Given: BD⎯⎯⎯⎯⎯ is an altitude of △ABC.Prove: sinAa=sinCcTriangle A B C with an altitude B D where D is on side A C. side A C is also labeled as small b. Side A B is also labeled as small c. Side B C is also labeled as small a. Altitude B D is labeled as small h. Select from the drop-down menus to correctly complete the proof.Statement ReasonBD⎯⎯⎯⎯⎯ is an altitude of △ABC. Given△ADB and △CDB are right triangles. Definition of right trianglesinA=hcand sinC=hacsinA=hand asinC=hMultiplication Property of EqualitycsinA=asinCcsinAac=asinCacsinAa=sinCcSimplify.

The value of x is \(\log_{3}(\frac{-4\pm \sqrt{82}}{3})\) approximately equal to -1.1219 or 1.5219 (approx).

The given equation has two values of x, i.e., \(\log_{3}(\frac{-4+ \sqrt{82}}{3})\) and \(\log_{3}(\frac{-4- \sqrt{82}}{3})\).

Given: 3^{x} \log _{2} 4^{8}+\log _{11} 11^{3^{x}}=17

Since \log_{a}b^{c}=c\log_{a}b\implies3^{x} \log _{2} 4^{8}+\log _{11} 11^{3^{x}}

=17\implies 3^{x} (8\log _{2} 4)+3^{x}=17\implies 3^{x}(3^{x}+8)

=17

Now, we will find out all the possible values of x one by one as:3^{x}(3^{x}+8)=17\implies 3^{2x}+8*3^{x}-17=0\implies 3^{x}=\frac{-8\pm \sqrt{8^{2}-4*3*(-17)}}{2*3}\implies 3^{x}

=\frac{-8\pm \sqrt{328}}{6}\implies 3^{x}

=\frac{-8\pm 2\sqrt{82}}{6}\implies 3^{x}

=\frac{-4\pm \sqrt{82}}{3}\implies x

=\log_{3}(\frac{-4\pm \sqrt{82}}{3})

Learn more about value from;

https://brainly.in/question/3918992

#SPJ11

P( X≥23.5) = 0.5 + A(0.277)

P( X≥23.5) = 0.5 + A(1.388)

Given that the mean of the Population = 26 weeks

The Standard deviation of the Population = 9 weeks

Let 'X' be a Normal distribution

Z = \(\frac{x-mean}{standard deviation}\)

Z = \(\frac{23.5-26}{9}\)

Z = -2.5/9

Z = -0.277

The probability that a single randomly selected value is greater than 23.5

P( X≥23.5) = P(Z≥-0.277)

P( X≥23.5) = 0.5 + A(-0.277)

P( X≥23.5) = 0.5 + A(0.277)              

Let 'X' be a Normal distribution

Z = \(\frac{x-mean}{\frac{standard deviation}{\sqrt{n} } }\)

Z = \(\frac{23.5-26}{\frac{9}{\sqrt{25} } }\)

Z = -2.5/9/5

Z = -2.5/1.8

Z = -1.388

The probability that a  sample of size randomly selected value is greater mean greater than 23.5

P( X≥23.5) = P(Z≥-1.388)

P( X≥23.5) = 0.5 + A(-1.388)

P( X≥23.5) = 0.5 + A(1.388)

Therefore,

P( X≥23.5) = 0.5 + A(0.277)

P( X≥23.5) = 0.5 + A(1.388)

To learn more about information visit Probability :

brainly.com/question/14747562

#SPJ4

On solving the provided question we can say that As a result, the credit equation limit of a client who has paid on time every year for the past ten years is $7,000.

A mathematical equation is a formula that links two statements and uses the equals sign (=) to indicate equality. In algebra, an equation is a statement that demonstrates the equality of two mathematical expressions. The equal sign divides the variables 3x + 5 and 14 in the equation 3x + 5 = 14, for instance.

The relationship between the two sentences that are located on opposite sides of a letter is explained by a mathematical formula. Frequently, the symbol and the single variable are identical. like in 2x - 4 = 2, for example.

The following equation determines the credit limit, Ln, of customers who have made on-time payments each year and are in the nth year of card ownership:

Ln = $2,000 + $500n

where Ln stands for the credit limit in the nth year and n is the number of years the cardholder has had it.

In the equation above, we substitute n=10 to get a customer's credit limit after ten years of card use:

L10 = $2,000 + $500(10)

L10 = $2,000 + $5,000

L10 = $7,000

As a result, a client with a ten-year history of on-time payments has a credit limit of $7,000.

To know more about equation visit:

brainly.com/question/649785

#SPJ1

Answer:

-2

Step-by-step explanation:

\(\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }\)

where (x₁, y₁) is the first coordinate and (x₂, y₂) is the second coordinate

Slope

\( = \frac{14 - 4}{ - 8 - ( - 3)} \)

\( = \frac{10}{ - 8 + 3} \)

\( = \frac{10}{ - 5} \)

= -2

Answer:

l = x · c / 360

l = 72 · 20 / 360

l = 1440 / 360

l = 4

Step-by-step explanation:

1. write down the arc length formula.

2. replace x and c by their values

3. multiply and then divide to get l

The percentage of $898.01 billion that is spent on $161.4 billion​ is equal to 17.97%.

In Mathematics, a percentage simply refers to any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.

In order to determine the percentage, we would use the following mathematical expression:

Percentage = 161.4/898.01 × 100

Percentage = 0.1797 × 100  

Percentage = 17.97%

Read more on percentage here: brainly.com/question/11360390

#SPJ1

Answer:

c(p) = {0.2 p ⇒ p < 1000

          0.24 p - 40 ⇒ 1000 ≤ p ≤ 2000

          0.29 p - 140 ⇒ p > 2000}

Step-by-step explanation:

* Lets explain how to solve the problem

- The profit is represented by p

1. If the profit is under $1,000,  the commission rate is 20%

∵ The profit is p < 1000

∵ 20% of p =  = 0.2 p

∵ c(p) is the function of the commission

∴ c(p) = 0.2 p when p < 1000

2. If the profit is at least $1,000 and less than or equal to  $2,000, the

 commission rate is 20% of the first $1,000 and 24% of the remainder

 of  the profit

- At least means greater than or equal

∵ The profit 1000 ≤ p ≤ 2000

- The commission is divided into 20% of first $1000 and 24% of

 the reminder

∵ 20% of 1000 =  = 200

∵ The remainder of the profit = p - 1000

∵ 24% of the remainder profit =

 = 0.24(p - 1000) = 0.24 p - 240

∴ The total commission = 200 + 0.24 p - 240

∴ The total commission = 0.24 p - 40

∴ c(p) = 0.24 p - 40 when 1000 ≤ p ≤ 2000

3. If the profit is above $2,000, the rate is 20% of the first $1,000

  of profit,  24% of the next $1,000 of profit, and 29% of the amount

  of profit over $2,000

∵ The profit p > 2000

- The commission is divided into 20% of first $1000 and 24% of the

 next $1,000 of profit, and 29% of the amount of profit over $2,000

∵ 20% of 1000 =  = 200

∵ 24% of 1000 =  = 240

- The amount of profit over $2,000 = p - 2000

∵ 29% of the amount of profit over $2,000 =

   = 0.29(p - 2000)

  = 0.29 p - 580

∴ The total commission = 200 + 240 + 0.29 p - 580

∴ The total commission = 0.29 p - 140

∴ c(p) = 0.29 p - 140 when p > 2000

* The commission function is:

c(p) = {0.2 p ⇒ p < 1000

           0.24 p - 40 ⇒ 1000 ≤ p ≤ 2000

           0.29 p - 140 ⇒ p > 2000}* Lets explain how to solve the problem

- The profit is represented by p

1. If the profit is under $1,000,  the commission rate is 20%

∵ The profit is p < 1000

∵ 20% of p =  = 0.2 p

∵ c(p) is the function of the commission

∴ c(p) = 0.2 p when p < 1000

2. If the profit is at least $1,000 and less than or equal to  $2,000, the

 commission rate is 20% of the first $1,000 and 24% of the remainder

 of  the profit

- At least means greater than or equal

∵ The profit 1000 ≤ p ≤ 2000

- The commission is divided into 20% of first $1000 and 24% of

 the reminder

∵ 20% of 1000 =  = 200

∵ The remainder of the profit = p - 1000

∵ 24% of the remainder profit =

 = 0.24(p - 1000) = 0.24 p - 240

∴ The total commission = 200 + 0.24 p - 240

∴ The total commission = 0.24 p - 40

∴ c(p) = 0.24 p - 40 when 1000 ≤ p ≤ 2000

3. If the profit is above $2,000, the rate is 20% of the first $1,000

  of profit,  24% of the next $1,000 of profit, and 29% of the amount

  of profit over $2,000

∵ The profit p > 2000

- The commission is divided into 20% of first $1000 and 24% of the

 next $1,000 of profit, and 29% of the amount of profit over $2,000

∵ 20% of 1000 =  = 200

∵ 24% of 1000 =  = 240

- The amount of profit over $2,000 = p - 2000

∵ 29% of the amount of profit over $2,000 =

   = 0.29(p - 2000)

  = 0.29 p - 580

∴ The total commission = 200 + 240 + 0.29 p - 580

∴ The total commission = 0.29 p - 140

∴ c(p) = 0.29 p - 140 when p > 2000

* The commission function is:

c(p) = {0.2 p ⇒ p < 1000

           0.24 p - 40 ⇒ 1000 ≤ p ≤ 2000

           0.29 p - 140 ⇒ p > 2000}

A type II error is a statistical term used to describe the failure to reject a false null hypothesis. It occurs when the null hypothesis is actually false but is not rejected because the statistical test failed to find significant evidence against it.

In other words, it happens when an alternative hypothesis is true, but we fail to reject the null hypothesis.

Types of errors in hypothesis testing

There are two types of errors in hypothesis testing:

Type I error: Rejecting a true null hypothesis

Type II error: Failing to reject a false null hypothesis.Type I error occurs when a true null hypothesis is rejected while Type II error occurs when a false null hypothesis is not rejected. These types of errors are inversely related, meaning that a decrease in one type of error causes an increase in the other.

You can learn more about type II errors at: brainly.com/question/30403884

#SPJ11

Answer: 8n

Step-by-step explanation:

Suppose the number is 'n'

Its product with number eight is given by

\(\Rightarrow n\times 8=8n\)

Answer:

8n

Step-by-step explanation:

edguenity 2020-2021

Answer:

5.025m

Step-by-step explanation:

The clothesline also creates an upside-down triangle with two sides being 5m, 0.5m, and the hypotenuse being the clothesline.

We can use the pythagorean theorem to find the length of the clothesline.

5 squared +.5 squared= the length of the clothesline squared

25+.25= the square root of 25.25

= 5.025

Answer:

Your answer would be:
5.025m

Step-by-step explanation:

5 sq + 0.5sq = the length of the clothesline sq

25 + 0.25= the square root of 25.25

= 5.025m



Have a great rest of your day
#TheWizzer

Answer:

yes

Step-by-step explanation:

The problem of unit root in standard regression and time-series models arises when a variable exhibits a non-stationary behavior, meaning it has a trend or follows a random walk. Unit root tests, such as the Dickey-Fuller and augmented Dickey-Fuller tests, are used to detect the presence of a unit root in a time series. These tests examine whether the coefficient on the lagged value of the variable is significantly different from one, indicating the presence of a unit root.

In standard regression analysis, it is typically assumed that the variables are stationary, meaning they have a constant mean and variance over time. However, many economic and financial variables exhibit non-stationary behavior, where their values are not centered around a fixed mean but instead follow a trend or random walk. This presents a problem because standard regression techniques may produce unreliable results when applied to non-stationary variables.

Time-series models, such as autoregressive integrated moving average (ARIMA) models, are specifically designed to handle non-stationary data. They incorporate differencing techniques to transform the data into a stationary form, allowing for reliable estimation and inference. Differencing involves computing the difference between consecutive observations to remove the trend or random walk component.

The Dickey-Fuller test and augmented Dickey-Fuller test are commonly used to detect the presence of a unit root in a time series. These tests examine the coefficient on the lagged value of the variable in a regression framework. The null hypothesis of the tests is that the variable has a unit root, indicating non-stationarity, while the alternative hypothesis is that the variable is stationary.

The Dickey-Fuller test is a simple version of the test that includes only a single lagged difference of the variable in the regression. The augmented Dickey-Fuller test extends this by including multiple lagged differences to account for potential serial correlation in the data. Both tests provide critical values that can be compared to the test statistic to determine whether the null hypothesis of a unit root can be rejected.

To learn more about regression click here: brainly.com/question/32505018

#SPJ11

Answer:

No, it is a irrational number

Step-by-step explanation:

Answer: Irrational or not rational

Step-by-step explanation:

square root of 7 is 2.64575131

Rational numbers are numbers that can be expressed in fractions.

Square root of 7 can't be made by dividing 2 integers.

The vertices of ΔFGH are F(-2,4), G(4,4), and H(1,-2), then the coordinates of the orthocenter of ΔFGH are ( 1 , 5/2 ) or ( 1 , \(2\frac{1}{2}\) ).        

Graph ΔFGH . To find the orthocenter, find the point where two of the three altitudes intersect.

Find an equation of the altitude from F to GH.

The slope of GH is,

= 4-(-2)/4-1

= 4+2/4-1

= 6/3

= 2

So the slope of the altitude, which is perpendicular to GH, is -1/2

y - \(y_{1}\) = m (x - \(x_{1}\))

y - 4 = -1/2 ( x - (-2) )

y - 4 = -1/2 (x+2)

y - 4 = -1/2x - 1

y = -1/2x -1 + 4

Find an equation of the altitude from F to GH.

The slope of FH is,

= -2-4/1-(-2)

= -6/1+2

= -6/3

= -2

So the slop of the altitude is, 1/2

y - \(y_{1}\) = m (x - \(x_{1}\))

y - 4 = 1/2 ( x - 4 )

y - 4 = 1/2x - 2

y = 1/2x -2 + 4

y = 1/2x + 2

Solve the resulting system of equations \(\left \{ {{y = -1/2x + 3} \atop {y = 1/2x + 2 }} \right.\)  to find the point of intersection of the altitudes.

Adding the two equations to eliminate \(x\) results in 2y = 5 or y = 5/2

y = 1/2x + 2

5/2 = 1/2x + 2  

1/2 = 1/2x

x = 1

Therefore,

The coordinates of the orthocenter of ΔFGH are ( 1 , 5/2 ) or ( 1 , \(2\frac{1}{2}\) ).

To learn more about information visit Orthocenter problems :        

brainly.com/question/19763099

#SPJ1

Answer:

12 additional sticks of butter

Step-by-step explanation:

First, create an equation. Let y represent the number of additional sticks of butter needed, and let x represent the number of cakes made.

y = \(\frac{x}{2}\) will be the equation.

Since she has already baked 17 cakes, she will need to bake 24 more cakes to make 41 cakes.

Plug in 24 as x into the equation, and solve for y:

y = \(\frac{x}{2}\)

y = \(\frac{24}{2}\)

y = 12

So, she will need 12 additional sticks of butter

Answer:

(6,3)

Step-by-step explanation:

I'm going to start with the second one.

x - 2y = 0

   +2y  +2y

x = 0 + 2y   which is the same as (x = 2y)

Now plug that in for the x-value in the other equation.

4(2y) - 3y = 15

8y - 3y = 15

5y = 15

Divide both sides by 5

y = 3

Here is where you are going to plug it back into the first one we did.

x - 2(3) = 0

x - 6 = 0

  +6   +6

x = 6

So the answer is (6,3)

Hope that helps and have a great day!

Answer:

23/20

Step-by-step explanation:

110% of 20 is 22/20, so 23/20 is more.

Step-by-step explanation:

23/20 = 1,15

110% = 1,1

1,15 > 1,1

⇒ 23/20 > 110%

Answer:

Step-by-step explanation:

5

Answer:

x = 1/a-b.

x is the reciprocal of the difference of a and b.

x is 1 over the difference of a and b.

x is the quotient of 1 and the difference of a and b.

Step-by-step explanation:

i did it

The transformation of the given equation ax = bx + 1 for the x will be 1/(a - b).

In the by substitution method, one of the equations is calculated for one of the variables, which is then transferred back into the other equation where the chosen variable is a replacement, and the second equation is then calculated for. The first variable is then home safely.

In other words, substitution is a method to find the value of variables x and y by just substituting x and y to another equation.

The substitution method is more good than the elimination method.

Given that the equation

ax = bx + 1

Transfer bx to the left side

ax- bx = 1

Take common x from the left-hand side

x(a - b) = 1

Divide a - b on both sides

x = 1/(a - b) hence it will be the correct transformation.

For more about the substitution method

https://brainly.com/question/22340165

#SPJ2

The ordered pair that could be the image point is (a) (2.5,1)

From the question, we have the following parameters that can be used in our computation:

Point C = (5, 2)

This means that

C = (5, 2)

The point is dilated using the origin as a center of the origin

So, the image point is

C = k(5, 2)

Let k = 1/2

So, we have

C = 1/2(5, 2)

Evaluate

C' = (2.5, 1)

Hence, the ordered pair that could be the image point is (a) (2.5,1)

Read more about dilation at

https://brainly.com/question/3457976

#SPJ1

Question

Triangle ABC is dilated with the origin as the center of the dilation. Which ordered pair could represent the image of point C(5, 2) after the dilation?

A (2.5,1)

B (5,−2)

C (7.5,4.5)

D (−1,−4)

x³-125= (x−5)(x^2+5x+25)

Hence, it has 1 real root and 2 imaginary roots.

Factors in polynomial equations with exactly two terms are called binomial factors. Because binomials are simple to solve and their roots are the same as the polynomial's roots, binomial factors are fascinating. Finding a polynomial's roots begins with factoring it.

Note that (x3 + a3 )may typically be factored as ( x -a ) ( x^2 + an x + a 2).

Similarly,

x^3-125

=( x^3-5^3 )

=( x−5) ( x^2 + 5 x + 25 ).

x³-125= (x−5)(x^2+5x+25).

Hence by solving this we get one real root as 5 and other two roots are imaginary.

We can get the roots by using discriminant formula.

Learn more about binomial factor here:

https://brainly.com/question/29198524

#SPJ4

In the analyze stage of the data life cycle, the data analyst will use the spreadsheet to aggregate the data and use the formulas to perform the calculations

The data life cycle is defined as the time period that that data exist in you system. Usually the data management experts finds the six or more stages in the data life cycle

The data analyst is the person who use the interpreted data and analyze the data in order to solve the problems

The analyze stage is the one of the main stages of the data life cycle. In the stage data analyst will use the spreadsheet to aggregate the data in the system and use the formulas to perform the calculations in the system

Therefore, the data analyst will use the spreadsheet to aggregate the data and use the formulas to perform the calculations

Learn more about data life cycle here

brainly.com/question/28039445

#SPJ4

Answer:

\(x=54^{o}\)

Step-by-step explanation:

Angles of straight line: 126 and x = 180

\(x+126=180\)

\(x=180-126\)

\(x=54^{o}\)

{CHECK: \(54+126=180\)}

hope this helps.....

The revenue from muffins was $8,000. To find the revenue from doughnuts: 4.5x = 4.5 * 8,000 = $36,000 Therefore, the cupcake delight shop sold $8,000 worth of muffins and $36,000 worth of doughnuts.

Let's use the given terms and set up a system of equations to solve this problem:

Let x be the revenue from muffins, and y be the revenue from doughnuts. We know the following:

1. y = 4.5x (Cupcake Delight Shop made 4 1/2 times as much revenue on doughnuts as muffins)
2. x + y = 44,000 (Total sales were $44,000)

Now we'll solve the system of equations step-by-step:

Step 1: Replace y with 4.5x in the second equation (using equation 1):
x + 4.5x = 44,000

Step 2: Combine the x terms:
5.5x = 44,000

Step 3: Divide both sides by 5.5 to solve for x:
x = 8,000

Step 4: Plug x back into equation 1 to find y:
y = 4.5 * 8,000
y = 36,000

So, Cupcake Delight Shop sold $8,000 worth of muffins and $36,000 worth of doughnuts.

to learn more about revenue click here:

https://brainly.com/question/23798931

#SPJ11

The dollar amount of muffins sold is $8,000, and the dollar amount of doughnuts sold is $36,000.

To solve this problem, let's assign variables to the revenue for doughnuts and muffins:
Let D = revenue from doughnuts
Let M = revenue from muffins
We are given that the shop made 4 1/2 times as much revenue on doughnuts as muffins:
D = 4.5M
We are also given that the total sales were $44,000:
D + M = 44,000
Now, we can solve for the dollar amount of each item sold:
Replace D with 4.5M in the second equation:
4.5M + M = 44,000
Combine like terms:
5.5M = 44,000
Divide by 5.5 to isolate M:
M = 44,000 / 5.5
M = 8,000
Plug the value of M back into the first equation to find the value of D:
D = 4.5M
D = 4.5 × 8,000
D = 36,000.

For similar question on dollar.

https://brainly.com/question/13199393

#SPJ11

Answer:

First Blank: 5

Second Blank: 5

Third Blank: -1

Fourth Blank: -1

Fifth Blank: 3

Step-by-step explanation:

10x+15y=15

-10x+2y=-32

__________

17y=-17

__   ___

17      17

y=-1

2x+3(-1)=3

2x-3=3

    +3  +3

________

2x=6

__  __

2     2

x=3

Answer:

Step-by-step explanation:

Domain is the independent variable (x)

Range is the dependent variable (y)

For each of these you would just put what x and y are equal to

For the Domain you would put:

0<=x<=3

<= is less than or equal to

For the Range you would put

1<=y<=4

The line is a function

To prove that xlogx is o(x^2), we need to show that there exists a positive constant c and a positive integer N such that for all x greater than N, we have:

|xlogx| ≤ cx^2

Let's start by rewriting xlogx as:

xlogx = xlnx

Now we can use integration by parts to find the antiderivative of xlnx:

∫xlnxdx = x^2/2 * ln(x) - x^2/4 + C

where C is the constant of integration. Since ln(x) grows slower than any positive power of x, we can see that xlogx is O(x^2).

To prove that x^2 is not o(xlog(x)), we need to show that for any positive constant c, there does not exist a positive integer N such that for all x greater than N, we have:

|x^2| ≤ c|xlogx|

Assume that such a constant c and integer N exist. Then, we have:

|x^2| ≤ c|xlogx|

Dividing both sides by |xlogx| (which is positive for x > 1), we get:

|x|/|logx| ≤ c

As x approaches infinity, the left-hand side of this inequality approaches infinity, while the right-hand side remains constant.

Therefore, the inequality cannot hold for large enough x, and we have shown that x^2 is not o(xlog(x)).

To know more about positive integer refer here:

https://brainly.com/question/18380011

#SPJ11

Answer:

130.25ft

Step-by-step explanation:

a^2+b^2=c^2

5.5^2+10^2=

30.25+100=

The probability of getting a tail on any given toss is 1/2.

The random variable X represents the number of tails in 44 tosses of a coin. Since there are two possible outcomes (heads and tails) for each toss, the probability of getting a tail on any given toss is 1/2.

We can use the binomial distribution formula to calculate the probability of getting a specific number of tails in 44 tosses. The formula is:

P(X = k) = (44 choose k) * (1/2)^44

where "k" represents the number of tails we want to calculate the probability for, and "44 choose k" represents the number of ways we can get k tails in 44 tosses.

Using this formula, we can calculate the probability of getting 0, 1, 2, ..., 44 tails, and we get the following probability distribution:

X = 0: P(X = 0) = (44 choose 0) * (1/2)^44 = 1/17592186044416

X = 1: P(X = 1) = (44 choose 1) * (1/2)^44 = 44/17592186044416

X = 2: P(X = 2) = (44 choose 2) * (1/2)^44 = 946/17592186044416

...

X = 42: P(X = 42) = (44 choose 42) * (1/2)^44 = 946/17592186044416

X = 43: P(X = 43) = (44 choose 43) * (1/2)^44 = 44/17592186044416

X = 44: P(X = 44) = (44 choose 44) * (1/2)^44 = 1/17592186044416

Note that the sum of all these probabilities is 1, which means that one of these outcomes must occur. Also, we can see that the distribution is symmetric around the mean (22 tails) since the probability of getting k tails is the same as the probability of getting 44-k tails.

For more questions like Probability click the link below:

https://brainly.com/question/30034780

#SPJ11

Using the cosine rule, the distance the plane has flown during Jack's phone call can be calculated by taking the square root of the sum of the squares of the initial and final distances, minus twice their product, multiplied by the cosine of the angle difference.

To determine the distance the plane has flown during Jack's phone call, we can use the cosine rule in trigonometry.

The cosine rule relates the lengths of the sides of a triangle to the cosine of one of its angles.

Let's denote the initial distance from Jack to the plane as d1 and the final distance as d2.

We know that the altitude of the plane remains constant at 2400 meters.

According to the cosine rule:

\(d^2 = a^2 + b^2 - 2ab \times cos(C)\)

Where d is the side opposite to the angle C, and a and b are the other two sides of the triangle.

For the initial angle of elevation (70°), we have the equation:

\(d1^2 = (2400)^2 + a^2 - 2 \times 2400 \times a \timescos(70)\)

Similarly, for the final angle of elevation (50°), we have:

\(d2^2 = (2400)^2 + a^2 - 2 \times 2400 \times a \times cos(50)\)

To find the distance the plane has flown, we subtract the two equations:

\(d2^2 - d1^2 = 2 \times 2400 \times a \times (cos(70) - cos(50))\)

Now we can solve this equation to find the value of a, which represents the distance the plane has flown.

Finally, we calculate the square root of \(a^2\) to find the distance in meters.

It's important to note that the angle of elevation assumes a straight-line path for the plane's movement and does not account for any changes in altitude or course adjustments that might occur during the phone call.

For similar question on cosine rule.

https://brainly.com/question/27613782  

#SPJ8