A private plane leaves the airport and flies 1.3 hours at 110 mph on a bearing if 40 degrees. Then it turns and continues another 1.5 hours at the same speed, but in a bearing if 130 degrees. Through what angle did the plane have to turn to head back to the airport?

Answers

Answer 1

Refer to the diagram shown below.

The first distance traveled is
a = (110 mi/h)*(1.3 h) = 143 mi
The second distance traveled is
b = (110 mi/h)*(1.5 h) = 165 mi

From geometry,
x = 40°
y = 180° - 130° = 50°
x + y = 40° + 50° = 90°
Therefore we have a right triangle.

By definition
tan θ = 165/143 = 1.1538
θ = tan⁻¹ 1.1538 ≈ 49°
Because the sum of angles in a triangle is 180°, therefore
z = 180° - (49° +90°) = 41°

The angle through which the plane has to turn to head back to the airport is
φ = 360° - (y + z)
= 360° - (50° + 41)°
= 269°

Answer: 269°

A Private Plane Leaves The Airport And Flies 1.3 Hours At 110 Mph On A Bearing If 40 Degrees. Then It

Answer 2

Heading = 269.09 degrees. Plane will turn through an arc of 139.09 degrees. First, lets calculate the length of the 2 legs we know of. Leg1 = 1.3 * 110 = 143 miles. Leg2 = 1.5 * 110 = 165 miles. These distances are short enough that we can ignore the curvature of the earth and stick with euclidean geometry. Let's convert the polar coordinate of (40, 143) to Cartesian. (143sin(40), 143cos(40)) = (91.92, 109.54) So we know the plane flew 109.54 miles to the north, and 91.92 miles east. Lets see about the second leg. (165sin(130), 165cos(130)) = (126.40, -106.06) So the plane then traveled 126.40 miles to the east, and 106.06 miles to the south. Adding those distances together gives (91.92 + 126.40, 109.54 - 106.06) = (218.32, 3.48) So the plane is now 218.32 miles to the east and 3.48 miles to the north of where it originally started. Let's calculate the angle needed to return by first calculating the tangent. 3.48 / 218.32 = 0.01594 atan(0.01594) = 0.91 degrees. Since the plane will have to be going almost due west, that means that the heading will be close to 270 degrees. And since it also needs to go slightly south, we'll subtract the 0.91 degrees from the 270 to get a heading of 269.09 degrees. In order to get to that new heading from it's current heading of 130 degrees, we simply subtract. So 269.09 - 130 = 139.09 degrees

Related Questions

i'm working at a distribution place and need help i'm supposed to be averaging 1000 units every hours if i do 4800 in a shift i'm 48 minutes behind schedule how many units per a hour am i averaging

Answers

Expected throughput is
1000 units/h

Therefore the expected time for 4800 units is
(4800 units)/(1000 units/h) = 4.8 hours = 288 minutes

Because the worker is 48 minutes behind schedule, the actual time is
288 + 48 = 336 minutes = 5.6 hours

The actual average throughput is
(4800 units)/(5. h) = 857 units per hour.

Answer: 857 units per hour.

Work out the value of 3x + 2y when x=4 and y=-5

Answers

3x + 2y =

3*4 + 2*-5=

12 + -10 = 2

Just substitute the equation with the given

The given are
x = 4 and y = -5
the equation is
3x + 2y
3 (4) + 2 (-5) = 12 - 10 = 2

I really need help on this problem can i get help on how to solve the problem please

Answers

you cannot assume that the angles are equal. there is no angle measure and nothing to say the lines are parellel.

Help me solve this please...in detail.

Answers

n+6 = 2*7
n+6 = 14
n= 14-6
n=8

Is it true that |3-8| and |3+8|

Answers

No, it is not true. If you solve them, the first one is 5, while the second one is 11.

To determine if |3-8| is equal to |3+8|, we calculate the absolute values: |3-8|=5 and |3+8|=11. Since 5 is not equal to 11, the statement is false.

To solve the given problem, we need to understand the properties of absolute values. Absolute value measures the distance of a number from zero on the number line, regardless of direction.

First, calculate the absolute value of each expression: |3-8| and |3+8|.For |3-8|:

3 - 8 = -5, and the absolute value of -5 is 5. Therefore, |3-8| = 5.

For |3+8|:

3 + 8 = 11, and the absolute value of 11 is 11. Therefore, |3+8| = 11.

In conclusion, it is not true that |3-8| equals |3+8|, as |3-8| = 5 and |3+8| = 11.

here is the full question-Is it true that |3-8| and |3+8| are equal?

Joseph’s garden is 9 feet wide and 12 feet long. Alana’s garden is 7 feet wide and 25 feet long.

How much greater is the area of Alana’s garden than Joseph’s garden?
Please help!! Will give 15 points!

Answers

area of Josephs garden = 9*12 = 108 square feet

area for Alana's garden = 7 *25 = 175 square feet

175/108 = 1.62

Alan's garden is 1.62 times larger

(−2+2i)⋅(5+5i)
Can you help me simplify

Answers

(−2+2i)⋅(5+5i)
FOIL
-10-10i+10i+10i²=-10+10i² this is the simplify answer
If you want the complete answer is
-10+10(-1)=-10-10=-20

If the ratio between the radii of the two spheres is 3 5 what is the ratio of their volumes

Answers

3^3 / 5^3 = 27 / 125

Answer:

The answer is 27:125

Cho welcome

Algebra Vocabulary Crossword help ?!

1. a relation described in word format? (17 letter)

9. a way to name a function identifying its input?
(16 letter)

Answers

1. a relation described in word format (17 letter) is "is direct variation"

9. a way to name a function identifying its input (16 letter) is "f of x equals x square"

Final answer:

The student is looking for the terms 'Verbal Description' and 'Function Notation' for their Algebra Vocabulary Crossword. These refer to a relation described in word format and a way to name a function identifying its input respectively.

Explanation:

Based on the number of letters you've indicated, it looks like you're looking for two vocabulary items in the field of Algebra.

First, a relation described in a word format is typically called a Verbal Description, which has 17 letters.

Second, a way to name a function identifying its input is called Function Notation, which has 16 letters.

In Algebra, Verbal Description is when you describe a mathematical relationship using words. For example, 'the sum of a number and three is seven.' This could be translated to the equation x+3=7.

Function Notation, on the other hand, is a way to name a function that is dependent on one or more inputs. For example, f(x) = x^2 is function notation, since the output 'f(x)' is dependent on the input 'x'.

Learn more about Algebra Vocabulary here:

https://brainly.com/question/17547766

#SPJ11

If a line is perpendicular to a line segment, what angle do they form at their intersection

Answers

If a line is perpendicular to a line segment, then they will form a right angle.

90 degree will be the answer cause its a right angle.

Based on research by barsh and colleagues (2000), _____ genes appear to be related to body weight regulation.

Answers

The answer is more than 40 genes. According to their research, these genes are transcripted into the DNA during the translation.One of these genes is called CYP19. Having more than one strand of this gene can possibly be the reason why people are slightly larger than the others.

The height of one square pyramid is 12 m. A similar pyramid has a height of 6 m. The volume of the larger pyramid is 400 m3. Determine each of the following, showing all your work and reasoning.

Scale factor of the smaller pyramid to the larger pyramid in simplest form

Ratio of the areas of the bases of the smaller pyramid to the larger pyramid

Ratio of the volume of the smaller pyramid to the larger

Volume of the smaller pyramid

Answers

[tex]\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{ccccllll} &Sides&Area&Volume\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array} \\\\ -----------------------------\\\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\ [/tex]

[tex]\bf \cfrac{smaller}{larger}\qquad \cfrac{\stackrel{height}{6}}{\stackrel{height}{12}}\implies \cfrac{1}{2}\impliedby \textit{scale factor of the pyramids}\\\\ -------------------------------\\\\ \cfrac{smaller}{larger}\qquad \cfrac{h}{h}=\cfrac{\sqrt{base}}{\sqrt{base}}\implies \cfrac{1}{2}=\sqrt{\cfrac{base}{base}}\implies \left( \cfrac{1}{2} \right)^2=\cfrac{base}{base} \\\\\\ \cfrac{1^2}{2^2}=\cfrac{base}{base}\implies \cfrac{1}{4}=\cfrac{base}{base}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \cfrac{smaller}{larger}\qquad \cfrac{h}{h}=\cfrac{\sqrt[3]{volume}}{\sqrt[3]{volume}}\implies \cfrac{1}{2}=\sqrt[3]{\cfrac{volume}{volume}} \\\\\\ \left( \cfrac{1}{2} \right)^3=\cfrac{volume}{volume} \implies \cfrac{1^3}{2^3}=\cfrac{volume}{volume}\implies \cfrac{1}{8}=\cfrac{volume}{volume}\\\\ -------------------------------\\\\ \cfrac{smaller}{larger}\qquad \cfrac{1}{8}=\cfrac{\stackrel{volume}{v}}{\stackrel{volume}{400}}\implies \cfrac{1\cdot 400}{8}=v[/tex]

The commission of selling each iPhone is $30 and the commission of selling each iPad is $20. If you one day sold 4 more iPhones than iPads and earned a total commission of $520, how many iPhones and iPads did you sell respectively?

Answers

lets assume number of iphones sold = a number of ipads sold = b i sold 4 iphones more than ipad that becomes a = b+4 then the equation of total commission becomes 30a+20b = 520 substituting a =b+4 in the above equation 30(b+4)+20b = 520 30b+120+20b = 520 50b =520-120 50b = 400 b = 400/50 b=8 number of iphones i sold = a = b+4 = 8+4 = 12 number of ipads i sold = 8 so i sold 12 iphones and 8 ipads to earn the commission of $520

By solving the system of equations which includes the total commission and difference in quantity of iPhones and iPads sold, we determine that the salesperson sold 8 iPads and 12 iPhones.

The student is tasked with solving a system of linear equations to determine how many iPhones and iPads were sold based on the commission earned. Let's define the number of iPads sold as x and the number of iPhones as x + 4.

The total commission for iPhones is $30 per iPhone and the total commission for iPads is $20 per iPad. The total commission earned from selling these products is $520.

We can set up two equations based on the given information:

Commission from iPhones: 30(x + 4)

Commission from iPads: 20x

Total Commission: 30(x + 4) + 20x = 520

By solving the equation 30(x + 4) + 20x = 520, we find:

30x + 120 + 20x = 520

50x + 120 = 520

50x = 400

x = 8

So, the number of iPads sold is 8. Since the number of iPhones sold is 4 more than iPads, we have:

Number of iPhones sold = x + 4 = 8 + 4

Number of iPhones sold = 12

Therefore, the salesperson sold 8 iPads and 12 iPhones respectively.

Critical thinking write a recursive rule for a sequence where every term is the same.

Answers

To do this, let f(1) = 5 and f(n) = f(n-1) for n greater than 1. This is recursive rule and each term is the same because it eventually becomes f(1), which is 5.

PLEASE ANSWER FAST!
Which statement best describes why the sale price is a function of the original price?
A:As the original price increases, the sale price also increases.
B:The sale price is always less than the original price.
C:For every original price, there is exactly one sale price.
D:The sales price is never less than zero.

Answers

Answer:

I think B,not sure

Step-by-step explanation:

Answer:

Step-by-step explanation:

Got it right

If f(x) = + 8, what is f(x) when x = 10?

Answers

f(x) = (x/2) + 8
f(10) = (10/2) + 8 ... replace every x with 10; now use PEMDAS
f(10) = 5 + 8
f(10) = 13

We plugged in x = 10 as the input to get the output of f(x) = 13

Answer: 13

Answer:

Step-by-step explanation:

it correct

You went shopping and found a pair of shoes that were $45.00 on sale for $27.50. what was the percent of decrease of the shoes? your answer should go 1 decimal place)

Answers

percent decrease = (original number - new number) / original number....* 100
= (45 - 27.5) / 45.....* 100
= 17.5 / 45....* 100
= 0.3888 * 100
= 38.9 % decrease <== thats rounded

Tali started a pool cleaning business. She purchased cleaning supplies and charged the same amount for each pool cleaned. The expression −243+24x represents the profit Tali has earned from cleaning pools.

Which expression represents the total amount Tali earns from pool cleaning?

24x

24

−243

x

Answers

Answer:

24x

Step-by-step explanation:

The variable x is used to represent the independent variable in a situation. In this situation, the independent variable would be the number of pools cleaned; this means that x represents the number of pools cleaned.

24x would then indicate that Tali charges $24 per pool cleaned; this makes 24x her total earnings from cleaning pools.

Answer:

A. [tex]24x[/tex]

Step-by-step explanation:

We have been given an expression [tex]-243+24x[/tex], which represents he profit Tali has earned from cleaning pools. We are also told that Tali purchased cleaning supplies and charged the same amount for each pool cleaned.

Upon looking at our expression we can see that [tex]-243[/tex] is constant term and it is negative, so it will represent the amount spent by Tali on supplies.

The term [tex]24x[/tex] contains independent variable [tex]x[/tex], which represents the number of pools cleaned and 24 represents Tali's earning from each pool.

Since Tali cleaned [tex]x[/tex] pools, so total amount of Tali's earning from cleaning [tex]x[/tex] pools will be [tex]24x[/tex] and option A is the correct choice.

1. what are some different types of numbers that you have herd of before?

2. why do you think it is important to classify (sort) different types of numbers

Answers

natural, whole

you need the different classifications that way it is easier to tell someone what you are talking about.

1. Some types of numbers I've heard about are: whole numbers, fractions, negative numbers, infinite numbers, irrational numbers, rational numbers, improper fractions, imaginative numbers, radical numbers, unknown numbers, etc.

2. I think it important to group or separate numbers out in order to apply them to the categories they apply to.

Name the property the equation illustrated
8 + 3.4 = 3.4 +8

Answers

8 + 3.4 = 3.4 +8
commutative property of addition

I'm sure it would only just be 0 so either 0 or no solution

At city high school,the sophomore class has 60 more students than the freshman class.the junior class has 50 fewer students than twice the students in the freshman class.the senior class is three times as large as the freshman class.if there are a total of 1,424 students at the city high school,how many students are in the freshman class?

Answers

S=f+60
J=Fx2-50
Senior=fx3

(f)+(f+60)+(fx2-50)+(fx3)=1424 (Parenthesis first)
f+f+60+2f-50+3f=1424 (rewrite)
2f+60+2f-50+3f=1424 (combine like variables)
7f+10=1424 (rewrite)
7f=1414 (isolate variable (take away 10 from each side))
1414/7
202=freshman

Answer:

The number of students in the freshman class are:

202

Step-by-step explanation:

Let the number of students in Freshman class = x

The sophomore class has 60 more students than the freshman class.

This means that the number of students in sophomore class = x+60

The junior class has 50 fewer students than twice the students in the freshman class.

This means that the number of students in junior class= 2x-50

The senior class is three times as large as the freshman class.

This means that the number of students in senior class are: 3x

There are a total of 1,424 students at the city high school.

This means that:

[tex]x+x+60+2x-50+3x=1424\\\\x+x+2x+3x+60-50=1424\\\\7x+10=1424\\\\7x=1424-10\\\\7x=1414\\\\x=\dfrac{1414}{7}\\\\x=202[/tex]

Need help ASAP real quick ????????????

Answers

The answer is 54. (36+72=108. 108/2 = 54)

If y = 44 when x = –264, what is y when x = –486

Answers

Final answer:

The value of 'y' when x equals -486 using the same ratio (1:6) as given in the original input is -81.

Explanation:

To solve this problem, we're given a ratio of y to x (1:6) when x is -264 and y is 44. This ratio implies that y is one-sixth of x. Utilizing this information, we can determine y for a different x value (-486). By maintaining the 1:6 ratio, we divide -486 by 6, resulting in -81. Therefore, when x is -486, y equals -81. This solution stems from understanding the proportional relationship between y and x, allowing us to calculate y for any given x value based on the established ratio. In this case, the ratio of 1:6 guides the computation, ensuring the accurate determination of y as -81 when x is -486.

Learn more about Ratios here:

https://brainly.com/question/32531170

#SPJ2

What is 39ft/min to yd/s?
Please explain using dimensional analysis.

Answers

Dimensional analysis simply means to arrange the units in the problem in a such a way that they cancel each other out and you're left with the units you need in the answer. We do this by using conversion ratios arranged like fractions, then multiplying across left to right.

In your problem, we're given ft/min and need to convert to yd/s. Start with feet and convert to yards for the numerator, then convert minutes to seconds for the denominator: (pretend the parentheses encompass the entire fractions - limitations of the answer box)
39 feet x ( 1 yard ) x (1 min)
1 min 3 feet 60 sec

Notice that feet cancel, and minutes cancel. We're left with yards in the numerator and seconds in the denominator.
Multiplying the numbers, we get 39/180, which simplifies to 0.217.
The final answer is ~0.22 yd/sec.

48 out of 120 equals what percent

Answers

48/120 = 40%

48 * 2,5 = 120

np ;)

The answer i got was 40 because you multiply 100 to 48 and then divide by 120.

Given the literal equation for the area formula of a trapezoid: A =12h(b1 + b2) solve for b1. Must show your work to receive full credit.

Answers

[tex]$ b_1 = \frac{A}{12h} - b_2 $[/tex] is the formula to solve for [tex]$ b_1 $[/tex] in the trapezoid area equation.

To solve for [tex]$ b_1 $ in the equation $ A = 12h(b_1 + b_2) $, where $ A $[/tex] is the area of the trapezoid, [tex]$ h $ is the height, $ b_1 $[/tex]is one of the bases, and [tex]$ b_2 $[/tex] is the other base, you can follow these steps:

1. Divide both sides of the equation by [tex]$ 12h $ to isolate $ (b_1 + b_2) $:[/tex]

[tex]\[ \frac{A}{12h} = b_1 + b_2 \][/tex]

2. Subtract [tex]$ b_2 $[/tex] from both sides of the equation:

[tex]\[ \frac{A}{12h} - b_2 = b_1 \][/tex]

So, the equation for [tex]$ b_1 $ in terms of $ A $, $ h $, and $ b_2 $[/tex] is:

[tex]\[ b_1 = \frac{A}{12h} - b_2 \][/tex]

Please can you help me

Answers

Answer:

5 : 1

Step-by-step explanation:

From your second-grade memorization of multiplication tables, you recognize that 15 = 3×5, so you know 3 is a factor of both numbers in the ratio. To reduce the ratio to simplest form, you divide out all common factors:

15 : 3 = (15/3) : (3/3) = 5 : 1

Is it possible for a composite number to have more than one prime factorization?

Answers

no The prime factorization of a composite number is the process of finding all the prime numbers that when multiplied together result in the composite number. Just rearranging the order of the prime numbers doesn't change the factorization. The Commutative Property of multiplication allows us to multiply the prime factors together in any order at all.

Which equation below represents a vertical line? y = x + 0, y = x – 0, y = 4, x = 4

Answers

a vertical line is represented by x = a number
so ur vertical line is : x = 4 <==

** and just so u know, a horizontal line is represented by y = a number.

[tex]x=4[/tex] is the answer
hope this has helped you

The LCD for the fraction 1/3 , 3/4 , 5/32 , and 8/9 Is?

A. 288
B. 24
C. 3,072
D. 64

Answers

the answer would be a. 288. hope that helped

2 is the biggest number, so to find the LCD check to see if it is divisible by 3, no, 4, yes, 9, no. Next number: 32x2=64. None of the numbers were divisible. Eventually, you'll find that the LCD is 288

Other Questions

The sun delivers an average power of 1.499 w/m2 to the top of neptune's atmosphere. find the magnitudes of vector e max and vector b max for the electromagnetic waves at the top of the atmosphere. Why is important to use reply instead of new message when answering e-mail which force causes an object to free falla) windb) fluid forcesc) friction d) gravity A teacher asked the class to solve the equation 3(x + 2) = 21. Robert wrote 3x + 6 = 21 as his first step. Which property did he use? (1) associative property (3) distributive property (2) commutative property (4) zero property of addition Pebbles caught in swirling eddies of water best describe ________. Fred completen 10 math problems This is 40 percent of the number of math problems he has to do How many math problems must he do After gave him a warm bath....now he sleep peacefully. It is correct grammar? you have a bottle of water with a leak. after 2 seconds there is 28 ounces left in the bottle. after 6 seconds there are 20 ounces left in the bottle. how much water was in the bottle initially What does the word quack likely mean What class of organic molecules does cholesterol belong to? What can be concluded about the atom from knowing that oxygen-18 has an atomic number of 8? A)An oxygen atom that includes 8 baryons, 9 prions, and 10 neutrons. B)This oxygen isotope contains 8 electrons, 8 protons, and 10 neutrons. C)It's an oxygen allotrope incorporates 7 electrons, 7 protons, and 7 quarks. D)The oxygen configuration consists of 6 electrons, 8 photons, and 10 neutrons. A chemical bond formed when two atoms of the same element share electrons is a _________________ _________________ bond. The sales tax rate on camping equipment is 7 percent. Olivia will buy a sleeping bag priced at $35.35 and a tent at $52.75. What amount will Olivia spend on the sales tax. One of the five characteristics of life is the need for energy. Which of the four basic needs meets this need? water air food a place to live The most rapid way that erythrocytes adapt to high altitudes is What consecutive numbers have a sum of 133? If $6000 is invested at 7% simple interest for 4 months, how much interest is earned? The conclusion paragraph has two jobs what are they Ordinary household bleach is an aqueous solution of sodium hypochlorite. what is the molarity of a bleach solution that contains 32.4 g of sodium hypochlorite in a total volume of 499 ml? Atp is generated during cellular respiration. in which stage is the most atp produced? Steam Workshop Downloader