A pilot is flying from Thunder Bay, Ontario to Dryden, Ontario a distance of approximately 320 km. As the plane leaves Thunder Bay, it flys 20° off course for exactly 80 km. After flying off-course how far is the plane from Dryden?
Answers
Answer: The plane is 246.4 kilometres from Dryden (approximately)
Step-by-step explanation: Please refer to the picture attached for further details.
The pilot was meant to fly from Thunder Bay which is marked as point T to Dryden which is marked as point D. The distance is given as approximately 320 kilometres as shown.
However upon departure, the pilot goes off course at an angle of 20 degrees and flies for 80 kilometres. When he has traveled for exactly 80 kilometres, he would find himself at point P as shown in the diagram. The plane which is now at point P, is t kilometres from Dryden (point D). To calculate the distance t, we shall apply the cosine formula, having been given two sides and an angle between.
The cosine rule states as follows;
c² = a² + b² - 2abCosC
Substituting for the given variables in this question, the formula can be expressed as follows;
t² = d² + p² - 2dpCosT
Substituting for the known values, we now have,
t² = 80² + 320² - 2(80*320)Cos20
t² = 6400 + 102400 - 2(25600)0.9396
t² = 108800 - (51200) * 0.9396
t² = 108800 - 48107.52
t² = 60692.48
Add the square root sign to both sides of the equation
√t² = √60692.48
t = 246.3584
t ≈ 246.4
Therefore, the plane is approximately 246.4 kilometres from Dryden.
Related Questions
12. The overtime rate of pay which is one-and-a-half times the basic rate of $240
per hour is
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Answer:
300 inches tall or a flat surface is the best way you could use it to be
Madeline is writing a computer program for class. The first day she wrote 5 lines of code. She wrote 15 lines of code on the second day and 45 on the third day. Find the total amount of lines of code written after all 6 days.
Answers
Answer:
1215
5×3,15×3,45×3,135×3,405×3=1215
Guess my rule. PLS HELP ME I BEG
Answers
Answer:
12,22,2002, 4x, 5x
Step-by-step explanation:
The rule is x2 +2
Not sure on the last 4
Sorry I answered late.
Which graph represents the function f(x) = 1/x+3
-2
Answers
Answer:
Step-by-step explanation:
To eliminate ambiguity please use parentheses when typing a function like this one. I'm going to assume that you meant
f(x) = 1 / (x + 3) - 2
Start with the graph of y = 1/x. Its vertical asymptote is the line x = 0. The graph never touches the x-axis.
Translating the entire graph 3 units to the left will give you the function
h(x) = 1 / (x + 3).
Translating the above graph 2 units down will give you the desired function g(x) = 1 / (x + 3) - 2.
Answer:
Graph B on Edge2022.
Have a great day.
Find the volume of a right circular cone that has a height of 6 ft and a base with a radius of 9.7 ft. Round your answer to the nearest tenth of a cubic foot.
Answers
Answer:
591.18
Step-by-step explanation:
A survey of 720 adults nationwide asked, "What irks you most about the actions of other motorists?" The response "tailgaters" was given by 231 people. What percent of those surveyed were most irked by tailgaters? Round to the nearest tenth of a percent
Answers
Answer: 32.08%
Step-by-step explanation:
From the question, a survey of 720 adults nationwide asked, "What irks them most about the actions of other motorists? and the response "tailgaters" was given by 231 people.
The percentage of people that responded with tailgaters will be the number of people who responded with tailgaters divided by the total survey of adults asked and then multiplying by 100. This can be mathematically written as:
= 231/720 × 100
= 32.08%
7. The length of a minute hand of a clock is 3.5cm. Find the angle it turns through if it
sweeps an area of 48 cm. (Taken=22/7)
(3 marks)
Page 2 of 3
Answers
Answer:
The angle it turns through if it sweeps an area of 48 cm² is 448.8°
Step-by-step explanation:
If the length of a minute hand of a clock is 3.5cm, to find the angle it turns through if it sweeps an area of 48 cm, we will follow the steps below;
area of a sector = Ф/360 × πr²
where Ф is the angle, r is the radius π is a constant
from the question given, the length of the minute hand is 3.5 cm, this implies that radius r = 3.5
Ф =? area of the sector= 48 cm² π = [tex]\frac{22}{7}[/tex]
we can now go ahead to substitute the values into the formula and solve Ф
area of a sector = Ф/360 × πr²
48 = Ф/360 × [tex]\frac{22}{7}[/tex] × (3.5)²
48 = Ф/360 × [tex]\frac{22}{7}[/tex] ×12.25
48 = 269.5Ф / 2520
multiply both-side of the equation by 2520
48×2520 = 269.5Ф
120960 = 269.5Ф
divide both-side of the equation by 269.5
448.8≈Ф
Ф = 448.8°
The angle it turns through if it sweeps an area of 48 cm² is 448.8°
A regular hexagon and a rectangle have the same perimeter, P. A side of the hexagon is 4 less than the length, l, of the rectangle. The width of the rectangle, w, is 2 less than the length of the rectangle. What is the perimeter of the hexagon?
A rectangle with a length of l and width of w. P = 2 l + 2 w. A hexagon with side lengths of s. P = 6 s.
Answers
Answer:
The perimeter of the hexagon is equal to 36 units
Step-by-step explanation:
Let
x-------> the length side of the hexagon
L-----> the length of the rectangle
W-----> the width of the rectangle
we know that the perimeter of the hexagon is equal to the perimeter of the rectangle is equal to so
-------> equation A
-------> equation B
-------> equation C
Substitute equation B and equation C in equation A
Solve for L
Find the value of x
Find the perimeter of hexagon
Answer:
36 units
ur welcome sis
Step-by-step explanation:
F
D
80°
E
B
160
G
NOTE: Angles not necessarily drawn to scale.
2=
PLEASE HELPPP!!!
Answers
Answer:
[tex] \boxed{x\degree = 80\degree} [/tex]
Step-by-step explanation:
Vertically opposite angles are equal.
[tex] = > x \degree + 80\degree = 160\degree \\ \\ = > x\degree = 160\degree - 80\degree \\ \\ = > x\degree = 80\degree[/tex]
Answer:
80°
Step-by-step explanation:
Look at the picture* *
how would i answer this?
Answers
Answer:
Option (B).
Step-by-step explanation:
Option (a). {(1, 2), (3, 4), (4, 5), (6, 7)}
Since in every ordered pair value of x corresponds a distinct value of y.
The given ordered pairs represent one-to-one function.
Option (b). {(0, 3), (1, 5), (3, 9), (1, 13)}
In the ordered pairs (1, 5) and (1, 13) value of x correspond to the two different values of y.
Therefore, its not a function.
Option (c). {(-2, 2), (-3, 3), (-4, -4), (-5, -5)}
For every value of x there is distinct value of y.
Therefore, given set of ordered pairs represent a one to one function.
Option (d). {(1, 2), (2, 2), (3, 5), (4, 8)}
Ordered pairs represent a function.
Option (B), will be the answer.
Please help will mark brainliest
Answers
Answer:
-1/5
Step-by-step explanation:
which graph represents a quadratic function with a vertex at (0,0)
Answers
Answer:
parabola On a coordinate plane, a parabola opens up. It goes through (negative 5, 6), has a vertex of (0, 0), and goes through (5, 6). On a coordinate plane, a parabola opens up.
Step-by-step explanation:
Answer: C) the third graph
Step-by-step explanation: i got 100% on my quiz, hope this helps!!
Please help me in this
Answers
Answer:
3
Step-by-step explanation:
as u add 2 + 1 from the 6 and 7 hours
Solve x4 − 7x2 − 18 = 0
Answers
Answer:
the answer is
x=±3,±√2
ı
Step-by-step explanation:
(x^2−9)(x2+2)=0
Based on an architectural drawing, a roof slopes to a drain
along the function represented in the table that defines the
edge of slope, where x is the horizontal distance in feet and
f(x) is the vertical distance in feet.
If the drain is at the minimum point, how far is it from the wall
defined by the y-axis?
A. O feet
B. 8 feet
C. 80 feet
D. 160 feet
Answers
Answer:
80 feet
Step-by-step explanation:
Given that x is the horizontal distance in feet and f(x) is the vertical distance in feet. The minimum point of a function is its lowest point. For a quadratic equation, at its minimum or maximum point, the slope of the graph is equal to zero.
For the table of the function given below, it can be seen that the lowest point occurs when x = 80 feet, at this point, the value of f(x) is at its lowest which is 0.
Therefore at the minimum point, it is 80 feet far from the wall .
Answer:
The answer is C!
Step-by-step explanation:
Your welcome
What is the perimeter of ABCDE, rounded to the nearest whole number?
Answers
Answer:
option B -> 23 units
Step-by-step explanation:
To solve this question we need to find the length of each side, and we can do this finding the distance between the pair of points that make a side, using the formula:
[tex]dist = \sqrt{(x_1 - x_2)^{2} + (y_1 - y_2)^{2} }[/tex]
Where the points are [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex].
So, using the points A = (-4, -2), B = (-1, 2), C = (2, 2), D = (5, -1) and E = (2, -4), we have that:
[tex]AB = \sqrt{(-4 - (-1))^{2} + (-2 - 2)^{2} } = 5[/tex]
[tex]BC = \sqrt{(-1 - 2)^{2} + (2 - 2)^{2} } = 3[/tex]
[tex]CD = \sqrt{(2 - 5)^{2} + (2 - (-1))^{2} } = 4.2426[/tex]
[tex]DE = \sqrt{(5 - 2)^{2} + (-1 - (-4))^{2} } = 4.2426[/tex]
[tex]EA = \sqrt{(2 - (-4))^{2} + (-4 - (-2))^{2} } = 6.3246[/tex]
So the perimeter of ABCDE is:
[tex]P(ABCDE) = AB + BC + CD + DE + EA[/tex]
[tex]P(ABCDE) = 5 + 3 + 4.2426 + 4.2426 + 6.3246 = 22.8098[/tex]
Rounding to nearest whole number we have:
[tex]P(ABCDE) = 23[/tex]
So the answer is the option B.
No rush. I need help on this question. I need an explanation pleaseeeeee. Thank you in advance!
Answers
Answer:
1) 275
2)60
Step-by-step explanation:
1) 55 x 5 =275
2) 12 x 5 = 60
Hope it helps!
Answer:
2 vans and 7 busses
Step-by-step explanation:
Let x=# of busses
Let y=# of vans
55x+12y=409
x=y+5
55(y+5)+12y=409
55y+275+12y=409
67y+275=409
134=67y
y=2
There were two vans, and y+5 (7) busses
please help me, with full explanation!!!!
Answers
Answer:
9.54 cm
Step-by-step explanation:
In triangle ABD, AD is the hypotenuse (longest side)
We know that according to Pythagoras theorem,
a^2+b^2=c^2
In the figure, c (10cm) and a (5cm) is given. So,
(5)^2 + b^2 = 100
25+b^2 = 100
b^2 = 75
So b is √75 = 8.66
Therefore BD is 8.66 cm
Now even BDC is a triangle
In it, the hypotenuse is missing but we know the value of other sides
so, in Pythagorean theorem,
a=4 (CD)
b=8.66 (BD)
c=x
Therefore,
(4)^2 + (8.66)^2 = x^2
16+74.99= x^2
x^2 = 90.99
x= 9.54 cm
Hope this helps!
The inverse of f(x) is a function
Answers
Answer:
Step-by-step explanation:
Not always. If, however, the given function passes the "horizontal line test," then the given function has an inverse which is also a function. The horizontal line test consists of drawing a horizontal line through the given graph; if the line intersects the graph in only one place, it "passes," and the given function has an inverse function.
Two parallel lines are crossed by a transversal. Horizontal and parallel lines p and q are cut by transversal m. At the intersection of lines p and m, the bottom left angle is b degrees. At the intersection of lines q and m, the top right angle is 128 degrees. What is the value of b?
Answers
Answer:
If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary . ... When two lines are cut by a transversal, the pairs of angles on either side of the transversal and outside the two lines are called the alternate exterior angles .
Step-by-step explanation:
hope this helps you :)
Answer:
The answer is 102
Step-by-step explanation:
Did it on edg hope this helps :)
Q4: Katie and Tyler are working at their lemonade stand. An hour ago, their pitcher of lemonade was 78 full. Since then, they have sold 12 of a pitcher of lemonade. What fraction of a pitcher do they have left?
Answers
Answer:
3/8 of the pitcher of lemonade remains.
Step-by-step explanation:
They tell us that at first they had 7/8 of a pitcher full of lemonade, and they ask us to know what fraction is left if they have taken 1/2 of the pitcher of lemonade for a while, which means that it would be a subtraction between what had at the beginning and what they have taken, would be:
7/8 - 1/2 = (14 - 8) / 8 * 2 = 6/16 = 3/8
Which means that 3/8 of the pitcher of lemonade remains.
the sum of the present ages of A and B is 60 years.5 years hence their ages will be in the ratio 4:3.What were their ages 5 years ago? please show the working
Answers
Answer:
A= 30 years old
B= 20 years old
Step-by-step explanation:
Let the present age of A be x years old.
Since the sum of the present ages of A and B is 60 years,
present age of B= (60-x) years old
In 5 years
A= x +5
B= 60 -x +5= 65-x
Since the ratio of A:B= 4:3,
A would represent 4 units and B would represent 3 units.
Thus [tex]\frac{3}{4}[/tex]A=B
[tex]\frac{3}{4}[/tex](x+5)= 65 -x
[tex] \frac{3}{4} x + \frac{15}{4} = 65 - x \\ \frac{3}{4} x + x = 65 - \frac{15}{4} \\ \frac{7}{4} x = 61.25 \\ 7x = 61.25 \times 4 \\ 7x = 245 \\ x = 245 \div 7 \\ x = 35[/tex]
Thus, present age of A
= x
= 35 years old
present age of B
= 60 -x
= 60 -35
= 25 years old
5 years ago
A= 35 -5= 30 years old
B= 25 -5= 20 years old
* under the section in 5 years, [tex]\frac{3}{4} A=B[/tex] because both would be equal to 3 units each. Since B is 3 units and A is 4 units, in order to make both value the same, we divide the 4 units of A by 4 then multiply by 3 to get 3 units. Thus, [tex]\frac{3}{4}[/tex] of A is equal to B.
Eduardo had 18 candies. 2/3 of the candies were butterscotch discs. How many were butterscotch discs?
Answers
Answer:
is 12
Step-by-step explanation:
2/3=18
18:3= 6
6 x 2=12
[tex]answer \\12 \\ solution \\ \\ \frac{2}{3} \times 18 \\ = 12 \\ \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
PLEASE HELP ASAP!!!
How is solving addition and subtraction equations similar to and different from solving multiplication and division equations?
Answers
Answer:
Here is what I think:
Addition and Multiplication are very similar. Multiplication is just repeated addition. If you do 3*2 its just adding 3, 2 times to each-other. The same goes for division. Its repeated subtraction. 15/3 If you subtract 3 from 15 how many times can you do it. There are also differences though. Multiplication is usually used to calculate different things though. It can calculate area and volume while addition usually doesn't. Division is used to find how much of something can fit into something. But subtraction usually is only used for subtracting other things. Those are similar things and different things for this.
A movie theater is giving away a souvenir poster to any customer with a concession stand receipt that exceeds 560. The theater
sells a bag of popcorn for $6 and bottle of soda for $3.50. Let x represent the number of bags of popcorn, and let y represent the
number of bottles of soda. Which Inear inequality can be used to find the quantities of popcorn and soda that should be purchased
to receive a poster?
Answers
Please help me Simplify 5+(z+2)
Maybe try to simplify
Answers
Answer:
7+z
Step-by-step explanation:
you can open the parentheses right away because it is addition. so you are left with 5+z+2. you can add both 5 and 2 together, so the final result will be 7+z
Find the surface area of the polyhedra
pls!! show how you got the surface area
Answers
Answer:
164 cm.
Step-by-step explanation:
First, I solved for the bottom and top. 10 times 3 is 30. Then I doubled it because it's the same answer for the bottom and top. I got 60.
Next I solved for the sides. 4 times 3 is 12. Then I doubled it because it's the same answer for both sides. I got 24.
Lastly I solved for the front and back. 10 times 4 is 40. Then I doubled it because it's the same answer for both the front and back. I got 80.
After all this, I added everything together. 60 + 24 + 80 = 164.
Sorry, I'm not the best at explaining things.
3 feet
12 feet
The ramp will be approximately
feet long
Answers
Answer:
36 feet long
Step-by-step explanation:
3 feet x 12 feet is 36 so it will be 36 feet long!
please mark brainliest and have a nice day :)
Which of the following is an angle shown in the drawing?
Answers
Answer:
ABE
DBC
CBE
Step-by-step explanation:
They all have B as the middle one, and B is the vertex
I think
A coordinate plane showing Nina's run. The x-axis shows Time in seconds and the y-axis shows Distance in meters. Four points plotted and labeled. The points are (4, 32), (6, 48), (8, 64), (10, 80). A two column table with four rows. The first column, Time in seconds, has the entries, 4, 6, 8. The second column, Distance in meters, has the entries, 35, 47.5, 60. Nina and Ryan each ran at a constant speed for a 100-meter race. Each runner’s distance for the same section of the race is displayed on the left. Who had a head start, and how big was the head start? had a head start of meters
Answers
Answer:
Ryan had a head start of 10 meters
Answer:
Ryan had a head start of 10 meters.
Have a great day!
Step-by-step explanation:
Please mark me brainliest!
