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
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Related Questions
Which equation represents a line that passes through (5, 1) and has a slope of 1/2?
Oy-5= 1/2(x-1)
oy- į = 5(x-1)
oy-1 = 1/2(x–5)
oy-1 = 5(x-1/2)
Answers
Answer:
C. y - 1 = 1/2(x - 5)Step-by-step explanation:
Use the point- slope form:
y - y₁ = m(x - x₁)Substitute know values:
y - 1 = 1/2(x - 5)The matching choice is C
The correct equation which represents a line that passes through (5, 1) and has a slope of 1/2 is,
y - 1 = 1/2(x - 5)
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
A equation of a line that passes through (5, 1) and has a slope of 1/2.
Now, Use the point- slope form:
⇒ y - y₁ = m(x - x₁)
Hence, Substitute all the values:
y - y₁ = m(x - x₁)
y - 1 = 1/2(x - 5)
Thus, The correct equation which represents a line that passes through (5, 1) and has a slope of 1/2 is,
y - 1 = 1/2(x - 5)
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A regular polygon has 20 sides
work out the sum of the interior angles of the polygon
work out the size of the interior angles
Answers
Step-by-step explanation:
The sum of the interior angles of a regular n-gon is given by the formula (n-2)180. Hence, in our case n=20 and we have the answer of 18(180)=3240 degrees.
Step-by-step explanation:
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What is the measure of an interior angle of a regular polygon with 20 sides?
Geometry Angles with Triangles and Polygons
1 Answer
mason m
Jan 2, 2016
162
˚
Explanation:
The sum of the interior angles in a regular polygon with
n
sides is found through the formula
180
˚
(
n
−
2
)
Here,
n
=
20
, so the sum of the interior angles is
180
˚
(
20
−
2
)
=
180
˚
(
18
)
=
3240
˚
To find just one angle, divide
3240
˚
by
20
since all
20
angles are congruent.
3240
˚
20
=
162
˚
The time, in minutes, that it takes Mark to bake cookies is given by t = 15 + 10d, where d is dozens of cookies. How long would it take Mark to bake 48 cookies?
Answers
Answer:
55
Step-by-step explanation:
15+10d
15+10(4)
15+40
55 minutes
It will take 55 minutes for Mark to bake 48 cookies.
15+10d
15+10(4)
15+40
55 minutes
How long does it take to bake a cookie?
Simply put, you can expect to bake cookies at 350 degrees Fahrenheit for 8-12 minutes. However, there are some things to consider when baking biscuits. The type of biscuit, the size of the biscuit, and the content of the fabric.
Preheat the oven to 350 ° F (or 325 ° F for a non-stick baking sheet). Place the cookie dough base about 2 inches apart on a non-oiled sheet pan. BRAKE for 10-14 minutes or until light brown. Cool 2 minutes; Remove from the top plate.
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If R is the midpoint of QS, QR = 6x – 51 and RS = 2x – 7, find QS.
Answers
Answer:
QS = 30
Step-by-step explanation:
Since R is the mid point QR = RS
Given QR = 6x – 51 and RS = 2x – 7 then
6x – 51 = 2x – 7, isolate like terms
6x -2x = 51 -7 , combine like terms
4x = 44, divide both sides by 4
x = 11
QS = QR + RS
QS = 6x -51 +2x -7 , combine like terms
QS = 8x - 58, substitute x= 11 in the equation
QS = 8*11 -58, multiply 8 and 11
QS = 88 -58
QS = 30
Translate to an equation and solve. Let x be the unknown number.
94 is 25% of what number?
What: x
Is: =
Of: multiple
Answers
Answer:
x= 376
Step-by-step explanation:
100/25=4
94*4=376
Flights 204 and 317 are both approaching Hartsfield Atlanta International Airport from directions directly opposite one another and at an altitude of 2.5 miles. The pilot on flight 204 reports an angle of depression of 17 degrees 47 minutes to the tower, and the pilot on flight 317 reports an angle of depression of 12 degrees 39 minutes to the tower. Calculate the distance between the planes.
Answers
Answer:
19.26 milesStep-by-step explanation:
Refer to attached picture. Not to scale.
The picture explains all the given parameters.
We need to find the distance d, which is the sum of x and y.
First convert minutes to degrees:
47 min = 47/90 deg = 0.52 deg39 min = 39/90 deg = 0.43 degFind x:
x/2.5 = cot (17.52°) ⇒ x = 2.5*3.1677 ≈ 7.92 miFind y:
y/25 = cot (12.43°) ⇒ y = 2.5*4.5369 ≈ 11.34 miThe distance between the planes:
7.92 + 11.34 = 19.26 miA rectangular park 60 yards long and 50 yards wide. Plans call for increasing both the length and the width by x yards.
a. Write a function to find the new length of the park.
b. Write a function to find the new width of the park.
c. Write a function to find the area of the park after increasing both the length and width.
Answers
Answer:
C
Step-by-step explanation:
If they are increasing w and l, they need a function for both.
Solve the equation :
7:x=2:3
Answers
Answer:
x=8
Step-by-step explanation:
Since 7-2 is 5, that means that both sides are increasing by 5.
3+5 = 8 so therefore 8 =x
How many corresponding pairs of parts do you have in a pair of triangles?
Answers
Answer:
Notice that when two triangles are congruent their three pairs of corresponding angles and their three pairs of corresponding sides are congruent.
Step-by-step explanation:
Answer:
three pairs of congruent corresponding sides
Is question 6 and question 7 is it correct
Answers
Answer:
6) a
7) c
Step-by-step explanation:
question 6 is incorrect because you have to find the distance between the two points. for question 6, you are finding the distance between -2 and 1. that is three!
Glenda wants to find out how often people in her town visit the cinema.
She collects data from 10 people standing in a queue outside a cinema.
Answers
Answer:
huh your questions make no sense there has to be more
Step-by-step explanation:
using quadratic regression what parabola uses the points (4,80), (-3,-11), (-1,-15)? i need help badly i don’t understand this at all
Answers
Answer:
How do you find a quadratic regression from points?
Image result for using quadratic regression what parabola uses the points (4,80), (-3,-11), (-1,-15)?
Quadratic regression is the process of determining the equation of a parabola that best fits a set of data. This set of data is a given set of graph points that make up the shape of a parabola. The equation of the parabola is y = ax2 + bx + c, where a can never equal zero
Step-by-step explanation:
Help me please i need help :( will name brainliest if the answer is correct :)
Answers
Answer:
What's the question?
Step-by-step explanation:
-
W H EN H_ DRIBBLE_
_ means blank
Answers
Answer:
whenhedribbles???
Step-by-step explanation:
what am i to do
Match the hotspots to their correct answers
Answers
[tex]\sf \large \boldsymbol {} 1) \ (4^0)^6= 4^{0\cdot 6}= 4^0\neq 4^6 \ False \\\\\\ 2) \ \dfrac{3^8}{3^{-2}} =3^{8-(-2)}=3^{8+2}=3^{10} \ \ True \\\\\\ 3) \ 2^{-5}\cdot 2^3=2^{-5+3}=2^{-2}=\dfrac{1}{2^2} \ \ True \\\\\\ 4) \ 6^4\cdot 3^4=(6\cdot 3)^4=18^4\neq 18^8 \ \ False[/tex]
Answer:
false, true, true, false
Step-by-step explanation:
(4^0)^6=1 is not equal to 4^6=4096
3^8/3^-2=59049 is equal to 3^10=59049
2^-5*2^3=0.25 is equal to 1/2^2=1/4=0.25
6^4*3^4=104976 is not equal to 18^8=11019960576
hope this helps!
x+2x+x+x+x+x= ????
Answers
Answer:
7x
Step-by-step explanation:
x +2x + x + x + x + x
= x + x + x + x + x + 2x
= 5x + 2x
= 7x
please answer i will give a thanks!
Answers
Answer:
21cm^2
Step-by-step explanation:
Formula for area of triangle = (base x height) / 2
in this triangle: base = 7 Height = 6
= (7 x 6) / 2
= 42 /2
= 21cm^2
Can someone pls help me out
Answers
Answer:
The answer is 8.
Step-by-step explanation:
If you multiply each of the measurments by 1.5 they equal the measurments on the larger trapazoid. I can't see the full question but im assuming It's asking for the measurment (2x-16). So 12 divided by 1.5 equals 8. And to get eight you replace x with 4. Hope I helped. :)
[tex]\\ \sf\longmapsto \dfrac{2x-16}{12}=\dfrac{12}{18}[/tex]
[tex]\\ \sf\longmapsto \dfrac{x-8}{6}=\dfrac{2}{3}[/tex]
[tex]\\ \sf\longmapsto 3(x-8)=12[/tex]
[tex]\\ \sf\longmapsto 3x-24=12[/tex]
[tex]\\ \sf\longmapsto 3x=36[/tex]
[tex]\\ \sf\longmapsto x=12[/tex]
Insert parentheses and brackets to make4x 8 - 4 + 1 = 12
Answers
Answer:
3
Step-by-step explanation:
Write the equation of the line that passes through the given point and is perpendicular to the given line
please explain if you can, but if you dont want to its okay
Answers
Answer:
y = 5Step-by-step explanation:
The line x = 3 is parallel to y- axis, the perpendicular line is going to be parallel to x- axis and will have an equation:
y = aSince it passes through the point (-2, 5), it will have a = 5:
y = 5 is the line we needthe diffrence between 4 and 1 on number line
Answers
Answer:
What is 3
Step-by-step explanation:
4 - 1 = 3.
what will be the ones digit in the square of the following number 21222
Answers
Answer:
4
Step-by-step explanation:
since the square of the number ending with 2 will give 4 at units place
sin^2020(x)+cos^2020(x)=1
Answers
Answer:
so this is really simpel x=1 thats it
Step-by-step explanation:\sin ^2\left(20^{\circ \:}\right)\left(x\right)+\cos ^2\left(20^{\circ \:}\right)\left(x\right)=1 \sin ^2\left(20^{\circ \:}\right)x+\cos ^2\left(20^{\circ \:}\right)x=1
pls someone help me! im giving brainlest!!!!!!
Answers
Answer:
True
Step-by-step explanation:
If (h + h) · (h. h) = 16, find the value of h.
— HELP ME PLEASEEEE
Answers
Answer:
h = 2
Step-by-step explanation:
I'm assuming your periods are multiplication signs.
(h + h) X (h X h) = 16
When adding two variables like the first set of parentheses, it would become 2h. When multiplying two like variables, you add the exponents. h is the same as writing h¹. So h¹ x h¹ gives you the answer of h².
So now your equation would look like:
2h X h² = 16
As above, when you multiply two like variables you would add the exponents. Also if any number are in front of the variable you would multiply those numbers. So you have 2h¹ x 1h² and that would be 2h³. If it had been
2h¹ x 2h², your answer would have been 4h³.
But so far you have 2h¹ x 1h² = 16
2h³ = 16
Dividing both sides by 2 you get
h³ = 8
To find h you have to take the cubed root of 8. What number multiplied by itself 3 times gives you 8? 2 x 2 x 2 = 8 2 x 2 = 4 and x 2 = 8.
h = 2
If you put this into the original equation you have:
(2 + 2) x ( 2 x 2) = 16
( 4 ) x ( 4 ) = 16
5x+6y=50
x=-26+6y
what is the solution as a coordinate pair
Answers
Answer:
póngalo en español como puedo yo poner lo en español por que todo me sale en inglés
f(x)=3x+10xg(x)=4x−2,(f−g)(x)
help please
Answers
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Let's find (f - g)(x) :
[tex]f(x) - g(x)[/tex][tex]3x + 10 - (4x - 2)[/tex][tex]3x + 10 - 4x + 2[/tex][tex] - x + 12[/tex]Answer:
f(x) = 3x + 10g(x) = 4x - 2(f - g)(x) = f(x) - g(x)
(f - g)(x) = (3x + 10) - (4x - 2)
(f - g)(x) = 3x + 10 - 4x + 2
(f - g)(x) = - x + 12
(f - g)(x) = - x + 12 is the right answer.What us 2 1/3 divided by 1 1/2 in mixed number form?
Answers
33/14 =2 5/14
Step-by-step explanation:
have a great day
Please help I have to get this in in 20 mins
Answers
Answer:
(x, y) = (4, 1)
Step-by-step explanation:
I'm pretty sure this is right but please check with someone else is possible. Hope this helped!
You are selling tickets for a high school play. Student tickets cost $5 and general admission tickets cost $7. You sell 103 tickets and make a total of $561. How many of each type of ticket did you buy?
Answers
Answer:
2876
Step-by-step explanation:
Let the student tickets be x
Let the generall Admission tickets be y
x+y=525
y=525-x
4x+6y=2876 (subsitute for y)
4x+6(525-x)=2876