You are looking at the New York ball drop on New Year’s Eve at a distance of 100 m away from the base of the structure. If the ball drops at a constant rate of 2 m/s, what is the rate of change of the
angel between you and the ball when the angle is ( ?
Answers
The question is an illustration of related rates.
The rate of change between you and the ball is 0.01 rad per second
I added an attachment to illustrate the given parameters.
The representations on the attachment are:
[tex]\mathbf{x = 100\ m}[/tex]
[tex]\mathbf{\frac{dy}{dt} = 2\ ms^{-1}}[/tex] ---- the rate
[tex]\mathbf{\theta = \frac{\pi}{4}}[/tex]
First, we calculate the vertical distance (y) using tangent ratio
[tex]\mathbf{\tan(\theta) = \frac{y}{x}}[/tex]
Substitute 100 for x
[tex]\mathbf{y = 100\tan(\theta) }[/tex]
[tex]\mathbf{\tan(\theta) = \frac{y}{100}}[/tex]
Differentiate both sides with respect to time (t)
[tex]\mathbf{ \sec^2(\theta) \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot \frac{dy}{dt}}[/tex]
Substitute values for the rates and [tex]\mathbf{\theta }[/tex]
[tex]\mathbf{ \sec^2(\pi/4) \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot 2}[/tex]
This gives
[tex]\mathbf{ (\sqrt 2)^2 \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot 2}[/tex]
[tex]\mathbf{ 2 \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot 2}[/tex]
Divide both sides by 2
[tex]\mathbf{ \frac{d\theta}{dt} = \frac{1}{100} }[/tex]
[tex]\mathbf{ \frac{d\theta}{dt} = 0.01 }[/tex]
Hence, the rate of change between you and the ball is 0.01 rad per second
Read more about related rates at:
https://brainly.com/question/16981791
Related Questions
What is the result when the number 40 is decreased by 50%
Answers
Answer:
20
Step-by-step explanation:
40 x 50% = 20
So 50% of 40 equals to 20. Now, since it says decreased by 50%, we have to subtract 20 from 40 because we already know that 20 is the 50%. So 40 - 20 gives you 20.
The length of a rectangle is six times its width.
If the perimeter of the rectangle is 70 cm, find its length and width.
Answers
Answer:
Length = 30
Width = 5
Step-by-step explanation:
So the formula for perimeter is
P = 2L+2W
And we know that:
L = 6W
So then we put in all the information that we do know
70 = 2(6W)+2W
And pop that into a calculator and you get W=5
So now we put that information into L = 6W to get:
L = 6×5
L = 30
Jamie saw 12 ducks on the lake. When Jamie said that 1/2 of the ducks swam away, how many ducks was that?
a) 8
b) 4
c)6
Answers
12 divided my 2 is 6
or 6 + 6 is 12.
Hope this helps
If a rhombus is inside a regular hexagon, what is the size of x
Answers
Answer: x = 60°
Step-by-step explanation:
The rest of the question is the attached figure.
Given: A rhombus inside a regular hexagon, work out the angle x.
As shown
ABCDEF is a regular hexagon.
The regular hexagon have 6 congruent angles, and the sum of the interior angles is 720°
So, the measure of one angle of the regular hexagon = 720/6 = 120°
So, ∠F = ∠BAF = 120°
AFEG is a rhombus.
The rhombus have 2 obtuse angles and 2 acute angles.
∠F is one of the obtuse angles of the rhombus = 120°
∠F and ∠FA G are supplementary angles
So, ∠F + ∠FA G = 180°
∴ ∠FA G = 180° - ∠F = 180 - 120 = 60°
∴ x = ∠GAB = ∠BAF - ∠FA G = 120 - 60 = 60°
So, the measure of the angle x = 60°
I need to finish this question very quickly and I’m confused, any help is greatly appreciated
Answers
Answer:
Step-by-step explanation:
a. sqrt(2x) = -x
b. (sqrt(2x))^2 = (-x)^2
2x = x^2
c. divide both sides by x. x = 2, 0
d. x = 2 does not satisfy the original equation, but x = 0 does.
Mr. Chu's cherry tree grew 12 inches in
3
4
of a year. At that rate, how much would it grow in 1 year?
Answers
Answer:
16 inches after one year
Step-by-step explanation:
in 3/4 a year tree grew 12 inches
divide by 3
multiply by 4
16 inches
If You Have 6 People At A Party And In Total You Have 18 Slices Of Pizza, How Much Dose Each Person Get?
Answers
Answer:
3 slices of pizza.
Step-by-step explanation:18/6=3
Find the 70th term of the arithmetic sequence 29, 17, 5, ...29,17,5,...
Answers
hijab day of doing a great day of doing a little bit more about the way for me the ch-2 ex is a very good time to be able to get the day of doing a great day when mother speaks it happens to be a good time to be a good time to be a good day please anyone who is in the day and in the way for me the way
find the value of k so that the two given lines are parallel. -5x+kx=4 2y-9x=11
Answers
The value of k so that the two given lines are parallel is; k = 22.5
First, the correct question is;
-5y+ kx = 4 and 2y-9x=11In line segment geometry;
The slopes of two or more parallel lines are equalFirst, we must determine the slope of the lines by rewriting the equations to resemble the equation of a line in the slope-intercept form; y = mx + c
Therefore, we have;
y = (k/5)x - 4/5.................eqn(1)and y = (9/2)x + 11/2....,........eqn(2)Evidently, the slope of the line in equation 2 is; 9/2.
And since the slope of parallel lines are equal;
k/5 = 9/2By cross product;
2k = 45k = 22.5
Read more:
https://brainly.com/question/12557573
Need help ASAP! Directions in picture;)
Answers
Answer:
[tex]x=61[/tex]
Step-by-step explanation:
We can find the angle directly above the [tex]2x+8[/tex].
We know that because they both lie on a straight line, the other angle is [tex]180-(2x+8)=172-2x[/tex].
Aha! We have a path to the solution!
[tex]172-2x=x-11[/tex] because of the parallel line angle theorem(I forget what it's called).
We then add [tex]2x[/tex] and [tex]11[/tex] to both sides to get [tex]183=3x[/tex].
Lastly, we divide by [tex]3[/tex] to get [tex]61=x[/tex].
So, [tex]\boxed{x=61}[/tex] and we're done!
You roll a number cube find the probability. P(3 or 4)
Answers
P(3 or 4) = 2\6 = 1/3 (ans)
What is 1 minus 1 divided by 5
Answers
Answer:
0.8Step-by-step explanation:
Remember PEMDAS
1-1:5=
1-0.2=
0.8
I need help pleaseee
Answers
Answer:
The hundred thousands place
Step-by-step explanation:
A train travels 170 miles in 4 hours. The train is traveling at a constant rate of speed. How many miles per hour does the train travel?
Record your answer. Be sure to use the correct place value.
Answers
Answer:
42.5 mph
Step-by-step explanation:
170 miles/4 hours= 42.5 mph
Your Welcome!
Kayden Kohl
8th Grade Student
Answer:
42.5
Step-by-step explanation:
170 divided by 4
42.5 miles per hour
The perimeters of the
square and the rectangle
below are the same. Write
and solve an equation to find
the value of x.
Answers
Answer:
[tex]x = 5[/tex]
Step-by-step explanation:
Find the side length of the square. The formula is for area is
[tex]a = {s}^{2} [/tex]
So take the square root to find the side length.
[tex] \sqrt{121} = \sqrt{ {s}^{2} } [/tex]
[tex]s = 11[/tex]
Now find the perimeter of the square.
[tex]11 \times 4 = 44[/tex]
setup the equation to solve for x. The left side is the perimeter of the rectangle and the right is the perimeter of the square.
[tex]3x + 3x + x - 2 + x - 2 = 44[/tex]
Collect like terms
[tex]8x - 4 = 44[/tex]
subtract 4 from both side
[tex]8x = 40[/tex]
divide both side by 8
[tex]x = 5[/tex]
What happens to the x and y coordinates in a 90-degree counterclockwise rotation?
Answers
Answer: hope this helps i didnt see any A, B, C, D etc options to choose from
each point of the given figure has to be changed from (x, y) to (-y, x)
Step-by-step explanation:
When we rotate a figure of 90 degrees counterclockwise, each point of the given figure has to be changed from (x, y) to (-y, x) and graph the rotated figure.
Example 1 :
Let F (-4, -2), G (-2, -2) and H (-3, 1) be the three vertices of a triangle. If this triangle is rotated 90° counterclockwise, find the vertices of the rotated figure and graph.
Solution :
Step 1 :
Here, triangle is rotated 90° counterclockwise. So the rule that we have to apply here is
(x, y) -------> (-y, x)
Step 2 :
Based on the rule given in step 1, we have to find the vertices of the rotated figure.
Step 3 :
(x , y) -----> (-y , x)
F(-4 , -2) -------> F'(2, -4)
G(-2, -2) -------> G'(2, -2)
H (-3, 1) -------> H'(-1, -3)
Step 4 :
Vertices of the rotated figure are
F'(2, -4), G'(2, -2) and H'(-1, -3)
Can someone PLEASE HELP ME ITS TRANSLATIONS PLEASEEEE
Answers
Answer:
What connects to what.
Step-by-step explanation:
"Vertices is the plural of the word vertex, which is the point at which two or more lines/edges meet. " QRS is like "1,2,3. " Not sure if this is what you mean??
5. I bought a $55 swimsuit, a $15 hat, and a $40 pair of shoes. I used a coupon that gave me 40% off my total bill. How much did | spend?
quickk pls
Answers
Answer:66 dollars
Step-by-step explanation:110 - 44 = 66
A REALITY OF RATIONAL ALGEBRAIC EXPRESSIONS
Answers
Rational equations can be used to solve a variety of problems that involve rates, times and work. Using rational expressions and equations can help you answer questions about how to combine workers or machines to complete a job on schedule.
Determine whether each expression is a monomial. Write yes or no. Explain your reasoning. 1. 21/27 2. 32/
Answers
Answer:
1. Yes and for 2. I don't know
Step-by-step explanation:
1. is a monomial because 21/27 is one group
Tom is deciding whether or not he should become a member gym to use their basketball courts. The membership cost is $135. Members pay $2 to rent out the basketball courts. Non-members can rent the court also, but they have to pay $11 each time. how many times would Tom need to rent the court in order for it be cheaper to be a member than a non member?
Answers
Answer:
16 times
Step-by-step explanation:
Membership cost:
C = 135 + 2x
Non-members:
C = 11x
____
135 + 2x = 11x
135 = 9x
x = 15
The cost would be the same after renting 15 times, so after 16 times the cost would be cheaper for a member.
Can I get help on 1,2 and 5?
Answers
Answer:
Question 1: [tex]x=4[/tex]
Question 2: [tex]x= \pm7[/tex]
Question 5: The dimensions of one face of the container are 6 by 6 inches.
Step-by-step explanation:
Hi there!
Question 1
[tex]x^3=64[/tex]
Rewrite 64 as a power of 3:
[tex]x^3=4^3[/tex]
(We could find that 4³ = 64 through trial and error)
This above equation makes it true that x=4. If aⁿ = bⁿ, then a=b:
[tex]x=4[/tex]
Question 2
[tex]x^2=49[/tex]
Rewrite 49 as a power of 2:
[tex]x^2=7^2[/tex]
Again, we could have found this through trial and error, or by looking at our multiplication tables.
[tex]x=7[/tex]
However, remember that positive and negative numbers will all square to be a positive number. So, therefore, x can be -7 OR 7 (since both, when squared, equal 49):
[tex]x= \pm7[/tex]
Question 5
Let x be equal to the length of one edge of the cube.
Volume of a cube formula: [tex]V=x^3[/tex]
Plug in the given information, when V is the volume:
[tex]216=x^3[/tex]
Rewrite 216 as a power of 3:
[tex]6^3=x^3[/tex]
^ We could have found this through trial and error.
[tex]x=6[/tex]
Therefore, the dimensions of one face of the container are 6 by 6 inches.
I hope this helps!
Given the following formula, with A = 27 and t = 3, solve for r.
Answers
Answer:
b
Step-by-step explanation:
can anyone explain this to me?
Answers
Answer:
The missing side would be 6.
And the area would be 54.
Step-by-step explanation:
The perimeter equals 30, that's the outside of the rectangle. They give you a part of the perimeter, 9ft. So 9ft and there's another 9ft on the bottom line, (because it is equal to the top width) Which equals 18. To get the other sides you need to subtract 18 from the whole perimeter, 30. Which gives you 12. And there's two sides left, so divide by 2, and you have 6 on each side(left and right sides) Perimeter is adding all the sides up.
And the Area formula is Area=Length times Width. Area=9ft×6ft Which equals 54.
Pls explain
Pls and thank
Answers
Step-by-step explanation:
A=l×w
A=3 3/4×1 1/2
A=5.625
Omggg pls help me with this question pls pls pls!!!!!!
Answers
Answer:
A
Step-by-step explanation:
A. is the answer I'm sure
8x2 – 24 = ?
Choose 1 answer:
A 8(22 – 3)
B.
8x (x2 – 3)
8(x – 3)
8x(x – 3)
Answers
8x² - 24 = 8 (x² - 3)
Write the equation of the line that is perpendicular to y = -5x + 1 and passes through the point (2,-1). slope intercept equation please help
Answers
Answer:
[tex]y = \frac{1}{5} x - \frac{7}{5} [/tex]
Step-by-step explanation:
Look at graph above⤴⤴⤴
Hope this helps :)
Which list shows the values of the changes in order, from least to greatest?Stock A, Stock B, Stock C, Stock DStock B, Stock D, Stock A, Stock CStock C, Stock A, Stock D, Stock BStock D, Stock C, Stock B, Stock A
Answers
Answer:
c
Step-by-step explanation:
edge 2022
Pls help what is 46743356644 x 5545445555
Answers
Answer: 52.288.802.199
