A lighthouse is located on a small island 5 km away from the nearest point P on a straight shoreline and its light makes six revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P? (Round your answer to one decimal place.)
Answers
Answer:
The beam of light is moving along the shoreline at a velocity of approximately 196 kilometers per second.
Step-by-step explanation:
The statement is described geometrically in the image attached below by means of a right triangle. All variables are described below:
[tex]OP[/tex] - Minimum distance between lighthouse and the straight shoreline, in kilometers.
[tex]PP'[/tex] - Distance along the straight shoreline, in kilometers.
[tex]\theta[/tex] - Angle of rotation of the lighthouse, in sexagesimal degrees.
To find the rate of change of distance along the straight shoreline ([tex]\frac{dPP'}{dt}[/tex]), in kilometers per minute, we use the following trigonometric relationship:
[tex]PP' = OP \cdot \tan \theta[/tex] (1)
Then, we differentiate this expression in time:
[tex]\frac{dPP'}{dt} = OP\cdot \dot \theta \cdot \sec^{2}\theta[/tex] (2)
Where [tex]\dot \theta[/tex] is the rate of change of the angle of rotation of the lighthouse, in radians per minute.
The angle at the given instant is calculated by (1): [tex]OP = 5\,km[/tex], [tex]PP' = 1\,km[/tex]
[tex]\theta = \tan^{-1} \left(\frac{PP'}{OP} \right)[/tex]
[tex]\theta \approx 11.310^{\circ}[/tex]
If we know that [tex]\dot \theta = 37.699\,\frac{rad}{min}[/tex], [tex]\theta \approx 11.310^{\circ}[/tex] and [tex]OP = 5\,km[/tex], then the rate of change is:
[tex]\frac{dPP'}{dt} \approx 196,035\,\frac{km}{min}[/tex]
The beam of light is moving along the shoreline at a velocity of approximately 196 kilometers per second.
Related Questions
HELP! WILL GIVE BRANLIEST + EXTRA POINTS!!!!
Answers
Answer:
130.25 ft.
Step-by-step explanation:
The semi circle has a length 1/2 of the circumference of the circle with a diameter of 25
C = πd = 3.14(25)
So, the semi circle has a length = 1/2(3.14)25) = 39.25
The distance for the rectangle = 33 + 25 + 33 = 91
Therefore, the total perimeter = 91 + 39.25 = 130.25
What is the range of the relation below?
{(-4,1), (-2,0), (8, -1)}
Answers
Answer:
Range: {-1, 0, 1}
General Formulas and Concepts:
Math
Number LineAlgebra I
Range is the set of y-values that are outputted by function f(x){Set Builder Notation}Step-by-step explanation:
Step 1: Define
[Relation] {(-4, 1), (-2, 0), (8, -1)}
Step 2: Identify
According to the relation, our y-values are 1, 0, and -1. These values would encompass our range.
-2=w/2+6
solve for w
Answers
Answer:
It is -16
Step-by-step explanation:
Have a great Day
To find the area of a triangle, you can use the expression b × h ÷ 2, where b is the base of the triangle and h is its height. What is the area of a triangle with a base of 6 centimeters and a height of 8 centimeters?
Answers
Answer:
Step-by-step explanation:
½×6×8 = 24 cm²
A sportswriter wishes to see if a football filled with helium travels farther, on average, than a football filled with air. To test this hypothesis, the writer uses 18 male subjects, randomly divided into two groups of 9 subjects each. Group 1 kicks a football filled with helium to the recommended pressure, while Group 2 kicks a football filled with air to the same pressure. The sample mean yardage for Group 1 was barx2 = 30 yards with a standard deviation of s1 = 8 yards. The mean yardage for Group 2 was barx2 = 25 yards with a standard deviation of s2 = 6 yards. Assume that the two groups of kicks are independent. Let μ1 and μ2 represent the mean yardage we would observe for the entire population represented by the volunteers if all members of this population kicked, respectively, a helium-filled football and an air-filled football. Let σ1 and σ2 be the corresponding population standard deviations. Assuming two-sample t procedures are safe to use, what is a 99% confidence interval for μ1 – μ2?
A) 4 ± 7.7 yards.B) 4 ± 11.2 yards.C) 4 ± 4.7 yards.D) 4 ± 6.2 yards.
Answers
Answer:
5 ± 9.74
Step-by-step explanation:
Confidence interval, two - sample, t procedure ;
μ1 - μ2 = (x1 - x2) ± Tcritical*S
S = sqrt[(s1²/n1) + (s2²/n2)]
n1 = 9 ; n2 = 9 ; s1 = 8 ; s2 = 6 ; x1 = 30 ; x2 = 25
S = sqrt[(8^2/9) + (6^2/9)]
S = sqrt[11.111111]
S = 3.333
Tcritical at 99% confidence interval
df = 18 - 2= 16
Tcritical = 2.92
(30 - 25) ± 2.92*(3.333)
5 ± 9.74
Which expression has the greatest value?
A: -2 x -2 divided by 1/2
B: -2 x -1/2 divided by 2
C: -2 x 1/2 divided by 1/2
D: -2 x 2 divided by 2
Answers
Answer:
A. -2 × -2 divided by 1/2
Step-by-step explanation:
-2 × -2 ÷ 1/2 =8
If 12 men or 15 women can finish a piece of work in 66 days, how long will 24 men and 3 women take to finish the work? Pls helppp thank you :)
Answers
Answer:
30 days
Step-by-step explanation:
Find the value of y.
Answers
Answer:
y = 6
Step-by-step explanation:
This is a special right triangle with angle measures 90° 60° 30°
the side length that sees angle measure 30 is represented with x
the side length that sees angle measure 90 is represented with 2x
and the side length that sees angle measure 60 is represented with x√3
the side length that sees angle measure 90 is given as 4√3 which means 2x = 4√3 divide both sides by 2
x = 2√3 now to find y, we need to multiply this value by √3
2√3 × √3 = 2 × 3
Find the measure of angles?
The equations to find the measure of ∠ ∠ are given. Use the definition of an angle bisector
to find the measure for those two angles.
Answers
Answer:
m<KNL = 65°
m<MNL = 65°
Step-by-step explanation:
An angle bisector divides an angle into two equal parts.
Thus:
m<KNL = m<MNL
Substitute
5x + 10 = 6x - 1
Collect like terms
5x - 6x = -10 - 1
-x = -11
Divide both sides by -1
x = 11
✔️m<KNL = 5x + 10
Plug in the value of x
m<KNL = 5(11) + 10 = 55 + 10
m<KNL = 65°
✔️m<MNL = 6x - 1
Plug in the value of x
m<MNL = 6(11) - 1 = 66 - 1
m<MNL = 65°
Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms. x+7–4x3
Answers
Friedman and Rosenman have suggested that personality type isrelated to heart disease. specifically, type A people, who arecompetitive, driven, pressured and impatient are more prone toheart disease. on the other hand, type B people, who are lesscompetitive and more relaxed are less likely to have heart disease.suppose that an investigator would like to examine the relationshipbetween personality type and disease. for a random sample ofindividuals, personality type is assessed witha standardizedtest. these people are then examined and categorized as to whetherthey have a heart disorder. the observed frequencies are asfollows: noheart disease heartdiseaseTypeA 32 18 50TypeB 128 22 150 160 40is there any relationship between personality and disorder? testat the .05 level of significance.
Answers
Answer:
since p value(0.001091 ) is less than less than alpha(0.05)
null hypothesis H₀ is rejected.
Hence, we conclude that there is a relationship between personality and disorder.
Step-by-step explanation:
Given the data in the question;
non-heart disease heart disease total
TypeA 32 18 50
TypeB 128 22 150
total 160 40
level of significance ∝ = 0.05
H₀ : There is no relationship between personality and disorder
H₁ : There is a relationship between personality and disorder
so
the computational table for x²
E₁ = 50×160 / 200 = 40
O E O-E (O-E)² (O-E)² /E
32 40 -8 64 1.6
18 10 8 64 6.4
128 120 8 64 0.5333
22 30 -8 64 2.133
∑ 10.667
so
X² = ∑( (O-E)² /E ) = 10.667
The contingency table is 2×2, since there are 2 rows and 2 columns
df = (2-1)(2-1) = 1
P Value from Chi-Square Calculator
Chi-square score: 10.667
DF : 1
p-value = 0.001091
since p value(0.001091 ) is less than less than alpha(0.05)
null hypothesis H₀ is rejected.
Hence, we conclude that there is a relationship between personality and disorder.
What is a chi-squared test?
Answers
Answer:
A chi-squared test, also written as χ² test, is a statistical hypothesis test that is valid to perform when the test statistic is chi-squared distributed under the null hypothesis, specifically Pearson's chi-squared test and variants thereof.
I hope it's helpful!
Evaluate: 63 + 7 X 4
Answers
Answer:
91
Step-by-step explanation:
Multiplication first, so 7x4 = 28
28+63=91
Answer:
91
Step-by-step explanation:
multiply the numbers
7×4=28
63+28=91
add the numbers
91
27
6 boys have a mean age of 10 years.
14 girls have a mean age of 5 years.
Work out the mean age of all 20 children.
Answers
not clear way ..... clear it
15 divided by 2 = 7.5
In the following problem, Emily tried to calculate EG. However, she has made a mistake in her work. You need to identify and explain the mistake. Then, you must provide the correct solution.
Answers
Answer:
x = 66
Step-by-step explanation:
Emily's mistake is that part of the line is only x - 6, but she put 6x - 6
The first 6 shouldn't be there.
x - 6 = 72
x = 66
The actual correct answer is:
x = 78
Step-by-step explanation:
Although the explanation above is correct, the answer is wrong. It's not 66 because you are subtracting 6 from x. This means x needs to be 6 above 72.
Here is my step-by-step solution:
x - 6 = 72 <-- Given; Corrected Equation
x - 6 + 6 = 72 + 6 <-- Addition Property of Equality
x = 78 <-- Result from Solution
19.14 = v + 1.5
v = ?
Answers
Answer:
V= 17.64
Step-by-step explanation:
7.
Mr. Aamodt bought a new lawn tractor for $3,350.
a.
The state sales tax on the lawn tractor purchase will be 6.5%. How much state
sales tax will Mr. Aamodt pay on the tractor? (2 points)
b.
Mr. Aamodt has applied for a 2-year loan at the bank for $3,350 to pay for
the new lawn tractor. The bank will charge him 8.4% simple interest on the
loan. What amount of interest will Mr. Aamodt pay on the loan? (2 points)
C.
What is the total cost of Mr. Aamodt's new lawn tractor, including the purchase
price, the loan interest, and the sales tax? (2 points)
Answers
Answer:
7. Mister as an umbrella a new lawn tractor for 3035 $0 a the state sales tax the lawn tractor purchase will be 6. 5% how much states sells tax will mr. pay for the tractor two points? mister I can apply for 2 years loan for the bank for new tra
Can anyone help me with my homework
Answers
2. Music class
3. 9 left and 5 down
4. Science and math
5. 1,4
6. Second quadrant, where the entrance is
Determine the solution to 8x = 32 that makes the equation true.
Answers
Answer:
4
Step-by-step explanation:
8x=32
x = 4
Any help would be nice
Answers
Hope this helps! Good luck!
Answer:
<CPB
Step-by-step explanation:
Because the rest make obtuse angles or a right angle, only angle CPB is less than 90 degrees.
HELP ME PLZ I NEED IT DONE
Answers
Answer:
-6 , 6, 11
Step-by-step explanation:
Set each part of the equation to zero, so that x-11= 0, and x^2 - 36 = 0. Solve each part, and you get -6, 6, and 11.
Hopefully this helps- let me know if you have any questions!
The amount of a radioactive substance remaining as it decays over time is A = A0(0.5)t/h ,where a represents the final amount
Ao represents the original amount, t represents the number of years, and h represents the half-life of the sibstance.
The half-life of the radioactive isotope carbon-14 is 5,730 years. Approximately how many years will it take a 50-gram mass of
carbon-14 to decay to 5 grams?
Answers
Ao represents the original amount, t represents the number of years, and h represents the half-life of the sibstance.
The half-life of the radioactive isotope carbon-14 is 5,730 years. Approximately how many years will it take a 50-gram mass of
carbon-14 to decay to 5 grams?
Carbon-14 will take 19,035 years to decay to 10 per cent.
What is the time of decay?
A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay.
An exponential decay can be described by the following formula:
[tex]N(t)=N_oe^{-\lambda t}[/tex]
Where:
No = The quantity of the substance that will decay.
N(t) = The quantity that still remains and has not yet decayed after a time t
[tex]\lambda[/tex] = The decay constant.
One important parameter related to radioactive decay is the half-life:
[tex]t_{1/2}=\dfrac{Ln(2)}{\lambda}[/tex]
If we know the value of the half-life, we can calculate the decay constant:
[tex]\lambda =\dfrac{ln(2)}{t_{1/2}}[/tex]
Carbon-14 has a half-life of 5,730 years, thus:
[tex]\lambda =\dfrac{ln(2)}{5730}[/tex]
[tex]\lambda[/tex] = 0.00012097
The equation of the remaining quantity of Carbon-14 is:
[tex]N(t)=N_oe^{-0.00012097t}[/tex]
We need to calculate the time required for the original amount to reach 10%, thus N(t)=0.10No
[tex]0.10N_o=-N_oe^{-0.00012097t}[/tex]
Simplifying:
[tex]0.10=e^{0.00012097t}[/tex]
Taking logarithms:
ln(0.10) = -0.00012097t
Solving for t:
[tex]t=\dfrac{Log0.10}{-0.00012097}[/tex]
t = 19035 years
Carbon-14 will take 19,035 years to decay to 10 per cent.
To know more about decay follow
https://brainly.com/question/25537936
#SPJ2
through: (-2, -1), slope = 3
Write the slope intercept form of the equation line through given point with given slope .
Answers
Answer:
y =3x + 5
Step-by-step explanation:
The slope intercept form of an equation is expressed as;
y = mx+c
m is the slope
c is the intercept
Get the intercept
Substitute m = 3 and (-2,-1) into y = mx+c
-1 = 3(-2)+c
-1 = -6 + c
c = -1+6
c = 5
Get the equation.
Recall that y = mx+c
y =3x + 5
This gives the required equation
FACTOR the expression 6x+3y-12 using the greatest common multiple.
Include Parentheses: ()
No spaces!
Put the multiple outside, to the left of the parentheses! Combine like terms and simplify the expression: -2+6x+4+4x
Answers
Answer:
Step-by-step explanation:
For 6x+3y-12 the greatest common factor is 3 so
3(2x+y-4)
For -2+6x+4+4x
10x+2 and 2 is greatest common factor so
2(5x+1)
There are 20%, percent more goblins than wizards in magic club. There are 120 goblins in magic club.
How many wizards are in the magic club?
Answers
Answer:
100
Step-by-step explanation:
Here is your answer
Let the number of wizards is x
20% more gobins than wizards.
ATQ
Hence Numbers of wizards are 100 in a magic club.
Answer:
480
Step-by-step explanation:
120 ------ [tex]\frac{20}{100}[/tex]
x ----------[tex]\frac{100}{100}[/tex]
x·[tex]\frac{20}{100} = 120\frac{100}{100}[/tex]
x= [tex]\frac{120}{0,2}[/tex]
x=600
600- 120= 480 wizards in the club
24 divided by [(6 divided by 2) - (4 divided by 2)
Answers
Answer:
Im pretty sure the answer is 6
Step-by-step explanation:
Leave the 24 aside for a sec. Focus on the 6÷2 and 4÷2. 6 divided by 2 is 3. And 4 divided by 2 is 2. So now its 24÷3= 8
8-2=6
A farmer has harvested 1.6 tons of sweet potatoes from one-quarter of an
acre. How many tons will he harvest from one acre
Answers
Answer: there is no pic
Step-by-step explanation:
Answer:
6.4 tons
Step-by-step explanation:
two number are in the ratio 5:6 if sum of three number is 132 . find the number.
Answers
I hope this help you
.........
15) Max has his eye on a new pair of sneakers that cost $120. He decided
he would not purchase the shoes until there was at least a 30% discount.
What was the cost Max was willing to pay for the sneakers?
Answers
This is for person to help me
Answers
Answer:
5. F
6. C
Step-by-step explanation:
5. the mode is all the variables added together which is 100 or 100% divided by the number of them which is 4. 100 divided by 4 is 25 or 25%. The one that's equal to 25% is F which is soccer.
6. The relative frequency from what I can tell is the percentages of each of them. You just have to see how much space each of them takes up. C should be the answer.
Hopefully these are correct.