At 1 P.M., ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 5 P.M.?

Answers

Answer 1
The distance between the ships is changing at a rate of 21.393 km/h

Step 1: First, you must draw an image to help better understand the problem 

The reason that ship A is moving -35km/h is because ship B acts as an "origin" and as things move closer to the "origin" they become negative and as things move away from the "origin" they become positive.

We know that the rate of Ship A is expressed as dAdt=−35 and the rate of Ship B is expressed as dBdt=25

Step 2: We want to figure out how many km Ship A and Ship B traveled in 4 hours

ShipA:−35kmh⋅4hr=−140km

Now if we take this −140km and add it to the 150km we can see that Ship A is now only 10km away from where Ship B began

ShipB:25kmh⋅4hr=100km

This means that Ship B is now 100km from where it originally started

We can now redraw our information

Step 3: We must use the Pythagorean Theorem to find the third side of the triangle

x2+y2=z2→102+1002=z2

z=√102+1002

Step 4: Now that we know z, we must differentiate the original equation in order to find the rate at which z in changing

x2+y2=z2→2xdxdt+2ydydt=2zdzdt

We can simplify by canceling out the 2's

xdxdt+ydydt=zdzdt

Step 5: Write down all the information and then plug into equation

x=10anddxdt=−35
y=100anddydt=25
z=√102+1002anddzdt=?

Now plug in the information

xdxdt+ydydt=zdzdt

10(−35)+100(25)=√102+1002dzdt

−350+2500=√102+1002dzdt

2150=√102+1002dzdt

21.393=dzdt

The distance between the ships are increasing at a rate of 21.393 km/h


Related Questions

What would a frog do if he could not find scissors to cut a coupon out of the newspaper?

Answers

lick it until it gets wet enough to rip it.

What is 0.306 in word form?

Answers

Three Hundred six thousandths 

Answer:

Three hundred six thousandths.

Step-by-step explanation:

We are asked to write 0.306 in word form.

We can see that our given number has 3 tenths, 0 hundredths and 6 thousandths.

To convert our given number in word form, we will write the number of thousandths in 0.306.

The number of thousandths for our given number are three hundred six thousandths, therefore, our number is three hundred six thousandths.

A campground has cabins that can each hold 28 campers. There are 148 campers that are visiting the campground. How many cabins are full if there are 28 campers in each cabin? Please help i'm desperate and i'm marking most brainliest.

Answers

Final answer:

To find the number of full cabins, divide the total number of campers by the number of campers in each cabin. Round the answer up to the nearest whole number.

Explanation:

To find the number of full cabins, you can divide the total number of campers by the number of campers in each cabin.

148 campers / 28 campers per cabin = 5.2857 cabins

Since we can't have fractional cabins, we round up to the nearest whole number, which is 6.

Therefore, there are  that are full.

Final answer:

There are 6 cabins that are full.

Explanation:

To find the number of cabins that are full, we need to divide the total number of campers by the number of campers each cabin can hold. In this case, there are 148 campers and each cabin can hold 28 campers.

We can solve this problem by dividing 148 by 28: 148 ÷ 28 = 5.2857.

Since we cannot have a fraction of a cabin, we round up to the nearest whole number. Therefore, there are 6 cabins that are full.

write division problem that will have a 2-digit quotient and another division problem that will have a 3-digit quotient. Explain how you chose the divisor and dividends.

Answers

300÷5=60
14000÷7=200
600÷30=20
2400÷3=800

• capital one is advertising a 60-month, 5.99% apr motorcycle loan. if you need to borrow $8000 to purchase your dream harley davidson, what will your monthly payment be?

Answers

Given:
P = $8000, the principal
r = 5.99% = 0.0599, the interest rate
t = 60 months = 5 years, the duration
Assume n = 12, monthly compounding.

n*t = 12*5 = 60
r/n = 0.0599/12 = 0.004992

The total value of the loan is
A = P(1 + r/n)⁶⁰
    = 8000(1.004992)⁶⁰
    = 10785.434

Monthly payment = 10785.434/60 = $179.76

Answer: $179.46

Answer:

The monthly payment  is $ 154.29

Step-by-step explanation:

Given : time period = 60 months

Annual interest rate = 5.99%

Amount to be borrowed = $8000

We have to calculate the monthly payment.

We know ,

[tex]P=\dfrac{A\cdot \frac{i}{12}}{1-(1+\frac{i}{12})^{-n}}[/tex]

We have,

interest rate = 5.99% = 0.0599

Amount = $8000

time period = 60 months

P is monthly payment.

[tex]P=\dfrac{8000\left(\frac{0.059}{12}\right)}{1-\left(1+\frac{0.059}{12}\right)^{\left(-60\right)}}[/tex]

Simplify, we get,

P = 154.29

Thus, the monthly payment  is $ 154.29

Using the first derivative test, find all relative extrema for f(x) g

Answers

jdxjvbjfjck kdjndkb kehckbksjckiv jcjuw

The yard behind the Cindy’s house is rectangular in shape
and has a perimeter of 72 feet. If the length  of the yard
is 18 feet longer than the width w of the yard, what is the
area of the yard, in square feet?

Answers

Length = x + 18

Width = x

Perimeter = 72

72 = 2(x + 18) + 2x

72 = 2x + 36 + 2x

72 = 4x + 36

72 - 36 = 4x

36 = 4x

36/4 = x

9 = x

The width is 9 feet.

The length is 9 + 18 or 27 feet.

Area = length • width

A = 27(9)

A = 243 ft^2

You decide to treat yourself to some of your favorite cookies. The box that you bought has 24 cookies. You eat 2 cookies each day as a snack. Which equation shows the number of cookies that you have left at the end of each day?

Answers

Answer:

-2X+24



Step-by-step explanation:


Answer:

[tex]y=-2x+24[/tex]

Step-by-step explanation:

Let

x------> the number of days

y----->the number of cookies which are left at the end of each day

we know that

[tex]y=-2x+24[/tex]

verify

For [tex]x=0\ days[/tex]

[tex]y=-2(0)+24=24\ cookies[/tex] -----> original amount of cookies

For [tex]x=1\ days[/tex]

[tex]y=-2(1)+24=22\ cookies[/tex]

For [tex]x=12\ days[/tex]

[tex]y=-2(12)+24=0\ cookies[/tex]


Trigonometric area formula: Area = 1/2 ab sin(c)

What is the area of triangle DEF? Round to the nearest tenth of a square unit.

10.3 square units
18.0 square units
20.0 square units
20.6 square units

Answers

Answer:

1.  10.3 square units.

Step-by-step explanation:  

The general formula for area of triangle is [tex]\frac{1}{2}(\text{ Base}\times\text{ Height}})[/tex]. We can also find area of a triangle using trigonometric area formula.

[tex]Area=\frac{1}{2} ab\text{ sin}(c)[/tex], where a represents length of base and height of triangle is represented by [tex]b\text { sin}(c)[/tex].  

We have been given two angle measures but we can only use sine of included angle whose two side lengths are given. In our triangle the angle that measures 31 degrees in included angle of sides EF and DF.  

Now let us substitute our given values in the above formula.  

[tex]Area=\frac{1}{2}\times 8\times 5\text{ sin}(31)[/tex]

[tex]Area=\frac{1}{2}\times 8\times 5\times 0.51503807491[/tex]

[tex]Area=4\times 5 \times 0.51503807491[/tex]

[tex]Area=20 \times 0.51503807491[/tex]

[tex]Area=10.3007614982\approx 10.3[/tex]

Therefore, the area of triangle DEF is 10.3 square units and 1st option is the correct choice.

Answer:

10.3= the awnser

Step-by-step explanation:

just took test and got it right.

what is 139.47 rounded to the nearest tenth?

Answers

the answer is 139.50
139.47 rounded to the nearest tenth is 139.5. It is that because the digit 4, is in the tenths place and the number to the right of it is 7, you would round up because 7 is greater than 4. So you would round up, to 139.50.

The owner of a candy store wants to mix some peanuts worth $3 per pound, some cashews worth $10 per pound, and some Brazil nuts worth $9 per pound to get 50 pounds of a mixture that will sell for $6.80 per pound. She uses 10 fewer pounds of cashews than peanuts. How many pounds of each did she use?

Answers

let
x = pounds of peanuts
y = pounds of cashews
z = pounds of Brazil nuts.

The total pounds is 50, therefore
x + y + z = 50                   (1)

The total cost is $6.60 per pound for 50 pounds of mixture.
The total is equal to the sum of the costs of the different nuts.
Because the cost for peanuts, cashews, and Brazil nuts are $3, $10, and $9 respectively, therefore
3x + 10y + 9z = 50*6.8
3x + 10y + 9z = 340         (2)

There are 10 fewer pounds of cashews than peanuts, therefore
x = y + 10                         (3)

Substitute (3) into (1) and (2).
y + 10 + y + z = 50
2y + z = 40                     (4)
3(y + 10) + 10y + 9z = 340
13y + 9z = 310                (5)

From (4),
z = 40 - 2y          (6)
Substitute (6) into (5).
13y + 9(40 - 2y) = 310
-5y = -50
y = 10
z = 40 - 2y = 40 - 20 = 20
x = y + 10 = 20

Answer:
Peanuts:     20 pounds
Cashews:   10 pounds
Brazil nuts: 20 pounds


How many unique triangles can be made when one angle measures 90° and another angle is half that measure?

Answers

in a right-triangle, if either of the other two angles are "half that measure", or half of 90°, that means 45°, then the last angle will also have to be a 45° one too, and the sides coming from the 90° angle, will be equal twins, and therefore they can only make up one type-length hypotenuse, and due to that, you can only make that one triangle.  Check picture below.


You order an entree for $12. You pay 0.78 in taxes. What is the tax rate

Answers

6.5% tax rate 12 x .065 = .78 

You pay $0.78 in tax, so the rate is 0.78/12×100%=78/12=6.5%.

A family pays $45 each month for cable television. The cost increases 7%.
a. How many dollars is the increase?
b. What is the new monthly cost?SHO
W YOUR WORK

Answers

3.15

Hope this helped

What is an equation of a line, in point-slope form, that passes through (1, −7) and has a slope of −2/3 ?

Answers

y+7=-2/3(x-1)
point-slope form- y + 7 = -2/3(x - 1)

Nora took 8 bottles of water to a picnic. Of those bottles of water, she and her friends opened a certain number of bottles. b. What expression can be used to determine the number of unopened bottles at the end of the picnic?



A .8 + b

B. b + 8


C 8 - b


D. b - 8


Answers

8 - b

8 is the total amount of bottles that they started out with.
b is the amount that Nora and her friends drank.

b cannot be greater than 8, since 8 is the limit

C. 8 - b is your answer

hope this helps

I really need help with this question!

Answers

First put the terms in order:

4x[tex] ^{7} [/tex] + 5x[tex] ^{6} [/tex] - 4x[tex] ^{4} [/tex] + 1.

So the first term would be 4x^7. Second is 5x^6. Third is -4x^4. Fourth is 1.

The coefficients are the numbers in front of each variable. 

Describe how the graph of y= x2 can be transformed to the graph of the given equation. y = x2 - 20

Answers

y = x² is the parent function

Apply a displacement or translation of  -20 units in the y direction to obtain
f(x) = x² - 20

Answer:
Apply a translation of - 20 in y.

translate to an algebraic expression 49 more than t

Answers

t + 49 This is the answer because by saying “more than” you are adding and the symbol for adding is “+”.

how do u find the initial value on a graph

Answers

First, you have to find the axis of symmetry and vertex. Next, make a function to model a linear relationship between the two quantities. Finally, find the rate of change and initial value of the function from a description of a relationship or from 2 (x , y) values, including reading these from graph or a table.
What you would need to do is:
1) Determine the rate of change
2)
Find the function
  (initial value) of x and y values.


Which are factors of x2 – 4x – 5? Check all that apply. (x – 5) (x – 4) (x – 2) (x + 1) (x + 5)

Answers

x^2 – 4x – 5 = (x - 5)(x + 1)
cause
(x - 5)(x + 1) = x^2 -5x +x - 5= x^2 -4x - 5

so (x - 5) and (x + 1) are factors

answer
(x - 5) and (x + 1) 
x² - 4x - 5
x          -5
x           1

(x-5)(x+1) is your answer

none of the others work, because they wont give you the desired number in the middle, -4x

hope this helps

what is the graph of the equation 4x-5y=15

Answers

Hello James!

Graph using the slope and y - intercept.
Slope: [tex] \frac{4}{5} [/tex]
Y-intercept: -3

The graph looks like this ↓↓↓

The correct answer I think is

A basket of laundry is being separated. Divide 48 pieces into 2 clothing groups so the ratio is 1 to 3

Answers

[tex]\bf 48\qquad 1:3\qquad \cfrac{1}{3}\qquad \qquad \cfrac{1\cdot \frac{48}{1+3}}{3\cdot \frac{48}{1+3}}\implies \cfrac{1\cdot 12}{3\cdot 12}\implies \cfrac{12}{36}[/tex]

btw, don't put the shirts in the same bundle as the socks, you may end up with an unwanted perfume.

a telephone pole needs a wire attached to its top and anchored to the ground at a point that is 56 feet less than the height of the pole. if the wire is to be 16 feet longer than the height of the pole what is the height of the pole

Answers

check the picture below.

[tex]\bf (y+16)^2=(y-56)^2+y^2 \\\\\\ \underline{y^2}+32y+16^2=y^2-112y+56^2+\underline{y^2} \\\\\\ 32y+256=y^2-112y+3136\implies 0=y^2-144y+2880 \\\\\\ 0=(y-24)(y-120)\implies y= \begin{cases} \boxed{120}\\ 24 \end{cases}[/tex]


it cannot be 24, because then the ground base area will be 24 - 56, which is a negative amount and unfeasible for the phenomena.

Will give brainliest.
The table below represents the displacement of a bird from its nest as a function of time: Time (hours) x Displacement from nest (miles) y 0 12 1 20 2 28 3 36 4 44 Part A: What is the y-intercept of the function, and what does this tell you about the bird? (4 points) Part B: Calculate the average rate of change of the function represented by the table between x = 1 to x = 3 hours, and tell what the average rate represents. (4 points) Part C: What would be the domain of the function if the bird continued to fly at this rate until it traveled 172 miles from the nest? (2 points)

Answers

Part A: y-intercept = 12 miles 


Part B: Find the average rate of change: 36 - 20/2 = 16/2 = 8 mph
This tells us that the bird can travel long distances. 


Part C: 172 - 12 = 160 miles at a rate of 8 mph
160 mi ÷ 8mph = 20 hrs

Domain of function = 0 ≤ x ≤ 20

the graph of y=x^2 is shifted 4 units to the right, vertically stretched by a factor of 6, reflected over the x axis and shifted 7 units downward

Answers

Use the vertex form: 

y = 6(-x-4)^2 -7

Answer:y=-6Vx-7

Step-by-step explanation:

Simplify the following expression. (3 + 8 x ) + 7 x
3 + 15
x 18
x 18 + x
11 x + 7

Answers

d . 3+4=11 so d is the only one with an 11 to shorten and simplify it,if it is wrong I'm sorry.

The simplified expression of 4 +9 "/" 3 "/" 2 x 3 + (3 + 1) x 4 is 17, following the order of operations or PEMDAS.

To simplify the given expression, follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

The original expression is 4 +9 / 3 / 2 x 3 + (3 + 1) x 4. First, address operations inside parentheses: (3+1) equals 4. The expression becomes 4 +9 / 3 / 2 x 3 + 4 x 4.

Next, handle the multiplication and division from left to right: 9 / 3 equals 3, and 2 x 3 equals 6. Then, 4 x 4 equals 16. This turns our expression into 4 + 3 - 6 + 16.

Finally, perform addition and subtraction from left to right: 4 + 3 equals 7, 7 - 6 equals 1, and 1 + 16 equals 17. Therefore, the simplified expression is 17.

complete the solution of the equation. find the value of y when x equals 15.

-x+2y=-1

Answers

-x + 2y = -1....when x = 15...so we sub in 15 for x and find y
-15 + 2y = -1
2y = -1 + 15
2y = 14
y = 14/2
y = 7 <==

Ned took a test with 25 questions. He lost 4 points for each of the 6 questions he got wrong and earned an additional 10 points for answering a bonus question correctly. How many points did Ned recieve or lose overall?

Answers

Ned lost 16 points for 4 questions, so he got 9 correct out of 25, the bonus he got 10 points so then the final answer is 19.


STEP BY STEP:
> up to 24 questions (which is every 6 question he got wrong) he got 4 questions wrong
> -16 points
> 25-16=9 ( IF EVERY QUESTION WAS WORTH 1 POINT, THEN HIS MIGHT BE THE RIGHT METHOD)
> bonus questions +10 points
> 10+9=19
OVERALL:
> Ned received 19 points (+19)
> Ned lost 16 points (-16)

I may be incorrect, I'm sorry I tried to figure his out, also, if I'm right then, HOPE THIS HELPED!

What percent of 18 is 36

Answers

So you just want to say 36/18 or 2.

So it's 2, or 200%.
100%/x%=18/36

(100/x)*x=(18/36)*x       - we multiply both sides of the equation by x

100=0.5*x       - we divide both sides of the equation by (0.5) to get x

100/0.5=x 

200=x 
x=200
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