A plane flying horizontally at an altitude of 1 mile and a speed of 460 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 2 miles away from the station. (Round your answer to the nearest whole number.)
Answers
Answer:
The rate increases at 398mi/h
Step-by-step explanation:
Given
[tex]\frac{dx}{dt} = 460mi/h[/tex] --- rate when [tex]y = 2[/tex] --- distance
The given parameters is represented with the attached figure
Using Pythagoras theorem [take the attached image as a point of reference]
[tex]y^2 = x^2 + 1^2[/tex]
[tex]y^2 = x^2 + 1[/tex]
Differentiate with respect to time (t):
[tex]2y \frac{dy}{dt} = 2x \frac{dx}{dt}[/tex]
Divide both sides by 2
[tex]y \frac{dy}{dt} = x \frac{dx}{dt}[/tex] --- (1)
When y = 2:
[tex]y^2 = x^2 + 1^2[/tex] --- Pythagoras Theorem
[tex]2^2 = x^2 + 1[/tex]
[tex]4 = x^2 + 1[/tex]
Collect like terms
[tex]x^2 = 4 -1[/tex]
[tex]x^2 = 3[/tex]
Solve for x
[tex]x = \sqrt 3[/tex]
So:
[tex]y \frac{dy}{dt} = x \frac{dx}{dt}[/tex]
Substitute: [tex]x = \sqrt 3[/tex], [tex]\frac{dx}{dt} = 460mi/h[/tex] and [tex]y = 2[/tex]
[tex]2 * \frac{dy}{dt} = \sqrt 3 * 460[/tex]
[tex]2 * \frac{dy}{dt} = 460\sqrt 3[/tex]
Divide by 2
[tex]\frac{dy}{dt} = 230\sqrt 3[/tex]
[tex]\frac{dy}{dt} = 230*1.7321[/tex]
[tex]\frac{dy}{dt} = 398.383[/tex]
[tex]\frac{dy}{dt} \approx 398[/tex]
Related Questions
Suppose that a news article refers to a poll that surveyed 886 registered voters and carries a margin of error of plus or minus 3.5 percentage points. Assume a 95% confidence level, and calculate the margin of error. Is your answer 3.5%
Answers
Answer:
no its not 3.5
Use the unit price of gasoline at both gas stations to determine which gas station charges more for gasoline (gallons). Be sure to include the unit prices in your answer. Show or explain your work.
Answers
Answer: Gas station P
Step-by-step explanation:
When you plot gas station M on the graph all the values are under the line meaning it gas at station M costs less than station G.
Gas station P charges more than gas station M.
What is unit rate?A unit rate means a rate for one of something.
Given is a table and a graph,
When we compare each, we get,
Gas station P is charging $20 for 5 gallons, and gas station M charges $19 for same.
Hence, gas station P charges more than gas station M.
For more references on unit rate, click;
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Playland Park charges $25 admission plus $2 per ride. Funland Park charges $35 admission plus $1 per ride. For what number of rides is the total cost the same at both parks?
Answers
Playland day cost is 25+2r
Funland day cost is 35+1r
Now plug in the same number to both and see if the answer is equal I always start with easy ones:
5
25+10=35
35+5=40
10
25+20=45
35+10=45
*Bingo*
So 10 is the number of rides that makes the parks cost the same.
Good luck! Brainliest would be greatly appreciated.
Previous data estimates the proportion of adults who are fully literate in Colombia to be 0.92. Suppose a random sample of adults from Columbia is to be taken and used to construct a 95% confidence interval for the proportion of adults who are fully literate. What is the MINIMUM sample size which should be used to construct this interval if the margin of error for the interval is to be 0.03 or less
Answers
Answer:
The minimum sample size which should be used is 315.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
Previous data estimates the proportion of adults who are fully literate in Colombia to be 0.92.
This means that [tex]\pi = 0.92[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
What is the MINIMUM sample size which should be used to construct this interval if the margin of error for the interval is to be 0.03 or less?
The minimum sample size that should be used is n for which M = 0.03. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.92*0.08}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.92*0.08}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.92*0.08}}{0.03}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.92*0.08}}{0.03})^2[/tex]
[tex]n = 314.2[/tex]
Rounding up
The minimum sample size which should be used is 315.
If a video game cost $60 and it's on sale for 10% off, how much is the discount?
Answers
Answer:
$6
Step-by-step explanation:
Percentages have a cool little trick where they can be reversed :) 10% of 60 is a little tough, but we can switch it to 60% of 10, which is much easier. 60% of 10 is 6, so the discount is $6
Giselle uses 2 ounces of pasta to make 2 over 3 of a serving of pasta. How many ounces of pasta are there per serving
Answers
NEED MAJOR HELP FAST GET HERE QUICK PLEASE
Answers
A 45 degree angle is 1/8 of a circle, so keep that in mind for later. You're looking for the circumference of that 1/8 fence, so you have to use the formula, circumference/diameter=pi. Now, the problem gives you half the diameter, a.k.a the radius, so double it to get 44 ft. then, you multiply that by 3.14 (pi) to get 138.16. Now take the 1/8, from before, of the circumfrence and you get your final answer, 17.27 ft!
Which set of points on the graph represents equivalent ratios?
70
60
F
50
40
30
.
20
10
1
2 3
4
5
6 7
Х
points C, D, and F
O points B, C, and D
points B, C, and F
O points A, C, and D
Ο Ο Ο
Answers
Answer:
C or otherwise BCD
Step-by-step explanation:
right on edge
Please help and will give brainliest
Answers
9514 1404 393
Answer:
12 m³
Step-by-step explanation:
The bottom platform has dimensions 2m × 4m × 3m, so a volume of ...
V = LWH
V = (2 m)(4 m)(3 m) = 24 m³
The top platform has dimensions 2m × 3m × 2m, so a volume of ...
V = (2 m)(3 m)(2 m) = 12 m³
The bottom platform has a larger volume by ...
24 m³ -12 m³ = 12 m³
The bottom prism has a 12 m³ larger volume.
Answer:
the answer is 12m squared
For estimation purposes, the shape formed by the sectors is considered to be a parallelogram. Which statement is true?
A.The height is approximately r units, and the base length is approximately mr units.
B.The height is approximately r units, and the base length is approximately 2 units.
C.The height is approximately r2 units, and the base length is approximately it units.
D.The height is approximately 2r units, and the base length is approximately it units.
Answers
Answer:
Step-by-step explanation: B
HELPPPPPPPPPPP!! SMART People?
Answers
its $1.07 my bad XD :P
Step-by-step explanation:
What is 5^5 equal to
Answers
Answer:
5^5 is equal to 3125
Step-by-step explanation:
5×5×5×5×5=3125 Hope this helps!
the answer is 10 alangan
A group of 140 students at an elementary school were asked if they prefer the color orange to the color green. The results are shown in the table below. Given that a randomly selected survey participant is a male, what is the probability that this student prefers the color green?
Enter your answer as a fraction.
Male Female Total
Orange 12 50 62
Green 5 73 78
Total 17 123 140
Provide your answer below:
$$
Answers
Answer:
1/28
Step-by-step explanation:
The probability that a male student picks green is 5 / 17
The randomly selected participant is a male which means that you should be looking at the probability that a male picks green not that a student picks green.
The probability that a male picks green is:
= Number of males who prefer green / Number of males in total
There are 17 males in total and 5 of them prefer green. Probability that a male picks green is:
= 5 / 17
In conclusion, the probability that a male picks green is 5 / 17.
Find out more at https://brainly.com/question/14682217.
Six friends go to lunch and the total cost of lunch is $41.12. After using a $5 coupon to reduce the bill, the friends split the cost of lunch evenly. How much does each friend owe?
A $6.20
B $6.02
C $6.85
Answers
Answer:
6.02
Step-by-step explanation:
(41.12 - 5) / 6
= 6.02
(its a practice question)
Answers
Answer:
your answer will be X=30
Step-by-step explanation:
[tex]85 = 3x - 5[/tex]
[tex]90 = 3x[/tex]
[tex]x = 30[/tex]
hope it helps you!!
What is 12 divided by 3/5
Answers
Answer:
20
Step-by-step explanation:
12 / 3/5
12 / 0.6
20
Answer:
12 divided by 3/5 = 20
Mr. Y gets paid $8.70 per hour. Yesterday he worked 6.5 hours. What will be his pay, assuming that he gets paid for exactly the time that he works.
Answers
Answer:
$56.55
Step-by-step explanation:
8.70*6.5=56.55
If (×+1 ) and(×+2) are factors of the expressionx^4+ax^2+b , find the value of and b, with these value of and factorize completely.
Answers
Answer:
Step-by-step explanation:
(x⁴+ax²+b) ÷ (x+1) = x³-x²+(a+1)x-(a+1) remainder b+(a+1)
Since x+1 is a factor, b+(a+1) = 0.
(x³-x²+(a+1)x-(a+1)) ÷ (x+2) = x²-3x+(a+7) remainder -3a-15
Since x+2 is a factor, -3a-15 = 0
a = -5
b = 4
x⁴+ax²+b = x⁴ - 5x² + 4 = (x²-4)(x²-1) = (x+2)(x-2)(x+1)(x-1)
I need these three and they shouldn’t be too hard.
Answers
Answer:
i dont know
Step-by-step explanation:
sorry my man my school is still just going into these kind of questions ):
The yield of a chemical process is being studied. Fromprevious experience, yield is known to be normally distributedand 3. The past five days of plant operation have resulted inthe following percent yields: 91.6, 88.75, 90.8, 89.95, and 91.3.Find a 95% two-sided confidence interval on the true mean yield.
Answers
Answer:
(87.85 ≤ μ ≤ 93.11)
Step-by-step explanation:
Given the data:
91.6, 88.75, 90.8, 89.95, 91.3
Mean, m = Σx / n
n = sample size = 5
Mean = 452.4 / 5 = 90.48
Standard deviation, σ = 3
Zcritical at 95% = 1.96
Confidence interval :
Mean ± Error margin
Error margin = Zcritical*σ/sqrt(n)
Error margin = 1.96 * 3/sqrt(5)
Error margin = 2.630
Lower boundary : 90.48 - 2.630 = 87.85
Upper boundary : 90.48 + 2.630 = 93.11
(87.85 ; 93.11)
Cup G has a diameter of 4 in. and a height of 8 in. Find the volume of Cup G.
Answers
Answer:
32pi
Radius=1/2 Diameter
radius=2
Area of circle= pi*radius^2= 4pi
4pi*8=32 pi
(3.14)(32)
v=100.48
Please let me know asap
Answers
Answer:
100
Step-by-step explanation:
Hello There!
∠4 and ∠8 are corresponding angles
corresponding angles are congruent so if ∠4 = 100 then ∠8 also equals 100
In 2018, there were about 32 million teenagers (aged 13-17) in the United States. They each sent
an average of 1200 text messages per month. About how many text messages did all of the
teenagers in the United States send each month? Express your answer using scientific notation.
Answers
Answer:
About 38,400,000,000 text
thirty eight billion + four hundred million
Step-by-step explanation:
Consider the following food chain:
Plants are eaten by grasshoppers, which are eaten by mice, which are eaten by snakes.
What will happen to the other members of the food chain if the grasshoppers are removed?
a.
the number of plants will increase, the number of mice will decrease, the number of snakes will decrease
b.
the number of plants will decrease, the number of mice will increase, the number of snakes will increase
c.
the number of plants will decrease, the number of mice will increase, the number of snakes will decrease
d.
the number of plants will increase, the number of mice will increase, the number of snakes will increase
Answers
Answer:
A
Step-by-step explanation:
the plant will increase because no grasshopper will be present to eat them without the grasshopper the mice cannot eat so the mice population will decrease....
If the grasshoppers are removed then the number of plants will increase, the number of mice will decrease, the number of snakes will decrease.
The correct answer is option a.
For the given Food chain:
If the grasshoppers are removed from the food chain, it will lead to a increase in the number of plants, as there will be no herbivores (grasshoppers) to consume them. This is because grasshoppers help control plant populations by feeding on them.
With the removal of grasshoppers, the mouse population is likely to decrease since their primary food source (grasshoppers) is no longer available.
As a consequence of the decreased mouse population, the snake population may also decrease because their primary food source (mice) has been affected.
Thus, the number of plants will increase, the number of mice will decrease, the number of snakes will decrease.
Thus, option a is correct.
Learn more about Food chain here:
https://brainly.com/question/26022932
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The mean monthly water bill for 44 residents of the local apartment complex is $104. What is the best point estimate for the mean monthly water bill for all residents of the local apartment complex?
Answers
Answer:
$104
Step-by-step explanation:
The computation of the best point estimate for the mean monthly water bill is shown below:
Given that
The mean monthly water bill is $104
and, the number of residents is 44
based on the above information
The best point estimate would be equivalent to the mean monthly water bill i.e. $104
hence, the same would be considered
Page 491 #s 6-8 6) Find the area of a square with side length 74 yard
Answers
Answer:
A=5476
Step-by-step explanation:
HOPE I HELPED
An expression is shown.
95-34
What is the value of the expression?
Answers
Answer:
61
Step-by-step explanation:
95
- 34
_______
61
A principal of $2900is invested at 3.25% interest, compounded annually. How much will the investment be worth after 9years? Use the calculator provided and round your answer to the nearest dollar.
Answers
Given:
Principal = $2900
Rate of interest = 3.25% compounded annually.
Time = 9 years.
To find:
The amount of investment after 9 years.
Solution:
The formula for amount is:
[tex]A=P\left(1+\dfrac{r}{n}\right){nt}[/tex]
Where, P is principal, r is rate of interest, n number of times interest compounded in an year and t is the number of years.
Substitute P=2900, r=0.0325, n=1 and t=9.
[tex]A=2900\left(1+\dfrac{0.0325}{1}\right)^{1\times 9}[/tex]
[tex]A=2900\left(1+0.0325\right)^{9}[/tex]
[tex]A=2900\left(1.0325\right)^{9}[/tex]
Using calculator, we get
[tex]A=3867.306[/tex]
[tex]A\approx 3867[/tex]
Therefore, the worth of the investment after 9 years will be $3867.
A circle has a diameter of 7 inches. Find the radius
Answers
Answer:
radius= 3.5 in
Step-by-step explanation:
Answer: 3.5
Step-by-step explanation:
The diameter is the length from one side of the circle to the other the radius is half that
.5% of what number is 15.8?
Answers
Answer:
316 should be your answer
Step-by-step explanation:
Answer:
3160
Step-by-step explanation:
.5% of what number is 15.8?
Let the unknown number be x.
0.5% * x = 15.8
0.005x = 15.8
x = 15.8/0.005
x = 3160