A plane flies at 350 mph in the direction 40° north of east, with a wind blowing at 40 mph in the direction 30° south of east. What is the plane’s drift angle?
5.90°
6.38°
45.89°
46.38°
If the plane flying in direction of 40° north of east at a speed of 350 mph and wind is blowing at 40 mph in the direction 30° south of east. then the drift angle will be 5.9 °.
Let's assume east as x axis and north as y axis.
Breaking velocity of plane into components
350 cos40° î + 350 sin40° ĵ
(350 × 0.76604) î + (350 × 0.64278) ĵ
268 î + 225 ĵ
Breaking velocity of wind into components
40 cos30° î - 40 sin30° ĵ
(40 × 0.86602) î - (40 × 0.5) ĵ
34.64 î - 20 ĵ
Now adding velocity of wind to velocity of plane as
The resultant velocity of the plane = initial velocity of plane + velocity of wind
( 268 + 34.64 ) î + ( 225 - 20 ) ĵ
302.64 î + 205 ĵ
So the final velocity of plane will be 302.64 î + 205 ĵ
Lets assume the angle of final velocity from east be θ
So Tan θ = perpendicular / base
So Tan θ = 205 / 302.64
Tan θ = 0.677
θ = Tan⁻¹(0.677)
θ = 34.12 °
As we know,
Drift angle is the difference of initial and final angle of the object measured from same reference.
Drift angle=| Initial angle of plane from east - final angle of plane from east |
Drift angle= | 40 - 34.12 |
Drift angle= 5.87 ° ≈ 5.9 °
So we used the concepts of vectors to solve the above question, first we find out the the final angle of plane from east and then takes the difference of initial and final angle from east to find the drift angle and that we got as 5.9 °.
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Simplify the exponential expression 48 ^1/2
O 2 (24^1/2)
O 3 (16^1/2)
O 4 (3^1/2)
O 16 (3^1/2)
Step-by-step explanation:
Hi There! Let me help you :)
To answer this question, we have to know about the way to simplify it. First, you find the factor of 48.
[tex] = {48}^{ \frac{1}{2} } [/tex]
[tex] = {(16 \times 3)}^{ \frac{1}{2} } [/tex]
[tex] = {16}^{ \frac{1}{2} } \times {3}^{ \frac{1}{2} } [/tex]
[tex] \: [/tex]
—Use the general formula of the exponential, where a^m/n = ^n√a^m.
[tex] \: [/tex]
[tex] = {16}^{ \frac{1}{2} } \times {3}^{ \frac{1}{2} } [/tex]
[tex] = \sqrt[2]{16} \times {3}^{ \frac{1}{2} } [/tex]
[tex] = 4 \times {3}^{ \frac{1}{2} } [/tex]
The answer is C.
how many spherical balls of diameter 15cm can be covered by 40 square metres of material
Answer:
It's very simple: divide the 40 m² area by area of 1 one sphere
[tex] \frac{40 \: m {}^{2} }{3.41 \times 15m {}^{2} } = 565[/tex]
Two similar triangles are shown below:
Two triangles are shown. The sides of the triangle on the left are marked 6, 4, 3. The sides of the triangle on the right are marked as 3, 2 and 1.5. For the triangle on the left, the angle between sides marked 4 and 6 is labeled as w, marked by a double arc, and the angle between the sides marked 6 and 3 is labeled as x, marked by a single arc. The third angle is marked by a triple arc. For the triangle on the right, the angle between sides marked 3 and 1.5 is labeled as y and the angle between the sides marked 2 and 3 is labeled as v, marked by a double arc. The angle between the sides 2 and 1.5 is labeled as z, marked by a triple arc, and it is also the angle on the top vertex of this triangle.
Which two sets of angles are corresponding angles?
∠w and ∠v; ∠x and ∠y
∠w and ∠y; ∠x and ∠v
∠w and ∠z; ∠x and ∠v
∠w and ∠z; ∠x and ∠y
Two sets of angles are corresponding angles will be ∠w = ∠v and ∠x = ∠y. Then the correct option is A.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
Two similar triangles are shown below:
Then two sets of angles are corresponding angles will be
∠w = ∠v and ∠x = ∠y
Then the correct option is A.
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what is 8.31752 to the correct 3 decimal places
Answer:
8.31752 to correct 3 decimal places =
Step-by-step explanation:
8.318
brainiest pls it helps
When given
Slope=4
Point= (2,-4)
What is this written in slope-intercept form?
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{y = 4x - 12}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{Slope = 4, Point = (2, -4)}[/tex]
Find: [tex]\textsf{The equation in slope-intercept form}[/tex]
Solution: We need to plug in the values into point-slope form and after simplifying, distributing, and solving for y we will have our equation in slope-intercept form.
Plug in the values
[tex]\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}[/tex][tex]\textsf{y - (-4) = 4(x - 2)}[/tex]Distribute and simplify
[tex]\textsf{y + 4 = 4(x - 2)}[/tex][tex]\textsf{y + 4 = (4 * x) + (4 * -2)}[/tex][tex]\textsf{y + 4 = 4x + (-8)}[/tex][tex]\textsf{y + 4 = 4x - 8}[/tex]Subtract 4 from both sides
[tex]\textsf{y + 4 - 4 = 4x - 8 - 4}[/tex][tex]\textsf{y = 4x - 8 - 4}[/tex][tex]\textsf{y = 4x - 12}[/tex]Using the information that was provided in the problem statement we were able to determine that the equation in slope-intercept form was y = 4x - 12.
Answer:
y = 4x - 12
Step-by-step explanation:
Given:
slope of 4, and point (2, -4)
Here, we're being asked to write the equation in Slope-Intercept Form. As we have been given the slope and a point on the line, we can use the Point-Slope Form to be able to find that equation.
First, know the two forms:
⇒ Point-Slope Form: y - y₁ = m(x - x₁)
where: m is the slope, and (x₁, y₁) is the given point
⇒ Slope-Intercept Form: y = mx + b
where: m is the slope, and b is the y-intercept
Now, substitute the given values into the Point-Slope Form:
⇒ y - y₁ = m(x - x₁)
⇒ y - (-4) = 4(x - 2) [simplify]
⇒ y + 4 = 4x - 8
Change to the Slope-Intercept Form:
⇒ y + 4 = 4x - 8 [subtract 4 from both sides]
⇒ y + 4 - 4 = 4x - 8 - 4
⇒ y = 4x - 12
Therefore, the equation of the line in slope-intercept form is: y = 4x - 12
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The average rate of the first part of Yi’s walk on a park loop was 4 miles per hour. She then met up with a friend and the two walked the rest of the way at an average rate of 5 miles per hour. The entire 3-mile walk took Yi 42 minutes (0.7 hour). Which equation can be used to solve for x, the time in hours that Yi spent walking before meeting her friend?
A table showing Rate in mile per hour, Time in hours, and Distance in miles. The first row shows Part 1 and has 4, x, and 4 x. The second row shows Part 2, and has, 5, 0.7 minus x, and 5 left-parenthesis 0.7 minus x right-parenthesis.
x = 0.7 – x
x + (0.7 – x) = 1
4x + 5(0.7 – x) = 1
4x + 5(0.7 – x) = 3
The equation can be used to solve for x, the time in hours that Yi spent walking before meeting her friend would be D; 4x + 5(0.7 – x) = 3.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Total distance covered = 3 miles.
The first part walked at the rate of 4 miles per hour.
Let us consider x hours was walked in the first part.
Total distance covered in x hours at the rate of 4 miles per hour will be 4x.
Now, the Second walk rate with meeting with friend will be 5 miles per hour.
The Total time is taken = 0.7 hours.
Therefore, time is taken in the second walk only = (0.7 - x) hours.
Distance covered in second walk = 5 (0.7 - x).
Total distance covered = distance covered in the first part + distance covered in the second part.
4x + 5 (0.7 - x) = 3 miles.
Hence, correct option is D; 4x + 5(0.7 – x) = 3.
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Answer:
its d
Step-by-step explanation:
Based on the graph, which statement is correct about the solution to the system of equations for lines A and B
Answer:
the answer is (3,4) is the solution to line A but not to line b
A pink crayon is made with 12\text{ mL}12 mL12, start text, space, m, L, end text of red wax for every 5\text{ mL}5 mL5, start text, space, m, L, end text of white wax. Which of the following wax mixtures will create the same shade of pink? Choose 2 answers: Choose 2 answers:
Mixtures D and E have a ratio of 5:12 and will create the same shade of pink. Options D and E are correct.
What is the difference between a ratio and a proportion?A ratio is an ordered pair of integers a and b expressed as a/b, with b never equaling 0. A percentage is a mathematical expression in which two ratios are specified to be equal.
Given data;
red wax = 12 ml
white wax = 5 ml
A red wax: white wax = 5:12
B. red wax: white wax=4:1
C red wax white wax = 13: 6
D. red wax: white wax=12:5
E. red wax white wax=12:5
Hence, mixtures D and E have a ratio of 5:12 and will create the same shade of pink.
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A carpenter started with a board that was 31 inches long. he cut 2 pieces that were each 3 inches long. he then cut 3 pieces that were each
Answer:
i don't know
Step-by-step explanation:
i
Eleven upright dominos of increasing height are lined up to be knocked down. The dominos are numbered 0 to 10. The smallest domino, #O, is 3.00 inches tall and will be top- pled by a person to start the chain reaction. Each subsequent domino is 19% taller than the one before. What is the height of domino #10?
The height of domino number 10 is 56.9 inches.
What is a function?A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.
The exponential function:-An exponential function is given by:
y = abˣ
where a is the initial value of y at x = 0, y, x are variables and b is the multiplication factor
Let y represent the height of the number x domino
Since the height of the smallest domino no 0 is 3 inches, hence a = 5. b = 100% + 19% = 1.19
y = 10(1.19)ˣ
For x = 10:
y = 10(1.19)¹⁰= 56.9 inches
Therefore the height of domino number 10 is 56.9 inches.
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Which function is graphed below?
-
Answer:
y=3 (1/3)x
Step-by-step explanation:
On a graph, the closest graph you pictured is this answer
Answer:
y = [tex]3 (\frac{1}{3} )^{x}[/tex]
Step-by-step explanation:
Step 1:
Check the y-intercept; in the graph, when x = 0, y = 3. Which equation satisfies this?
y = [tex]\frac{1}{3}[/tex] [tex](3)^{x}[/tex] = [tex]\frac{1}{3}[/tex] [tex](3)^{0}[/tex] = [tex]\frac{1}{3}[/tex] ❌
y = [tex]3 (\frac{1}{3} )^{x}[/tex] = [tex]3 (\frac{1}{3} )^{0}[/tex] = 3 ✅
y = [tex](\frac{1}{2} )^{x}[/tex] + 2 = [tex](\frac{1}{2} )^{0}[/tex] + 2 = 3 ✅
So the last two equations are possible.
Step 2:
Now check the y-value on the graph for any other x-value, whose corresponding y-value can be easily estimated from the graph.
For example, when x = 2, the y-value is between 0 and 1.
• 2nd equation: y = [tex]3 (\frac{1}{3} )^{x}[/tex] = [tex]3 (\frac{1}{3} )^{2}[/tex] = 0.333 ✅
• 3rd equation: y = [tex](\frac{1}{2} )^{x}[/tex] + 2 = y = [tex](\frac{1}{2} )^{2}[/tex] + 2 = 2. 25 ❌
∴ 2nd equation (y = [tex]3 (\frac{1}{3} )^{x}[/tex] ) is the one being represented by the graph.
Find the reflection of the point (25, 25) across the y-axis.
Answer:
(-25, 25)
Step-by-step explanation:
let me know if you want an explanation!
he tables represent the functions f(x) and g(x). A table with 2 columns and 7 rows. The first row, x, has the entries, negative 3, negative 2, negative 1, 0, 1, 2. The second row, f(x), has the entries, negative 5, negative 3, negative 1, 1, 3, 5. A table with 2 columns and 7 rows. The first row, x, has the entries, negative 3, negative 2, negative 1, 0, 1, 2. The second row, g(x), has the entries, negative 13, negative 9, negative 5, negative 1, 3, 7. Which input value produces the same output value for the two functions?
A function assigns the values. The input value that produces the same output value for the two functions is 1.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
For the given tables the x is the input while f(x) and g(x) are the outputs of the respective functions. Therefore, the input for which the two given functions will return the same output is 1.
Hence, the input value that produces the same output value for the two functions is 1.
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Please help!!!!!!!
picture below
Answer:
the first equation could be something along the lines of [tex]y=3x^{2}[/tex] then the second is [tex]y=3x^{2} -3\\[/tex]
Step-by-step explanation:
this is how shifting works
Find X = Find Y= please help ty :)
Answer:
X = 125° and Y = 75°
Step-by-step explanation:
Y = 75° because the line the bisects two parallel lines. When this happens, the angles at the corners are identical.
To find the value of "X", I first found the value of the last angle in the triangle. I found this by performing the following:
180° - 55° - 75° = 55°
The value of this missing angle is 55°. To find "X", I subtracted this value from 180°. I did this because lines always equal 180°
180° - 55° = 125°
decimal form of rational numbers 1/11
Answer:
1/11 = 0.090909090909090909........................
There are 5 types of fruit in a basket. There are 3 apples, 2 bananas, 4 oranges, 5 kiwi,
and 1 passionfruit. You ask a friend to bring you a piece of fruit. What is the probability of them bringing you an apple?
The probability of bringing an apple is 0.20
How to determine the probability?The distribution of the fruits is given as:
3 apples2 bananas4 oranges5 kiwi,1 passion fruit.The probability of bringing an apple is:
P(Apple) = Apple/Total
This gives
P(Apple) = 3/(3 + 2 + 4 + 5 + 1)
Evaluate
P(Apple) = 0.20
Hence, the probability of bringing an apple is 0.20
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I’m not good at math PLEASE HELP
4 hours minus 1 hour, 59 minutes, 58 sec-
onds equals
A. 2 hours, 2 seconds.
B. 3 hours, 1 minute, 2 seconds.
C. 2 hours, 1 minute, I second.
D. 3 hours, 2 seconds.
a suvery shows that 55℅
Answer: No. The intervals defined by the margin or error overlap
Step-by-step explanation:
If we think about it, with the worst margins, 55% could be 48% and then the 45% would be 52%, showing there is no clear yes or no and it is possible that the intervals could overlap
Find the value of X.
Answer:
x=6
Step-by-step explanation:
check the scale factor by the fraction 10/5
after/before
it simplifies to 2 meaning that the second triangle is two times the size of the first
then take 3 fron segment AB to the similar segment DE and times it by the scale factor(2)
2×3=6
Answer:
6
Step-by-step explanation:
since AC = 5. and DF = 2(5) = 10
FW = 2(4)=8 DE= 2(3) = 6
therefore x = 6
The swimming pool at Spring Valley High School is a rectangle with a width of 70 meters and a length of 30 meters. Around the perimeter of the pool is a tiled floor that extends w meters from the pool on all sides. Find an expression for the area of the tiled floor.
The expression for the area of the rectangular swimming pool is given as follows:
A = w² + 100w + 2100.
What is the area of a rectangle?The area of a rectangle of length l and width w is given by the multiplication of these measures, that is:
A = lw.
In this problem, considering the width of 70 meters and a length of 30 meters, plus the floor of w meters, we have that:
l = 30 + w.wi = 70 + w.Hence the area is given as follows:
A = l x wi = (30 + w)(70 + w) = w² + 100w + 2100.
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Instructions: Simplify the algebraic expression.
[tex]4(-4x-\frac{3}{2} )[/tex]
What do you consider to be the advantages of the numerical values? What do you consider to be the advantages of the visual representations? Which do you prefer working with, and why?
Visual representation is preferable for working for its attractive charts, graphs etc.
The advantages of the numerical values :
1. Numerical values are present in numerical methods. Numerical methods are easier to calculate with the help of mathematical operations like addition, subtraction, multiplication, division & others.
2. No analytical solution is present in numerical methods, only the numerical values are there. So, this is an advantage of numerical values.
The advantages of the visual representations
1. Visual representation gives us an easier way of understanding.
2. Visual representation makes something more interesting to read or solve.
3. Visual representation is best to arrange quantitative datas by using charts, graphs, attractive colors etc.
Which is preferable for working and why?
Visual representation is preferable for working. Because it is more easier way to solve something. The gained interest from visual representation also help to solve something quicker.
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Answer:
I myself prefer visual representation because to me it helps to see things visually and for understanding and working with charts and graphs.
Numerical methods make equations easier to calculate because they give us help of mathematical operations like in addition, subtraction, multiplication, division & others.
Visual representations give us easier ways of understanding and makes something more interesting to read or solve by simply looking at the visual.
Step-by-step explanation:
Which system of equations can be used to find the roots of the equation 4x/2=x/3+2x
The system of equation can be used to find the root of the equation is y= x³-4x² +2x and y=0 , y=4x² and y= x³+2x
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
y=-4x²
y= x³+2x
By equating the above equation we have
-4x²=x³+2x
Now, y= x³-4x² +2x
and y=0
By equating the above equation we have
x³-4x² +2x=0
y=4x²
y= -x³-2x
By equating the above equation we have
4x²=-x³-2x
Lastly,
y=4x²
y= x³+2x
By equating the above equation we have
4x²=x³+2x
Hence, the equation can be used is y= x³-4x² +2x and y=0 ,
y=4x² and y= x³+2x
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x + 4 is prime x2 – 9 can be factored using the formula.
Answer:
difference-of-squares
Step-by-step explanation:
Please help!!!!!!!
picture below
Answer:
This would shift the equation to the right by 5
Step-by-step explanation:
In the year 1999, the surface elevation of Lake Powell was 3893 feet above sea level. In the year 2005, the surface elevation of Lake Powell was 3425.6 feet above sea level. Interpret the rate of change in this situation.
Answer:
Rate of Change = -77.9 feet/year
My interpretation: "Is Bad."
Step-by-step explanation:
The rate of change is the number of feet that Lake Powell dropped, divided by the number of years the drop took place. We want a value with a unit of feet/year.
Year Feet
1999 3893
2005 3425.6
Change
Year = (2005 - 1999) or 6 years
Feet = (3425.6 - 3893) or -467.4 feet
Rate of Change = (-467.4 feet)/(6 years)
Rate of Change = -77.9 feet/year
=======================
FYI: Lake Powell is 22.39 feet lower today (June 23, 2022) than it was 1 year ago.
Which answer choice shows the decimal 23.476 written in expanded form?
Answer: 23.476 = 20+3+0.4+0.07+0.006
Step-by-step explanation:
I think you were supposed to write down the choices but I will guess the answer is this one:
23.476 = 20+3+0.4+0.07+0.006
Hope I helped!
