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 ( ?
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
a. Describe the three ways in which two lines may be related
a. Which of the following is the correct way to relate two lines? Select all that apply.
A. congruent
B. skew
C. parallel
D. intersecting
E. collinear
NEED HELP! John wrote the numbers 678,901 and 67,890. How many times greater is the value of 7 in 678,901 than the value of 7 in 67,890?A. 10,000B. 1,000C. 100D. 10
Which of the following describes distributive property? *
12 + 10 = 22
12 + 10 = 10 + 12
5( 7 + 4) = 35 + 20
5( 7 + 4) = 35 + 5
deu ruim aqui pq eu não sei
Step-by-step explanation:
Alex and 3 of his friends are playing in a class math competition. Each player can score up to 10 points per round. Choose the equation or inequality to represent the number of points Alex’s team scores in one round.
A. p = 40
B. p = 30
C. p ≤ 40
D. p ≤ 30
E. p ≥ 40
F. p ≥ 30
A.p:40 his friends alex
Answer:
the answer is p<40
Step-by-step explanation:
(: ur welcome
What is the result of subtracting the second equation from the first? 5x-y=6 and -2x+y=8
Answer:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Point Form:
(2,−4)
Equation Form: x= 2, y = −4
Step-by-step explanation:
I did the math
can somebody answer this? thankyu
Answer:
1. 3, 12, 48, 192, 768 Ratio: x4
2. 8, 16, 32, 64, 128 Ratio: x2
3. 120, 60, 30, 15, 7.5 Ratio: ÷2
4. 5, 10, 20, 40, 80, 160 Ratio: x2
5. 1.3?, 4, 12, 36, 108, 324 Ratio: x3
Hope this helps!
I'm not sure about the first one on question 5 though.
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?
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.
PLEASE ANSWER SO I DON’T FAIL THIS
Copy Z DEF to the line so that S is the
vertex.
This task will be complete when you have
constructed an angle with vertex S that is
congruent to ZDEF..
Val started watching a live video on social media. The equation Y + 20 = 120(X + 1) represents Y, the total number of people watching the video as a function of X, the number of minutes since Val started watching.
A - List the slope and what it represents.
B - Write the equation in slope-intercept form.
C - How many people were watching the video when Val started watching? how do you know?
Help asap
Answer:
y = 120x + 100
x = y/120 - 5/6
Step-by-step explanation:
(sec^2 - 1) (cse^2 -1) Show work please
what do you want us to do because we can
-solve for S
-solve for E
-solve for C
-multiply them together
-find the intercepts of any
-turn any into others
-more
If you invest $7,000 for 5 years, and you earn 4% interest, how much interest overall
will you earn, assuming the interest is NOT compounding? (Hint: I=PRT)
Show your answer as a whole number (no decimals).
The interest earned in five years is $1400.
What is simple interest?
Simple interest is interest calculated on the principal portion of a loan or the original contribution to a saving account.
Formula for simple interestA = P(1 + rt)
Where,
A is the final amount
P is the initial principal balance
r is the annual interest rate
t is time(in years)
According to the given question
We have
Initial Principal balance, P = $7000
Time, t = 5years
Annual interest rate, r = 4% = 0.04
Therefore, the amount in five years is given by
A = 7000(1 + 0.04(5))
A = 7000(1 + 0.2)
A = 7000(1.2)
A = $8400
Now, the interest earned in five years
S.I = A - P
⇒ S.I = $8400 - $7000
⇒ S.I = $1400
Hence, the interest earned in five years is $1400.
Learn more about simple interest here:
https://brainly.com/question/17959107
#SPJ2
The Kitten Korner animal shelter buys cat food in 64-can crates. Each can holds 6 ounces of cat food. If the animal shelter orders 2 crates of cat food at a time, how many pounds of cat food are in each order?
Which division problem does the number line below best illustrate?
Answer: A
Step-by-step explanation:
x−5/8=2x−1 solve for x
Answer:
[tex] if \: \frac{x - 5}{8} = 2x - 1) \times 8 \\ x - 5 = 16x - 8 \\ 15x = 3 \\ x = \frac{15}{3} \\ \therefore \: x = 5 \\ if \: your \: quetion \: is \\ x - \frac{5}{8} = 2x - 1) \times 8 \\ 8x - 5 = 16x - 8 \\ 8x = 3 \\ x = \frac{3}{8} \\ try \: to \: use \: brackets \: next \: time[/tex]
what law would you use to simplify (2xy)^(2)
Answer:
(2xy)²
Step-by-step explanation:
please mark me as brainliest
The deer population is estimated to be 17,600 in northern
Illinois, but an actual count was 21,300. What is the percent
error?
The percentage error in the deer population is 17%
Actual population = 21300
Estimated population = 17600
The percentage error will be calculated by subtracting the estimated population from the actual population and then dividing the result. This will be:
= (Actual population - Estimated population) / Actual population × 100
= (21300 - 17600) / 21300 × 100
= 3700/21300 × 100
= 0.17 × 100
= 17%
Therefore, the percentage error in the deer population is 17%
Read related link on:
https://brainly.com/question/24988697
What is the reason for each step in the solution of the equation?
12−5x+6x=4
Drag and drop the reasons into the boxes to correctly complete the table.
12−5x+6x=4
12+x=4
x=−8
The correct reason for each step in the solution of the equation would be as follows:
12 − 5x + 6x = 4 - Given
12 + x = 4 - Combine Like Terms
x= −8 - Subtraction Property of Equality
Hope this answers the question. Have a nice day.
Need help with math question. Please. I’ll give 5 stars
Answer:
The domain is -11 < x < 4 or in interval notation it is (-11, 4).
Step-by-step explanation:
The domain is the set of possible values of x.
Here the open circles at each end mean that these values are not included.
In 2012 Joe had $ 104
in his bank account. BY
2017 he had $889 in his
account. Determine
the annual rate of
change.
Answer:
$157Step-by-step explanation:
The amount of change is:
889 - 104 = 785The time difference in years:
2017 - 2012 = 5The annual rate of change is the ratio of the difference in amount to the time difference:
785/5 = 157
Paula orders 3.75 pounds of
macaroni salad and 2.25
pounds of coleslaw. How
many more pounds of
macaroni salad does she
have than coleslaw?
Answer:
1.5 pounds more.
Step-by-step explanation:
3.75 - 2.25
= 1.50.
Answer:
1.50 pounds
Step-by-step explanation:
Paula orders a macaroni salad and coleslaw each weighing 3.75 and 2.25 pounds respectively
so, to find how many more pounds of macaroni salad than coleslaw we do,
3.75-2.25=1.50
therefore, macaroni salad has 1.50 pounds more than coleslaw.
PLS MARK BRAINLIEST
PLZZZ HELPPPP ILL MARK BRAINLIEST TO FIRST AND CORRECT ANSWER THAT HAS WORK AND A THX TO SECOND AND CORRECT ANSWER.
Answer:
well I think it is none of these because the square root would be 9^2
Step-by-step explanation:
Answer:
9^2
Step-by-step explanation
if the are is 81 then you have to think for th numbers like if the are was 20
it would be 5x4=20cm sorry i can't type in anything special ti won'y let me
Luigi incorrectly solved the following equation. Explain the error in Luigi's work.
Complete your work in the space provided or upload an image of your work completed on paper.
Answer:
the error(s) is from the step 2
Step-by-step explanation:
3r - 12 = 2r - 3 +4r
3r - 4r -2r = 12 - 3
-3r = 9
r = 9 : (-3)
r = -3
--------------------------
the error(s) is from the step 2
This right circular cone has a volume of 75 cubic inches. The height of the cone is 9 inches. What is the length of the radius? A. 4 in. B. 5 in. C. 6 in. D. 8 in.
Answer:
B. 5 in.
Step-by-step explanation:
Answer:
either 8 or 4
Step-by-step explanation:
because it can't be 6 or 5
30 POINTS AND BRAINLIST TO GRAPH
Graph the equation by translating y=|x|.
y=|x+5|
Answer:
Please refer to the attached photo.
Step-by-step explanation:
Table of values
[tex]\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline \sf x &\sf -8 &\sf -7 &\sf -6 &\sf -5 &\sf -4 &\sf -3 &\sf -2 &\sf -1 &\sf 0 &\sf 1 &\sf 2 \\\hline \sf y &\sf 3 &\sf 2 &\sf 1 &\sf 0 &\sf 1 &\sf 2 &\sf 3 &\sf 4 &\sf 5 &\sf 6 &\sf 7 \\\hline \end{array}[/tex]
A laptop has a listed price of $503.98 before tax if the sales tax rate is 7.5% find the total cost of the laptop with sales tax included
Answer:
The tax would be roughly $37.79, which means the laptop would be overall $541.77.
HELP ME ASAP!!!!!!
See pic attached
Step-by-step explanation:
a ) 9 × 2 = 18 → 18 + 3 = 21
o/p = 21
b) 17 - 3 = 14 → 14/2 = 7
i/p = 7
hope this answer helps you dear!
factorise using the formula
Answer:
please find answer attached
Step-by-step explanation:
what is the midpoint of 0.2 and 0.3
Answer:
0.25
Step-by-step explanation:
Half of a tenth in 5 hundredths.
To find the midpoint of 0.2 and 0.3, think of it as 20 and 30.
What would be the midpoint of 20 and 30? 25.
Therefore, 0.25 would be the midpoint of 0.2 and 0.3
-kiniwih426
4 Jamyra4555 (follow her)
Answer:
b
Step-by-step explanation:
10*10=100
100+140=240
240/5=48
Answer:
it's BBBBBBBBBBBBBBBBBB) 48
Step-by-step explanation: