes an angle with the axis.

Given the vector makes a 35° angle to the left of the +y-axis, this effectively means it is 35° above the -x-axis (or equivalently, 55° from the +x-axis in the second quadrant). We can calculate the components as follows:

y-component: Dy = D*cos(35°) = 9.0 km * cos(35°) = 9.0 km * 0.8191 = 7.37 kmx-component: Dx = -D*sin(35°) = -9.0 km * sin(35°) = -9.0 km * 0.5736 = -5.16 km (negative because it's in the direction of the -x axis)

The negative sign in the x-component indicates that the direction is towards the negative x-axis. Therefore, the x- and y-components of the vector are -5.16 km and 7.37 km, respectively.

Answer 2

1. [tex]\(\mathf{d}\): \(d_x = -3.8 \text{ km}, d_y = 8.2 \text{ km}\)[/tex]

2. [tex]\(\mathf{v}\): \(v_x = -4.0 \text{ cm/s}, v_y = 0\)[/tex]

3. [tex]\(\mathf{a}\): \(a_x = 10.3 \text{ m/s}^2, a_y = -14.7 \text{ m/s}^2\)[/tex]

To find the [tex]\( x \)[/tex]- and [tex]\( y \)[/tex]-components of vectors given in terms of magnitude and direction, we need to decompose the vectors using trigonometric functions. Let's go through each problem step by step.

1. Find the [tex]\( x \)[/tex]- and [tex]\( y \)[/tex]-components of the vector [tex]\( \mathf{d} = (9.0 \text{ km}, 25^\circ \text{ left of } +\mathbf{y}\text{-axis}) \)[/tex].

First, understand that "25° left of +[tex]\( y \)[/tex]-axis" means the vector is rotated 25° counterclockwise from the [tex]\( y \)[/tex]-axis.

Decomposition:

- Magnitude, [tex]\( d = 9.0 \text{ km} \)[/tex]

- Angle from the [tex]\( y \)-axis, \( \theta = 25^\circ \)[/tex]

To find the components:

- [tex]\( d_x = d \sin(\theta) \)[/tex]

- [tex]\( d_y = d \cos(\theta) \)[/tex]

However, since the angle is counterclockwise from the [tex]\( y \)-axis[/tex] and to the left, the [tex]\( x \)[/tex]-component is negative.

Therefore:

- [tex]\( d_x = -9.0 \sin(25^\circ) \)[/tex]

- [tex]\( d_y = 9.0 \cos(25^\circ) \)[/tex]

Calculating these:

- [tex]\( d_x \approx -9.0 \times 0.4226 \approx -3.8 \text{ km} \)[/tex]

- [tex]\( d_y \approx 9.0 \times 0.9063 \approx 8.2 \text{ km} \)[/tex]

So, the components are:

- [tex]\( d_x \approx -3.8 \text{ km} \)[/tex]

- [tex]\( d_y \approx 8.2 \text{ km} \)[/tex]

2. Find the [tex]\( x \)[/tex]- and [tex]\( y \)[/tex]-components of the vector [tex]\( \mathf{v} = (4.0 \text{ cm/s}, -x \text{-direction}) \).[/tex]

Since the vector is given in the [tex]\(-x\)[/tex]-direction, it means the entire magnitude is in the [tex]\( x \)[/tex]-direction and negative.

Decomposition:

- Magnitude, [tex]\( v = 4.0 \text{ cm/s} \)[/tex]

- Direction: [tex]\(-x\)[/tex]

Therefore:

- [tex]\( v_x = -4.0 \text{ cm/s} \)[/tex]

- [tex]\( v_y = 0 \text{ cm/s} \)[/tex]

So, the components are:

- [tex]\( v_x = -4.0 \text{ cm/s} \)[/tex]

- [tex]\( v_y = 0 \text{ cm/s} \)[/tex]

3. Find the [tex]\( x \)[/tex]- and [tex]\( y \)[/tex]-components of the vector [tex]\( \mathbf{a} = (18 \text{ m/s}^2, 35^\circ \text{ left of } -y \text{-axis}) \)[/tex].

"35° left of -[tex]\( y \)[/tex]-axis" means the vector is rotated 35° counterclockwise from the negative [tex]\( y \)[/tex]-axis.

Decomposition:

- Magnitude, [tex]\( a = 18 \text{ m/s}^2 \)[/tex]

- Angle from the [tex]\(-y \)[/tex]-axis, [tex]\( \theta = 35^\circ \)[/tex]

To find the components:

- [tex]\( a_x = a \sin(\theta) \)[/tex]

- [tex]\( a_y = -a \cos(\theta) \)[/tex]

However, since the angle is counterclockwise from the [tex]\(-y \)[/tex]-axis and to the left, the [tex]\( x \)[/tex]-component is positive.

Therefore:

- [tex]\( a_x = 18 \sin(35^\circ) \)[/tex]

- [tex]\( a_y = -18 \cos(35^\circ) \)[/tex]

Calculating these:

- [tex]\( a_x \approx 18 \times 0.5736 \approx 10.3 \text{ m/s}^2 \)[/tex]

- [tex]\( a_y \approx -18 \times 0.8192 \approx -14.7 \text{ m/s}^2 \)[/tex]

So, the components are:

- [tex]\( a_x \approx 10.3 \text{ m/s}^2 \)[/tex]

- [tex]\( a_y \approx -14.7 \text{ m/s}^2 \)[/tex]

The correct question is:

1. Find the [tex]$x$[/tex] - and [tex]$y$[/tex]-components of the vector [tex]$d \boxtimes=(9.0 \mathrm{~km}, 25 \boxtimes$[/tex] left of [tex]$+\mathrm{y}$[/tex]-axis).

2. Find the [tex]$\mathrm{x}$[/tex] - and [tex]$\mathrm{y}$[/tex]-components of the vector [tex]$\mathrm{v} \boxtimes=(4.0 \mathrm{~cm} / \mathrm{s},-\mathrm{x}$[/tex]-direction [tex]$)$[/tex].

3. Find the [tex]$x$[/tex] - and [tex]$y$[/tex]-components of the vector [tex]$a \boxtimes=(18 \mathrm{~m} / \mathrm{s} 2,35 \boxtimes$[/tex] left of [tex]$-y$[/tex]-axis [tex]$)$[/tex].


Related Questions

I need help with #18 c-i

Answers

c - one is -4 due to that when y=0 the x coordinate shows -4, the other is when 4-x^2=0, and the square root of 4 is 2

d - x intercepts

e - it's 4 due to that 4 is shown where x=0 on the graph

f - y intercept

g - Since x>0, we do 4-x^2. x=1, and 1^2=1, so 4-1=3. 1 is x and 3 is f(x), or y, so the coordinates are (1,3)

h - Since it's <0, -1+4=3, and since 3 is the output the coordinates are (-1,3)

i - Since -3 <0, we do -3+4=1

A gardener has 27 pansies and 36 daisies. He plants an equal number of each type of flower in each row.What is the greatest possible number of pansies in each row?

Answers

There are 27 pansies.
The factors of 27 are (3,9)
Therefore,
Either (a) plant 3 pansies in 9 rows, or
           (b) plant 9 pansies in 3 rows.

There are 36 daisies.
The factors of  36 are (3,12), (6,6) or (9,4).
Therefore
Either (a)  plant 3 daisies in 12 rows, or
           (b) plant 12 daisies in 3 rows, or
           (c) plant 6  daisies in 6 rows, or
           (d) plant 9 daisies in 4 rows, or
           (e) plant 4 daisies in 9 rows.

Because each row has an equal number of pansies and daisies, the only common arrangements are
(a) 9 pansies and  12 daisies in 3 rows, or
(b) 3 pansies and 4 daisies in 9 rows.

To have the greatest number of daisies in each row means planting 9 pansies and 12 daisies in 3 rows.

Answer: 
The greatest number of pansies per row is 9.
Plant 9 pansies and 12 daisies in 3 rows.

In the diagram below, what is the approximate length of the minor arc ? 

Answers

arc length = given angle/360 x 2 x PI x radius

120/450 x 2 x 3.14 x 23 = 48.17

 round to 48 cm

Answer:

Option A is correct

the approximate length of the minor arc is, 48 cm

Step-by-step explanation:

Length of an arc is given by:

[tex]l = r \theta[/tex]              .....[1]

here r is the radius of the circle from the center and [tex]\theta[/tex] is the angle in radian.

From the given figure, we have;

r = 23 cm

Use conversion:

1 degree = 0.0174533 radian

then

120 degree = 2.094396

[tex]\theta = 2.094396[/tex] radian.

Substitute these in [1] we have;

[tex]l = 23 \cdot 2.094396 = 48.171108[/tex] cm

Therefore, the approximate length of the minor arc is, 48 cm

Which equation is not equivalent to the formula m = ca?
A: [tex]c = \frac{m}{a} [/tex]
B: [tex]a = \frac{c}{m} [/tex]
C: [tex]a = \frac{m}{c} [/tex]
D: m = ac

Answers

m = ca

If we find a, we must do c = m/a and if we find c we must do a = m/c

The bigger measure over the known one.

Answer B

Answer:m=ca i remember my teacher telling me how to do this.

Step-by-step explanation:

Evaluate f(x) when x=9

Answers

if x = 9 then f(x) = 12

answer
12
that is in the range 9≤x<13

f(x) in that range is equal to 12

so f(9)=12

When a line has an undefined slope what will any two points on the line have in common

Answers

y-coordinate
Good luck and have a nice day.
I think it y or k coordinate most likely y coordinate
 

3. Simplify log3 20 - log3 5

Answers

[tex]\log_320-\log_35=\log_3\dfrac{20}{5}=\log_34[/tex]

A line passes through the point (-8,3) and has a slope of 5/4.

Write an equation in slope-intercept form for this line.

Answers

y = mx + b
3 = 5/4(-8) + b
3 = -10 + b
b= 13


equation

y = 5/4x + 13
y - y1 = m(x - x1)
y - 3 = (5/4) ( x + 8)
y - 3 = 5/4x + 10
add 3 to both sides
y = 5/4 x + 13

Find the greatest common factor of the following monomials 28g5h2 12g6h5
Also explain step by step how to solve these problems please

Answers

28g^5h^2 and 12g^6h^5

first, we find the GCF of the coefficients 28 and 12. What is the highest number that will go into both 28 and 12 evenly ? That number is going to be 4.

now, we look at our variables....to find the GCF of the variables, pick the lowest exponent.
another words, the lowest exponent of ur variable h is h^2...and the lowest exponent of ur variable g is g^5

therefore, the GCF of these monomials is : 4h^2g^5

A surface on which all points are at the same potential is referred to as

Answers

equipotential, equi=equal

The measure of an inscribed angle is 110°. What is the measure of the intercepted arc? 55° 110° 220°

Answers

the measurement of an inscribed angle is half of the measure of the intercepted arc.

the inscribed angle is 110 degrees, so we multiply 110 by 2.

110*2 = 220 degrees

The measure of the intercepted arc is 220 degrees

220° is the measure of the intercepted arc

Can someone help me

Answers

2.89-2.84 = 0.05 cent increase

0.05/2.84 = 0.0176

0.0176 = 1.8% increase

price increase = (new number - original number) / original number....* 100
                       = (2.89 - 2.84) / 2.84...* 100
                      = 0.05 / 2.84....* 100
                      = 0.0176 ...* 100
                      = 1.76  rounds to 1.8% <===

Can you use the ASA Postulate or the AAS Theorem to prove the triangles congruent?

Answers

Answer:

ASA only

Step-by-step explanation:

Given is a picture of two triangles with one side and one angle congruent.

Comparison of these two triangles given

side = side

one angle = one angle (given)

Second angle = second angle (Vertically opposite angles)

Thus we find here that two angles and one corresponding side are congruent.

HEnce we say that these two triangles are congruent by ASA theorem

ASA theorem can be applied here because the equal side is between the two congruent angles.  

Instead if the side is not between the congruent angles but corresponding side then we can only use AAS

SO here ASA is correct.

Answer:

ASA only

Step-by-step explanation:

We are given that  two triangles in which

An angle of triangle is equal to its corresponding angle of second triangle.

One side of a triangle is equal to one side of other triangle.

ASA  postulate: It states that two angles and included side of one triangle are congruent to its corresponding angles and corresponding side of other triangle , then the two triangles are congruent.

AAS postulate: It states that two angles and non- included side of one triangle are congruent to its corresponding two angles and its corresponding side of another triangle, then the triangles are congruent by AAS postulate.

In triangle AOB and COD

[tex]\angle AOB= \angle COD[/tex]  (Vertical angles are equal )

[tex]\angle ABO=\angle CDO[/tex] ( Given )

[tex]OB=OD[/tex] (Given )

[tex]\triangle AOB\cong \triangle COD[/tex] ( ASA Postulate )

Answer: ASA only

Solve cos x +sqrt2 = -cos x for x over the interval (0,2pi) .

Answers

Final answer:

The equation cos x + sqrt(2) = -cos x is solved by combining like terms and isolating cos x, resulting in the solutions x = 3π/4 and 5π/4 over the interval (0,2π).

Explanation:

To solve the equation cos x + sqrt(2) = -cos x for x over the interval (0,2π), first combine like terms by adding cos x to both sides of the equation, resulting in:

2 cos x + sqrt(2) = 0

Isolate cos x by subtracting sqrt(2) from both sides:

2 cos x = -sqrt(2)

Divide both sides by 2 to solve for cos x:

cos x = -sqrt(2)/2

The value of cos x = -sqrt(2)/2 corresponds to angles in the second and third quadrants. So, the solutions for x in the interval (0,2π) are:

x = 3π/4, 5π/4

Which is a counterexample that disproves the conjecture? After completing several multiplication problems, a student concludes that the product of two binomials is always a trinomial.

Answers

When you make the product of a binomial of the kind x + a times other binomial that is of the kind x - a, you obtain another binomial (not a trinomial), so any example with that form will be a counterexample that disproves the conjecture:

(x + a) * (x - a) = x^2 - a^2

For example, (x +3) * (x - 3) = x^2 - 9. So, not always the product of two binomials is a trinomial.

HELP! Type the correct answer in each box. Use numerals instead of words, if necessary, use / for the fractions bar(s)

Answers

The piecewise function is:

[tex]\[ f(x) = \begin{cases} 4 & \text{if } -1 \leq x \leq 1 \\ x - 1 & \text{if } 3 \leq x \leq 5 \end{cases} \][/tex]

To determine the piecewise function represented by the given coordinates, let's examine the points and their corresponding intervals.

The coordinates are (-1, 4), (1, 4), (3, 2), and (5, 4).

The points (-1, 4) and (1, 4) have the same y-coordinate, indicating that on the interval [tex]\(-1 \leq x \leq 1\)[/tex], the function has a constant value of 4. Therefore, the piecewise function for this interval is f(x) = 4 for [tex]\(-1 \leq x \leq 1\).[/tex]

The points (3, 2) and (5, 4) indicate that on the interval [tex]\(3 \leq x \leq 5\)[/tex], the function is a line passing through these two points. We can find the slope (m) and y-intercept (b) for this line.

[tex]\[ m = \frac{\text{change in } y}{\text{change in } x} = \frac{4 - 2}{5 - 3} = \frac{2}{2} = 1 \][/tex]

Using the point (3, 2), we can find the y-intercept:

2 = 1(3) + b

b = -1

Therefore, the equation for the line on the interval [tex]\(3 \leq x \leq 5\) is \(f(x) = x - 1\) for \(3 \leq x \leq 5\).[/tex]

Putting it all together, the piecewise function is:

[tex]\[ f(x) = \begin{cases} 4 & \text{if } -1 \leq x \leq 1 \\ x - 1 & \text{if } 3 \leq x \leq 5 \end{cases} \][/tex]

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The variable Z is inversely proportional to X. When X is 6, Z has the value 2. What is the value of z . When x = 13
Round to at least the thousandths place if needed.

Answers

Given that z is inversely proportional to x, then:
z α 1/x
hence;
z=k/x
where:
k is the constant of proportionality; 
when x=6, z=2
therefore;
2=k/6
hence;
k=2*6=12

Therefore:
z=12/x
the value of z when x=13 will be:
z=12/13
the answer is 12/13

What is the equation of the line?

Answers

First find the slope of the line. Slope is defined as the change in y over the change in x.

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Find two ordered pairs and plug them into the slope formula.

After looking at the graph, I found two points: (0, 1) and (4, 4)

[tex]\frac{4 - 1}{4 - 0} = \frac{3}{4}[/tex]

Now find where the line intersects the y-axis.

After looking at the graph, I found out that the line intercepts the y-axis at
(0, 1)

Now build the slope-intercept equation.

General form: y = mx + b
Where m is the slope and b the y-intercept

So, the answer is y = 3/4m + 1

Identify the cross section shown.

circle


trapezoid


rectangle


pentagon

Answers

The cross section shown in the picture below include the following: B. rectangle.

In Mathematics and Euclidean Geometry, a rectangle refers to a type of quadrilateral or polygon in which its opposite sides are equal and all the angles that are formed are right angles.

Generally speaking, a circle has no edge or sides. A trapezoid is a type of quadrilateral that has one pair of parallel sides and one pair of non-parallel sides. Additionally, a pentagon is a regular polygon that comprises 5 sides.

By critically observing the cross section shown in the picture below, we can logically deduce that it represents a rectangle because its opposite sides are equal.

Using the graph, find this information about the child’s movement in the vertical (y) direction:
1. the best trigonometric function to start with
2. the amplitude
3. the period
4. any horizontal displacement of the graph.
5. any vertical displacement of the graph.

Type your response here:

Answers

1. The sine and cosine function are sinusoidal waves such that they form waves when you graph them on a cartesian plane. The only difference between them is that the crest comes first followed by the trough in the sine function. The opposite is true for the cosine function. The graph in the picture is a sine function.

2. The amplitude is the measure from crest to crest, or from trough to trough. The amplitude in the graph is 1.5.

3. The period is the reciprocal of amplitude. Therefore,itis 1/1.5 or 2/3.

4. There is no horizontal displacement because the wave only moves in a vertical direction.

5. The vertical displacement is from crest to trough which is 1 unit.

Evaluate. 5.4 - 1.3

Answers

5.4-1.3=4.1 is ur answer.
5.4 - 1.3= 4.1 is your answer

The initial temperature of a cup of tea is 200ºF. The surrounding temperature is 70ºF, and the value of the constant k is 0.6.
Applying Newton's cooling model, the temperature of the tea after 2 hours will be ___
ºF. round to the nearest integer.

Answers

Newton's Law of Cooling states that the change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature over time.

Therefore when expressed mathematically, this is equivalent to:

dT = - k (T – Ts) dt

dT / (T – Ts) = - k dt

Integrating:

ln [(T2– Ts) / (T1– Ts)] = - k (t2 – t1)

Before we plug in the values, let us first convert the temperatures into absolute values R (rankine) by adding 460.

R = ˚F + 460

T1 = 200 + 460 = 660 R

Ts = 70 + 460 = 530 R

ln [(T2– 530) / (660 – 530)] = - 0.6 (2 - 0)

T2 = 569.16 R

T2 = 109 ºF

Answer: After 2 hours, it will be 109 ºF

Answer:

109 degrees

Step-by-step explanation:

Find the angle between the given vectors to the nearest tenth of a degree. u = <-5, 8>, v = <-4, 8>

Answers

Answer: 5.4 degrees

Step-by-step explanation:

look up online "how to find the angle between 2 vectors, and it'll show you how"

Find the exact values of sin A and cos A. Write fractions in lowest terms. A right triangle ABC is shown. Leg AC has length 15, leg BC has length 20, and hypotenuse AB has length 25.

Answers

sin A = opposite / hypotenuse = BC/AB = 20/25 = 4/5

cos A = adjacent / hypotenuse = AC/AB = 15/25 = 3/5

In the right triangle with sides 15, 20, and 25, the exact values of sin A and cos A are 4/5 and 3/5, respectively.

In the right triangle ABC, we can use the given side lengths to find the trigonometric ratios for angle A. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (AB) is equal to the sum of the squares of the lengths of the legs (AC and BC).

Let's denote the angle A as angle A:

Find sin A:

sin A = (opposite / hypotenuse) = BC / AB = 20 / 25 = 4/5.

Find cos A:

cos A = (adjacent / hypotenuse) = AC / AB = 15 / 25 = 3/5.

So, the exact values are sin A = 4/5 and cos A = 3/5.

In summary, in the right triangle ABC with side lengths AC = 15, BC = 20, and AB = 25, the exact values of sin A and cos A are 4/5 and 3/5, respectively.

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The sum of 2 numbers is 7. if one number is subtracted from the other, the result is -1. find the numbers

Answers

Let the two numbers be x and y.

Given,

x + y = 7

x = 7 - y

Also given,

x - y = -1

7 - y - y = -1

-2y = -8

y = 4

x = 7 - y = 7 - 3 = 4

Hence, the numbers are 3 and 4.

Use Gauss-Jordan elimination to solve the following linear system: 5x – 2y = –2 –x + 4y = 4 A. (–6,–5) B. (2,0) C. (0,1) D. (–1,0)

Answers

Im pretty sure its A.

The answer is C.(0,1)

5x - 2y = -2 -x + 4y = 4

5(0) - 2(1) = -2 -(0) + 4(1) = 4

If four times a number plus 3 is 11, what is the number

Answers

4x + 3 = 11
4x = 11 -3
4x = 8
x =8/4
x =2

answer
the number is 2
4x + 3 = 11
4x = 11-3 = 8
x = 2

number is 2

Quadrilateral ABCD is a parallelogram. ,  bisects , and . What is the best name for quadrilateral ABCD?

A.

rectangle

C.

isosceles trapezoid

B.

rhombus

Answers

C. Isosceles trapezoid

Determine the common ratio and find the next three terms of the geometric sequence.



3/4,3/10,3/25,...

Answers

to find the common ratio, divide the 2nd term by the 1st term
(3/10) / (3/4) = 3/10 * 4/3 = 12/30 = 2/5 <==

In a geometric sequence, the next term is found by multiplying the term by the common ratio.
3/25 * 2/5 = 6/125 <==
6/125 * 2/5 = 12/625 <==
12/625 * 2/5 = 24/3125 <==

The next three terms of the sequence are 6/125, 12/625 and 24/3125

Geometric sequence

The nth term of a geometric sequence is given as:

Tn = ar^n-1

Given the geometric sequence

3/4,3/10,3/25,...

Find the common ratio

r = 3/10 * 4/3

r = 2/5

Find the 4th, 5th and 6th terms

T4 = (3/4)(2/5)^3
T4 = 3/4 * 8/125
T4 = 6/125

T5 = (3/4)(2/5)^4
T5 = 3/4 * 16/625
T5 = 12/625

T6 = (3/4)(2/5)^5
T6 = 3/4 * 32/3125
T6 = 24/3125

Hence the next three terms of the sequence are 6/125, 12/625 and 24/3125

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Two containers, one for 3 liters and one for 5 liters, how would you measure 4 liters

Answers

Fill the 5-liter container, pour water from that into the 3 liter container until that is full,  You will now have 2 liters left in the 5 liter container.

Empty the 3-liter container, and then transfer the 2 liters from the 5-liter container into it.

Now fill the 5-liter container again, then pour water carefully from the 5-liter container into the 3-liter container until it is full - exactly one more liter.

The 5-liter container now has 4 liters in it.
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