A boat sails directly toward a 250-m skyscraper that stands on the
edge of a harbor. The angular size of the building is the angle
formed by lines from the top and bottom of the building to the
observer (see figure). Complete parts (a) and (b) below.
Answers
a) The value of [tex]\theta[/tex] as a function of "x" is [tex]\theta = tan^{-1}\frac{250}{x}[/tex]
b) The rate of change of the angle with respect to x is -0.000308rad/m
Find the complete question and diagram attached
Form the right-angled triangle shown:
Adjacent side = x
Opposite side = 250m
angle of elevation = [tex]\theta[/tex]
Using the SOH CAH TOA identity
[tex]tan\theta = \frac{opposite}{hypotenuse} \\tan \theta = \frac{250}{x} \\\theta = tan^{-1}\frac{250}{x}[/tex]
Hence the value of [tex]\theta[/tex] as a function of "x" is [tex]\theta = tan^{-1}\frac{250}{x}[/tex]
b) If x = 450m
[tex]\theta = tan^{-1}\frac{250}{x}\\tan \theta = \frac{250}{x}\\[/tex]
Differentiate both sides with respect to "x"
[tex]sec^2 \theta \frac{d\theta}{dx} = \frac{-250}{x^2} \\ \frac{d\theta}{dx} = \frac{1}{sec^2\theta} \times \frac{-250}{x^2}[/tex]
Substitute x = 450m and [tex]\theta = 60^0[/tex] into the resulting expression to have:
[tex]\frac{d\theta}{dx} = \frac{1}{sec^260^0} \times \frac{-250}{450^2}\\\frac{d\theta}{dx} = (cos60)^2\times \frac{-250}{202,500}\\\frac{d\theta}{dx} = 0.5^2\times \frac{-250}{202,500}\\\frac{d\theta}{dx} =-0.000308[/tex]
Hence the rate of change of the angle with respect to x is -0.000308rad/m
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Related Questions
What did you learn in this lesson about the value of leaving the money invested for long periods of time? How can you apply this to retirement?
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Answer:
65435675e
Step-by-step explanation:
12456764 br5654365
3. Simplify the expression (x3 - 5x2 + 7x - 12) = (x – 4) using long division. Show your work.
Answer:
Answers
Answer:
x^2-x+3
Step-by-step explanation:
(x^3-5x^2+7x-12)÷(x-4)
x^3−5x^2+7x−12
Factors of 12,
1,2,3,4,6,12
Substitute 4 into x. Since the result is 0, x-4 is a factor..
4^3−5×4^2+7×4−12=0
x-4
x^2 -x 3
x-4 | x^3 -5x^2 7x -12
x^3 -4x
-x^2 7x -12
-x^2 4x
3x -12
3x -12
x^2−x+3
(x^2−x+3)(x−4)
x−4
(x^2−x+3)
Answer = x^2-x+3
Hopes this helps
The center of the circle whose equation is (x + 2)² + (y - 3)² = 25 is
Answers
Answer:
The center of the circle is at: C=(−2,3).
The radius of the circle is r=5.
Step-by-step explanation:
A circle with center at (h,k) and a radius of r has equation (x−h)2+(y−k)2=r2.
In this example our circle equation can be written as:
(x−(−2))2+(y−3)2=(5)2
So, we have: h=−2 , k=3 and r=5.
kia worked 30 hours and 15 minutes this weekend . if she makes $15.60 per hours ,how much did she make?
Answers
30 x 15.60 = 468 (total full hours x amount per hour)
60 / 15 = 1/4 (60 minutes per hour divided by the 15 minutes they worked = amount of the hour)
15.60 x 1/4 = 3.9 (amount for the 15 minutes worked)
468 + 3.9 = 471.9 (total full hours + 15 minutes total)
Answer:
$471.90 dollars
Step-by-step explanation:
First, we need to find out how many hours she's working.
There are 60 minutes in an hour so 15/60 is 0.25.
Thus, adding that to the 30 hours gives us 30.25.
If she makes $15.60 per hour we just multiply that by 30.25 hours and get the answer.
[tex]\frac{15.60}{hour}*30.25 hours = 471.9\\[/tex]
The [tex]\frac{}{hour}[/tex] comes from the wording of per hour, and since the unit is in the denominator, when we multiply it by the 30.25 hours, the units cancel out. Thus all we are left with is the amount of dollars made, which is $471.90.
Given that lines a and b are parallel:
If m48 = (-x + 13), and
= +
m42 = (9x - 27),
Answers
Answer:
[tex]x= 9m+69 ,m 48 =− 9m + 316[/tex]
Consider the following two loans for P=$12,000.
Loan A: 5 year loan, annual interest rate of 5%.
Loan B: 3 year loan, annual interest rate of 8%.
Answers
Answer:
Simple interest-?
Step-by-step explanation:
P= 12000
T=5yrs
R=5%
Now,
Simple interest - PTR/100
= 12000*5*5/100
= $3000
Again,
P=12000
T=3yrs
R=8%
Now,
Simple interest - PTR/100
= 12000*3*8/100
= $2880
Hope this helps.
The table lists recommended amounts of food to order for 25 party guests. and are hosting a graduation party for 40 guests. They know there will also be guests stopping by who may have come from other parties. For ordering purposes, they will count each of these 45 "drop-in" guests as half a guest. How much of each food item should and order for a graduation party with drop-in guests?
Answers
Answer:
667
Step-by-step explanation:
Answer:
It will be
1. 3
2.2
3.5
Step-by-step explanation:
HOpe this helps!
The degree of the polynomial function f(x) is 4.The roots of the equation f(x)=0 are −6, −2, 1, and 3.Which graph could be the graph of f(x)?
Answers
Slope of -3 passes through the point (2,1)
Answers
Answer:
Linked the work I did on a scientific calculator :)
( How to write it as an equation )
Step-by-step explanation:
Austin and his wife go out to dinner. Their bill is $59.36. They want to leave a 19%
tip, and there is a sales tax of 5.5%. What is the final amount they will pay?
$62.62
$73.90
$74.49
$70.64
Answers
Answer:
The final amount they will pay is $74.49
Step-by-step explanation:
59.36(Check)*0.19(19% tip rate)=11.27
59.36+11.27=70.62 Check+Tip
70.62(Check total)*0.055(5.5% tax)=3.87
70.62+3.87=74.49 Total check, tip & tax
what is square root of 50
Answers
Answer:
7.071067811865475
Step-by-step explanation:
Customer account “numbers” for a certain company consists of 2 letters followed by 2 single-digit numbers. How many different account numbers are possible if repetition of letters and digits are allowed?
Answers
Answer:
67600Step-by-step explanation:
Let the format be:
LLDD- where L stands for letter and D- digitFor each L we have 26 (English alphabet) and for each D we have 10 options.
Number of possible accounts:
26*26*10*10 = 67600(20 Points) What is the value of x?
Answers
heeelllllllllpppppppp meeeeee
Answers
Answer:
32
Step-by-step explanation:
36-4
Use Pythagorean theorem
Answer:
B=4
Step-by-step explanation:
The bearing of point Y from point X is 070°.
The bearing of point Z from point Y is 145°.
The bearing of point Z from point X is 100°.
Find the bearing of point X from point Z.
Answers
Answer:
i cant understand sorry
You deposit $200 in a savings
account that pays a simple
interest rate of 3.25% per year.
How much interest will you earn
after 5 years?
Answers
Answer:
$16.25
Step-by-step explanation:
First, you have to find 3.25*5 which is 16.25.
16.25 is the percent rate of your total interest over the course of 5 years.
In other words, you have to do 200*0.1625 which is 32.5.
So, your answer is $16.25.
Good luck!
Paloma decided to divide 1,292 by 31 using partial quotients. She uses 30 as her first partial quotient. Which are the partial quotients Paloma should show in her work
A 20, 10
B 30, 10,1
C 10,10,10,1
D 10,10,10,10,1
Answers
What is the radius of a hemisphere with a volume of 94 m", to the nearest tenth of a
meter?
Answers
Answer:
3.553774
Step-by-step explanation:
[tex] \frac{2}{3} \pi {r}^{3} = 94[/tex]
h
works out to 3.553774
The radius of the hemisphere with a volume of 94 m³ is :
r = [tex]$\sqrt[3]{\frac{141}{\pi } }[/tex]
What is a hemisphere? What is a mathematical function, equation and expression? hemisphere : a hemisphere is half of a sphere.function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is hemisphere with a volume of 94 m³.
The volume of sphere is : V{S} = (4/3)πr³.So, the volume of hemisphere will be : V{S}/2 = V{H} = (2/3)πr³.So, we can write as :(2/3)πr³ = 94
πr³ = (94 x 3/2)
πr³ = 47 x 3
πr³ = 141
r³ = (141/π)
r = [tex]$\sqrt[3]{\frac{141}{\pi } }[/tex]
Therefore, the radius of the hemisphere with a volume of 94 m³ is :
r = [tex]$\sqrt[3]{\frac{141}{\pi } }[/tex]
To solve more questions on hemispheres, visit the link below -
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1) Eight times the difference between a number and seven, is the same as when five times
the number is increased by four. Find the number.
Answers
Tip: Go step-by-step
Let the number = x
Eight times the difference between a number and seven.. = 8(x-7)
is the same as... =
the number increased by 4.. x+4
8(x-7)=x+4
Distribute
8x-56=x+4
Subtract x from both sides
7x-56=4
Add 56 to both sides
7x=60
x=60/7
I NEED A 100% ACCURATE ANSWER FOR THIS QUESTION ASAP NO LINKS !!!
Answers
Answer:
w= 8/7
Step-by-step explanation:
1. divide the numbers
[tex]12w-1*10=6-2w[/tex]
2. multiply the numbers
[tex]12-10=6-2w[/tex]
3. rearrange terms
[tex]12-10=-2w+6[/tex]
4. add 10 to both sides of the equation
[tex]12w-10+1-=-2w+6+10[/tex]
5. simplify
[tex]12w=-2w+16[/tex]
6. add 2w to both sides of the equation
[tex]12w+2w=-2w+16+2w[/tex]
7. simplify
[tex]14w=16[/tex]
8.divide both sides of the equation by the same term
14w/14 = 16/14
9. simplify
w = 8/7
Answer:
[tex]w = 2[/tex]
Step-by-step explanation:
[tex] \frac{(12w - 20)}{2} = 6 - 2w[/tex]
[tex]6w + \frac{ - 20}{2} = 6 - 2w[/tex]
[tex]6w + \frac{( - 10.2)}{(1.2)} = 6 - 2w[/tex]
[tex]6w + 10 = 6 - 2w[/tex]
[tex]6w - 10 + 2w = 6 - 2w + 2w[/tex]
[tex]6w + 2w - 10 = 6 - 2w + 2w[/tex]
[tex]8w - 10 = 6 - 2w + 2w[/tex]
[tex]8w - 10 = - 2w + 2w + 6[/tex]
[tex]8w - 10 = 6[/tex]
[tex]8w - 10 + 10 = 6 + 10[/tex]
[tex]8w = 6 + 10[/tex]
[tex]8w = 16[/tex]
[tex] \frac{8w}{8} = \frac{16}{8} [/tex]
[tex]w = \frac{16}{8} [/tex]
[tex]w = \frac{2.8}{1.8} [/tex]
[tex]w = 2[/tex]
[tex]Thank \: you!!![/tex]
PLEASE HELP ME WITH THIS!!!
Answers
Answer:
6. Bobby makes more money than John
Step-by-step explanation:
John's profits
(4.2 × [tex]10^{5}[/tex]) + (3.2 × [tex]10^{6}[/tex])
= 36.2 x 10^5
= 3.62 x 10^6
Bobby's profits:
323659000 = 3.23659 x 10^8
3.23659 x 10^8 > 3.62 x 10^6
John and Jill collect 280 stamps. Out of this John collected three time as many as
Jill. How many stamps did Jill collected?
Answers
Answer:
Jill collected 70 Stamps
John collected 210 Stamps
Step-by-step explanation:
280/4=70
Please allow me to know if my answer helped you with a thank you!
<3Miss Hawaii
Ajar contains 3 red and 5 green balls identical in all aspects except color. If two balls are drawn at random, then the probability that the two balls drawn are not green is
Answers
Answer:
3/28.
Step-by-step explanation:
Total of 8 balls in the jar.
Prob (first one not green (= that its red) = 3/8
Prob ( Second one is also red) = 2/7.
So probability that both are not green = 3/8 * 2/7
= 6/56
= 3/28.
Helpppp plzzzzzzzzzzzzz
Answers
Answer:
x=90 possibly
Step-by-step explanation:
3x all at 30 degrees. but not posative so please check elsewhere.
Determine the domain and the range of the function.
f = {(4, 8),(19,-3),(33, 8),(54,3)}
The domain is {}.
Answers
Answer:
By definition: domain is set of x coordinates = {4, 19, 33, 54}, By definition: range is set of y coordinates = {8, -3, 8, 3} = {8, -3, 3}
Step-by-step explanation:
6) Find the equation of a line that is parallel to y = 2x + 3 and passes through (-1,-1).
A) y = 2x + 1
B) y = 2x + 3
C) y = 4x + 3
D) y = 4x + 5
Answers
Answer:
A Y=2X + 1
Step-by-step explanation:
2x wouldn't the same because of the fact that is Is a parallel line and setting the slope to 1 caused it to pass through (-1,-1)
It is well known that Yan Limeng can be called "beauty" in Asian aesthetics, but why I call it "Sleeping Beauty" is because she slept a lot of Americans, so she called it "Sleeping Beauty"."Sleeping Beauty" Yan Limeng
Answers
Answer:
It is well known that Yan Limeng can be called "beauty" in Asian aesthetics, but why I call it "Sleeping Beauty" is because she slept a lot of Americans, so she called it "Sleeping Beauty".
Step-by-step explanation:
It is well known that Yan Limeng can be called "beauty" in Asian aesthetics, but why I call it "Sleeping Beauty" is because she slept a lot of Americans, so she called it "Sleeping Beauty".
help pls!!
#420hehsh
Answers
Answer:
It's gonna be probably A
Z=8-i ^ w=12+3i, entonces ZxW, es:
a) 99-12i
b)93+12i
c)99+12i
d)93-12i
Necesito ayuda urgente!!
Answers
Answer:
21
Step-by-step explanation:
what is the LCD of 5/7, 1/6, and 11/12
Answers
Answer:
celluar resperation
Step-by-step explanation: