Part A- The linear form of the vectors are as follows:
Airplane vector: (-127.05 mph, 290.97 mph)
Wind vector: (20 mph, 34.64 mph)
Part B- The sum of the vectors is (-107.05 mph, 325.61 mph).
Part C- The true speed of the airplane is approximately 346.68 mph, and the true direction is approximately -72.044°.
Part A:
To express the vectors in linear form, we'll break them down into their horizontal (x) and vertical (y) components.
Airplane vector:
Magnitude: 300 mph
Direction: 100°
We can find the horizontal component (x) using cosine:
x = magnitude × cos(direction)
x = 300 × cos(100°)
x ≈ -127.05 mph (rounded to two decimal places)
We can find the vertical component (y) using sine:
y = magnitude × sin(direction)
y = 300 × sin(100°)
y ≈ 290.97 mph (rounded to two decimal places)
Wind vector:
Magnitude: 40 mph
Direction: 60°
Horizontal component (x):
x = magnitude × cos(direction)
x = 40 × cos(60°)
x = 20 mph
Vertical component (y):
y = magnitude * sin(direction)
y = 40 × sin(60°)
y ≈ 34.64 mph (rounded to two decimal places)
Therefore, the linear form of the vectors are as follows:
Airplane vector: (-127.05 mph, 290.97 mph)
Wind vector: (20 mph, 34.64 mph)
Part B:
To find the sum of the vectors, we simply add their corresponding components.
Horizontal component (x):
-127.05 mph + 20 mph = -107.05 mph
Vertical component (y):
290.97 mph + 34.64 mph = 325.61 mph
Therefore, the sum of the vectors is (-107.05 mph, 325.61 mph).
Part C:
To find the true speed and direction of the airplane, we'll calculate the magnitude and direction of the resultant vector.
Magnitude (speed) of the resultant vector:
speed = √([tex]x^2 + y^2[/tex])
speed = √((-107.05 mph[tex])^2[/tex] + (325.61 mph[tex])^2[/tex])
speed ≈ 346.68 mph (rounded to three decimal places)
Direction (angle) of the resultant vector:
angle = arctan(y / x)
angle = arctan(325.61 mph / -107.05 mph)
angle ≈ -72.044° (rounded to three decimal places)
The true speed of the airplane is approximately 346.68 mph, and the true direction is approximately -72.044°.
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Write an equation of the line that passes through the point (8, 1) with slope 5. A. y - 1 = 5(x − 8) B. y − 1 = - -5(x − 8) - C. y - 8 = -5(x - 1) OD. y - 8 = 5(x − 1) Question Progress
Answer:
[tex]y-1=5(x-8)[/tex]
A polygon has the coordinates A (3, 4), B (3, 1), and C (5, 1). Identify the type of polygon
The type of polygon is a triangle
How to identify the type of polygon?The coordinates are given as:
A (3, 4), B (3, 1), and C (5, 1).
The above shows that the number of vertices in the polygon is 3
A polygon that has 3 vertices is a triangle
Hence, the type of polygon is a triangle
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From the given graph, use two points to write an equation in point-slope form and then
change to slope-intercept form.
Step 1: Use the two points to find the slope.
Step 2: Use the slope and one point to complete point-slope form.
y-y₁ = m(x-x₁)
Step 3: Change point-slope form into slope intercept form by solving for y. Show your
work!
y=mx+b
Step 1
Using the points (2,0) and (-2, -3), we get the slope is
[tex]\frac{-3-0}{-2-2}=\frac{3}{4}[/tex]
Step 2
Using the point (2,0), the equation is
[tex]y=\frac{3}{4}(x-2)[/tex]
Step 3
Using the distributive property, we get [tex]y=\frac{3}{4}x-\frac{3}{2}[/tex].
BP = _______ BC = ________ 13. AP = 3.5, PD = 6, PC = 4
Find BP and BC.
The measure of the length BP and BC are 6 and 10 respectively
Circle theoremThe given figure is a circle containing two chords AD and BC. From the given diagram, the following are true
AP = PC
BP = PD
BC = BP + PC
Circle theorem includes the concept of tangents, sectors, angles, the chord of a circle and proofs. A circle is the locus of all points in a plane which are equidistant from a fixed point.
Given the following parameters
AP = 3.5,
PD = 6,
PC = 4
According to the expression above;
BP = PD = 6
BC = BP + PC
BC = 6 + 4
BC = 10
Hence the measure of the length BP and BC are 6 and 10 respectively
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what formula would i need to use to graph the relationship of volume of surface area of a cylinder?
The formula is illustrated below:
Volume of cylinder = πr²hSurface area = 2πrh + 2πr²How to illustrate the information?It should be noted that a cylinder simply means a three dimensional solid which holds two parallel bases that are joined by a curved surface.
In this case, it can be seen that the formula that can be used to calculate the volume and the surface area of the cylinder is illustrated above.
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Graph the quadratic function by transforming the graph of f(x) = x^2. Give the minimum or maximum
vertex value and the equation for the axis of symmetry.
For the function g(x) we have:
Maximum y = 5Vertex (-2, 5)Axis of symmetry: x = -2.How to find the graph of g(x)?
The function g(x) is given by applying transformations to f(x), the transformations are:
A reflection: g(x) = -f(x)A translation of 2 units to the left: g(x) = -f(x + 2)A translation of 5 units up: g(x) = -f(x + 2) + 5The function is:
[tex]g(x) = -(x + 2)^2 + 5[/tex]
The graph is the one you can see below:
There you can see that the vertex is at (-2, 5), then the line of symmetry is:
x = -2.
And we have a maximum at the vertex, which is y = 5.
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Yasmin designed a square table using a scale drawing. The actual length of each side was 4 feet and the scale factor was 1 inch : 2 feet. Choose the figure with the new side length if Yasmin changed the scale factor to 1 inch : 3 and two-thirds feet.
The figure with the new side length if Yasmin changed the scale factor to 1 inch : 3 and two-thirds feet is a square with side lengths of 7 and one third feet.
How to calculate the length?From the information given, the actual length of each side was 4 feet and the scale factor was 1 inch : 2 feet.
The new length will be:
= 2 × 3 2/3
= 7 1/3
Therefore, the new length is 7 1/3 feet.
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WILL MAKE BRAINLIEST!!Determine if two triangles are congruent if they are state the triangle congruence statement.
Answer:
Yes they are congruent by SSS criterion Explanation:AC=DC. (Given in figure)
AB=BD. (Given in figure
BC=BC. (Common)
that means triangle BAC is congruent to triangle BDC by SSS criterion
Help pls :’( ASAPP!!!
“Complete the proof”
1) [tex]\overline{AB} \cong \overline{CD}[/tex], [tex]\overline{AD} \cong \overline{CB}[/tex], [tex]\overline{AX} \perp \overline{BD}[/tex], [tex]\overline{CY} \perp\overline{BD}[/tex] (given)
2) [tex]\overline{BD} \cong \overline{BD}[/tex] (reflexive property)
3) [tex]\triangle ABD \cong \triangle ACDB[/tex] (SSS)
4) [tex]\angle ADB \cong \angle CBY[/tex] (CPCTC)
5) [tex]\angle CYB[/tex] and [tex]\angle AXD[/tex] are right angles (perpendicular lines form right angles)
6) [tex]\triangle CYB[/tex] and [tex]\triangle AXD[/tex] are right triangles (a triangle with a right angle is a right triangle)
7) [tex]\triangle AXD \cong \triangle CYB[/tex] (HA)
8) [tex]\overline{AX} \cong \overline{CY}[/tex] (CPCTC)
Practice with Laws of Logic
Provide the valid conclusion to the argument below.
If I am sick, then I will not come to school.
If I do not come to school, then I am sad.
Answer:
if I am sick, then I will not come to school.
Step-by-step explanation:
There are 400 beads in a box. 20% of them are red, 35% of them are yellow and the rest are green. How many green beads are there in the box
Step-by-step explanation:
400 is the whole = 100%
20% (= 20 out of 100 equal parts of 100%) are red.
how many are that ?
well, again, 400 = 100%
1% = 100%/100 = 400/100 = 4
20% = 20×1% = 20×4 = 80
when you combine these 2 steps, you see you get 20% by multiplying the 100% by 20/100 or 0.20.
400 × 0.2 = 80
now,
35% are yellow.
35% = 35×1% = 35×4 = 140
or
400×0.35 = 140
red + yellow = 80 + 140 = 220
the rest are green
400 - 220 = 180
we would get this also by seeing that
red + yellow = 20% + 35% = 55%.
so, green has then the remaining 100-55 = 45%
and again
45% = 45×1% = 45×4 = 180
or
400×0.45 = 180
I need help with this!!
Answer: $18.51
Step-by-step explanation:
1015cm^3/7.95cm^3/g = 127.67g
127.67g/1000g = .128
.128*$.29 = $.037
$.037*500 = $18.51
Answer:
$1170
Step-by-step explanation:
1. We know that each steel part has a volume of 1015 cubic centimeters, and the machinist wants to make 500 of these. Then the total volume of the steel part the machinist will make will be 1015 x 500.
--> 1015 x 500
--> 507500 cubic centimeters.
2. The density of the steel part is 7.95 grams per one cubic centimeter. Then the total density of the 500 steel parts will be 507500 x 7.95.
--> 507500 x 7.95
--> 4,034,625 grams.
3. For every kilo of steel part, the cost is $0.29. We should first change the 4,034,625 gram to kilo. Since 1000 grams is a kilo, we divide 4,034,625 by 1000.
--> 4,034,625 grams / 1000 = 4034.625 kilograms.
Now we multiply 4034.625 by 0.29 to find the total cost.
--> 4034.625 x 0.29
--> 1170.04125.
Since the question specifically asked to round it to the nearest dollar, our final answer becomes $1170.
Use substitution to find the integral. (Remember to use absolute values where appropriate.) square root x / x-4
Answer:
Step-by-step explanation:
here is a solution and verify
Find a linear differential operator that annihilates the given function. (Use D for the differential operator.) 4 ex cos 3x
If the function is
[tex]y = 4 e^x \cos(3x)[/tex]
then we have derivatives
[tex]Dy = 4 e^x \cos(3x) - 12 e^x \sin(3x)[/tex]
[tex]D^2y = -32 e^x \cos(3x) - 24 e^x \sin(3x)[/tex]
Now consider the linear ODE
[tex]aD^2y + bDy + cy = 0[/tex]
Substituting [tex]y[/tex] and its derivatives reduces the equation to
[tex](-32a + 4b + 4c) \cos(3x) + (-24a - 12b) \sin(3x) = 0[/tex]
Now,
[tex]-24a - 12b = 0 \implies b = -2a[/tex]
[tex]-32a + 4b + 4c = 0 \implies c = 10a[/tex]
Then the minimal ODE with the given solution is
[tex]aD^2y -2a Dy + 10ay = 0[/tex]
or
[tex]\boxed{D^2y -2 Dy + 10y = 0}[/tex]
Que tanto por ciento es 20 de 80
Answer:
Step-by-step explanation:
40 por ciento
Find the measure of angle C.
D
118°
C
The measurement of angle C in the given figure is 118°.
Given that are two lines intersecting at a point making 4 angles, 118°, C, D and B.
B and D are opposite to each other and C and 118° are opposite to each other.
We need to find the measurement of angle C.
To find the measurement of angle C, we can use the concept of vertical angles.
Vertical angles are a pair of non-adjacent angles formed when two lines intersect.
They are always congruent, meaning they have the same measure.
In this case, angle 118° and angle C are vertical angles. So, their measures are equal:
Angle C = 118°
Therefore, the measurement of angle C is 118°.
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A square has a side of length 2xcm. in terms of X, what is the area
Answer:
4x^2
Step-by-step explanation:
2x(2x) It is a square so we multiply the side by the side to get the area.
=2*x*2*x
=4*x2
=4x^2
Pls help solve for part b)iii.
Given that the distance and angle of elevation of the tree from P are 50 m. and 32°, and Q is 100 m. from P, we have;
a. The height of the tree is approximately 31.2 m.
b. i. The distance of Q from the base of the tree is 50•√5 m.
ii. The angle of elevation of the top of the tree from Q is approximately 15.6°
iii. The bearing of the tree from Q is 296.565°
How can the distances and bearing of the tree from Q be found?a. tan(32°) = Height/50
Height = 50 × tan(32°) = 31.243 m.
Height of the tree ≈ 31.2 m.b. i. The distance, d, of Q from the base of the tree is given by Pythagorean theorem as follows;
d = √(100² + 50²) = 50•√5
The distance of Q from the base of the tree, d = 50•√5 m.ii. The angle of elevation is given by trigonometric ratios as follows;
[tex]tan (\theta) = \frac{31.243}{50 \cdot \sqrt{5} } [/tex]
Which gives;
[tex]\theta= arctan \left( \frac{31.243}{50 \cdot \sqrt{5} } \right) \approx 15.6 ^{ \circ} [/tex]
The angle of elevation of the top of the tree from Q ≈ 15.6°iii. The angle formed at Q by the lines from Q to the point P and Q to the tree is found as follows;
Angle = arctan(50/100) ≈ 26.565°
The angle between the direction north of Q and a line from Q to the tree is therefore;
90° - 26.565° = 63.435°
The bearing, which is the angle described clockwise from the direction north of Q and the direction from Q to the tree, is therefore;
Bearing = 360° - 63.435° = 296.565°
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Write an equation of the line that passes through (-1,3) and has a slope of 2.
Answer: y = -2x + 1.
Step-by-step explanation:
From (-1, 3) follow the line to go 1 to the right and 2 down (because the slope is -2). That takes you to (0, 1). So the y-intercept is 1 and the equation is y = -2x + 1.
A sweatshirt costs $48 at Hollister. The sales tax rate is 7%. How much will it cost to buy the sweatshirt?
Answer:
$ 51.36
Step-by-step explanation:
To find the sales tax multiply the tax rate by the cost of the product and then add to the cost.
Sales tax = tax rate * cost price
= 7% * 48
= 0.07 * 48
= $ 3.36
Cost price = cost of product + sales tax
= 48 + 3.36
= $ 51.36
Mrs karki purchased a sari for rs 8000 and sold it for Rs 11300 with 13% VAT , find her profit and loss percent.
The profit Mrs karki made from the Sari she sold at RS 11300 was 28.25%
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
VAT = 13% = 0.13 * 8000 = 1040
Selling price - VAT = 11300 - 1040 = 10260
Profit = [(10260 - 8000)/8000] * 100% = 28.25%
The profit Mrs karki made from the Sari she sold at RS 11300 was 28.25%
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suppose you are performing an experiment where you randomly assign people to one of three experimental conditions
The analysis which would be most appropriate for randomly assign people to one of three experimental conditions (Treatment A, Treatment B, Control) are-
ANOVAthe general linear modelWhat is ANOVA?A statistical test called an analysis of variance, or ANOVA, is used to compare the means of more than two groups.
One independent variable is used in a one-way ANOVA, while two independent variables are used in a two-way ANOVA.A statistical technique called analysis of variance, or ANOVA, divides observed variance data into various components for use in further testing. When there are three or more data groups, a one-way ANOVA is used to find out how the dependent and independent variables are related.What is general linear model?A helpful framework for analysing how various variables affect various continuous variables is the general linear model (GLM).
GLM generalises the ANOVA's linear model by enabling any other kind of resual distribution id(and optimises the likelihood function, which only allows a t-test based on an estimated error of the coefficients). An GLM is therefore an ANOVA, but a GLM is not exclusively a GLM.To know more about ANOVA, here
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The complete question is -
Suppose you are performing an experiment where you randomly assign people to one of three experimental conditions (Treatment A, Treatment B, Control). Which analysis would be most appropriate?
Pls help me !!! due today:(
Answer:
x = 20 units
Step-by-step explanation:
See attached.
Answer:
[tex]x = 94[/tex]
Step-by-step explanation:
To find the value of [tex]x[/tex], we have to first find the lengths of the sides of the squares and add them.
The formula for area of a square is as follows:
[tex]{area = (length \space\ of \space\ side)^2}[/tex]
This means the length of a side of a square can be found by:
[tex]\boxed {length \space\ of \space\ side = \sqrt{area}}[/tex]
Now we can find the lengths of sides of each of the squares:
• Length of side of larger square = [tex]\sqrt{8100}[/tex]
= 90
• Length of side of smaller square = [tex]\sqrt{16}[/tex]
= 4
Next we can just add the lengths of the sides to get the value of [tex]x[/tex] :
[tex]x = 90 + 4[/tex]
⇒ [tex]x \bf = 94[/tex]
please help me !! due today:(
Answer:
[tex]\huge\boxed{\sf x = 65 \textdegree}[/tex]
Step-by-step explanation:
Using trigonometric ratio cos.
Here,
Theta = θ = xAdjacent = 12Hypotenuse = 28Finding x:[tex]\displaystyle cos \theta =\frac{adjacent}{hypotenuse} \\\\cos \ x =\frac{12}{28} \\\\cos \ x = 0.43\\\\x = cos^{-1} 0.43\\\\x = 65 \textdegree\\\\\rule[225]{225}{2}[/tex]
What is the height of a cylinder with a volume of 315 pi cubic meters and a radius of 6 meters?
8.75 meters
12.25 meters
26.25 meters
52.5 meters
The height of the cylinder is (a) 8.75 meters
How to determine the height?The given parameters are:
Volume = 315[tex]\pi[/tex]
Radius, r = 6
The volume of a cylinder is:
[tex]V = \pi r^2 h[/tex]
So, we have:
[tex]315\pi = \pi * 6^2 * h[/tex]
Divide both sides by 36[tex]\pi[/tex]
h = 8.75
Hence, the height of the cylinder is (a) 8.75 meters
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Which expression illustrates the associative property of addition? (3 19) – 12 = (3 12) – 19 3 (19 – 12) = 3 (19 12) (3 19) – 12 = 3 (19 – 12) 3 (19 –12) = 3 – (19 12)
Answer:
Associative Property
For multiplication, the rule is "a(bc) = (ab)c"; in numbers, this means 2(3×4) = (2×3)4.
Answer:
3rd Option!
Step-by-step explanation:
EDGE 2022; good luck
I drive from town a to my home and then to town b. the journey time is 50 minutes what is the average speed?
The average speed can be shown as (A + B)/50 miles per minute, where the distance between town A and his home is A miles, and that from his home to town b is B miles, and the total time is 50 minutes.
The average speed of any object is given as the ratio of the total distance traveled by the body, to the total time taken.
Average Speed = Total Distance/Total Time.
In the question, we are informed that the person drove from town a to his home and then to town b, with the total journey time as 50 minutes.
We are asked to find the average speed of the person.
We assume the distance from town a to his home to be A miles.
We assume the distance from his home to town b to be B miles.
Thus, the total distance traveled = A + B miles.
The total time taken by the person is given to be 50 minutes.
We know that the average speed of any object is given as the ratio of the total distance traveled by the body, to the total time taken.
Thus, the average speed of the person can be shown as:
Average Speed = (A + B)/50 miles per minute.
Thus, the average speed can be shown as (A + B)/50 miles per minute, where the distance between town A and his home is A miles, and that from his home to town b is B miles, and the total time is 50 minutes.
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On a number line, point D is at -3, and point E Is at 6. The point F lies on DE. The ratio of Df to FE ls 2:3. Where does point F lie on the
number line?
Point F is at
. All rights reserved.
on the number line.
Helppp me please
The point F as described in the task content is at point; 0.6 on the number line.
Where does point F lie on the number line?Since it follows from.tge task content that; point D is at -3, and point E Is at 6, it follows that the length of segment, DE is; |-3-6| = 9.
Consequently, since the ratio of Df to FE ls 2:3
It follows that point F is at -3 + (2/5) × 9.
Point F is therefore at 0.6 on the number line.
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Look at the rectangle and the square:
A rectangle PQRS and square LMNO are drawn side by side. The length SR of the rectangle is labeled as 14 inches, and the width QR is labeled as 7 inches. The side LM of the square is labeled as 7 inches.
Anna says that the length of diagonal SQ is two times the length of diagonal OM.
Is Anna correct? Justify your answer and show all your work. Your work should state the theorem you used to find the lengths of the diagonals.
Answer:
Incorrect
Step-by-step explanation:
Formula:
the Diagonal of a square with side square of lengths a
is equal to a√2.
=============
Then
Diagonal of LMNO : 7√2
Then
OM = 7√2
…………………………………………
Using the Pythagorean theorem:
The diagonal of the rectangle PQRS is equal to :
√(14²+7²) = √245 = 7√5
Then
SQ = 7√5
………………
Conclusion:
7√5 ≠ 2×(7√2)
Therefore
Anna is not correct.
the imax screen at the michigan science center is 22 meters wide and 16.1 meters tall. what is diagonal length of the screen? use a calculator, do the work. round to nearest tenth of a meter. a 29.2 m b 743.2 m c 26.2 m d 27.2 m e 28.2 m