an airplane, flying horizontally at 200 mph at an altitude of 3 miles, passes over a radar station. what is the rate of change of the angle of elevation between the radar station and the plane 3 minutes after the plane passes over the radar station? (the angle of elevation is the angle between the horizontal and a line between the radar station and the airplane.)
The rate of change of angle of elevation between the radar station and airplane is
[tex]\displaystyle \frac{-10}{109} \left(\frac{rad}{min}\right)[/tex]
The airplane is flying at the speed of 200 mph
The airplane is at an altitude of 3 miles over the radar station
The distance travelled by the airplane after 3 mins
distance = speed x time
= 200 mi/hr x 3 min
Since the speed is hour let us convert it to mins
= 200 x 3 x 1/60
= 600 / 60
= 10 miles
So , let us assume that the airplane is exactly at the top of the radar station at an altitude of 3 miles
Then the elevation angle of the between radar station and airplane can be find by
tan θ = O / A
where O is the opposite side to the angle of elevation
A is the adjacent side to the angle of elevation.
But we need the find the rate of change of angle of elevation , so let us differentiate on both side with respect to time
[tex]\displaystyle sec^{2}\theta\frac{ d\theta }{dt} = \frac{A \frac{dO}{dt} - O \frac{dA}{dt} }{A^{2}}[/tex]
[tex]\displaystyle \frac{ d\theta }{dt} = \frac{A \frac{dO}{dt} - O \frac{dA}{dt} }{sec^{2}\theta A^{2}}[/tex]
[tex]\displaystyle \frac{d\theta}{dt} = \frac{10 (0) - 3 (200 mi/hr)}{sec^{2}(10)^{2}}[/tex]
The altitude is gonna be a constant , thus the derivative of altitude will be zero whereas , the the distance travelled by airplane is changing with respect to time.
[tex]\displaystyle \frac{d\theta}{dt} = \frac{10 (0) - 3 (200 mi/hr)}{\frac{109}{100}(10)^{2}}[/tex]
We had found the value of sec²θ = (hyp/adj)²
[tex]\displaystyle \frac{d\theta}{dt} = \frac{-600}{109} \frac{rad}{hr}[/tex]
Now , let us convert in terms of rad/min
[tex]\displaystyle \frac{d\theta}{dt} = \frac{-600}{109} \left(\frac{1}{60}\right)[/tex]
[tex]\displaystyle \frac{d\theta}{dt} = \frac{-10}{109} \left(\frac{rad}{min}\right)[/tex]
Therefore , the rate of change of angle of elevation is -10/109 (rad/min)
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A line passes through the points (-18, -2) and (9, 10). Find this line's equation in point-slope form. Using the point (-18, -2), this line's point-slope form equation is [ ]Using the point (9, 10), this line's point-slope form equation is [ ]
We know that the point-slope formula is given by:
y − y₁=m(x − x₁)
where the terms: m, y₁ and x₁ are numbers.
Given that the line passes through a given points we have that:
m is the slope of the line
y₁ is the y value of that given point
x₁ is the x value of that given point
Finding the slopeWe want to find the slope m, having that
(x₁, y₁) = (-18, -2)
(x₂, y₂) = (9, 10)
The slope is always a rate of change. It is:
m = Δy/Δx,
where Δ means "change"
Step 1: finding the change of each term x and y
Δy = change of y = y₂ - y₁
Δy = 10 - (-2) = 12
Δx = change of x = x₂ - x₁
Δx = 9 - (-18) = 27
Step 2: dividing the found quantities
Then
m = Δy/Δx = 12/27
m = 4/9
Step 3: replacing in the equation
Using the equation, we have that
y − y₁ = m(x − x₁)
replacing m:
y − y₁= 4/9(x − x₁)
Step 4: replacing each pointFor the first point: (-18, -2)
We have that (x₁, y₁) = (-18, -2)
since the equation is
y − y₁ = 4/9(x − x₁)
replacing each term for each number of the given coordinate
y − (-2) = 4/9(x − (-18))
y + 2 = 4/9(x + 18)
Equation: y + 2 = 4/9(x + 18)
For the second point: (9, 10)
We have that (x₂, y₂) = (9, 10)
since the equation is
y − y₂ = 4/9(x − x₂)
replacing each term for each number of the given coordinate
y − (10) = 4/9(x − (9))
y - 10 = 4/9(x - 9)
Equation: y - 10 = 4/9(x - 9)
Kyle just graduated from college and got his first job, he has $45,000 in student loan debt, wants to buya new car, and is considering opening up a retirement account. He has a disposable income of$300/month, what would you recommend he do with this money? Why?
Problem
Kyle just graduated from college and got his first job, he has $45,000 in student loan debt, wants to buy a new car, and is considering opening up a retirement account. He has a disposable income of $300/month, what would you recommend he do with this money? Why?
Solution
For this case the best option would be put the $45000 in a bank with a compound interest
And with the earnings each month of 300$ he can put the half of this into the account and the remain to spend on other things
Hi can someone help me with this?Writing the algebraic equation for the phrase below.. 1. The sum of X and 96 equals half of X .
Given:
1. The sum of X and 96 equals half of X.
To determine the algebraic equation, we note that the sum of x and 96 would be:
x+96
Next, half of x must be like this:
x/2
Then, the phrase equals means we set x+96 equals to x/2.
Therefore, the answer is:
[tex]x+96=\frac{x}{2}[/tex]A parabola can be drawn given a focus of (7,-3) and a directrix of y=-7. Write
the equation of the parabola in any form.
State if the three side lengths form an acute obtuse or a right triangle
Given three side lengths form an acute obtuse or a right triangle 17, 21, & 28
Check Right triangle
[tex]\begin{gathered} Hyp^2=opp^2+adj^2 \\ 28^2=17^2+21^2 \\ 28^2\text{ = 289 +441} \\ 784\text{ }\ne\text{ 730} \end{gathered}[/tex]Not a Right triangle
An obtuse triangle is a triangle with one obtuse angle and two acute angles. Since a triangle's angles must sum to 180° in Euclidean geometry.
Not an Obtuse triangle
[tex]\begin{gathered} \sin \text{ A= }\frac{opp}{hyp} \\ \sin \text{ A = }\frac{17}{28} \\ A=sin^{-1}\text{ }\frac{17}{28} \\ A=37.4^0\text{ (less than 90)} \end{gathered}[/tex][tex]\begin{gathered} \cos \text{ B = }\frac{adj}{hyp} \\ \cos \text{ B = }\frac{21}{28} \\ B=cos^{-1}\frac{21}{28} \\ B=41.4^0\text{ (less than 90)} \end{gathered}[/tex][tex]\begin{gathered} \tan \text{ C = }\frac{opp}{adj} \\ \tan \text{ C = }\frac{17}{21} \\ C=tan^{-1\text{ }}\frac{17}{21}\text{ } \\ C=38.9^0\text{ (less than 90) } \end{gathered}[/tex]Hence it is acute angle because all angles are less than 90°
4.(06.07 HC)A teacher is assessing the correlation between the number of hours spent studying and the average score on a science test. The table below shows the data:Number of hours spent studying 0 0.5 1(x)1.5 2 2.5 33.54Score on science test(y)57 62 67727782 879297Part A: Is there any correlation between the number of hours students spent studying and the score on the science test? Justify your answer. (4 points)Part B: Write a function which best fits the data. (3 points)Part C: What does the slope and y-intercept of the plot indicate? (3 points)(10 points)
For part A. One way to know if there is a correlation between the data is to graph the data set, like this
Then, as can you see the data presents a positive linear correlation.
For part B. You can take the coordinates of two points and find the slope of the line using the formula
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}[/tex]If you take
[tex]\begin{gathered} (x_1,y_1)=(1,67) \\ (x_2,y_2)=(3,87) \\ \text{ You have} \\ m=\frac{87-67}{3-1} \\ m=\frac{20}{2} \\ m=10 \end{gathered}[/tex]Now, using the slope formula, you can find the equation of the line in its slope-intercept form
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-67=10(x-1) \\ y-67=10x-10 \\ \text{ Add 67 on both sides of the equation} \\ y-67+67=10x-10+67 \\ y=10x+57 \end{gathered}[/tex]Therefore, the function that best fits the data is
[tex]y=10x+57[/tex]For part C. The slope of the plot is 10 and indicates that for every hour students spend time studying, they get 10 more points on the science test.
The y-intercept of the plot is 57 and indicates that if students study 0 hours for the science test, they will obtain 57 points as a grade.
Miguel is going to see a movie and is taking his 5 kids. Each movie
ticket costs $12 and there are an assortment of snacks available to
purchase for $5 each. How much total money would Miguel have to
pay for his family if he were to buy 5 snacks for everybody to share?
How much would Miguel have to pay if he bought a snacks for
everybody to share?
Total cost with 5 snacks:
Total cost with a snacks:
Pls give me a good answer
The total cost for 6 movie tickets and 5 snacks is $97
The total cost for 6 movie tickets and x snacks is $(72 + 5x)
Given,
Miguel is going to see a movie with his 5 kids.
Number of people = 6
Cost for one ticket = $12
Cost of one snack = $5
Number of snacks = 5
We have to find the total cost spend by Miguel:
For tickets and 5 snacks:
For tickets and x snacks:
Now,
Total cost for tickets = 6 × 12 = $72
Cost for 5 snacks = 5 × 5 = $25
Therefore,
Total cost = 72 + 25 = $97
Next,
Cost for x snacks = 5x
Then,
Total cost = 72 + 5x
That is,
The total cost for 6 movie tickets and 5 snacks is $97
The total cost for 6 movie tickets and x snacks is $(72 + 5x)
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help quick 30 points
Answer:
y = -5x + 6
Step-by-step explanation:
Looking at the graph it looks that the slope of the line is -5
and the y intercept is (0, 6)
So the slope intercept form is y = -5x + 6
this should be correct hope this helps
A box of cereal states that there are
78 calories in a
3
4
-cup serving. What is the unit rate for calories per cup? How many calories are there in
4 cups of the cereal?
The unit rate for the cereal is 104 calories per cup and there are 416 calories in 4 cups
How to determine the unit rate for the cereal?From the question, the given parameters are
Calories = 78 calories
Size of cups = 3/4-cup
The unit rate of the calories per cup is calculated as
Unit rate = Number of Calories/Size of cup
Substitute the known values in the above equation
So, we have the following equation
Unit rate = 78/(3/4)
Evaluate the quotient
So, we have the following equation
Unit rate = 104
So, the unit rate is 104 calories per cup
For four cups of cereal, we have
Calories = 104 x 4
Evaluate
Calories = 416
So, the number of calories is 416 calories
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Brynn rides her bike 84 miles in 4 hours.
a. Create a ratio of Brynn's miles per hour.
b. Using the ratio you found in part a, determine
how far Brynn can ride in 7 hours.
c. If Brynn rides 57 miles at the rate indicated,
how long will she ride? Justify your response.
Part (a)
distance = rate*time
rate = distance/time
rate = 84/4
rate = 21
Answer: 21 mph
==================================================
Part (b)
distance = rate*time
distance = 21*7
distance = 147
Answer: 147 miles
==================================================
Part (c)
distance = rate*time
time = distance/rate
time = 57/21
time = 2.71428571428571
time = 2.714
Answer: Approximately 2.714 hours
Answer;
A.21:1
B:147 Miles
C.2.7 hours or 182 minutes
2. Dexter needs to find each angle in this figure that is adjacent
to LLON. He claims that LMON is adjacent to LLON.
a. List each angle that is adjacent to LLON.
мор
b. Why is Dexter's claim incorrect?
Answer:
It would be MOP is adjacent
Step-by-step explanation:
What is the midpoint between (-3,-2) and (4-7)
The midpoint between the given figures are -2.5 and 5.5 respectively.
What is a midpoint ?A midpoint is defined as that particular point that divides two separate figures into two equal halves or the centre of two endpoints on a number line.
That is;
point a + point b/2
The figures given are :
Point a = -3
Point b = -2
= -3 + -2/ 2
= -5/2
= -2.5
For points 4 and 7 ;
= 4 + 7 / 2
= 11/2
= 5.5
Therefore, the middle or midpoint of -3 and -2 is -2.5 and the midpoint for 4 and 7 is 5.5.
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A ball was dropped from the Empire State Building observatory. The height of the ball in feet is described by the function f(x) = 1048 - 16[tex]x^{2}[/tex], where x is the time in seconds.
Find the inverse function [tex]f^{-1}[/tex](x) and explain its meaning.
[tex]f^{-1} (x) = \sqrt{65.5 - 0.0625x }\\[/tex] is the inverse function and it means the time in seconds it will take the ball to attain a certain height in feet.
What is the inverse function f^-1(x) and its meaning?
Given:
[tex]f(x) = 1048 - 16x^{2}[/tex]
Since the function f(x) is the height (h), we can write the function as :
[tex]h = 1048 - 16x^{2}[/tex]
We will make x the subject:
[tex]16x^{2} = 1048 - h[/tex]
[tex]x^{2} = \frac{1048 - h}{16}[/tex]
[tex]x = \sqrt{\frac{1048 - h}{16} }[/tex]
[tex]x = \sqrt{65.5 - 0.0625h }[/tex]
Since:
[tex]x = f^{-1} (h) = \sqrt{65.5 - 0.0625h }[/tex]
Thus:
[tex]f^{-1} (x) = \sqrt{65.5 - 0.0625x }\\[/tex]
Therefore, the inverse function is [tex]f^{-1} (x) = \sqrt{65.5 - 0.0625x }\\[/tex] and it is a function describing the amount of time (in seconds) it takes for the ball to reach a height of h feet.
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suppose that the miles per gallon (mpg) rating of passenger cars is a normally distributed random variable with mean of 33.8 mpg and standard deviation of 3.5mpg. what is the probability that a randomly selected car gets less than 40 mpg?
The probability that a randomly selected car gets more than 40 mpg is equal to 0.771.
Let us assume that the miles-per-gallon rating of passenger cars be represented by random variable X. According to the question we know that X ≈ N (μ = 33.8 mpg and σ² = 3.5² mpg). Now, to compute the probability that a randomly selected passenger will gets less than 40 mpg will be given as
P(X < 40) = P(X - μ/σ > 40 - 33.8/3.5)
= P(Z < 1)
= P(Z > 1) - 1
= 1.771 - 1
= 0.771 which is the required probability.
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Write an expression for the calculation triple 4 and then add 6 times 6
Answer:
4x3+6x6=48
Step-by-step explanation:
PEMDAS
4x3=12
6x6=36
12+36=48
therefore, the answer is 48
Bob is planning to start an it business, servicing computers that are infected with viruses. to start his new enterprise, bob estimates that he will need to spend $5,000 on equipment $6,000 on premises, $4,000 on advertising. all of these costs are fixed. he is planning on charging his customers $250 each to fix an infected computer. for each computer that he fixes, he must spend $25 on parts and software. suppose we let x be the number of computers that bob fixes. if bob only fixes 50 computers, what is his total loss?
If Bob only fixes 50 computers, his total loss is $3,750.
What is the total loss?The total loss results from the negative difference between the total revenue and the total costs.
The total costs consist of variable and fixed costs.
The result is a loss when the total costs exceed the total revenue. This result becomes a profit or income when the total revenue exceeds the total costs.
Fixed Costs:Equipment = $5,000
Premises = $6,000
Advertising = $4,000
Total fixed costs = $15,000
Variable cost per unit = $25
Selling price per unit = $250
Total number of computers fixed = 50
The total variable cost for 50 units = $1,250 (50 x $25)
The total costs (fixed and variable) = $16,250
The sales revenue for 50 units = $12,500 (50 x $250)
Loss = $3,750 ($12,500 - $16,250)
Thus, Bob will incur a total loss of $3,750 if he fixes only 50 computers based on his fixed and variable costs.
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when atc has not imposed any climb or descent restrictions and aircraft are within 1,000 feet of assigned altitude, pilots should attempt to both climb and descend at a rate of between a. 500 feet per minute and 1,500 feet per minute. b. 1,000 feet per minute and 2,000 feet per minute. c. 500 feet per minute and 1,000 feet per minute.
In the absence of ATC restriction on climb or descent, and aircraft are within 1,000 feet of assigned altitude. pilots should attempt to both climb and descend at a rate of between 500 fpm and 15000 fpm. (Option A)
An Air Traffic Controller (ATC) clearance refers to an authorization by ATC for the purpose of preventing known aircraft collision. The rate of climb or descend expected by ATV is when an aircraft is within 1000 feet of assigned altitude, descend, or climb at an optimum rate consistent with the operating characteristics of the aircraft to 1,000 feet above or below the assigned altitude, and then attempt to descend or climb at a rate of between 500 and 1,500 fpm until the assigned altitude is reached.
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Mai runs around a 400-meter track at a constant speed of 250 meters per minute. How many minutes does it take Mai to complete 4 laps of the track? Write your answer as an improper fraction
The minutes it take Mai to complete 4 laps of the track would be 6 minutes 24 seconds.
What is speed?Speed can be calculated as the ratio of distance traveled to the time taken.
Speed = distance /time
Also, Time = distance/ speed
In this case, the distance is 4 laps of 400 meters, so;
4 x 400=1600 meters
Speed = 250 per minute
Now,
Time =1600 meters /250 meter per minute
= 6,40 minutes is the same 6 minutes 24 seconds
Hence, the minutes it take Mai to complete 4 laps of the track would be 6 minutes 24 seconds.
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Use the order of operations to find the value of the expression.12÷2*3-(7-5)O A.0O B.6O C.16O D.19
Given:
given expression is
[tex]12\div2\ast3-(7-5)[/tex]Find:
The main objective is to evaluate the expression.
Explanation:
we will use BoDMAS formula for evaluating the expression.
[tex]\begin{gathered} 12\div2\ast3-(7-5)=12\div2\ast3-2 \\ =6\ast3-2 \\ =18-2 \\ =16 \end{gathered}[/tex]Conclusion:
Therefore, correct option is C.16
Please help
3. In the formula A = lw, find A when I is
5 inches and w is 25 inches.
Answer:
125 inches squared
Step-by-step explanation:
A=lw
A=(5)(25)
A=125
HELP IMMEDIATELY I WILL GIVE 75 BRAINLIST
Answer:
Step-by-step explanation:
(4x + 50)° = 150°
4x = 150° - 50°
4x = 100°
x = 100° / 4 = 25°
Which relation is a function?
Responses
(1, 0), (3, 0), (1, 1), (3, 1), (1, 3)
(1, 0), (3, 0), (1, 1), (3, 1), (1, 3)
(1, 1), (2, 2), (3, 3), (4, 4), (5, 8)
(1, 1), (2, 2), (3, 3), (4, 4), (5, 8)
(2, 7), (6, 5), (4, 4), (3, 3), (2, 1)
(2, 7), (6, 5), (4, 4), (3, 3), (2, 1)
(9, -3), (9, 3), (4, -2), (4, 2), (0, 0)
Answer:{(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}
Step-by-step explanation: hope this helps
The line perpendicular to y=-3x+4 that passes through the point (-3,-7)
Answer:
Step-by-step explanation:
A perpendicular line will have a sope that is the negative inverse of the reference line. The reference line is y = -3 + 4, with a slope of -3. The negative inverse would be -(-1/3) or (1/3).
The new line will take the form of y = (1/3)x + b, where b is the y-intercept (the value of y when x=0). We want the new line to go through point (-3,-7). We;ll need a value of b that will make that happen. To find b, enter the given data point and solve for b:
y = (1/3)x + b for (-3,-7).
-7 = (1/3)(-3) + b
-7 = -1 + b
b = -6
The new equation is y = (1/3)x - 6
See the attached graph.
The table shows the distances between major cities.
New York to Paris 3,636 miles
Los Angeles to Toronto 2,171 miles
Mr. Santiago has a flight from Los Angeles to Toronto. If the plane travels at 520 miles per hour, how many hours long is the flight?
__ hours
Answer:
The time take for the journey can be calculated by dividing the total distance by the distance travelled in an hour.
Which is 2171 (Total distance) / 520 (Distance travelled in a hour)
[tex]2171/520 = 4.175[/tex]
Which can be rounded of to 4.2
It takes 4.2 hours for the flight between Los Angeles and Toronto
What is the answer to this question
Is the given trinomial, 4x squared -20x + 25, a perfect square trinomial?
Yes, 4x² - 20x + 25 = (2x+5)² is a perfect square trinomial.
What is perfect square trinomial?
A trinomial that may be expressed as the square of a binomial is referred to as a perfect square trinomial. Remember that the square of the first term, twice the product of the first two terms, and the square of the final term are the results of squaring a binomial.
The perfect squared trinomials are always in the form:
[tex]a^2 +- 2ab + b^2 = (a+-b)^2[/tex]
The given equation can also be written as:
(2x)² - 2(2x)(5) + 5² = (2x+5)²
This equation is similar to the ideal equation for perfect square trinomial.
Here, a = 2x, b = 5
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Complete Question
Is the given trinomial, 4x² - 20x + 25 = (2x+5)² , a perfect square trinomial?
An artist is going to cut four similar righttriangles from a rectangular piece of paperlike the one shown to the right. What is thedistance from B and D to the diagonal AC?Write an equation and solve, showing ALLthe work.
First let's find the length of AC using the Pythagorean theorem in the right triangle with legs of 5 and 12:
[tex]\begin{gathered} AC^2=5^2+12^2 \\ AC^2=25+144 \\ AC^2=169 \\ AC=13 \end{gathered}[/tex]So the diagonal of the rectangle is 13 units. Now, since the area of a triangle is calculated as the product of a base and the corresponding height, we can use the legs as base and height or we can use the segment AC and the corresponding height, and the result is the same, so we have:
[tex]\begin{gathered} A=\frac{b\cdot h}{2} \\ A=\frac{5\cdot12}{2} \\ A=\frac{13\cdot h}{2} \\ \\ \frac{5\cdot12}{2}=\frac{13\cdot h}{2} \\ 60=13h \\ h=\frac{60}{13} \end{gathered}[/tex]So the distance from B or D to the diagonal AC is 60/13 units.
true or false: (justify/explain your answer) state whether a or b is the true statement below and then explain why the other statement is false. a. with a large random sample, the sample histogram will closely resemble the normal curve. b. with a large random sample, the probability density function of the sample mean will close resemble the normal curve.
By central limit theorem ,with a large random sample, the sample histogram will not closely resemble the normal curve but with a large random sample, the probability density function of the sample mean closely resembles the normal curve.
The central limit theorem for samples says that if we keep drawing larger and larger samples and calculating their means, the sample forms their own normal distribution (the sampling distribution). The normal distribution will have the same mean as the original distribution and a variance that equals the original variance divided by the sample size. The variable n is the number of values that are averaged together,and not the number of times the experiment is done.
Hence,with a large random sample, the sample histogram will not resemble the normal curve but with a large random sample, the probability density function of the sample mean will closely resemble the normal curve.
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v/8 - 3.1 = -15.9 solve for v
Hello!
So, we are given the following to solve.
Solve for v.
[tex]\frac{v}{8}-3.1=-15.9[/tex]
To solve for v, we to do as follows:
1. Add 3.1 to both sides.
[tex]\frac{v}{8}-3.1+3.1=-15.9+3.1[/tex]2. Simplify.
[tex]\frac{v}{8} =-12.8[/tex]3. Multiply both sides by 8.
[tex]\frac{8v}{8}=8(-12.8)[/tex]4. Simplify.
[tex]v=-102.4[/tex] ← Hence, our solution.Hope this helps!
