1. (5 points) At 6pm, ghost A is 5 kilometers due west of ghost B. Ghost A is flying westat 15 km/hr and ghost B is flying north at 20 km/hr. How fast is the distance between
the ghosts changing at 10pm?

Answers

Answer 1

Answer:

Answer:

The distance between the ghost changes at 10 pm approximately at a rate of 24.981 kilometers per hour.

Step-by-step explanation:

At first we assume that north and east directions both represent positive quantities. Let suppose that $\vec r_(A,o) = (0\,km,0\,km)$ and $\vec r_(B,o) = (5\,km, 0\,km)$ . If both ghosts moves at constant velocity such that $\vec v_(A) = \left(-15\,(km)/(h), 0\,(km)/(h) \right)$ and $\vec v_(B) = \left(0\,(km)/(h),20\,(km)/(h) \right)$ , then the final positions of both ghosts are, respectively:

Ghost A

$\vec r_(A) = \vec r_(A,o)+t\cdot \vec v_(A)$ (Eq. 1)

Ghost B

$\vec r_(B) = \vec r_(B,o)+t\cdot \vec v_(B)$ (Eq. 2)

Where $t$ is the time, measured in hours.

Then, the equations of motion of each ghost are, respectively:

Ghost A

$\vec r_(A) = (0\,km,0\,km)+t\cdot \left(-15\,(km)/(h), 0\,(km)/(h) \right)$

$\vec r_(A) = \left(-15\cdot t, 0)\,\,\,\left[km \right]$

Ghost B

$\vec r_(B) = (5\,km, 0\,km)+t\cdot \left(0\,(km)/(h), 20\,(km)/(h) \right)$

$\vec r_(B) = (5, 20\cdot t)\,\,\,\left[km\right]$

Then, the distance between both ghosts is:

$\vec r_(B/A) = (5,20\cdot t)-(-15\cdot t, 0)\,\,\,[km]$

$\vec r_(B/A) =(5+15\cdot t, 20\cdot t)\,\,\,[km]$ (Eq. 3)

The magnitude of the relative is represented by the following Pythagorean identity:

$r^(2)_(B/A) = (5+15\cdot t)^(2)+(20\cdot t)^(2)$

Then, we find the rate of change of the relative distance ( $\dot r_(B/A)$ ), measured in kilometers per hour, by implicit differentiation:

$2\cdot r_(B/A)\cdot \dot r_(B/A) = 2\cdot (5+15\cdot t)\cdot 15+2\cdot (20\cdot t)\cdot 20$

$r_(B/A)\cdot \dot r_(B/A) = 15\cdot (5+15\cdot t)+20\cdot (20\cdot t)$

$\dot r_(B/A) = (75+625\cdot t)/(r_(B/A))$

$\dot r_(B/A) = \frac{75+625\cdot t}{\sqrt{(5+15\cdot t)^(2)+(20\cdot t)^(2)}}$ (Eq. 4)

If we know that $t = 4\,h$ , then the rate of change of the relative distance at 10 PM is:

$\dot r_(B/A) = \frac{75+625\cdot (4)}{\sqrt{[5+15\cdot (4)]^(2)+[20\cdot (4)]^(2)}}$

$\dot r_(B/A) \approx 24.981\,(km)/(h)$

The distance between the ghost changes at 10 pm approximately at a rate of 24.981 kilometers per hour.

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There were 3 squirrels and 18 acorns on Josh's back porch. What was the ratio of acorns to squirrels? Enter your answer in reduced form.

Nine yards of ribbon are cut into 8 equal pieces what is the length of each piece of ribbon. Write a division expression to represent the problem and solve

Answers

Answer:

$x=(9)/(8)\ yards$

$x=1.125\ yards$

Step-by-step explanation:

Let's call x the length of each piece in yards

If the ribbon is cut into 8 equal pieces then the sum of the pieces is:

$x+x+x+x+x+x+x+x=8x$

Then:

$8x=9\ yards$

Now we solve the equation for x

$8x=9\ yards$

Divide both sides of equality by 8

$(8)/(8)x=(9)/(8)\ yards$

$x=(9)/(8)\ yards$

So the length of each piece is $(9)/(8)$ of a yard.

This is: 1.125 yards

Find mH to the nearest degree. HELP PLEASE! URGENT!!!!!!
GRADEPOINT

Answers

i believe it would be 23

Sales of Volkswagen's popular Beetle have grown steadily at auto dealerships in Nevada during the past 5 years. The sales manager has predicted in 2004 and 2005 sales would be 410 VW's. Using exponential smoothing with a alpha = 0.30 develop a forecast for 2006 through 2010. What is the forecast value for 2010?Please answer to one decimal place. (Example: 466.1)Formula: Ft = Ft-1 + alpha(At-1 - Ft-1)Actual sales data:2005 = 4502006 = 4952007 = 5182008 = 5632009 = 584

Answers

Answer:

Step-by-step explanation:

Given the data:

Year___Actual sale (At) ___forecast(Ft)

2005__450_____________410

2006__495____________ 422

2007__518____________ 443.9

2008_ 563____________ 466.1

2009_584____________ 495.2

2010__

Using the formula :

Ft = Ft-1 + alpha(At-1 - Ft-1)

Ft-1 = previous year forecast

At-1 = previous year actual

Alpha = 0.3

Forecast:

2006:

410 + 0.3(450 - 410) = 422.0

2007:

422 + 0.3(495 - 422) = 443.9

2008:

443.9 + 0.3(518 - 443.9) = 466.1

2009:

466.1 + 0.3(563 - 466.1) = 495.2

2010:

495.2 + 0.3(584 - 495.2) = 521.8

Forecasted value for 2010 = 521.8

Final answer:

By utilizing the method of exponential smoothing with alpha=0.3 and applying the forecasting formula iteratively, the forecasted sales of Volkswagen Beetles for 2010 in Nevada is 525.7 units.

Explanation:

The exponential smoothing method is commonly used in business and economics for forecasting future data in situations where historical data is available. The forecast value for 2010 using exponential smoothing with alpha = 0.30 can be obtained by implementing the provided formula in an iterative manner. This formula takes into account the actual data point from the previous year (At-1) and the forecasted data point for that year (Ft-1).

Let us use the forecast value for 2004 and 2005, which was predicted as 410 for each year, as our initial forecast value (F1).

By applying the formula Ft = Ft-1 + alpha * (At-1 - Ft-1) iteratively for each year from 2006 to 2009, we get:

Forecast for 2006 (F_2006) would be 410 + 0.30*(450-410) = 422.
Then, the forecast for 2007 (F_2007) is 422 + 0.30*(495-422) = 443.9.
The forecast for 2008 (F_2008) is 443.9 + 0.30*(518-443.9) = 466.1.
For 2009 (F_2009), the forecast is 466.1 + 0.30*(563-466.1) = 496.37.

Using these forecasted rates, we then forecast for the year 2010. The forecast for 2010 (F_2010) is calculated by 496.37 + 0.30*(584-496.37) giving 525.67 (rounded to one decimal place). Hence the forecast for the year 2010 using exponential smoothing with the alpha as 0.30 is estimated to be 525.7 VolksWagen Beetles.

Learn more about Exponential Smoothing here:

brainly.com/question/31358866

#SPJ3

Equivalent ratio of 30:36=5:_

Answers

30:36 is equivalent to 5:6

30:36 (divide by 6) = 5:6
56:36 (divide by 4) = 14:9
15:18:9 (divide by 3) = 5:6:3

When solving ratios divide by greatest common factor of the numbers(GCF).

Example: 2:4:6
GCF=2
Divide by 2
Answer=1:2:3

I hope this was helpful to you!

The volume of an object is given as a function of time by V = A + B t + C t4 . Find the dimension of the constant C