An airplane is flying overhead at a constant elevation of 4090 ft. A person is viewing the plane from a position 3010 ft from the base of a radio tower. The airplane is flying horizontally away from the person. If the plane is flying at the rate of 700 ft/s, at what rate is the distance between the person and the plane increasing when the plane passes over the radio tower
Answers
Answer:
415 ft/s
Step-by-step explanation:
I've attached a diagram showing the triangle formed between the plane, the person and the radio tower.
From the attached diagram, x represents the position between the person and the position on the ground directly below the airplane while s represents the distance between the person and the plane.
The constant elevation remains 4090 ft while the value of x and s varies with time.
Thus, x varies with respect to time as dx/dt while s varies with respect to time as ds/dt.
Now, we are told that the plane is flying at the rate of 700 ft/s. This means that; dx/dt = 700 ft/s
Now we want to find the rate at which the distance between the person and the plane is increasing when the plane passes over the radio tower.
This means that we want to find ds/dt when x = 3010 ft
From pythagoras theorem if x = 3010 ft and the Elevation remains 4090 ft, we can find s as;
s = √(4090² + 3010²)
s = √25788200
s ≈ 5078.21 ft
Since we want to find ds/dt at x = 3010 ft, from the diagram, we can say from pythagoras theorem that;
x² + 4090² = s²
Differentiating x and s with respect to t, we have;
2x(dx/dt) = 2s(ds/dt)
2 will cancel out to give;
x(dx/dt) = s(ds/dt)
ds/dt = (x/s)(dx/dt)
Plugging in 700 for dx/dt, 3010 for x and 5078.21 for s, we have;
ds/dt = (3010/5078.21) × 700
ds/dt ≈ 415 ft/s
Related Questions
students in a science class recorded lengths of a streched spring, as shown in the table. determine if each statement is true or false.
(Look at picture above)
A. The relationship represents a constant rate of change. True or false?
B. The slope of the relationship is 6 grams per centimeter. True or false?
C. The equation that represents the relationship is y = x + 10. true or false?
Answers
Answer:
Step-by-step explanation:
Solve each of the following equations for the missing variable.
-2.5x – 10 = 40
O x = 20
O x= -20
O 50
-50
Answers
Answer:
-20
Step-by-step explanation:
-2.5x = 40 + 10
- 2.5x = 50
x = 50/-2.5 = -20
An avant-garde clothing manufacturer runs a series of high-profile, risque ads on a billboard on Highway 101 and regularly collects protest calls from people who are offended by them. The company has no idea how many people in total see the ad, but it has been collecting statistics on the number of phone calls from irate viewers:
Answers
Answer and Step-by-step explanation:
Please find attached
GIVING OUT BRAINLLEST:What is the slope of the line that goes through the points (1,-2) and (3,6)?
Question 1 options:
-4
4
1
2
Answers
answer is 4
brainliest plz :)
Solve problem:
8-6•4+10/2
Answers
Answer:
[tex]8 - 6 \times 4 + \frac{10}{2} \\ = 8 - 6 \times 4 + 5 \\ = 8 - 24 + 5 \\ = 8 + 5 - 24 \\ = 13 - 24 \\ = - 11[/tex]
it is 200% correct answer..
It helps you ☺️Thank you ☺️
janelle has 25 pictures on her cell phone.she takes 7 more pictures, and then deletes 9 pictures . how many pictures does she have ?
Answers
Answer:
23
Step-by-step explanation:
Answer: 23 pictures
Step-by-step explanation:
25 + 7 = 32
32 - 9 = 23
Your answer will be 23 pictures.
Hope this helps!
Leon was asked to repaint the sign for his mother's ice cream shop, so he needs to figure out how much paint he will need. Determine the area of the ice cream cone on the sign. Round to the nearest tenth. 6 in 12 in.
Answers
Answer:
50.1
The area of the composite figure is 50.1
Trust me
I WILL BRAINLIST ITS ONLY ONE PROBLEM !!!!!!!!!!!!!!!
Answers
Answer:
11/200
Step-by-step explanation:
This is the correct answer boo
* Pending
This map shows the organization that was
association of nearly 30 countrior
Answers
Darnell uses 1 1/4 packages of beads to make 10 bracelets. He wants to make 25 bracelets. How many packages of beads will he use?
Answers
Answer:
I believe the answer is 3 1/8
Step-by-step explanation:
Since he uses 1 1/4 packages just to make 10, we can start with him making the 20. That would mean he uses 2 1/2 packages. Now all we have left is the 5 in 25. 5 is half of 10 and since you use 1 1/4 to make 10 bracelets, use half of it to make 5. Add up all the package use and you get 3 1/8. This was kinda rushed so I'm not 100% sure, but I'm like 95% sure. Hope this helps!
3¹/₈ packages of beads are required to make 25 bracelets
What is proportion ?
A proportion is an equation based on the equality of two ratios.
Here it is given that :
Darnell uses 1 1/4 packages of beads to make 10 bracelets that is :
1 ¹/₄ = 5/4 packages of beads requires to make = 10 bracelets
Now, divide both side by 10 we get :
to make 1 bracelets = 5/40 = 1/8 packages of beads are required
Now, to find the numbers packages of beads to make 25 bracelets multiply both side by 25 :
to make 25 bracelets = 25/8 = 3¹/₈ packages of beads are required.
Therefore, 3¹/₈ packages of beads are required to make 25 bracelets
Read more about ratio at:
https://brainly.com/question/17869111
#SPJ5
You play a game using fair dice and fair coins. First you flip 72 coins. For each coin that is a heads, you roll 5 six-sided dice. You sum all the six-sided dice you roll to calculate your total score. What is the expected total score from this game
Answers
Answer:
630
Step-by-step explanation:
Given that:
First flip = 72 coins
For each coin which is a head, you roll = 5, six-sided dice
Thus, the expected sum on a single six-sided dice = [tex]\sum x P(x)[/tex]
[tex]\sum x P(x)[/tex] = [tex]\dfrac{1}{6}\times (1+2+3+4+5+6)[/tex]
[tex]\sum x P(x)[/tex] = 3.5
Thus, the expected sum on the five six-sided dice = 5 × 3.5 = 17.5
However, for a single flip :
The expected sum = P(heads) × expected sum on 5 dice + P(tails) × expected sum on 0 dice.
Expected sum = [tex]\dfrac{1}{2} \times 17.5 + \dfrac{1}{2} \times 0[/tex]
Expected sum = 8.75
Hence, the expected total score from this game = 72 × 8.75 = 630
Eliza walked 1 1/2 miles in 2/3 of a hour. what is her walking rate in miles per hour?
Answers
Choose the equation that represents the line passing through the point -3 and -1 with a slope of 4
Answers
Answer:
y=4x+11
Step-by-step explanation:
y=mx+b.
-1=4(-3)+b
-1= -12+b
+12 +12
11=b
Answer:
y = 4x + 11
Step-by-step explanation:
factorise 3x^3-4x^2-28x-16
Answers
Answer:
i just saw that on google, but i'm not sure if that's what you are looking for
Answer: -2
Step-by-step explanation:
Hope it help you
Stayhomestaysafe
REAL NAME - SHRESTH DUBEY
Write each phrase as an expression.
Double the sum of x and 4.
Answers
your answer should be 2(x+4)
Can someone help me please
Answers
Answer:
your on the right one it's -7.5
Answer:
the answer is -7.5
Step-by-step explanation:
the answer is -7.5 because whenever you add a negative plus a negative it changes the equations symbol so it would be -4 minus 3.5 and the answer would be -7.5.
hope this helps :)
- by chance may i get brainliest
Need help on these two questions ♡
Answers
Answer:
for question 5 it is the last option
for question 6 it is the 3rd option down
Step-by-step explanation:
Help me please!!!!!!!!
Answers
Step-by-step explanation:
To solve the equation for s we've got to leave s alone
[tex]n = \frac{s + 360}{180} \\ 180n = s + 360 \\ 180n - 360 = s[/tex]
Does anyone know this answer !!!!!!
Answers
Answer:
13
Step-by-step explanation:
5x + 25 = 7x - 1
-7x. -7x
-2x + 25 = -1
-25. -25
-2x = -26
-2. -2
x = 13
Which rule describes a composition of transformations that maps pre-image PQRS to image P"Q"R"S"?
270 degree rotation about point 0 composition. Translation of negative 2 units x, 0 units y.
Translation of negative 2 units x, 0 units y composition 270 degree rotate about point 0.
270 degree rotation about point 0 composition reflected across the y-axis
Reflected across the y-axis composition 270 degree rotation about point 0.
Answers
Answer:
270 degree rotation about point 0 composition .translations of negative 2 units
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Took the test
A push lawnmower is priced at $299.50. There is an 8% sales tax rate. What is the sales tax of the pusher lawnmower in dollars and cents?
Answers
Answer:
$323.46
hope this helped :)
$299.50 + 23.96 = 323.46
Write each fraction as a percent. Use a model if needed. V-2
7/10
21/25
3/5
18/25
Answers
21/25 = 84%
3/5 = 60%
18/25 = 72%
21/25 is 84%
3/5 is 60%
18/25 is 72%
Multiply. Do not round your answer.
2.48x8.62 =?
Answers
Answer:
21.3776
Step-by-step explanation:
Answer: 21.3776
This is what I got for the answer hope it helps.
Planes X and Y and points C, D, E, and F are shown.
Which statement is true about the points and planes?
С
VX
The line that can be drawn through points C and D is
contained in plane Y.
O The line that can be drawn through points D and E is
contained in plane Y.
O The only point that can lie in plane X is point F.
O The only points that can lie in plane Y are points D
and E.
E
.
Save and Exit
Next
Submit
Mark this and return
Answers
Answer:
The answer is below
Step-by-step explanation:
The planes are shown in the image below.
From the image, points D and E are on plane Y, while point F is on plane X.
A) The line that can be drawn through points C and D is contained in plane Y.
This statement is wrong because point C is not in plane Y
B) The line that can be drawn through points D and E is contained in plane Y.
Correct. Since both points D and E are on plane Y, hence The line that can be drawn through points D and E is contained in plane Y.
C) The only point that can lie in plane X is point F.
This statement is correct because from the image only point F is on plane X.
D) The only points that can lie in plane Y are points D and E.
This statement is correct because from the image only point D and E is on plane Y.
If an angle measuring 18 ° is bisected to form two new angles , what is the measure of each new angle ?
Answers
Answer:
9 degrees
Step-by-step explanation:
18/2=9
please answeeeerrrrrr
Answers
I’m pretty sure the answer is D: 91 light bulbs
Hope this helps :)
Assume the number of customers who order a dessert with their meal on a given night at a local restaurant has the probability distribution given below. The variance for the random variable x is _____. a. .77
Answers
Complete question :
X: 3, 4, 5, 6
f(x): .25, .55, .15, .05
Answer:
0.60
Step-by-step explanation:
Given the data:
Variance (s) :
Σx²*f(x) - E(x)²:
E(x) = (3*0.25) + (4*0.55)+(5*0.15)+(6*0.05) = 4
Σx²*f(x) - E(x)²: [(3^2 * 0.25)+(4^2 * 0.55)+(5^2 * 0.15)+(6^2 * 0.05)] - 4²
16.6 - 16 = 0.6
2x^2+2=3x complete the square i need full explaination ASAP
Answers
Answer:
x = 3/4 + √7i/4
x = 3/4 - √7i/4
Step-by-step explanation:
2x² + 2 = 3x
Subtract 3x from both sides so it equals 0:
2x² - 3x + 2 = 0
Divide both sides by 2:
x² - 3/2x + 1 = 0
Subtract 1 from both sides:
x² - 3/2x = -1
Take -3/2 and multiply it by 1/2 then square it:
(-3/2 • 1/2)²
9/16
Add this to both sides:
x² - 3/2x + 9/16 = -1 + 9/16
Rewrite the perfect square on the left and add the terms on the right:
(x - 3/4)² = -7/16
Square root both sides to get rid of the square:
x - 3/4 = ± √-7/16
Simplify the radical:
x - 3/4 = ± √7i/4
Add 3/4 to both sides:
x = 3/4 ± √7i/4
Your two solutions are:
x = 3/4 + √7i/4
x = 3/4 - √7i/4
You can also convert to decimal if you need to (but I don’t recommend it):
x = 0.75 + 0.661438i
x = 0.75 - 0.661438i
Hope this helps!
What is the answer tho
Answers
Answer:
to?
Step-by-step explanation:
When multiplying the factors 2/3 and 4/7 what is the product of the denominators
Answers
Answer:
21
Step-by-step explanation:
When multipling fractions you go straight across so, all you have to do in the furture is multiply the demonators, anyways all i had to was 3x7 which is 21. Hope this helps and have a wonderful day!
Answer:
21
Step-by-step explanation:
2/3+4/7= 8/21
the top number is the numerator and the bottom number is the denominator.