A lighthouse is located on an island 33 miles from the closest point on a straight shoreline. If the lighthouse light rotates clockwise at a constant rate of 99 revolutions per minute, how fast does the beam of light move towards the point on the shore closest to the island when it is 5252 miles from that point
Answers
Question:
A lighthouse is located on an island 3 miles from the closest point on a straight shoreline. If the lighthouse light rotates clockwise at a constant rate of 9 revolutions per minute, how fast does the beam of light move towards the point on the shore closest to the island when it is 52 miles from that point
Answer:
The beam of light moves at [tex]16278\pi[/tex] miles/min
Step-by-step explanation:
This question is illustrated with the attached image
Taking the instructions in the question, one at a time.
A revolution of 9 per minute implies that:
[tex]\frac{d\theta}{dt} = \frac{9 * 2\pi\ rad}{1\ min}[/tex]
[tex]\frac{d\theta}{dt} = 18\pi \frac{rad}{min}[/tex]
Take tan of the angle in the attachment:
[tex]tan(\theta) =\frac{52}{3}[/tex]
Differentiate both sides with respect to time
[tex]\frac{d\ tan(\theta)}{dt} =\frac{52}{3} * \frac{dx}{dt}[/tex]
Rewrite as:
[tex]\frac{d\ tan(\theta)}{d\theta} * \frac{d\theta}{dt} =\frac{52}{3} * \frac{dx}{dt}[/tex]
In calculus:
[tex]sec^2(\theta) =\frac{d\ tan(\theta)}{d\theta}[/tex] -- Chain rule
So:
[tex]sec^2(\theta) *\frac{d\theta}{dt} =\frac{52}{3} * \frac{dx}{dt}[/tex]
In trigonometry:
[tex]sec^2(\theta) = tan^2(\theta) + 1[/tex]
So:
[tex](tan^2(\theta) + 1)\frac{d\theta}{dt} =\frac{52}{3} * \frac{dx}{dt}[/tex]
Recall that:
[tex]tan(\theta) =\frac{x}{3}[/tex]
[tex]((\frac{52}{3})^2 + 1)\frac{d\theta}{dt} =\frac{1}{3} * \frac{dx}{dt}[/tex]
[tex](\frac{52^2}{9} + 1)\frac{d\theta}{dt} =\frac{1}{3} * \frac{dx}{dt}[/tex]
[tex](\frac{2704}{9} + 1)\frac{d\theta}{dt} =\frac{1}{3} * \frac{dx}{dt}[/tex]
[tex](\frac{2704+9}{9})\frac{d\theta}{dt} =\frac{1}{3} * \frac{dx}{dt}[/tex]
[tex](\frac{2713}{9})\frac{d\theta}{dt} =\frac{1}{3} * \frac{dx}{dt}[/tex]
Recall that: [tex]\frac{d\theta}{dt} = 18\pi \frac{rad}{min}[/tex]
[tex](\frac{2713}{9}) * 18\pi =\frac{1}{3} * \frac{dx}{dt}[/tex]
[tex]2713 * 2\pi =\frac{1}{3} * \frac{dx}{dt}[/tex]
Multiply both sides by 3
[tex]3 * 2713 * 2\pi =\frac{1}{3} * \frac{dx}{dt} * 3[/tex]
[tex]3 * 2713 * 2\pi =\frac{dx}{dt}[/tex]
[tex]16278\pi =\frac{dx}{dt}[/tex]
[tex]\frac{dx}{dt} = 16278\pi[/tex] miles/min
Hence:
The beam of light moves at [tex]16278\pi[/tex] miles/min
Related Questions
How does lack of sleep affect risk of injury?
O A. It causes illness.
B. It causes distractions.
C. It interferes with hearing.
D. It interferes with motor responses.
Answers
Answer:
D. It interferes with motor responses
Step-by-step explanation:
Don't ask why I know this
Mr. Moretti is making welcome bags to give to the 18 students in his homeroom on the first day of school. He puts m mechanical pencils in each bag. He puts twice as many regular pencils in each bag. What is the total number of pencils that Mr. Moretti gives to his students if he puts 3 mechanical pencils in each bag?M
Answers
Answer:
The total number of pencils that Mr. Moretti gives to his is 162.
Step-by-step explanation:
He puts 3 mechanincal pencils in each bag.
In each bag, there is also twice as many regular pencils, that is, 3*2 = 6 regular pencils.
So in each bag, 3 + 6 = 9 pencils.
What is the total number of pencils that Mr. Moretti gives to his students if he puts 3 mechanical pencils in each bag?
18 students, and each gets 9 pencils.
18*9 = 162
The total number of pencils that Mr. Moretti gives to his is 162.
Answer:
162 pencils
Step-by-step explanation:
i did the i ready lesson!
An information technology service at a large university surveyed 200 students from the College of Engineering and 100 students from the College of Arts. Among the survey participants, 91 Engineering students and 73 Arts students owned a laptop computer. Construct a 98% confidence interval for the difference between the proportions of laptop owners among Engineering and Arts students.
Answers
Answer:
CI = ( 0,1433 ; 0,4067 )
Step-by-step explanation:
College of Engineering
sample size n₁ = 200
sample proportion ( with laptop ) p₁ = 91/ 200 p₁ = 0,455 q₁ = 1 - p₁
q₁ = 0,545
College of Arts
sample size n₂ = 100
sample proportion ( with laptop ) p₂ = 73/ 100 p₂ = 0,73 q₂ = 1 - p₂
q₂ = 0,27
CI = 98 % significance level α = 2 % α = 0,02 α/2 = 0,01
From z-table we find z(c) for 0,01
z(c) = 2,328
CI = [ ( p₂ - p₁ ) ± z(c) * √ (p₁*q₁)/n₁ + (p₂*q₂)/n₂ ]
CI
[ ( 0,73 - 0,455 ) ± 2,328 * √ (0,455*0,545)/ 200 + ( 0,73*0,27)/100
CI = ( 0,275 ) ± 2,328 *√0,00123 + 0,001971
CI = ( 0,275 ± 2,328* 0,0566)
CI = ( 0,275 - 0,1317 ; 0,275 + 0,1317 )
CI = ( 0,1433 ; 0,4067 )
The values of the CI for the difference are always positive meaning that the proportion of students of Arts is greater than the proportion of students of Engineering
Helpppppppppppppppppp
Answers
The number on top of sigma is the number of terms.
The answer is C. 8 terms.
6x+12 in its simplest form?
Answers
Answer:
It is already in simplest form.
Step-by-step explanation:
Answer:
Already in simplest form
Step-by-step explanation:
I mean you could do 6(x+2) but its already in its simplest form.
Answer this correctly and I will give brainslist + 10 points from question (:
Answers
Answer:
a
Step-by-step explanation:
A company receives shipments from two factories. Depending on the size of the order, a shipment can be in 1 box for a small order, 2 boxes for a medium order, 3 boxes for a large order. The company has two different suppliers. Factory Q is 60 miles from the company. Factory R is 180 miles from the company. An experiment consists of monitoring a shipment and observing B, the number of boxes, and M, the number of miles the shipment travels. The following probabity model describes the experiment:
Factory Q Factory R
small order 0.3 0.2
medium order 0.1 0.2
large order 0.1 0.1
a. Find PB M(b, m), the joint PMF of the number of boxes and the distance.
b. What is E[B], the expected number of boxes?
c. Are B and M independent?
Answers
Answer:
A) PB M(b, m), we have;
b = 1
b = 2
b = 3
B) E(B) = 1.7
C) No they are not independent
Step-by-step explanation:
A) We are told that a shipment can be in 1 box for a small order, 2 boxes for a medium order, 3 boxes for a large order. Thus;
For PB M(b, m), we have;
b = 1
b = 2
b = 3
B) Factory Q is 60 miles from the company. Thus, under factory Q in the table, m = 60
Factory R is 180 miles from the company. Thus under factory R in the table, m = 180
Now;
P_B (b) for b = 1 which is small order is;
P_B (b) = 0.3 + 0.2 = 0.5
P_B (b) for b = 2 which is medium order is;
P_B (b) = 0.1 + 0.2 = 0.3
P_B (b) for b = 3 which is large order is;
P_B (b) = 0.1 + 0.1 = 0.2
Thus;
E(B) = Σb•P_B (b) = (1 × 0.5) + (2 × 0.3) + (3 × 0.2)
E(B) = 0.5 + 0.6 + 0.6
E(B) = 1.7
C) No, they are not independent. This is because from the table we are given, P_B,M at b = 1 and m = 60 is given as 0.3.
Whereas, for B and M to be independent, P_B,M at b = 1 and m = 60 has to be equal to (P_M(m) under m = 0.3) multiplied by P_B(b) for b = 1.
Instead what we have is P_M(m) under m = 0.3 as; 0.3 + 0.1 + 0.1 = 0.5. Which means (P_M(m) under m = 0.3) multiplied by P_B(b) for b = 1 gives;
0.5 × 0.5 = 0.25 which is not equal to P_B,M = 0.3 at b = 1 and m = 60
your friend earns $10 babysitting. This is 3 more than you earn for washing the car. How much do you make for washing the car
Answers
Answer:
$7
Step-by-step explanation:
$10 - $3 = $7
help help help help help help
Answers
The members of a youth dance company were asked their favorite ice cream flavors for
an upcoming party to celebrate a competition win. The results are displayed in the bar
graph below.
Based on the information in the graph, which of the following statements are true?
Choose one. 10 points
Favorite Ice Cream Flavors
10
8
6
Amount
4
2
0
Vanilla - 6
Strawberry - 5
Cookies & Cream - 9
Butter pecan - 3
Chocolate - 2
Answers
Answer:
2
Step-by-step explanation:
find the product (ab-3)^2
Answers
Answer:
a^2b^2 -6ab + 9
Step-by-step explanation:
Which regression equation best fits these data?
х
y
1-2, 16).16)
15
-5
11
21.15)
-3
14
.6314
.(-5.11
10
(372)
- 2
16
4,9)
-1
16
1
15
3
12
6
4.
9
5
6
O A. y = -0.59x + 12.5
B. y = 0.30x2 + 0.48x + 15.83
C. y = 12.00 0.94%
Answers
Answer:
a will be the correct answer bro be sure
The Regression equation best fits these data is ŷ = -0.58939x + 12.52235
We have the table as from which can be calculated as
Sum of X = 2
Sum of Y = 99
Mean X = 0.25
Mean Y = 12.375
Sum of squares (S[tex]S_x[/tex]) = 89.5
Sum of products (SP) = -52.75
As, Regression Equation
ŷ = b x + a
where b = SP/S[tex]S_x[/tex]
b = -52.75/89.5
b = -0.58939
and, a = MY - b MX
a = 12.38 - (-0.59)(0.25)
a = 12.52235
So, the required equation is ŷ = -0.58939x + 12.52235
Learn more about Regression line here:
https://brainly.com/question/7656407
#SPJ7
Silvia wants to mix a 20% apple juice drink with pure apple juice to make 4 L of a juice drink that is 80% apple juice. How much pure apple juice should she use?
Answers
95141 1404 393
Answer:
3 liters
Step-by-step explanation:
There's a simple and effective "visual" way to solve mixture problems that makes short work of this.
In the attached, the concentrations of the contributors are listed on the left. It can work well to put the largest contributor on top (though that is not strictly necessary). The target concentration is put in the middle between them, and the differences along the diagonals are computed.
The diagonal differences are reduced to lowest terms as a ratio in the right-hand column. These numbers can be compared to the problem statement to see how they relate.
In this case, the total is 4 L of juice, and the total of the ratio units is 4. Then the ratio units are the number of liters of the corresponding contributor:
3 L of 100% juice1 L of 20% juiceLine r and m are parallel. Find the value of y.
Answers
Answer:
y=8
Step-by-step explanation:
the angle that is equal to 10x-3 and the angle that is equal to 7x+45 are equal to each other because they are corresponding angles so we setup an equation which would be
10x-3=7x+45
step 1
add 3 to each side
-3+3 = they cancel out
45+3=48
now we have
10x=7x+48
step 2
subtract each side by 7x
7x-7x cancels out
10x-7x=3x
3x=48
step 3
divide each side by 3
3/3 cancels out
48/3=16
so x =16
now we plug it into to 10x+3
10x16=160 160-3= 157
so the angle that is equal to 157 and the one that is equal to 3-y are supplementary angles so they will add up to equal 180 so to solve y we setup the equation which would be
180=157+3y-1
step 1 combine like terms
157-1=156
180=156+3y
step 2 subtract each side by 156
156-156 cancels out
180-156=24
so now we have
24=3y
next we divide each side by 3
3/3 cancels out
24/3=8
y=8
hope this makes sense :D
What happen when you multiply a number by it's reciprocal?
Answers
Answer:
When you multiply the number by its reciprocal the numerator of the one becomes the denominator of the other and is equals to 1 .
Please help ASAP please and thank you have a great and blessed day!
Answers
Answer:
I RLY HOPE THIS IS CORRECT WISH THE BEST OF LUCK
Answer:
12.08
Step-by-step explanation:
If you order these numbers from least to greatest, you would get...
12.08, 12.087, 12.7, 12.78, 12.807
The least second it took to complete the race is 12.08
hope you have a wonderful day too! <3
Daniel started a video game with 30 tokens. He earned 8 more tokens 0/10
for jumping on a star, but lost 6 tokens for falling into a hole. When he
passed a checkpoint, his number of tokens doubled! Then he spent20
tokens to buy a flashlight. Which expression shows how many tokens he
has left?
2x(30+8-6-20)
2x(30+8)-(20-6)
2x30+8-6-20
2x(30+8-6)-20
Answers
Answer:
2x(30+8-6)-20
Step-by-step explanation:
i need help with this
Answers
Answer:
12.5%
Step-by-step explanation:
Please help with this math question'
Answers
Answer:
h = 1296 feet
Step-by-step explanation:
Given that,
The vertical position of the object is :
[tex]h(t)=-16t^2+160t+896[/tex] .....(1)
We need to find the highest height reached by the object. For highest height,
Put dh/dt = 0
[tex]\dfrac{d}{dt}(-16t^2+160t+896)=0\\\\-32t+160\\\\t=\dfrac{160}{32}\\\\t=5\ s[/tex]
Put t = 5 in equation (1).
[tex]h(5)=-16(5)^2+160(5)+896\\\\=1296\ ft[/tex]
So, the height reached by the object is 1296 feet.
What is the domain and range as an inequality and if you could explain how you got it that would be great
Answers
Answer:
As per the graph, the function starts at point (0, -2) point it self not included.
The graph is extended down and right, so the given point is maximum of the function.
The domain:
x > 0 or x = (0, +∞)The range:
y < -2 or (- ∞, -2)Range
Set of y values
(-oo,-2)As -2 is not included (open dot)
Domain
Set of x values
(0,oo)0 is not included (open dot)
Milan is putting money into a savings account. He starts with $750 in the savings account, and each week he adds $70
Let "s" represent the total amount of money in the savings account (in dollars), and let "W" represent the number of weeks Mila
has been adding money. Write an equation (y = mx + b), relating "s" to "W". Then, use this equation to find the total amount of
money in the savings account after 12 weeks." (10 points)
Answers
Answer:
equation: s = 70W + 750
answer for 12 weeks: 1590
Step-by-step explanation:
You replace W with 12 to get the total amount per 12 weeks.
Write an expression for the following statement:
“Twice a number is subtracted from eighteen”
Answers
Answer:
Expression of the statement = 18 - 2x
Answer:
18 - 2x
Step-by-step explanation:
please very soon I offer the crown !!! + 10 points urgently !!!
Answers
Answer:
swdfghjkl;'[
Step-by-step explanation:
asdfghjkl;'iy7u6j54hy3feqdwsrtfyuiop;lkjhgf
Answer:
nbmmmmmmmmmmmmmmmmmm
Step-by-step explanation:
Trying to help my daughter can't figure this out.
The perimeter of a rectangle is 72 meters. The width of the rectangle is 4meters less than the length. Find the length and width of the rectangle. (use l for the length)
Answers
Answer:
width equals 16
length = 20
Step-by-step explanation:
Hello there!
we know that the perimeter is 72 m
and the width is 4 m less then the length
perimeter is 2w+2l
w=width and l = length
72 + (2x-4) = 72+8 = 80
80 / 4 (because there are 4 values, w, w, l, l ) = 20
so now...
20 - 4 = w
16 = w
and 20 = l
16+16 = 32
20+20 = 40
32+40 = 72
I need help please =)
Answers
Answer:
27
Step-by-step explanation:
111÷4=27.75
Hope this helps!
Answer:
27
Step-by-step explanation:
111/4 = 27
Many manufacturers have quality control programs that include inspection of incoming materials for defects. Suppose a computer manufacturer receives computer boards in lots of five. Two boards are selected from each lot for inspection. We can represent possible outcomes of the selection process by pairs. For example, the pair
(1, 2) represents the selection of boards 1 and 2 for inspection.
(a) List the ten different possible outcomes.
(b) Suppose that boards 1 and 2 are the only detective boards in a lot of five. Two boards are to be chosen at random. Define X to be the # of defective boards observed among those inspected. Find the pmf.
Answers
Answer:
a) S = {(1,2), (1,3), (1,4), (1,5), (2,3), (2,4), (2,5), (3,4), (3,5), (4,5)}
b) p(x) = 0.3 if x = 0
= 0.6 if x = 1
= 0.1 if x = 2
= 0 otherwise
Step-by-step explanation:
Given - Many manufacturers have quality control programs that include inspection of incoming materials for defects. Suppose a computer manufacturer receives computer boards in lots of five. Two boards are selected from each lot for inspection. We can represent possible outcomes of the selection process by pairs. For example, the pair (1, 2) represents the selection of boards 1 and 2 for inspection.
To find - (a) List the ten different possible outcomes.
(b) Suppose that boards 1 and 2 are the only detective boards in a lot of five. Two boards are to be chosen at random. Define X to be the # of defective boards observed among those inspected. Find the pmf.
Proof -
(a)
Given that there are 5 computer boards
Let,
The Boards are 1, 2, 3, ,4 and 5.
Now,
Total Number of possible ways of selecting 2 boards out of 5 by inspection = ⁵C₂ = [tex]\frac{51}{2! (5-2)!}[/tex] = [tex]\frac{5!}{2! 3!}[/tex] = [tex]\frac{5.4.3!}{2! 3!}[/tex] = [tex]\frac{5.4}{2.1}[/tex] = 10
And the choices be
Choice I -
Boards 1 and Board 2
Choice II -
Board 1 and Board 3
Choice III -
Board 1 and Board 4
Choice IV -
Board 1 and Board 5
Choice V -
Board 2 and Board 3
Choice VI -
Board 2 and Board 4
Choice VII -
Board 2 and Board 5
Choice VIII -
Board 3 and Board 4
Choice IX -
Board 3 and Board 5
Choice X -
Board 4 and Board 5
And
These outcomes becomes
S = {(1,2), (1,3), (1,4), (1,5), (2,3), (2,4), (2,5), (3,4), (3,5), (4,5)}
(b)
Given that, X be the number of defective boards
And there are only two defective boards (Board 1 and Board 2) in the lot
Therefore,
X can be 0, 1, and 2.
Now,
If X = 0
⇒ There is no defective boards
⇒ Possible outcomes be - { (3,4), (3,5), (4,5) }
So,
P(X=0) = [tex]\frac{3}{10}[/tex] = 0.3
Now,
If X = 1
⇒ There is one defective board
⇒ Possible outcomes be - { (1,3), (1,4), (1,5), (2,3), (2,4), (2,5) }
So,
P(X=1) = [tex]\frac{6}{10}[/tex] = 0.6
Now,
If X = 2
⇒ There is two defective boards
⇒ Possible outcomes be - { (1,2) }
So,
P(X=2) = [tex]\frac{1}{10}[/tex] = 0.1
And
P(x) = 0 if x ≠ 0, 1, 2
SO, The pmf be
p(x) = 0.3 if x = 0
= 0.6 if x = 1
= 0.1 if x = 2
= 0 otherwise
Shirts are on sale for $12 at a clothing store. How many shirts can you buy with $48?
Answers
Answer:
4 if no tax is included because 4 times 12 equals 48
hope this helps
Step-by-step explanation:
Answer:
4 shirts in total,
12x4=48
Step-by-step explanation:
Hope this helps!
Tell whether x and y show direct variation, inverse variation or - y/4 = 2x
Answers
9514 1404 393
Answer:
direct variation
Step-by-step explanation:
The given equation can be written in the direct variation form ...
y = kx
y = -8x . . . . rewrite of the given equation (multiply by -4)
This is an example of direct variation.
find the area of the trapezoid. if the answer is not an integer, leave it in simplest radical form, The figure is not to scale. (image included)
Answers
Answer:
420 ft^2
Step-by-step explanation:
[tex]h = \sqrt{25 ^{2} - 7 } [/tex]
[tex] = \sqrt{570} [/tex]
[tex] = 24[/tex]
[tex]a = \frac{1}{2} (b1 + b2)h[/tex]
[tex] = \frac{1}{2} (14 + 21)(24)[/tex]
[tex]answer = 420ft ^{2} [/tex]
Answer:
245 ft sq
Step-by-step explanation:
Find the are of the triangle and the square seperatly.
Area of a square is A = s * s
A = 14 * 14 = 196 ft sq
Focusing on the triangle, the dotted line is the same length as the bottom of the square. 14 ft
Area of a triangle is A = 1/2 * b * h
A = 1/2 * 14 * 7
A = 7 * 7
A = 49 ft sq
So, 196 + 49 = 245
c
Solve for m:
3/4m - 3 = 9
May I please have help!
Answers
Answer:
m=16
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 3/4*m-3-(9)=0
Step 1: Simplify 3/4
Equation at the end of step 1: ((3/4 x m) - 3) - 9 = 0
Step2: Subtracting a whole from a fraction
Rewrite the whole as a fraction using 4 as the denominator :
3 3 • 4
3 = — = —————
1 4
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
3m - (3 • 4) 3m - 12
—————4——————— = ———4————
When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
3•(m-16)
———————— • 4 = 0 • 4
4
Now, on the left hand side, the 4 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
3 • (m-16) = 0
6.2 Solve : 3 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solve : m-16 = 0
Add 16 to both sides of the equation :
m = 16