Linda goes water-skiing one sunny afternoon. After skiing for 15 min, she signals to the driver of the boat to take her back to the dock. The driver steers the boat toward the dock, turning in a parabolic path as it nears. If Linda lets go of the towrope at the right moment, she will glide to a stop near the dock. Let the vertex of the parabola travelled by the boat be the origin. The dock is located 30 m east and 30 m north of the origin. The boat begins its approach to the dock 30 m west and 60 m north of the origin.a) If Linda lets go of the towrope when she reaches point A, where is she headed relative to the dock? Use an equation to describe the path. (Hint: She will travel in a straight line.) b) If Linda lets go of the towrope when she reaches point B, where is Linda headed relative to the dock?c) If Linda waits until point C, how close will her trajectory be to the dock?d) At what point should Linda release the towrope to head straight for the dock?e) What assumptions have you made?f) To make this situation more realistic, what additional information would you need? Create this information, and solve part d) using what you have created. As you work through the task, be sure to explain your reasoning and use diagrams to support your answers.A

Answers

Answer 1
60 = a * (-30)^2
a = 1/15
So y = (1/15)x^2


abc)
The derivative of this function is 2x/15. This is the slope of a tangent at that point.
If Linda lets go at some point along the parabola with coordinates (t, t^2 / 15), then she will travel along a line that was TANGENT to the parabola at that point.
Since that line has slope 2t/15, we can determine equation of line using point-slope formula:
y = m(x-x0) + y0
y = 2t/15 * (x - t) + (1/15)t^2
Plug in the x-coordinate "t" that was given for any point.


d)
We are looking for some x-coordinate "t" of a point on the parabola that holds the tangent line that passes through the dock at point (30, 30).
So, use our equation for a general tangent picked at point (t, t^2 / 15):
y = 2t/15 * (x - t) + (1/15)t^2
And plug in the condition that it must satisfy x=30, y=30.
30 = 2t/15 * (30 - t) + (1/15)t^2
t = 30 ± 2√15 = 8.79 or 51.21
The larger solution does in fact work for a tangent that passes through the dock, but it's not important for us because she would have to travel in reverse to get to the dock from that point.
So the only solution is she needs to let go x = 8.79 m east and y = 5.15 m north of the vertex.

Related Questions

Given that IG FT which of the following statements is true

Answers

Answer:

C

Step-by-step explanation:

Please help please please

Answers

Answer:

C. y = 2x + 8

Step-by-step explanation:

✔️First, find the slope of the line that goes through points (-2, 4) and (6, 20):

Slope (m) = ∆y/∆x = (20 - 4) / (6 - (-2))

Slope (m) = 16/8

m = 2

✔️Find the y-intercept (b):

To do this, substitute (x, y) = (6, 20) and m = 2 into y = mx + b

Thus:

20 = 2(6) + b

20 = 12 + b

20 - 12 = b

8 = b

b = 8

✔️Write the equation by substituting m = 2 and b = 8 into y = mx + b

Thus:

y = 2x + 8

PLEASEEEE HELPPP
Ben Frank is an electrician who installs lighting fixtures. He charges (in dollars) his clients 15h +40f
where h is the number of hours worked and f is the number of fixtures installed.
How much does Ben Frank charge when he works 7 hours and installs 9 fixtures?

Answers

Answer:

465 Dollars

Step-by-step explanation:

15h+40f = Amount Charged

if: h = 7

   f = 9

15(7)+40(9) = Amount Charged

105 + 360 = Amount Charged

465 = Amount Charged

He will charge 465 dollars.

Answer:$465Steps and explanation of why:

Ben works 7 hours installing 9 fixtures. This tells us that h = 7, and f = 9. So, let's substitute h = 7 and f = 9 into the expression and evaluate:

Step 1:

15h + 40f

Step 2:

= 15(7) + 40(9)

Step 3:

= 105 + 360

Step 4:

= $465

Hope this helps!! Remember to get good grades, and to stay safe :))

Also, please mark as brainliest..I'm trying to get to, "Virtuoso," which is a level on here that's really important to me.. But- I'm not forcing you so..don't feel pressured into doing it, but if you do, then, thanks so much!! I love you!!

Give me 3 equivalent fractions for 10/30

Answers

Answer:

1/3, 100/300, 20/60

Step-by-step explanation:

Just multiply or divide the numerator and denominator with the same number.

Hope this helps you :)

The total length of a beach towel is 28 inches. If there are 6 beaches towels laid right next to each other side-by-side, what is the total length of the towels?

Answers

Answer:168 inches

Step-by-step explanation:

the answer is 168 inches because 28 times 6 is equivalent to 168 and then u have to put the inches on the end.

Caleb bought raisins in bulk $2.50 per round. He spent a total of $5.75. How many pounds of raisins did he buy?

Answers

$5.75 divided by $2.50= 2.3 pounds

Answer:

2 1/3 I believe

Step-by-step explanation:

The population of a city has increased by 15% since it was last measured. If the current population is 64,400 what was the previous population

Answers

about 50 000 i think

Answer:

73600

Step-by-step explanation:

Add

Simplify the expression please with step
[tex] \sqrt{13 - 4 \sqrt{3} } [/tex]

Answers

Answer:

[tex] \huge \boxed{ \boxed{ \red{2 \sqrt{3} - 1}}}[/tex]

Step-by-step explanation:

to understand thisyou need to know about:redicalsimplifying redicalPEMDASgiven:[tex]\tt \sqrt{13-4\sqrt{3}}[/tex]to do:

simplificationtips and formulas:(a-b)²=a²-2ab+b²√(a)²<=>|a|let's do:

[tex]step - 1 : define [/tex]

[tex] \tt \sqrt{13 - 4 \sqrt{3} } [/tex]

[tex]step - 2 : simplify[/tex]

[tex] \tt use \: the \: 1 \: formula : \\ \tt \sqrt{ 1 + 12 - 4 \sqrt{3} } \\ \tt \sqrt{1 - 4 \sqrt{3} + 12} \\ \tt \sqrt{ {(1)}^{2} - 2.1.2 \sqrt{3} + {(2 \sqrt{3}) }^{2} } \\ \sqrt{ \tt (1 - 2\sqrt{3} {)}^{2} } [/tex][tex] \tt use \: the \: 2 \: formula : \\ \tt |1 - 2\sqrt{3} | \\ \tt - (1 - 2 \sqrt{3} ) \\ - 1 + 2 \sqrt{3} \\ 2 \sqrt{3} - 1[/tex]

a system of equations is shown on the graph below. what is the solution to the system of equations?

Answers

Answer:

Step-by-step explanation:

solution is the point of intersection, (0,1)

Solution of the system of equations is, (0, 1)

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A system of equations is shown on the graph.

Now, We have seen that;

Both the graph intersect at a point (0, 1), which is solution of the graph.

Hence, Solution of the system of equations is, (0, 1)

Thus, Solution of the system of equations is, (0, 1)

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ7

Multiply 7/16 x 2 2/7reduced to lowest terms

Answers

The product of the fraction reduced to the lowest term is 1

Product of fractions

Fractions are written as a ratio of two integers. Given the products of fractions below

7/16 x 2 2/7

Convert mixed to improper

7/16 x 16/7

Take the product

7/16 x 16/7 = 7/7 * 16/16

7/16 x 2 2/7 = 1

Hence the product of the fraction reduced to the lowest term is 1

Learn more on product of fractions here: https://brainly.com/question/6109670
#SPJ1

PLEASE HELP!!!!!! ILL GIVE BRAINLIEST *EXTRA 40 POINTS** !! DONT SKIP :((

Answers

Answer:

B is the answer

Step-by-step explanation:

not staright line so not linear. but it is a function

Answer:

Step-by-step explanation:

it is non-linear; function

Aspen has 10 pairs of white socks and 1 pair of red socks. What is the chance that Aspen wears a pair of black socks?

Answers

Answer:

no chance

Step-by-step explanation:

he doesn't have any black socks

Answer:

Step-by-step explanation:

Of the ten socks,

10/11 chance of wearing white socks

1/11 chance of wearing red socks

0/11 chance of wearing any OTHER color

Black socks fall into the final row, which is the OTHER color, meaning there is no chance he can wear black socks.

Solve (y–3)2 – 32 = 0, where y is a real number.
Simplify your answer as much as possible.
If there is more than one solution, separate them with commas.
If there is no solution, click "No solution."
y = 0
Х

Answers

Answer:

[tex] \sqrt{32} + 3[/tex]

[tex] - \sqrt{32} + 3[/tex]

Step-by-step explanation:

Use foil method

[tex](y - 3) {}^{2} [/tex]

[tex](y - 3)( y - 3)[/tex]

First multiply y and y

[tex]y \times y = {y}^{2} [/tex]

Next Multiply Outer term y and -3.

[tex]y \times - 3 = - 3y[/tex]

After that ), Multily inner tern -3 and y

[tex] - 3 \times y = - 3y[/tex]

Finally multiply -3 and -3 and you get 9.

Then combine all

[tex] {y}^{2} - 6y + 9 - 32 [/tex]

[tex] {y}^{2} - 6y - 23[/tex]

Now I'm going to complete the square. First get only the y value on the left side so we first set this equal to zero then move add 23 on both sides.

[tex] {y}^{2} - 6y - 23 = 0[/tex]

Add 23

[tex]y {}^{2} - 6y = 23[/tex]

Apply formula

[tex] (\frac{b}{2} ) {}^{2} [/tex]

where b is the coefficient.

plug it in

[tex]( \frac{ - 6}{2}) {}^{2} [/tex]

Which is -3 squared which equal 9.

Then add 9 on both sides

[tex] {y}^{2} - 6y + 9 = 23 + 9[/tex]

23+9=32

Now let factor the left side

the only number that adds to -6 and multiply to 9 is

-3 so we would rewrite the left side as

[tex](x - 3) {}^{2} = 32[/tex]

Now take the sqr root of 32

[tex] \sqrt{(x - 3) {}^{2} } = \sqrt{32} [/tex]

Then add 3 on both sides

[tex]x + - 3 + 3 = \sqrt{32} + 3[/tex]

A sqr root of a number can be positive or negative so

the answer is

[tex] - \sqrt{32} + 3[/tex]

[tex] \sqrt{32} + 3[/tex]

pls bro i need help asap

Answers

Answer:

Step-by-step explanation:

i suck at math um i have no life

find the x and y-intercept of this function: 2x+y=-2

Answers

Answer:

x- intercept:(-1,0)

y-intercept:(0,-2)

Step-by-step explanation:

A standard six-sided die is rolled.
What is the probability of rolling a number greater than or equal to 3? Express your answer as a simplified fraction or a decimal rounded to four decimal places.
Tables
Keypad

Answers

Answer:

Step-by-step explanation:

There are six sides on the die...

1, 2, 3, 4, 5, 6

Greater than or equal to 3 includes 3, 4, 5, 6

This means 4 out of 6, or 4/6

4/6 simplified is 2/3

Hope this helps!

someone help me lol..

Answers

Answer:

1/3x + 3 is the correct answer, hope it help

1. Escribe dos semejanzas dadas en la estructura de la
circunferencia y la elipse.​

Answers

Un círculo es una forma curva cerrada que es plana. Es decir, existe en dos dimensiones o en un plano. En un círculo, todos los puntos del círculo están igualmente lejos del centro del círculo. Una elipse también es una forma curva cerrada que es plana.

~~Espero que esto ayude~~

Assume a test for a disease has a probability 0.05 of incorrectly identifying an individual as infected (False Positive), and a probability 0.01 of incorrectly identifying an individual as uninfected (False Negative). Assume furthermore that the probability of an individual being infected is 0.000001 (1 in 1 million). If a person tests positive for this disease, what is the probability of actually having the disease

Answers

Answer:

0.00002 = 0.002% probability of actually having the disease

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Positive test

Event B: Having the disease

Probability of having a positive test:

0.05 of 1 - 0.000001(false positive)

0.99 of 0.000001 positive. So

[tex]P(A) = 0.05*(1 - 0.000001) + 0.99*0.000001 = 0.05000094[/tex]

Probability of a positive test and having the disease:

0.99 of 0.000001. So

[tex]P(A \cap B) = 0.99*0.000001 = 9.9 \times 10^{-7}[/tex]

What is the probability of actually having the disease

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{9.9 \times 10^{-7}}{0.05000094} = 0.00002[/tex]

0.00002 = 0.002% probability of actually having the disease

Plsss help mee quickkk !!

Answers

Answer:

2.5 overtime hours

Step-by-step explanation:

90$+195$=285

390-285=105$

105/42=2.5 overtime hours

Answer:

h=2.5 hours

Step-by-step explanation:

take the 30x3=90 then 195-90= 105 finally, divide 105 and 42 to get 2.5 hours!

30x3

195-90

105/2.5

hope this helps!

find the slope of the line​

Answers

Answer:

1/2

Step-by-step explanation:

(2,1)(4,2)

x1-y1/x2-y2

slope:m=1/2

Compute the Gross Pay for these situations:
1. Regular Hours Worked: 40
Overtime Hours Worked: 4
Regular Rate of Pay: $7.50/hour

Answers

62525262626

Step-by-step explanation:

52525252+45541537948-5751576544+4246-5484-24848+2757%

Write a word description of the set.
{10, 11, 12, 13, ...}

Answers

this set of numbers counting by ones or the addition of one each time
It would be the addition of one.

10 Six years ago Jon was one-sixth the age of his mother
and in four years time his age doubled and increased
by 10 will match his mother's age. How old is Jon
now?​

Answers

Answer:

Jon is 11 years old

Step-by-step explanation:

We write the following equations describing the sentences of the problem, using the letter M to represent Jon's mom's current age, and j to represent his current age.

First sentence: "Six years ago Jon was one-sixth the age of his mother."

translates into:

J - 6 = (M - 6) / 6

Second sentence: "in four years time his age doubled and increased

by 10 will match his mother's age."

2 * (J + 4) + 10 = M + 4   which removing parentheses gives: 2 J + 18 = M + 4

We solve for "M" in the first equation

6 (J - 6) = M - 6

6 J - 36 = M - 6

M = 6 J - 30

and now use this result to substitute for M in the second equation

2 J + 18 = (6 J - 30) + 4

and work on solving for J

2 J + 18 = 6 J - 30 + 4

18 + 26 = 6 J - 2 J

44 = 4 J

J = 44 / 4

J = 11

Annika is painting a rectangular wall. She paints 1/2of the wall yellow. Then, she changes her mind and paints 1/4 of the yellow part blue. What
fraction of the wall does Annika paint blue?

Answers

Answer:

3/4

Step-by-step explanation:

(½-¼)+½=

¼+½=

¾

Nasa book po nmin yan

describe a family member in 3-5 sentences (use nouns) make it easy and simple please!!

Answers

Ok! ———- is ———- because of ————. They have ———- hair color and ———— eye color. I think they are ———— because of ————. They like to —————- because —————.

what is -10 as a percent

Answers

-1,000%

Hope I helped you!Success!

-0.1 is your answer!

When plotting points on the coordinate plane below, which point would lie on the x-axis?



(6, 0)
(0, 2)
(3, 8)
(5, 5)

Answers

Answer: (6,0)

Coordinate points are always written in pairs of the x- and y-coordinate: (x, y). Knowing this, the point would need to have a y-value of 0 in order to lie on the x-axis (otherwise, it would be on a random spot on the grid). The only coordinate point with a y-value of 0 is (6, 0). Therefore, the coordinate point (6, 0) lies on the x-axis.

Please refer to the attached graph below to see all the coordinate points.

What additional information must be known to prove the triangles similar to SAS?

Answers

Answer:

Option A) is the right answer because for SAS property we need to verify that the sides are equal to each other in the triangles.

IS THIS A FUNCTION ? YES OR NO ????

ILL GIVE 40 POINTS DONT LIE !!

Answers

Answer:

no it is not a function. .

Answer:

Step-by-step explanation:

No, it does not pass the  vertical line test

Other Questions
1. Which medical career was the highest on this list? A. Physician assistant B. Dentist C.nurse practitioner D. Occupational therapist 2. According to the same list what does it have listed as the median Salary for physical therapist A. 67k B.86k C.70k D.43k 3. According to the report which of these careers have the most projected of jobs in the future?A. Physical therapistB.Respiratory therapistC.Registered nurseD.Speech-language pathologist 4. US news and world report also published a 2019 list for best paying jobs how many of the top 10 carriers are considered medical careers?A.2B.5C.8D.105. The top six Careers on the best paying jobs listed all made this average median salary. A.108k B.140k C.180k D.208k6.What is the name of the agency that is responsible for measuring labor market activity, working conditions, and price changes in the Economy A.Occupational safety and health administration B.Federal communications commission C. The United States department of the interior 7. bos.gov has a chart with the fastest growing occupation in the US which medical career does it predict to be the highest in demand? A.Physical therapist assistants B.Medical assistants C.Massage therapist D.Home health aide In naming the compound PCl5, the prefix used with the second element is ____________________. Find the ratio of x to y.5x = 8y 3. A $50 pair of shoes is discounted by 15% What will be the newprice of the shoes? Mitchell cycled a total of 4 kilometers by making 2 trips to work. After 4 trips to work, how many kilometers will Mitchell have cycled in total? Assume the relationship is directly proportional. HURRY PLZ BRAINLIEST IF CORRECT which approach is preferred by sociologists and why? system-blame approach or person-blame approach Tell whether (4, 27) is a solution of y=3x+15 Paige had 18 dollars. She spent 6 of these dollars How does Chielo take Ezinma to the cave? What is an indicator that the universe is exapanding? Use the Distributive Property to solve the equation.3 = 3/4 ( b - 8 ) What are mutual funds? Explain the associated risks. explain why you think the vaccine is effective or not effective? I am play football. Change into passive voice ?????????????????????? pls help me ASAP!! what is the surface area of this design? a) 288in b) 256in c) 96in d) 160in Tom and Katie are discussing the sequence 3n - 4Tom says 34 is a term in the sequence.Katie says 41 is a term in the sequence. Maggie says that if the expression was 123to the second power, you would divide before simplifying 3 to the second power. Is she right? Explain A letter to your friend in another town telling him about the developmantal activities going on in your area