A line perpendicular to a plane, would intersect the plane at one point.
Perpendicular linesWhen a line is perpendicular directly away from the plane, the line will tend to intersect the plane at one points or single points.
The reason why the line intersect the plane is because the line cannot point to other places except directly away from the plane.
Therefore a line perpendicular to a plane, would intersect the plane at one point.
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Find the x- and y-components of the vector d⃗ = (9.0 km , 35 ∘ left of +y-axis).
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.
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].
If f(x)=4^x , which statements are true of g(x)? Check all that apply
The true statements about functions f(x) and g(x) are:
b. g(x) = 4^x - 1d.The function f(x) is translated 1 units down to get the function g(x) How to determine the true statements?The function f(x) is given as:
f(x) = 4^x
From the table of values, we can see that the function g(x) is 1 less than the function f(x).
This means that:
g(x) = f(x) - 1
This can be rewritten as:
g(x) = 4^x - 1
In transformation, it means that the function f(x) is translated 1 units down to get the function g(x)
Hence, the true statements are: b and d
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Determine the growth factor corresponding to 25% increase.
a.
1.75
c.
25
b.
1.25
d.
0.25
Answer:
Step-by-step explanation:
Alright, lets get started.
The given increase is 25 %.
Which means in terms : [tex]25*\frac{1}{100}[/tex]
That will be equal to : [tex]0.25[/tex]
So, the growth of 0.25 means the complete term will be :
[tex]1+0.25=1.25[/tex]
Hence the growth factor of 25 % will be equal to 1.25 : Answer
Hope it will help :)
The table below shows 10 data values:
88
92
94
80
85
90
72
83
93
91
What is the five-number summary for these data?
Minimum = 72, Q1 = 83, median = 89, Q3 = 92, maximum = 94
Minimum = 80, Q1 = 85, median = 89, Q3 = 91, maximum = 93
Minimum = 80, Q1 = 83, median = 90, Q3 = 92, maximum = 93
Minimum = 72, Q1 = 85, median = 90, Q3 = 91, maximum = 94
If ON = 9x – 4, LM = 8x + 7, NM = x – 3, and OL = 4y – 8, find the values of x and y for which LMNO must be a parallelogram.
The area of a triangle is 92 cm2. the base of the triangle is 8 cm. what is the height of the triangle?
a. 11.5 cm
b. 23 cm
c. 4 cm
d. 46 cm
Answer: b. 23 cm
Step-by-step explanation:
We know that area of a triangle is given by :-
[tex]\text{Area}=\dfrac{1}{2}bh[/tex], where b is the base of triangle and h is the height of the triangle.
Given : The area of a triangle is [tex]92\ cm^2[/tex]
The base of the triangle = 8 cm
Let h be the height of the triangle , then we have
[tex]92=\dfrac{1}{2}(8)h\\\\\Rightarrow\ h=\dfrac{92}{4}\\\\\Rightarrow\ h = 23[/tex]
Hence, the height of the triangle = 23 cm
What are the rigid transformations that will map
△ABC to △DEF?
Translate vertex A to vertex D, and then reflect
△ABC across the line containing AC.
Translate vertex B to vertex D, and then rotate
△ABC around point B to align the sides and angles.
Translate vertex B to vertex D, and then reflect
△ABC across the line containing AC.
Translate vertex A to vertex D, and then rotate
△ABC around point A to align the sides and angles.
Answer:
The answer above is correct! The answer is option D.
Step-by-step explanation:
Hope this helped clarify :D
Translating vertex A to vertex D, and then rotate △ABC around
point A to align the sides and angles will bring about a rigid
transformation.
What is Rigid transformation?This is the transformation which preserves the Euclidean
distance between every pair of points. This could be as a result
of the following:
RotationReflectionTranslation etc.Option D when done will preserve the distance between the
points when vertex A is translated to vertex D as they contain
the same angle with other sides and angles being made to
align.
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If a radius of a circle bisects a chord which is not a diameter, then ______
Answer:
the radius is perpendicular to the chord.
Step-by-step explanation:
The geometry is drawn in the image shown below in which AB is the chorh and O is the centre of the circle. Om is the radius which bisects the chord.(Given) So, AN = NB
From the image, considering ΔAON and ΔBON,
AO = BO (radius of circle)
AN = NB (given)
ON = ON (common)
So,
ΔAON ≅ ΔBON
Hence, ∠ANO = ∠BNO
Also, ∠ANO + ∠BNO = 180° (Linear Pair)
So,
∠ANO = ∠BNO = 90°
Hence, it is perpendicular to the chord.
Jonathan sets a camera on a tripod to film birds in a nest. The camera is 1.8 m off the ground and 16.4 m away from the tree. The angle of elevation from the camera to the bird’s nest is 29°. How far above the ground is the bird’s nest? Round your answer to the nearest tenth of a meter. 7.3 m 9.1 m 10.9 m 14.3 m
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 24, leg BC has length 32, and hypotenuse AB has length 40.
In this question , it is given that
A right triangle ABC is shown. Leg AC has length 24, leg BC has length 32, and hypotenuse AB has length 40.
And we have to find the values of sin A and cos A .
[tex]sin A = \frac{opposite}{hypotenuse} = \frac{32}{40}[/tex]
[tex]sin A = \frac{4}{5}[/tex]
And
[tex]cos A = \frac{adjacent}{hypotenuse} = \frac{24}{40}[/tex]
[tex]cos A = \frac{3}{5}[/tex]
And these are the required values of sin A and cos A .
Solve the equation by extracting the square roots. when a solution is irrational, list both the exact solution and its approximation rounded to two decimal places.
Find the distance between the points (13, 20) and (18, 8).
Answer: 13 units
Step-by-step explanation:
The distance formula to calculate distance between two points (a,b) and (c,d) is given by :-
[tex]d=\sqrt{(d-b)^2+(c-a)^2}[/tex]
Given points : (13, 20) and (18, 8)
Now, the distance between the points (13, 20) and (18, 8)is given by ;-
[tex]d=\sqrt{(8-20)^2+(18-13)^2}\\\\\Rightarrow\ d=\sqrt{(-12)^2+(5)^2}\\\\\Rightarrow\ d=\sqrt{144+25}\\\\\Rightarrow\ d=\sqrt{169}\\\\\Rightarrow\ d=13\text{units}[/tex]
Hence, the distance between the points (13, 20) and (18, 8) is 13 units.
D is (8,4) it just got cut off
Find the radius of a circle with an x-intercept of -2 if the circle’s center is (2,3) on a coordinate plane.
5
25
16
9
Radius of the circle is option (1) 5 units
What is radius?A radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length.
What is circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center
Center of the circle is (2,3) on a coordinate plane,
Radius of the circle with an x intercept of -2
There for the point is (-2,0)
Distance between the (2,3) and (-2,0) = Radius of the circle
Distance between (2,3) and (-2,0)
D= [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]
Substitute the values
[tex]D=\sqrt{(-2-2)^{2}+(0-3)^{2} }\\D=\sqrt{16+9} \\D=\sqrt{25}\\ D=5[/tex]
Hence, the radius of the circle is option (1) 5 units
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The graph shows the distance, y, that a car traveled in x hours:
A graph is shown with x axis title as Time in hours. The title on the y axis is Distance Traveled in miles. The values on the x axis are from 0 to 5 in increments of 1 for each grid line. The values on the y axis are from 0 to175 in increments of 35 for each grid line. A line is shown connecting ordered pairs 1, 35 and 2, 70 and 3, 105 and 4, 140. The title of the graph is Rate of Travel.
What is the rate of change for the relationship represented in the graph?
fraction 1 over 35
fraction 1 over 34
34
35
Answer: 35
Step-by-step explanation:
The rate of change of a graph is given by :-
[tex]k=\dfrac{\text{Change in y avlues}}{\text{Change in x values}}[/tex]
For points : (1, 35) and (2, 70)
The rate of change for the relationship in the graph is given by :-
[tex]k=\dfrac{70-35}{2-1}=35[/tex]
Hence, the rate of change for the relationship represented in the graph = 35.
The rate of change of the relationship shown in the graph is 35 miles per hour.
Linear equationLinear equation is in the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the y intercept.
Let y represent the elevator height after x seconds.
From the graph using points (0, 0) and (4, 140):
m = (140 - 0)/(4 - 0) = 35
The rate of change of the relationship shown in the graph is 35 miles per hour.
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A dress is priced at $21.42. The store is having a 30%-off sale. What was the original price of the dress?
Find all complex solutions of 4x^2-5x+2=0.
(If there is more than one solution, separate them with commas.)
find the area of a regular nonagon with a side length of 7 and an apothem of 5
A computer training institute has 625 students that are paying a course fee of $400. Their research shows that for every $20 reduction in the fee, they will attract another 50 students. What fee should the school charge to maximize their revenue?
$275
$380
$320
$325
Answer: it’s D $325
Step-by-step explanation:
the fee the school should charge to maximize their revenue is $325
You make $30,000.00 and your spouse makes $35,000.00. using the 20% range, calculate the least and greatest amount you spend on housing
30,000 x 0.20 = $6,000 least amount
30,000 +35,000 = 65,000
65000 x 0.20 = $13,000 greatest amount
The following table shows information collected from a survey of students regarding their grade level and transportation they use to arrive at school. What is the probability that a randomly selected eighth grader takes the bus?
How to find the area of region composed of rectangles and/or right triangles?
How do you solve
8(x-1)-2x=-(x+50)
The solution to the equation 8(x-1) - 2x = -(x + 50) is x = -6.
To solve the equation 8(x-1) - 2x = -(x + 50).
First, distribute the 8 to the terms inside the parentheses:
8x - 8 - 2x = -(x + 50)
Simplify the left side of the equation:
6x - 8 = -(x + 50)
Distribute the negative sign to the terms inside the parentheses:
6x - 8 = -x - 50
Isolate the x terms on one side and the constant terms on the other side:
6x + x = -50 + 8
Combine like terms:
7x = -42
Divide both sides of the equation by 7:
7x / 7 = -42 / 7
x = -6
Therefore, the solution to the equation 8(x-1) - 2x = -(x + 50) is x = -6.
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A pet store has k tanks of fish. Each tank has 30 fish. Using k, write an expression for the total number of fish in the store.
which of the following functions are graphed below
Answer:
The equation of given graph is f(x)=[x]-6
C is correct
Step-by-step explanation:
We are given a graph and to find the equation of graph.
It is a graph of greatest integer function or floor function.
Parent function of greatest integer function:
[tex]f(x)=[x][/tex]
For x = 0 to x= 1 , f(x)=0
For x =1 to x=2 , f(x)=1
We are given a function,
For x = 0 to x= 1 , f(x)=-6
For x = 1 to x= 2, f(x) = -5
If we shift 6 unit down the parent function. We will get original function.
[tex]f(x)=[x]-6[/tex]
Hence, The equation of given graph is f(x)=[x]-6
#3 In the figure below, the measure of Arc AC is 65 degree and if angle abc is equal to 78 degree.
True or false
False, The measure of Arc AC is not 65 degree if angle ABC is equal to 78 degree.
What is Circle?
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The statement is,
The measure of Arc AC is 65 degree if angle ABC is equal to 78 degree.
Now,
Since, Sum of Measure of arc AC and angle ABC is equal to 360 degree.
So, In angle ABC is 78 degree.
Then, Measure of arc AC = 360 - 78
= 282 degree.
Thus, The measure of Arc AC is not 65 degree if angle ABC is equal to 78 degree.
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The Cool Company determines that the supply function for its basic air conditioning unit is S(p) = 40 + 0.008p^3 and that its demand function is D(p) = 200 - 0.16p^2, where p is the price. Determine the price for which the supply equals the demand.
A line has no width and extends infinitely far in _____ directions.
If sam walks 650 meters in x minutes then write an algebraic expression which represents the number of minutes it will take sam to walk 1500 meters at the same average rate.
Find the midpoint of A and D. Simplify completely.
option 5 is none of these.
A = (1,3)
D= (5,0)
midpoint = (x1+x2)/2 , (y1+y2)/2
5+1=6/2 =3
3+0=3/2 = 3/2
(3,3/2)