an airplane is flying from montreal to vancouver. the wind is blowing from the west at 60km/h. the airplane flies at an airspeed of 750km/h and must stay on a heading of 65 degrees west of north. what heading should the pilot take to compensate for the wind? what is the speed of the airplane relative to the ground?
Answers
In order for the airplane to maintain a heading of 65° west of north, it actually heads at (65° +x) west of north at a speed of 750 km/h, to compensate for the wind blowing from west t east at 60 km/h.
The actual speed of the airplane relative to the ground is V km/h.
From geometry, obtain the triangle shown.
The speed of 750 km/h is opposite an angle of 155°, and the unknown angle x is opposite the wind speed of 60 km/h.
From the Law of Sines, obtain
[tex] \frac{sin(x)}{60}= \frac{sin(155^{o}}{750} \\ sin(x)= (\frac{60}{750})sin(155^{o})=0.0338[/tex]
[tex]x=sin^{-1}0.0338=1.937^{o}[/tex]
The heading that the pilot should take is 65 + 1.937 = 66.94° west of north.
The third angle of the triangle is 180 - (155 + 1.937) = 23.063°.
Use the Law of Sines to calculate V.
[tex] \frac{V}{sin(23.063^{o})}= \frac{750}{sin(155^{o})} [/tex]
[tex]V=( \frac{sin(23.063)}{sin(155)} )750=695.21\,km/h[/tex]
Answer:
The pilot heads approximately 67° (nearest integer) west of north.
The speed of the airplane relative to ground is 695.2 km/h (nearest tenth)
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can someone please help me?
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WILLL GIVEEEEE BRAINLIEST PLZ HELPPPPPPPP!!!!!!!!
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29 out of 74 do not like rap
29/74 = 0.39
31 out of 74 do not like hip hop
31/74 = 0.42
0.39+0.42 = 0.81
answer is 0.81
Suppose you have a normally distributed set of data pertaining to a standardized test. The mean
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A paint store has 35 gallons of paint in storage, 2/5 of which are for outdoor use. The others are for indoor use. If each gallon costs$22, what is the total cost of the indoor paint in storage?
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-6•(-18).......help this is due tomorrow
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108 is the answer
hope this helped, xx
Remember : A negative times a negative is a POSITIVE.
So, the negatives cross each other out.
So, we simply pretend that there are NO negatives in this question.
So, what is 6 × 18?
6 × 18 = 108
Therefore, -6·(-18) = 108
~Hope I helped!~
Which statement best describes the expression 3 + 2 ÷ y?
The quotient of y and the sum of 3 and 2
The quotient of the sum of 3 and 2 and y
The sum of 3 and the quotient of 2 and y
The sum of 3 and the quotient of y and 2
best answer will get BRAINLIEST!!!!!
Answers
Answer:
C. The sum of 3 and the quotient of 2 and y
Step-by-step explanation:
Given : 3 + 2 ÷ y
Solution:
First consider the BODMAS rule
solving any equation we need follow this sequence (BODMAS)
B - Bracket
O - Of
D- Division
M- Multiplication
A - Addition
S - Subtraction
So, in the given equation we first consider the division after that the addition
i.e. division of 2 by y (quotient of 2 and y) and then addition of 3 in the result of division of 2 by y
So, we can say it as The sum of 3 and the quotient of 2 and y
Answer:
The answer is just c
Step-by-step explanation:
A carton of juice shaped like a rectangular prism measures approximately 8 inches high and 4 inches along each edge. A cylindrical glass that is 3 inches in diameter is filled to a height of 3.5 inches. Approximately how many glasses of this juice can be poured from a full container? Use π π = 3.14.
Answers
V = length × width × height
The volume of the carton juice is
V = 4 × 4 × 8 = 128 in³
Volume of a cylinder is
V = Area of circular base × height = [tex] \pi r^{2} [/tex]×h, where [tex]r[/tex] is the radius of the circular base
The volume of the cylindrical glass is
V = (1.5)² × 3.14 × 3.5 = 24.7275 in³
Hence, the number of glasses that can be filled with the juice from the carton is:
128 ÷ 24.7275 = 5.18 ≈ 5 glasses
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workers have painted 920 square feet of an office they have completed 80% of their job how many square feet do they need to. paint in all
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80% = 0.80
divide the area done by the percentage:
920/0.80 = 1150
total area is 1150 square feet
Find the area of a triangle with a base of 10 meters and a height of 6 meters
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A = (1/2) * 10 * 6 = 30 m²
given
base=10
height=6
area=1/2 times 10 times 6
area=5 times 6
area=30 squaer meters
Which set of side lengths is a Pythagorean triple?
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11² = 121
60² = 3600
121 + 3600 = 3721
√3721 = 61
how many miles can you get on one tank of gas if your tank holds 18 gallons and you get 22 miles per gallon
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Given that a is the longest side length in the triangle, which of the following inequalities would make the triangle above an obtuse triangle?
A. a2+b2< c2 B. a2+b2>c2 C. b2+c2< a2 D. b2+c2>c2
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If the sum of the squares of the shorter sides is smaller compared to the square of the hypotenuse then, the triangle is OBTUSE. The answer therefore to this item is letter A.
Answer:
it is abtuse triangle
Step-by-step explanation:
no step
Which of the following are properties of the incenter of a triangle? Check all that apply. A. The incenter is where all of the bisectors of the angles of the triangle meet. B. The incenter of a triangle is always inside it. C. The incenter of a right triangle lies on the side opposite the right angle. D. The incenter is where all of the perpendicular bisectors of the sides intersect.
Answers
Incenter is nothing but a point inside a triangle where all interior angle bisectors intersect. So, the correct options are A) and B).
Incenter is nothing but a point inside a triangle where all interior angle bisectors intersect.
According to the definition of incenter the correct statement from the given options will be:
A). The incenter is where all of the bisectors of the angles of the triangle meet.
B). The incenter of a triangle is always inside it.
For more information, refer the link given below:
https://brainly.com/question/15103242
Option A and B
Incenter of a Triangle Properties:
A. The incenter is where all of the bisectors of the angles of the triangle meet.B. The incenter of a triangle is always inside it.Step-by-step explanation:
The incenter is where the angle bisectors intersect, making choice A true.The incenter lies inside the triangle, making choice B accurate.The incenter doesn't necessarily lie on the right triangle's side opposite the right angle, making choice C incorrect.The incenter is not where all the perpendicular bisectors of the sides intersect, making choice D false.Nine cards numbered 1-9 are flipped upside down. What is the probability of flipping up an even number?
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Write an expression that is equivalent to
(23.6-7.1a-4.2b)-(5.8b-9a)
Answers
(23.6 - 9a - 5.8b)
Explanation:Steps to simplify the expression:
Combine constant terms:
(23.6 - 7.1a - 4.2b) - (5.8b - 9a) = 23.6 - 7.1a - 4.2b - 5.8b + 9a
Group terms by variable:
(23.6 - 4.2b - 5.8b) + (-7.1a + 9a)
Combine like terms:
19.6 - 10b + (-7.1a + 9a) = 19.6 - 10b + 2a
Rewrite the expression with the simplified terms:
(19.6 - 10b) + 2a
Therefore, the equivalent expression is (19.6 - 10b) + 2a.
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Answers
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In a parallelogram, the opposite sides are parallel. If you draw a diagonal inside the parallelogram, it acts as a transversal line crossing the parallel lines. Therefore, the angles it forms at the corners are equal to each other, meaning the opposite angles have the same measure.
Learn more about Parallelogram here:https://brainly.com/question/31342904
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True or false. A trapezoid has congruent diagonals and one set of opposite sides that have equal slopes.
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A trapezoid has congruent diagonals and one set of opposite sides that have equal slopes.
Explanation:A trapezoid is a quadrilateral with one pair of parallel sides. It has two diagonals that connect opposite vertices. The diagonals of a trapezoid are not necessarily congruent because they have different lengths. However, one set of opposite sides of a trapezoid will always have equal slopes.
To see this, we can consider the equation of a line and the formula for slope. Let's say we have a trapezoid with vertices A, B, C, and D. The equation of the line passing through points A and B can be written as y = mx + b, where m is the slope of the line and b is the y-intercept. Similarly, the equation of the line passing through points C and D can be written as y = nx + c. Since the opposite sides of the trapezoid are parallel, the slopes m and n will be equal.
Therefore, the statement is true. A trapezoid has congruent diagonals and one set of opposite sides that have equal slopes.
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A lotion is made from an oil blend costing $1.50 per ounce and glycerin costing $1.00 per ounce. Four ounces of lotion costs $5.50.
A=(4-g) 1.5
B=(4-g) + 1.5
C= 4g-g(1.5)
D=(4-g)g
Answers
Answer:
A=(4-g) 1.5
Step-by-step explanation:
Let g be the amount of glycerin in the lotion. We know that there are 4 ounces total of lotion; this means that there are 4-g ounces of the oil blend.
The oil blend costs $1.50 per ounce; this gives us the expression (4-g)1.5 for the oil blend.
Answer:
the awnser is A
Step-by-step explanation:
I did the test
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n someone answer this question for me please : how can I write repeated multiplication using powers ?
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Alejandro has two marbles. One weighs 0.56 grams, and the other weighs 0.825 grams. How much more does the second marble weigh?
0.265 grams
0.355 grams
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1.385 grams
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0.265 grams
The pair of numbers whose difference is 18 and whose product is as small as possible is? The minimum product is?
Answers
So the product will be x(x-18) = x^2 - 18x = (x-9)^2 - 81
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Describe how the sizes of the 1/2 strip and the 1/6 strip compare. Then descrube how the denominators of the fractions 1/2 and 1/6 are related
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In order to have a clear understanding of how to write 500 words essay, you need to have at least the foggiest idea of what 500-word scholarship essay actually is! Let’s have a closer look at this type of the academic assignment.
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To compare the sizes of the 1/2 strip and the 1/6 strip, we should visualize the strips as portions of the same whole. Imagine a bar divided into 2 equal parts; one of those parts is the 1/2 strip. Now imagine the same bar divided into 6 equal parts; one of those parts is the 1/6 strip. It's evident that the 1/2 strip is larger than the 1/6 strip because when you divide something into fewer parts, each part is larger.
The denominators of the fractions 1/2 and 1/6 are related through the concept of divisibility and the number of equal parts into which a whole is divided. The denominator 2 in the fraction 1/2 tells us that the whole is divided into 2 equal parts, while the denominator 6 in the fraction 1/6 indicates that the whole is divided into 6 equal parts. Because 6 is a multiple of 2, each part of the 1/6 strip is smaller than each part of the 1/2 strip.
Solve the compound inequality. 7x > -35 and -5x > -50
Answers
x > -35/7
x > -5
-5x > -50
x < -50/-5
x < 10
-5 < x < 10 <==
Rectangle ABCD is similar to rectangle JKLM. AB = 10, BC = 8, CD = 10, DA = 8, and JK = 15. The area of rectangle JKLM is ____u2
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Two equations are given below: m + 5n = 20 m = n − 4 What is the solution to the set of equations in the form (m, n)? (3, 7) (0, 4) (5, 1) (2, 6)
Answers
m+5n=20
m=n-4
sub n-4 for m in other equation
n-4+5n=20
6n-4=20
add 4 both sides
6n=24
divide by 6 both sides
n=4
sub back
m=n-4
m=4-4
m=0
(m,n)
(0,4)
Answer:
(m,n) = (0,4)
Step-by-step explanation:
We have
m + 5n = 20 -----------------------eqn 1
m = n - 4 ----------------------------eqn 2
eqn 1 - eqn 2
m + 5n - m = 20 - ( n- 4 )
6n = 24
n = 4
Substituting in eqn 2
m = 4 - 4
m = 0
So the correct set is (0,4)
(m,n) = (0,4)
what is a function?
Answers
it is an expression involving one or more variables
examples:
2x +5
x^2
a+b
Simplify 5 • 2 • (–4) + 6 ÷ 2
Answers
paranthesis
exponents/roots
multiplication/division
addition/subtraction
so your question: 5 x 2 x (-4) + 6 divided by 2
5 x 2 x (-4)= -40
-40 / 2 = -20
-20 + 6 = -14
your answer is -14
hope this helps :D