A pilot in a rescue helicopter spots a person stranded on an island. The angle of depression to the island is 40°. If the helicopter is flying at an altitude of 100 ft, how far is the helicopter from the island
Answers
Answer:
Step-by-step explanation:
Step-by-step explanation:
the situation establishes 2 triangles :
1 has the corners at the helicopter, then straight down on the water, and then the island.
the other had the corners at the helicopter, then the island, and then from there 100ft straight up in the air.
we have enough information to know all angles, we know one side (100 ft altitude). so, we can use the law of sine to get the other sides (incl. the side representing the distance to the island).
a/sin(A) = b/sin(B) = c/sin(C)
where the angles are always opposite of the corresponding sides.
I personally prefer the first triangle.
the angle between the line of sight helicopter-island and the straight down altitude line is complementary to the angle of depression : 90 - 40 = 50°
then the angle between the straight down altitude line and the ground distance to the island is a right angle (90°).
and the angle between the ground distance and the line of sight is then 180 - 90 - 50 = 40°
(remember, the sum of all angles in a triangle is always 180°)
so,
altitude line / sin(40) = ground distance / sin(50)
ground distance = altitude line × sin(50)/sin(40) =
= 100 × sin(50)/sin(40) = 119.18 ft
Related Questions
Write an
explicit formula for An, the nth
term of the sequence 22, 17, 12, ....
Answers
Answer:
-5n + 27
Step-by-step explanation:
The difference is -5.
The first term is 22.
Use the formula for nth term.
an = dn + (a - d)
a is the first term.
d is the difference.
an = - 5n + (22 - ( - 5 ))
an = -5n + (22 + 5)
an = -5n + 27
Answer:
27 - 5n.
Step-by-step explanation:
This is arithmetic with common difference = 17 - 22 = -5 (also 12 - 17 = -1).
nth term an = a1 + d(n - 1)
= 22 - 5(n - 1)
Which simplifies to 27 - 5n
find two unit vectors that make an angle of 60° with v = 6, 8 .
Answers
Answer:
((3-4√3)/10, (4+3√3)/10)((3+4√3)/10, (4-3√3)/10)Step-by-step explanation:
You want two unit vectors that make an angle of 60° with v(6, 8).
Unit vectorAfter we normalize v to a unit vector, we can find the two desired vectors by adding or subtracting 60° from its angle. The normalized vector v is ...
v = (6, 8)/√(6² +8²) = (3/5, 4/5)
RotatedThis can be rotated 60° CCW by the transformation ...
(x, y) ⇒ (x·cos(60°)-y·sin(60°), x·sin(60°)+y·cos(60°)) = (x-y√3, x√3+y)/2
(3/5, 4/5) ⇒ ((3-4√3)/10, (3√3+4)/10) . . . . 60° CCW from v
It can be rotated 60° CW by the transformation ...
(x, y) ⇒ (x·cos(60°)+y·sin(60°), -x·sin(60°)+y·cos(60°)) = ((x+y√3, -x√3+y)/2
(3/5, 4/5) ⇒ ((3+4√3)/10, (4-3√3)/10)
__
Additional comment
When the vector is written as a complex number, it can be rotated by multiplying by 1∠±60° = (cos(60°)±i·sin(60°). That is what the calculator did.
<95141404393>
A police officer marries a bank teller. What is their
combined income each month?
Help please help help please please
Answers
Answer:
The combined income each month should be $4,515.08. If it needs to be rounded, then it's just 4,515.
Step-by-step explanation:
All you needed to do was add.
Hope this helps you out
True/False. the amount of rainfall in your state last month is an example of discrete data.
Answers
Answer: False
Step-by-step explanation:
Discrete means secret and that data is not discrete as it can be acess by anyone.
True. The amount of rainfall in your state last month is an example of discrete data.
Explanation:The answer to the question is True. The amount of rainfall in a state last month is an example of discrete data.
Discrete data is a type of data that can only take on specific values. In this case, the amount of rainfall can be measured in specific units, such as inches or millimeters, and cannot have values between those units.
Other examples of discrete data include the number of students in a classroom, the number of cars passing through a toll booth, or the number of coins in a piggy bank.
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graph f(x) = x^2 and g(x) = 2^x for x
Answers
Answer:
Step-by-step explanation:
C) Find the probability of rolling an odd number given you have spun a red section:
P(odd numberjred). 0.5 or 50%
2) A different game requires players to spin a five-section spinner and roll a six-sided
standard die to make a move. The spinner has sections of equal area, with each
section containing one of these numbers: 1, 2, 3, 4, and 5. The player gets to move
based upon the sum of the two numbers-one from the spinner and one from the
die.
A) Make a table to display the sample space of the compound events representing
the players making moves during the game.
I
1
2
- Make the columns correspond to the possible rolls of the dice and the
rows correspond to the possible spinner numbers.
For each cell entry, write the sum of the row value and the column value.
B) Find the probability of getting a sum of 4, 5, or 6.
Answers
The probability of rolling an odd number given you have spun a red section is 1/3 or approximately 33.33%.
The probability of getting a sum of 7 is 20%.
How to calculate the probabilityThere are three equally likely outcomes when you spin a red section: roll an odd number, roll an even number, or roll a 1. Of these three outcomes, only one corresponds to rolling an odd number. The probability will be:
= 1/3
= 33.33%
There are 5 possible outcomes when you spin the spinner and 6 possible outcomes when you roll the die, so there are 5 x 6 = 30 equally likely outcomes when you play this game. Therefore, the probability of getting a sum of 7 is 6/30 = 1/5 or 20%.
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An investment of \$2,500 doubles in value every 15 years. The function f defined by f(x) = 2, 500(2 ^ (rx)) represents the value of the investment , in dollars, years after the investment is made , where r is a constant. What is the value of r? R =
Answers
Answer:
\(\dfrac{1}{15}\)
Step-by-step explanation:
Given that:
Investment amount = $2500
Time in which it gets doubled = 15 years
Amount after 15 years = $5000 (As per given statement as it gets doubled)
Value of investment in dollars after \(x\) years if investment:
\(f(x) = 2, 500(2 ^ {rx})\)
\(r\) is a constant.
To find:
Value of \(r\).
Solution:
We are given that:
\(f(x) =\$5000\)
\(x=15\ years\)
Putting all the values in the given equation:
\(5000 = 2500(2 ^ {r\times 15})\\\Rightarrow 2 = 2 ^ {r\times 15}\\\Rightarrow r\times 15=1\\\Rightarrow r =\bold{\dfrac{1}{15}}\)
Therefore, the value of \(r\) is:
\(\dfrac{1}{15}\)
Factor to write an equivalent expression
36a - 16
Answers
Answer:
4(9a-4)
Step-by-step explanation:
36a - 16
We can factor 4 from each expression.
4*9a - 4*4
4(9a-4)
Imagine the point (square root 2/2, negative square root 2/2) on
the terminal side of an angle.
Find the value for the sine of this angle.
A positive
B negative
Answers
The sine of the angle formed by the point (square root 2/2, negative square root 2/2) on the terminal side is negative.
To find the sine of the given angle, we need to determine the y-coordinate of the point on the unit circle where the terminal side intersects. Since the given point lies in the third quadrant of the unit circle and has a negative y-coordinate, we know that the sine value will also be negative.
We can use the Pythagorean theorem to find the length of the hypotenuse of the right triangle formed by the given point, the origin, and the point where the terminal side intersects the unit circle. The length of the hypotenuse is 1 since all points on the unit circle have a distance of 1 from the origin. Using the y-coordinate of the given point (-sqrt(2)/2), and the length of the hypotenuse (1), we can calculate the sine value as -sqrt(2)/2, which is negative. Therefore, the final answer is B) negative.
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A mathematical model was created and solved using linear programming. The optimal values were determined: x1 = 10 and x2 = 10. If one of the constraints is: 4x1 + 2x2 >= 55, you can conclude that:
A.this is a binding constraint, so there is no slack or surplus
B.there are 15 units of surplus
C.there are 15 units of slack
D.there are 5 units of slack
E.there are 5 units of surplus
Answers
In mathematics, linear programming is a technique for maximizing operations under certain restrictions.
Why does a mathematical model of a linear programming problem is important?Using the mathematical modeling technique of linear programming, a linear function is maximized or minimized depending on the restrictions it is subjected to. This method has proved helpful for directing quantitative judgments in business planning, industrial engineering, and—to a lesser extent—in the social and physical sciences.
In mathematics, linear programming is a technique for maximizing operations under certain restrictions. Maximizing or minimizing the numerical value is the primary goal of linear programming. It comprises of linear functions that are subject to restrictions in the form of inequalities or linear equations.
Therefore, the correct answer is option A. this is a binding constraint, so there is no slack or surplus.
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In the coordinate plane, which of the following functions dilates by a factor of 3
about the point (9, 6)?
A. (, ) = (3 + 9, 3 +6)
B. (, ) = (3( + 9), 3( + 6))
C. (, ) = (9+ 3( − 9), 6 + 3( −6))
D. (, ) = (9+ 3(9− ), 6+ 3(6 − ))
Answers
numbers that do not form a fact family
Answers
The numbers that do not form a fact family are solved
Given data ,
A fact family consists of a set of related addition and subtraction facts that use the same numbers. For example, the numbers 3, 5, and 8 form a fact family because:
3 + 5 = 8
5 + 3 = 8
8 - 5 = 3
8 - 3 = 5
Numbers that do not form a fact family are any set of numbers that do not follow this pattern. For example, the numbers 2, 4, and 7 do not form a fact family because no combination of addition and subtraction using these numbers produces the other two numbers.
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Question 10(Multiple Choice Worth 5 points)
(Identifying Functions LC)
The graph represents a relation where x represents the independent variable and y represents the dependent variable.
a graph with points plotted at negative 5 comma 1, at negative 2 comma 0, at negative 1 comma 3, at negative 1 comma negative 2, at 0 comma 2, and at 5 comma 1
Is the relation a function? Explain.
No, because for each input there is not exactly one output.
No, because for each output there is not exactly one input.
Yes, because for each input there is exactly one output.
Yes, because for each output there is exactly one input.
Answers
Is the relation a function:
No, because for each input there is not exactly one output.How to know if the relation is a functionTo determine if the relation is a function, we need to check if there is exactly one output for each input.
Looking at the given set of points, we see that there are two points with an x-coordinate of -1: (-1, 3) and (-1, -2).
This means that there are two outputs for the same input, so the relation is not a function.
Therefore, the correct answer is: "No, because for each input there is not exactly one output."
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a hospital director is told that 56% of the emergency room visitors are insured. the director wants to test the claim that the percentage of insured patients is below the expected percentage. a sample of 160 patients found that 80 were insured. determine the p-value of the test statistic. round your answer to four decimal places.
Answers
The p-value of the test statistic will be equal to -1.5.
What is Test statistic?A statistic employed in statistical hypothesis testing is known as a test statistic. A hypothesis test is often defined in terms of a test statistic, which can be thought of as a numerical summary of a data set that distils the information into a single value that can be used to conduct the test.
The formula for test statistics:
Test statistic = z =
A sample of patients n = 160
Patients insured =x =80
P = x/n
P = 80/ 160
P = 1/2
P = 0.5
P₀ = 56/100
P₀ = 0.56
Putting the values we get:
\(Z =\dfrac{P-P_o}{\sqrt{\dfrac{P_o-(1-P_o)}{n}}}\)
\(Z =\dfrac{0.5-0.56}{\sqrt{\dfrac{0.56-(1-0.56)}{150}}}\)
Z= -0.06/0.04
Z = - 1.5
Therefore, the p-value of the test statistic will be equal to -1.5.
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Question 20 (5 points)
Ruby wrote the standard form of a linear equation as 4x – y =
= 7. Jennifer told her that the equation was not yet in standard form and
gave her the right advice for how to fix it. What advice did Jennifer give to Ruby?
O
Multiply both sides of the equation by 3. The standard form of the equation is 12x - 2y = 21.
Oь
Jennifer told Ruby her equation is already in standard form and there is nothing to correct.
Oc
Multiply both sides of the equation by 3. The standard form of the equation is 12x - 2y = 7
Multiply both sides of the equation by 3 and then divide both sides by 2. The standard form of the equation is 6x - y = 10.5.
Od
Answers
Answer:
Step-by-step explanation:
What you gave 4x – y = 7 is in standard form
The problem on screen
4x-2/3y=7
The standard form is 12x-2y=21
Answer is A
Help asp thank you show your work if you want
Answers
Answer:
\(y=-\frac{2}{3}x+1\)
Step-by-step explanation:
Parallel means same slope.
\(y=-\frac{2}{3}x+b\)
\(5=-\frac{2}{3} (-6)+b\)
5 = 4 + b
b = 1
\(y=-\frac{2}{3}x+1\)
Two numbers are co-prime if they do not have any prime factors in common. List all
possible numbers that are co-primes with the following numbers that are < 50:
(a) 390
(b) 210
(c) 49335
Answers
All possible numbers that are co-primes with the following numbers are mentioned below in detail. The possible co-primes of 390 are 1, 7, 11, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, and 49.
What are co-prime numbers?Co-prime numbers are pairs of numbers that only share the factor 1 in common. They are additionally referred to as reasonably prime numbers.
In the given question,
(a) 390
The prime factors of 390 are 2, 3, 5, and 13. All of the numbers that are co-prime with 390 are those that do not share any of these prime factors. This includes the numbers 1, 7, 11, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, and 49.
(b) 210
The prime factors of 210 are 2, 3, 5, and 7. All of the numbers that are co-prime with 210 are those that do not share any of these prime factors. This includes the numbers 1, 11, 13, 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 47, and 49.
(c) 49335
The prime factors of 49335 are 5, 7, 11, and 13. All of the numbers that are co-prime with 49335 are those that do not share any of these prime factors. This includes the numbers 1, 2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, and 49.
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Using the following weights:.3, 2, .5 find the forecast for the next period. Month 1 – 381, Month 2-366, Month 3 - 348. O a. 143 O b. 241 O c. 360 O d. 421
Answers
The forecast for the next period using the following weights: 0.3, 2, 0.5 is Option d. 421.
To compute the forecast for the next period, we'll use the weighted moving average (WMA) formula.WMA formula:
WMA = W1Yt-1 + W2Yt-2 + ... + WnYt-n
Where, WMA is the weighted moving average
W1, W2, ..., Wn are the weights (must sum to 1)
Yt-n is the demand in the n-th period before the current period
As we know Month 1 – 381, Month 2-366, and Month 3 - 348.
Weights: 0.3, 2, 0.5
We'll compute the forecast for the next period (month 4) using the data:
WMA = W1Yt-1 + W2Yt-2 + W3Yt-3WMA
= 0.3(381) + 2(366) + 0.5(348)WMA
= 114.3 + 732 + 174WMA
= 1020.3
Therefore, the forecast for the next period is 1020.3, which rounds to 421. Hence, option d is correct.
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Suppose the coefficient matrix of a linear system of five equations in five variables has a pivot in eachcolumn. how many solutions can the system have? why?
Answers
The system will be consistent and will have unique solution.
Given,
Coefficient matrix of 5 equation in 5 variables.
Here,
Let A be a 5x5 coefficient matrix such that its each column has a pivot element, then
Rank A = 5, rank of augmented matrix [A|b] = 5 and number of unknowns = 5
Rank A = rank of augmented matrix [A|b] = number of unknowns = 5
Hence , System is consistent
There is a unique intersection point of all three lines, so values of variables is unique.
Hence, solution of system if unique.
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find the total area between the curve and x-axis over rhegiven
interval. ( that is the absolute value of all areas
Answers
The total area between the curve and the x-axis over a given interval is the sum of the absolute values of all the individual areas.
To calculate the total area between the curve and the x-axis, we need to consider the areas both above and below the x-axis separately. First, we identify the x-values where the curve intersects the x-axis within the given interval. These points act as boundaries for the individual areas.
For each interval between two consecutive intersection points, we calculate the area by integrating the absolute value of the curve's equation with respect to x over that interval. This ensures that both positive and negative areas are included.
If the curve lies entirely above the x-axis or entirely below the x-axis within the given interval, we only need to calculate the area using the curve's equation without taking the absolute value.
Finally, we sum up the absolute values of all the calculated areas to find the total area between the curve and the x-axis over the given interval.
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30 points! Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Slope of the line: ___
Answers
Answer:
m = 5/4
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (0, -3) (4,2)
We see the y increase by 5 and the x increase by 4, so the slope is
m = 5/4
An environmental engineer measures the amount (by weight) of particulate pollution in air samples (of a certain volume) collected over the smokestack of a coal-fueled power plant. Let X denote the amount of pollutant per sample when a certain cleaning device on the stack is not operating, and let Y denote the amount of pollutants per sample when the cleaning device is operating under similar environmental conditions. It is observed that X is always greater than 2Y, and the relative frequency of (X,Y) can be modeled byf(x,y) = k for 0 ≤ x ≤ 2, 0 ≤ y ≤, 2y ≤ xand 0 elsewhere(X and Y are randomly distriibutied over the region inside the tricanle bounded by x=2, y=0 and 2y=x)a) Find the value of k that makes this a probability desnsity functionb) Find P
Answers
a) The value of k that makes this a probability density function is 1.
b) P(X > 1.5, Y < 0.5) = 3/4.
The given problem provides information about the relative frequency of (X,Y), the amount of pollutant per sample when a certain cleaning device on the stack is not operating (X), and the amount of pollutants per sample when the cleaning device is operating under similar environmental conditions (Y). We are given that X is always greater than 2Y, and the relative frequency of (X,Y) can be modeled by f(x,y) = k for 0 ≤ x ≤ 2, 0 ≤ y ≤ 2y ≤ x and 0 elsewhere.
To find the value of k that makes this a probability density function, we need to integrate f(x,y) over the entire region and set it equal to 1:
∫∫ f(x,y) dxdy = ∫∫ k dxdy = k ∫∫ dxdy = k(1/2)(2)^2 = k(2)
Since f(x,y) must integrate to 1 over the region, k must be 1/2.
To find P(X > 1.5, Y < 0.5), we need to integrate f(x,y) over the given region. We first need to identify the limits of integration. The region is a triangle bounded by x = 2, y = 0, and 2y = x. This can be rewritten as y = x/2. Thus, the limits of integration are 0 ≤ y ≤ 1 and 2y ≤ x ≤ 2.
After setting up the limits of integration, we can perform the integration to find P(X > 1.5, Y < 0.5). The final answer is 3/4.
Solution: ∫∫(2y ≤ x) f(x,y) dxdy = ∫∫(2y ≤ x) dxdy
= ∫0^1 ∫0^(2y) 1 dxdy + ∫1^2 ∫0^(1/2) 1 dxdy
= ∫0^1 2y dy + ∫1^2 1/2 dy
= ¾
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Please Help I Don't Understand!
Answers
Answer:
Step-by-step explanation:
Area of rhombus = (small diagonal · big diagonal)/2
small diagonal = AH +AH = 6+6 = 12
big diagonal = BH +BH = 10+10 = 20
Area of rhombus = (12·20)/2 = 120 units²
due today, pleaseee helppp
Answers
What is the volume of the rectangular prism?
PLEASE HELP ASAP
Answers
Answer:
7yd^2
Step-by-step explanation:
Calculate for volume as if its 1yd for cube, divide it by a third because each cube is 1/3 of a yard, square it.
Result: 7yd^2
Solve 2(x + 1) = 2x + 2.
- All real numbers
- No solution
- 0
- 1
Answers
Explanation: 2(x+1) *distribute 2 to x and 1
2x+2=2x+2 *now subtract 2x+2 to the other side
Select the correct
function
that represents
this data.
A. f(x) = -6x +1
B. f(x) = 6x +1
C. f(x) = -6x - 1
Answers
Answer:
Step-by-step explanation:
o find the vertex of f(x)=x2−8x+7 , there are several things you can do. You could complete the square to get the equation into vertex ...
evaluate 10/16 ÷ 5/16
Answers
Answer:
2
Step-by-step explanation:
10/16 ÷ 5/16
0.625 ÷ 0.3125
2
hi guys I am from india . can anybody solve this x+2c
Answers
2c + x
ANSWER:⇒ 2c + x
Jermaine spent $204 dollars on
shirts for his 21 employees while he
was on his vacation. Large shirts
were $12 and small shirts were $8.
How many larges did he buy?
Answers
Jermaine bought 9 large shirts for $12, and 12 small shirts for $8 for his 21 employees.
Let's represent the number of large shirts Jermaine bought as "L" and the number of small shirts as "S". We can set up a system of equations based on the information given:
L + S = 21 (equation 1, the total number of shirts is 21)
12L + 8S = 204 (equation 2, the total cost of the shirts is $204)
To solve for L, we need to eliminate S. We can do this by multiplying equation 1 by 8 and subtracting it from equation 2:
12L + 8S = 204
8L + 8S = 168 (multiply equation 1 by 8)
4L = 36
Dividing both sides by 4, we get:
L = 9
Therefore, Jermaine bought 9 large shirts for his 21 employees. We can find the number of small shirts by substituting L = 9 into equation 1:
L + S = 21
9 + S = 21
S = 12
So, by using linear equation system we find that Jermaine bought 9 large shirts and 12 small shirts for his 21 employees.
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