1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lutik1710 [3]
2 years ago
8

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 b

all 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 ( ?
Mathematics
1 answer:
Fofino [41]2 years ago
8 0

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:

\mathbf{x = 100\ m}

\mathbf{\frac{dy}{dt} = 2\ ms^{-1}} ---- the rate

\mathbf{\theta = \frac{\pi}{4}}

First, we calculate the vertical distance (y) using tangent ratio

\mathbf{\tan(\theta) = \frac{y}{x}}

Substitute 100 for x

\mathbf{y = 100\tan(\theta) }

\mathbf{\tan(\theta) = \frac{y}{100}}

Differentiate both sides with respect to time (t)

\mathbf{ \sec^2(\theta) \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot \frac{dy}{dt}}

Substitute values for the rates and \mathbf{\theta }

\mathbf{ \sec^2(\pi/4) \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot 2}

This gives

\mathbf{ (\sqrt 2)^2 \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot 2}

\mathbf{ 2 \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot 2}

Divide both sides by 2

\mathbf{ \frac{d\theta}{dt} = \frac{1}{100} }

\mathbf{ \frac{d\theta}{dt} = 0.01 }

Hence, the rate of change between you and the ball is 0.01 rad per second

Read more about related rates at:

brainly.com/question/16981791

You might be interested in
Yall are doing great thanks sm for the help
blondinia [14]

Answer:

That is an obtuse isosceles

4 0
3 years ago
If p(q) = q^2 4q- 12 then what is p(-1)
guapka [62]

Answer:

\bold{p(q) = q^2 4q- 12 }  \\  \bold{p( - 1) =  {( - 1)}^{2} \times 4 \times ( - 1) - 12} \\  = \bold {1 \times ( - 4) - 12} \\  \bold{  = ( - 4) - 12} \\  \bold{ p( - 1)=  - 16}

5 0
2 years ago
Read 2 more answers
The first row I️n the auditorium has 42 seats.each row after the first has 3 more seats than the row before I️t
grandymaker [24]
A. 117 seats
B. row 16
4 0
3 years ago
Read 2 more answers
Find the coordinates of the point three tenths<br><br> of the way from A(-4, -8) to B(11, 7)
Leviafan [203]

let's first off take a peek at those values.

let's say the point with those coordinates is point C, so C is 3/10 of the way from A to B.

meaning, we take the segment AB and cut it in 10 equal pieces, AC takes 3 pieces, and CB takes 7 pieces, namely AC and CB are at a 3:7 ratio.


\bf ~~~~~~~~~~~~\textit{internal division of a line segment}&#10;\\\\\\&#10;A(-4,-8)\qquad B(11,7)\qquad&#10;\qquad \stackrel{\textit{ratio from A to B}}{3:7}&#10;\\\\\\&#10;\cfrac{A\underline{C}}{\underline{C} B} = \cfrac{3}{7}\implies \cfrac{A}{B} = \cfrac{3}{7}\implies 7A=3B\implies 7(-4,-8)=3(11,7)\\\\[-0.35em]&#10;~\dotfill\\\\&#10;C=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em]&#10;~\dotfill


\bf C=\left(\cfrac{(7\cdot -4)+(3\cdot 11)}{3+7}\quad ,\quad \cfrac{(7\cdot -8)+(3\cdot 7)}{3+7}\right)&#10;\\\\\\&#10;C=\left( \cfrac{-28+33}{10}~~,~~\cfrac{-56+21}{10} \right)\implies C=\left( \cfrac{5}{10}~~,~~\cfrac{-35}{10} \right)&#10;\\\\[-0.35em]&#10;\rule{34em}{0.25pt}\\\\&#10;~\hfill C=\left( \frac{1}{2}~,~-\frac{7}{2} \right)~\hfill

4 0
3 years ago
There are 10 dogs and 4 leave.What is the percent change?<br><br> But can you explain it to me plzz
Vera_Pavlovna [14]

Answer:

the percent change would be 40 percent

Step-by-step explanation:

think of 10 as a base so like 100 ok and you know if 50 of that is 50 percent 40 would just be forty percent

8 0
3 years ago
Read 2 more answers
Other questions:
  • Josh has a savings account at a bank that charges a $10 fee for every month his balance falls below $1,000. What will his balanc
    6·1 answer
  • Evaluate X + Y when X = 13.1 and Y = 2.2<br> A. 10.9<br> B. -10.9<br> C. 35.1<br> D. 15.3
    15·1 answer
  • Given the following two points calculate the rate of change: (3,10) (7,10)
    8·1 answer
  • PLEASE help! this is so difficult! i literally cannot solve it to save my effing life.
    7·1 answer
  • Please help with last 2 domain and range
    7·1 answer
  • Help please if you can
    9·1 answer
  • I NEED HELP WITH THIS QUESTION ASAP
    11·1 answer
  • 9 - 0.5x = 15 <br> solve for x and show your work.
    13·2 answers
  • I put a picture of the question but I am confused on how to find the value of x.If you could provide a explanation that would be
    8·2 answers
  • A dairy needs 365 gallons of milk containing 7% butterfat. How many gallons each of milk containing 9% butterfat and milk contai
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!