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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PLEASE HELP ME TO ANSWER THIS QUESTION THANK YOU!
Answer:
Step-by-step explanation:
a. 4cm * 9cm * 2cm = 72 cm^3
b. 5m * 4m * 9m = 180 m^3
c. 10dm * 36 dm^2 (because the square could also be represented as 6cm * 6cm) =360 dm^3
d. (56mm)^3 = 175616 mm^3
e. 10 m * 1 m^2 (because of the square) = 10m^3
To tell which cubic unit of measure that should be used:
⇒ we should examine the unit of the side lengths
First question (a):
a rectangular prism that is 4cm by 9 cm by 2cm⇒ must use cm³ as cubic unit of measure
⇒ as all sides are centimeters
⇒Answer: cubic centimeters or cm³
Second question(b):
a rectangular prism that is 5m by 4m by 9m⇒ must use m³ as cubic unit of measure
⇒ as all sides are meters
⇒Answer: cubic meters or m³
Third question(c):
a rectangular prism that gives only two side length: 10dm, 6dm⇒must use dm³ as cubic unit of measure
⇒ as all of the sides given are in decimeter
⇒Answer: cubic decimeter or dm³
Fourth question(d):
a cube that gives only one side length: 56mm⇒ must use mm³ as cubic unit of measure
⇒ as all the given sides with side lengths are in millimeters
⇒ Answer: cubic millimeters or mm³
Fifth question(e):
a rectangular prism with two side length: 1m, 10m⇒ must use m³ as cubic unit of measure
⇒ as all given sides with side lengths are in meter
⇒Answer: cubic meter or m³
In general:
⇒ when faced with these problems
⇒ look to the unit of measure of the majority of the side lengths
⇒ look to the unit of measure that the problem wants for the answer
Hope that helps!
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Which is the graph of y = 3√x+1-2?
Answer:
I'm not sure how to interpret "y = 3√x+1-2."
I'll assume y = 3[tex]\sqrt{x+1}[/tex] - 2
Step-by-step explanation:
Use the free online app DESMOS. Either enter the equation, or make a table of individual points and plot them as ordered pairs.
GRAPH: See attached image
PLOT: Calculate a few points, mark them on the graph and then connect the dots. I selected a few values of x and calculated y from the equation. Each calculation provides a (x,y) ordered pair which can be marked on the graph and the dots are then connected. Note that x values less than -1 result in a value of y that includes i, an imaginary number. So the graph ends abruptly at that point.
please help me answer this matrices question ASAP
The value of a₃₂ is 7 , Option A is the correct answer.
What is a Matrix ?Matrix is an array or an arrangement of numbers or expression in rows and column format.
The matrix is given
For a matrix of size mxn , m is the row and n is the column of the matrix.
a₃₂ = This term means 3rd row and 2nd column of the matrix
which is 7
Therefore the value of a₃₂ is 7 , Option A is the correct answer.
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3. Choose the equation that correctly shows the Commutative Property of Multiplication. 5 × 1 3 = 1 3 ÷ 5 5 × 1 3 = 5 × 1 3 5 + 1 3 = 1 3 × 5
According to the commutative property of multiplication, changing the order of components has no effect on the product. The correct option is B.
What is the commutative property of multiplication?According to the commutative property of multiplication, changing the order of components has no effect on the product.
For example: 4 × 8 = 8 × 4 = 32
The equation that correctly shows the Commutative Property of Multiplication is,
5 × 1 3 = 5 × 1 3
Hence, the correct option is B.
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The nth term of a sequence is given by 3n²
What is the position of the term in the sequence that is the first one with a value greater than 1000?
The 19 th term of the sequence is the first term of the sequence having value greater than 1000.
Given that the n-th term of the sequence is given by,
[tex]a_n=3n^2[/tex]
Let the p-th term be the first term which have value greater than 1000 in the sequence.
The p-th term of the sequence is, [tex]a_p=3p^2[/tex]
According to the condition,
[tex]3p^2 > 1000[/tex]
[tex]\Rightarrow p^2 > \frac{1000}{3}[/tex]
[tex]\Rightarrow p > +\sqrt{\frac{1000}{3}}[/tex], as number of term cannot be negative so we ignore the negative value of square root here
[tex]\Rightarrow p > 18.25\\\Rightarrow p\geq19[/tex]
Hence the first term which has value greater than 1000 is 19 th term of the sequence.
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Kylie is ordering 9 pizzas for her party. Each pizza is either thin crust or deep dish. Each thin crust pizza costs $20, and each deep dish pizza costs $8 more. If her total including 10% tax is $242, how many thin crust pizzas did she order?
A. 2
B. 3
C. 4
D. 5
E. 8
Answer:
the answer is A. 2 thin crust pizzas
Helppppppppp plssssss
8. If a conditional is true and its hypothesis is true, then its_____ is true.
A school has 320 girls and 250 boys the probity that a girl is left handed 0.2 the probity that a boy is left handed is 0.1 estimate the number of left handed students
Probability helps us to know the chances of an event occurring. The estimated number of left-handed persons in the school is 89.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Given the number of girls is 320, the probability that a girl is left-handed is 0.2. Therefore, the number of girls who are left-handed is,
Number of left-handed girls = (320×0.2) = 64
Given the number of boys is 250, the probability that a boy is left-handed is 0.1. Therefore, the number of boys who are left-handed is,
Number of left-handed boys= (250×0.1) = 25
Hence, the estimated number of left-handed persons in the school is 89.
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PLEASE HELP ASAP!!!!!!!1
Consider the series 1/4+3/2+11/4+4+21/4+....
Does the series converge or diverge?
Select answers from the drop-down menus to correctly complete the statements.
The series _____ (diverges or converges). You Consider conclude this because the series is _________ (Arithmetic, Geometric and the absolute value of the common ratio is greater than 1, Geometric and the absolute value of the common ratio is less than 1, neither arithmetic nor geometric)
The series diverges. You Consider concluding this because the series is in arithmetic progression.
What is an arithmetic sequence?An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.
The explicit formula for any arithmetic series is given by the formula,
[tex]a_n = a_1 + (n-1)d[/tex]
where d is the difference and a₁ is the first term of the sequence.
The given series of numbers 1/4+3/2+11/4+4+21/4+.... is an arithmetic series because the difference between any two consecutive terms is 5/4. Therefore, the blanks can be filled as,
The series diverges. You Consider conclude this because the series is in arithmetic progression.
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what value of x makes this equation true , use numerals instead of words.
-2x+3=-15
Answer:
x = 9
Step-by-step explanation:
-2x + 3 = -15
-2x = -18
x = 9
Answer:
9Step-by-step explanation:
what value of x makes this equation true , use numerals instead of words.
-2x+3=-15
-2x + 3 = -15
-2x = -15 - 3
-2x = -18
x = -18 : (-2)
x = 9
--------------------
check
-2 * 9 + 3 = -15
-18 + 3 = -15
-15 = -15
the answer is good
Do the fractions and convert to repeating or terminating decimal numbers?
It should be noted that 16/25 can be converted to a terminating decimal number is 0.64.
How to explain the fraction?
Do the fractions 6/7 and 16/25 convert to repeating or terminating decimal numbers.
In this case, 6/7 converts to repeating decimal numbers. You could represent it, so you don't have to repeat the decimals infinitely, by putting a bar over the repeating decimals like 0.857142 with a bar going over from the 8 to the 2.
Also, 16/25 can be converted to a terminating decimal number which is 0.64.
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Which choice is equivalent to the expression below?
450
OA. 45²
OB. 0
OC. 45
O D. 1
Answer:
D is the answer because according to the law any number which has 0 at their power is equal to 1.
The correct value of this expression is 1. Letter D
We know that a power is the multiplication of equal factors - according to the exponent. That is, we just multiply the sentence by itself with the value given by the exponent.
Therefore, any number raised to the power of zero will be 1.
Round to the nearest hundredth
48.849
PLEASE HELP
If the discriminant of an equation is zero, which of the following is true of the equation?
A. It has one complex solution
B. It has two complex solutions
C. It has one real solutions
D. It has two real solutions
Considering the discriminant of zero for a quadratic equation, the correct option is given by:
C. It has one real solutions.
What is the discriminant of a quadratic equation and how does it influence the solutions?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The discriminant is:
[tex]\Delta = b^2 - 4ac[/tex]
The solutions are as follows:
If [tex]\mathbf{\Delta > 0}[/tex], and it is a perfect square, it has 2 rational solutions.If [tex]\mathbf{\Delta > 0}[/tex], and it is not a perfect square, it has 2 irrational solutions.If [tex]\mathbf{\Delta = 0}[/tex], it has 1 rational solutions.If [tex]\mathbf{\Delta < 0}[/tex], it has 2 complex solutions.Discriminant of zero is [tex]\Delta = 0[/tex], hence option C is correct.
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If angle 2 is 5x plus 5 degrees and angle 6 is 30 degrees then what is x
The value of x is 5.
What is Adjacent angle?Two angles that have the same vertex and a side in common.
Here, m∠2 = m∠6
5x + 5 = 30
5x = 25
x = 25/5
x = 5
Thus, The value of x is 5.
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What is the range of possible sizes for side x?
I dont need a long answer
Answer:
1.3 < x < 6.7
Explanation:
Given two sides of a triangle: 2.7 and 4.0
If 'x' will be the largest side:
third side < sum of two sidesx < 2.7 + 4.0x < 6.7If 'x' will be smallest side:
third side > difference between two sidesx > 4.0 - 2.7x > 1.3Hence range of possible size: 1.3 < x < 6.7
can someone help me with this question with details
Answer:
I think the answer is 5 ( if wrong then do a low rating)
Step-by-step explanation:
The way I found the answer was by using PEDMAS so first I handled [(4 - (-5)) x (-7)] which is the same as 4 + -5 which equals -1 and when multiplied by -7 equals positive 7 because whenever you multiply 2 negatives you get a positive.
Next I solved 6 / (-3) which is -2 since whenever a positive is divided by a negative the quotient is negative. Now the equation is:
-2 + 7 and when solved is -2 + 7 = 5
find the length of each arc and round the answer to the nearest tenth
PLEASE HURRY IF YOU CAN
The length of arc for the options 1,2,3 and 4 willl be 60.39,61.23,10.4 and 7.851 respectively.
What is angle measurement?An angle measure is the measurement of the angle created by two rays or arms at a shared vertex in geometry. A protractor is used to measure angles in degrees (°).
As a result, when measuring angles in radians,
The length of the arc is:
[tex]\rm l = r \theta[/tex]
Unit conversions;
1 π = 180°
1° = 180/π
315°= 5.49 rad
270° = 4.71 rad
60° = 1.04 rad
150°=2.617 rad
The measure of the length of arc for the given radius;
[tex]\rm L_1 = R_1 \theta \\\\ L_1 = 1 \times 5.49 \\\\\ L_1 = 60.39 \\\\ L_2 = 13 \times 4.71 \\\\ L_2 = 61.23 \\\\ L_3 = 10 \times 1.04 \\\\ L_4 = 10.4 \\\\ L_4 = 3 \times 2.617 \\\\ L_4 = 7.851[/tex]
The length of arc for the options1,2,3 and 4 willl be 60.39,61.23,10.4 and 7.851 respectively.
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GIVING BRAINLIEST TO CORRECT ANSWER What rotation about the origin is equivalent to R-200°
A. R-160
B. R560
C. R160
D. R200
The rotation about the origin that is equivalent to R-200° is; C. R160
How to find the angle of rotation?We are given;
Origin = -200°
Now, even if we add and also subtract a complete rotation of 360° (or even several rotations of 360°), we will want to have the similar rotation.
Thus;
By adding 360° to -200°, we have;
α = -200° + 360°
α = 160°
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The absolute value of 5.8 is _________.
Answer:
5.8
Step-by-step explanation:
Sketch the graph of y = x^2+2x-15 using your graphing calculator. What are the x-intercepts of this graph?
The intercept is 3 and 5
What is intercept?The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
To find x- intercept, y=0
x² + 2x -15=0
x² -5x + 3x -15=0
x(x-5) - 3(x-5) = 0
(x-5)(x-3)=0
Hence, the x- intercept is 3 and 5.
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Determine if the following scenarios are mutually exclusive or overlapping. Explain your reasoning.
1. You are taking a multiple choice test. Event A is you choose the correct answer. Event B is you choose D as the answer.
2.You survey students in your school about what grade they are. Event A is the person is a senior. Event B is the person is a junior.
An Event is the set of results from an experiment in probability. Assume you do an experiment by tossing a coin.
What is an event in probability?An Event is the set of results from an experiment in probability. Assume you do an experiment by tossing a coin. This experiment results in the coin landing 'heads' or 'tails.' These are the events that are associated with the experiment.
Scenario 1: You are taking a multiple-choice test. Event A is you choose the correct answer. Event B is you choose D as the answer.
The two of the given events will overlap since there is a possibility that the correct answer is option D.
Scenario2: You survey students in your school about what grade they are in. Event A is the person is a senior. Event B is the person who is a junior.
The two of the given events are mutually exclusive events since a person can not be a senior and a junior at the same time.
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Mason can type 210 words in 6 minutes. find the unit rate ( words per mintute )
Answer:
Step-by-step explanation:
words type per minute =210/6
=35
Which set of graphs can be used to find the solution set to 3e* > >-x?m
The green-colored area of the graph attached below shows the solution set to 3eˣ>(-1/2)x.
Inequality is the relationship between two expressions showing the relationships like greater than, lesser than, lesser than equals to, and greater than equals to.
Here assume f is a function which is given by f(x)=3eˣ
and g be another function which is given by g(x)= (-1/2)x
Here we have to find the solution graph showing the relationship
f(x) > g(x)
Let at point (a,b) the f(x) and g(x) meet each other.
After that intersection point, g(x) will decrease as g(x) is a decreasing function. and f(x) will increase.
So in the solution set will contain the area where g(x) is larger than f(x).
Therefore the solution graph of this inequality is the green-colored area as shown below,
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Carl scored a total of 24 points by making 6 two-point baskets and some three-point baskets. Which equation can be used to find the number of three-pointers he scored, and how many three-point shots did Carl score?
A. 3p + 12 = 24
Carl made 12 three-point baskets.
B. 3p + 12 = 24
Carl made 4 three-point baskets.
C. p + 6 = 24
Carl made 18 three-point baskets.
D. p + 6 = 24
Carl made 30 three-point baskets.
Answer:
A.3p+12=24
Step-by-step explanation:
carl Made 12 three-pint baskets.
need answer Asap! Lots of points!
Answer:
1
Step-by-step explanation:
Via calculator inputs.....
ABCD is a square. Triangle DEF is equilateral. Triangle ADE is isosceles with AD = AE. CDF is a straight line. Showing all your steps, calculate the size of angle AEF
Answer:
90°
Step-by-step explanation:
the sum of all angles in a triangle is always 180°.
in an equilateral triangle also all 3 angles are equal and therefore 180/3 = 60°.
angle EDF = 60°.
angle DEF = 60°
all angles in a square are 90°.
so, angle ADC = 90°.
and therefore, ADF = 90°.
the angle ADE is then 90-60 = 30°.
the triangle ADE is isoceles (both legs are equal, and both angles of the legs with the baseline are equal).
so, the angle AED = angle ADE = 30°
the angle AEF is then angles AED + DEF = 30 + 60 = 90°
Please help! I am stuck on this
Answer:
c.
Step-by-step explanation:
Assuming we are not restricting the domain of f, the inverse isn't a function
[tex] \frac{1}{ {x}^{2} } - 7[/tex]
[tex]y = \frac{1}{ {x}^{2} } - 7[/tex]
[tex]x = \frac{1}{ {y}^{2} } - 7[/tex]
[tex]x + 7 = \frac{1}{ {y}^{2} } [/tex]
[tex] {y}^{2} = \frac{1}{x + 7} [/tex]
[tex]y = \sqrt{ \frac{1}{x + 7} } [/tex]
Since square root are Positve or negative, the function will not be a function.
The correct answer is c.
can 18 7 10 make a triangle
Answer:
No, 18 7 10 are can not make a triangle.
Step-by-step explanation:
First of all, what does a Triangle?
A flat geometric figure that has three sides and three angles. OR something that has three sides and three angles a triangle of land.
Three sides form a triangle : if sum of length of two sides is greater than the third side. But here
10+7=17 < 18.
That is the sum of two sides (10+7) is less than the third side i.e 18
So that 18 7 10 are can not make triangle.
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Answer:
18 7 10 are can not make a triangle.
Step-by-step explanation:
Definition of a Triangle
A figure that has three sides and three angles is knows as a triangle
And a property of a triangle is that the sum of length of two sides should always be greater than the third side.
We have given the length of sides as : 18 7 10
now check it :
(i) 18 + 7 = 25 which is greater than 10
(ii) 18 + 10 = 28 which is greater than 7
(iii) 7 + 10 = 17 which is lesser than 18
so the sum of two sides (10+7) is less than the third side 18
Therefore 18 7 10 are can not make triangle.
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