Mathematics High School

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

Answer 1

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

Related Questions

Describe the transformation of y=-2/x

Answers

Answer:

This transformation is known as a vertical stretch. This is the graph of a transformation of \begin{align*}y=x^2\end{align*}. The points are plotted from the vertex as right and left one and down one-half, right and left 2 and down two, right and left three and down four and one-half

AHH HELPPPP !!!!
-In the following diagram, two parallel lines are cut by a transversal. The measure of which angle is equal to the measure of angle 1 ?
a - angle 2
b - angle 3
c - angle 4
d - angle 6

Answers

Answer:

angle 4

Step-by-step explanation:

1 and 4 are vertical angles

∠1 = ∠4

This according to the vertical angle theorem

Hope this helps!!

Solve:
3(4 - 2x) = -x +1
13
X =
5
O B. x = 11
O C. x= -1
x-5
D. X

Answers

Step-by-step explanation:

[tex]3(4 - 2x) = - x + 1 \\ 12 - 6x = - x + 1 \\ 12 - 1 =6x - x \\ 11 = 5x \\ \frac{11}{5} = x \\ 2 \frac{1}{5} = x \\ [/tex]

The solution of the equation is x = 11/5

What is an Equation?

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

The given equation is,

3 (4 - 2x) = -x + 1

We have to solve the equation.

Distributive property states that, for three numbers, a, b and c,

a(b + c) = ab + ac

So, 3 (4 - 2x) = (3 × 4) - (3 × 2x)

= 12 - 6x

Substituting,

3 (4 - 2x) = -x + 1

12 - 6x = -x + 1

-6x + x = 1 - 12

-5x = -11

x = 11/5

Hence the solution is x = 11/5.

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divide the given equation By 5 5x² - 4x- 3 = 0 .

Answers

Answer:

x^2 - 4/5x - 3/5 = 0

Step-by-step explanation:

5x^2/5 - 4x/5 - 3/5 = 0/5

x^2 - 4/5x - 3/5 = 0

[tex]\\ \sf\longmapsto \dfrac{5x^2-4x-3=0}{5}[/tex]

Divide each variable by 5

[tex]\\ \sf\longmapsto \dfrac{5x^2}{5}-\dfrac{4x}{5}-\dfrac{3}{5}=\dfrac{0}{5}[/tex]

[tex]\\ \sf\longmapsto x^2-\dfrac{4}{5}x-\dfrac{3}{5}=0[/tex]

We are done!

Use the graph to estimate the value of y when x = 2.5

Answers

Answer:

y=7

y will equal to 7 when x is 2.5

Write the equation of the line that passes through the points (0,0) and (7,8). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line

Answers

Answer:

PLS MARK BRAINLIEST

Step-by-step explanation:

m= y2 - y1/ x2 - x1( slope of a line)

m = 8 -0 / 7- 0

8/7 = m

m = 1.1

since m =y - y1/ x - x1

1.1 = y - 0/ x-0

1.1 = y/x(cross multiply)

y = 1.1 x

y -1.1 x = 0

y - 8/7 x = 0

plz help me with this im so confused

Answers

Answer:

1.) x = -5

y = -4

Point to graph: (-5, -4)

2.) x = 0

y = -6

Point to graph: (0, -6)

3.) x = 5

y = 8

Point to graph: (5, 8)

Step-by-step explanation:

Substitute x for the given value, then find y.

1.) -2(-5)-5y = 30

10-5y = 30

-5y = 20

y = -4

2.) -2(0)-5y = 30

-5y = 30

y = -6

3.) -2(5)-5y = 30

-10-5y = 30

-5y = 40

y = -8

Answer:

y values are

-4

-6

-8

Step-by-step explanation:

WILL GIVE BRAINLIEST

When you draw one marble from a bag, and don't put it back into the bag for the second draw, what kind of probability is it?

Answers

Answer:

it is a dependant event without placement

Step-by-step explanation:

you dont replace the marble so it is dependant. and without replacement is when you dont put it back in the bag

Solve the rational equation x divided by 2 equals x squared divided by quantity x minus 2 end quantity, and check for extraneous solutions.

No solution
x = 0 and x = −2
x = −2; x = 0 is an extraneous solution
x = 0; x = −2 is an extraneous solution

Answers

The value of x in the equation [tex]\frac{x}{2} = \frac{x^2}{x - 2}[/tex] are x = 0 and x = -2

How to solve the rational expression?

The expression is given as:

[tex]\frac{x}{2} = \frac{x^2}{x - 2}[/tex]

Cross multiply

[tex]x(x - 2) =2 * x^2[/tex]

Open the bracket

[tex]x^2 - 2x =2x^2[/tex]

Collect like terms

[tex]- 2x =2x^2 - x^2[/tex]

Evaluate the like terms

[tex]- 2x =x^2[/tex]

Rewrite as:

[tex]x^2 + 2x =0[/tex]

Factor out x

x(x + 2) =0

Expand

x = 0 or x + 2 = 0

Solve for x

x = 0 or x = -2

Hence, the value of x are x = 0 and x = -2

Answers

Answer:

2/3

Step-by-step explanation:

The probability that it will rain on wednesday will be 0.75.

What is a expression? What is a mathematical equation? What is Probability?

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. The formula to calculate the probability of occurrence of an event 'A' can be written as -

P(A) = n(A)/n(S)

where -

n(A) = Number of outcomes favorable to event A.

n(S) = Total number of outcomes.

We have a meteorologist who says that there is a 50% greater chance of rain than no rain on Wednesday.

Assume that the probability that it will rain on wednesday be [x]. Now, we can write -

P[R] = P[N.R.] + 1/2

P[R] + P[R] = P[N.R.] + P[R] + 1/2

2 P[R] = 1 + 1/2

2 P[R] = 1.5

P[R] = 1.5/2

P[R] = 0.75

Therefore, the probability that it will rain on wednesday will be 0.75.

To solve more questions on Probability, visit the link below -

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-12+x=8 properties of equality

Answers

-12+x=8 , value of X is 20

Answer:

x=20

Step-by-step explanation:

-12+x=8

Add 12 on both sides (-12 + 12 + x = 8 + 12)

which crosses out -12

and then you get x=20

9(b - 1) = 63
what is b? show your work will give brainlyiest

Answers

The answer is b=8 I hope it helps you should download photos math

Write the equation in slope intercept form. what are the slope and y-intercept? -3x - 10y = 7

Answers

slope intercept is basically solve for y y=mx+b m=slope b=yintercept -3x-10y=7 add 3x to both sides -10y=3x+7 divide both sides by -10

help with the top one please?

Answers

Answer:

30 pages per hour.

Step-by-step explanation:

Okay so they read 1 1/2 pages per hour right. And you need 20/20 to make 1 hour right. So all you have to do is multiply 1 1/2 by 20 and you got your answer.

how can my questions be marked brainliest

Answers

Answer:

Step-by-step explanation:

If you want to give brainliest, you have to wait for two answers then pick the best answer to get brainliest by clicking the little crown icon on the bottom right.

If you want to get brainliest, try to give a really good answer to a question and if the person asking thinks you gave the best answer,you will receive brainliest.

Answer:

Questions are marked brainliest by whoever asked the question. That person chooses which answer they received is the most helpful/correct, and then awards that answer with the brainliest crown.

Step-by-step explanation:

micheal jordan has 72 basketballs,84 baseballs and 48 gold balls and he wants to group them together so that he can donate them to schools in his hometoen.What is the largest number of identicsl groups he can put together without hahing any balls left over

Answers

They all can be divided by 12 which is the largest number they can be divided by so 12

In a certain state, % of adults indicated that sausage is their favorite pizza. Suppose a simple random sample of adults in the state of size is obtained and the number of adults who indicated that sausage is their favorite pizza was . What are values of the parameters n, p, and x in the binomial probability experiment?

Answers

Literally, binomial probability represents an experiment which has two possible outcomes.

The values of the parameters n, p, and x are 25, 50% and 16 respectively

The representations in binomial probability are:

n represents the sample sizex represents the selected samplep represents the proportion that supports the experiment

From the complete question, we have:

25 adults are selected as the sample size50% of adults indicated that sausage is their favorite pizza16 adults indicate that sausage is their favorite pizza

The above highlights mean that:

[tex]\mathbf{n = 25}[/tex]

[tex]\mathbf{x = 16}[/tex]

[tex]\mathbf{p =50\%}[/tex]

Read more about binomial probabilities at:

https://brainly.com/question/19578146

what is the slope of a line that passes through (-3,-3) (-5-2)

Answers

Answer:

- 1/2

Step-by-step explanation:

Given points:

(-3,-3) and (-5-2)

Use slope formula:

[tex]m=(y_2-y_1)/(x_2-x_1)=(-2-(-3))/(-5-(-3))=1/-2=-1/2[/tex]

(-3,-3)(-5,-2)

[tex]\\ \sf\longmapsto Slope=m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{-2+3}{-5+3}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{1}{-2}[/tex]

how many 4-digit natural numbers are there?

Answers

Answer:

9000

Step-by-step explanation:

There are 4 numbers (any number from 0-9) in a 4-digit number and the starting number should be 1 or bigger than 1. The thousands place in a 4-digit number cannot be 0. The smallest 4 digit number is 1000 and the greatest 4 digit number is 9999. There are 9000 four-digit numbers in all

what is 46+56+3+17+30+

Answers

Answer:

152

Step-by-step explanation:

46+56=102

102+3=105

105+17+130=152

The area of the rectangle is (18r - 12) square inches. Write an expression that represents the length of the rectangle (in inches).

Answers

Answer:

L = (18r - 12)/W

Step-by-step explanation:

A = L * W

18r - 12 = L * W

(18r - 12) = L * W

(18r - 12)/W = L

I really need help from you brainy users.
I don't expect you to write out a whole entire paragraph but give me some tips regarding moving out of my parents house before I turn 18.

Answers

Answer:

well, i guess ill tell you the way i did it. i rented a storage space, rented my apartment and bought all of my furniture before moving out of my parents house so i was totally ready to move out. then, when the day came to move out, i planned the entire day beforehand, planned where my furniture would go and did all the planning before actually leaving. anything else you wanna know? ill answer any questions

Step-by-step explanation:

It depends. Let’s say if your forced to leave the house then you should probably start looking for houses but you needa get a job too. You should get a small house a normal house yk? Because they’re less expensive and if like I trnna run away or something then you should wait because you won’t have any place to stay unless at your friends house or something, if your being abused or something that isn’t right for you you should just call the police and then you leave make sure you get some food too but it’s up you good luck

What is the slope of the line that passes through (-12, -5) and (0, -8)?

Answers

Answer:

-1/4

Step-by-step explanation:

Use the slope formula

m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\frac{-8-(-5)}{0-(-12)}[/tex]

Which equals -1/4

if 1 ft = 1.894 x 10 -4miles, convert 20.0 inches to miles

Answers

Answer:

3.1567 * 10^-4 miles

Step-by-step explanation:

1 ft = 1.894 * 10^-4 miles , so

1 inch = 1.894 * 10^-4 / 12 miles

= 0.15783 * 10^-4

= 1.5783* 10^-5 miles ( in scientific form).

Multiplying this by 20 we get

31.567 * 10^-5

= 3.1567 * 10^-4 miles.

So, I have a math problem, the problem is,16x^0+2x^2*y^-1,How do I solve if x = 2 and y = 4?

Answers

Answer:

Given x = 2 and y =4

so 16[tex]x^{0}[/tex]+2[tex]x^{2}[/tex][tex]y^{-1}[/tex]

= 16*[tex]2^{0}[/tex] + 2*[tex]2^{2}[/tex]*[tex]4^{-1}[/tex]

= 16 + (2*4)/4

=16 + 8/2

16 + 2

=18

Step-by-step explanation:

Item 5
What is the length of the line segment with endpoints (10.8, −5.3) and (−15.6, −5.3) ?

Answers

Step-by-step explanation:

since both points are on the same horizontal line (same y coordinate), we can save the detour via the Pythagoras approach. we only need to look at the difference of the x coordinates to get the distance :

10.8 - -15.6 = 10.8 + 15.6 = 26.4

solve the equation: -2(n+3)=13

Answers

Answer:

n is -9.5 ....hyuibgtyujhff

The ratio of blue marbles to white marbles in a bag is 4 to 5. At this rate how many blue marbles are there if there are 15 white marbles

Answers

Answer:

Step-by-step explanation:

ratio of blue marbles to white marbles = 4:5

15/5=3

4x3:5x3

ratio if there are 15 white marbles= 12:15

denoting that 12 blue marbles would be there

Factor completely
[tex]3x²+20x-7[/tex]
Please show all workings

Answers

Answer:

(x + 7)(3x - 1)

Step-by-step explanation:

See the steps below:

3x² + 20x - 7 = 3x² + 21x - x - 7 = 3x(x + 7) - (x + 7) = (x + 7)(3x - 1)

Explanation:-

First Method: (By splitting the middle term)

We have to find p and q such that p+q = 20 and

pq = 3×(-7) = -21

Let us looks for the pair of factors of -21 such that their sum is 20 and product is -21.

20 = 21 - 1 and -21 = 3(-7)

∴ 3x² + 20x - 7 = 3x² + 21x - 1x - 7

= 3x(x + 7) -1(x + 7)

= (x + 7)(3x - 1)

Second method: (Using the factor theorem)

8/5 minus 1/6 their are four answers 22/15 43/30 1/6 or 48/30

Answers

Answer:

43/30

Step-by-step explanation:

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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

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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 ( ?