Two boats leave the same place at the same time. The first boat heads due north at 10 kilometers per hour. The second boat heads due west at 16 kilometers per hour. After 2.5 hours, how fast is the distance between the boats increasing

Answers

Answer 1

Answer:

18.87 km/hr

Step-by-step explanation:

First boat is heading North with a speed of 10 km/hr.

Second boat is heading West with a speed of 16 km/hr.

Time for which they move = 2.5 hours

To find:

The speed at which the distance is increasing between the two boats.

Solution:

Let the situation be represented by the attached diagram.

Their initial position is represented by point O from where they move towards point A and point B respectively.

[tex]Distance = Speed \times Time[/tex]

[tex]Distance\ OA = 10 \times 2.5 = 25\ km[/tex]

[tex]Distance\ OB = 16 \times 2.5 = 40\ km[/tex]

We can use Pythagorean Theorem to find the distance AB.

AB is the hypotenuse of the right angled [tex]\triangle AOB[/tex].

According to Pythagorean theorem:

[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow AB^{2} = OA^{2} + OB^{2}\\\Rightarrow AB^2 = 25^2 + 40^2\\\Rightarrow AB^2 = 2225^2\\\Rightarrow AB^2 \approx 47.17\ km[/tex]

The speed at which distance is increasing between the two boats is given as:

[tex]\dfrac{47.17}{2.5} \approx 18.87\ km/hr[/tex]

Two Boats Leave The Same Place At The Same Time. The First Boat Heads Due North At 10 Kilometers Per

Related Questions

we have 2 fractions 5/8 and 5/4

Answers

Is there more context or information?

Due Today, Help me pls. I will MARK AS BRAINLIEST.

Answers

BAD, ADB, DBA, DA, DB, BA :)

What are the solutions of the equation x4 - 5x2 - 14 = 0? Use factoring to solve.
x = +/- √7 and x = +/- √2
x = +/- i√7 and x = +/- i √2
x = +/- i √7 and x = +/- √2
x = +/- √7 and x = +/- i √2

Answers

Answer:D

Step-by-step explanation:

The solution is: x = +/- √7 and x = +/- i √2  are the solutions of the equation x^4 - 5x^2 - 14 = 0.

What is  simplification?

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

given that,

we have to factorize the equation,

The given equation is

x^4 - 5x^2 - 14 = 0

To factor this expression, we can change variables to make easier to see the solution.

x^4 = y^2

and

x^2 = y

Applying the change, we have

y^2 - 5y - 14 = 0

Now, you can observe that to factor this expression, we just need to find two number which product is 14 and which difference is 5, such numbers are 7 and 2.

y^2 - 5y - 14 = 0

or, (y-7) ( y+2) = 0

However, remember that , y = x^2

so, (x^2-7) ( x^2+2) = 0

Applying the zero property, we have

x = +/- √7

and x = +/- i √2

As you can see, the equation has two real solutions and two complex solutions.

Therefore, the right answer is the last choice.

To learn more on simplification click:

brainly.com/question/28996879

#SPJ7

Help I’m being timed!!!

Answers

Answer:

50.24 square inches

Step-by-step explanation:

A circles area is:

[tex]\pi r^{2}[/tex]

Insert the values:

(3.14)(4^2)

3.14(16)

50.24 square inches

95 to 155 as a percentage

Answers

Answer:

61.290322580645% or 61%

Step-by-step explanation:

I put your question into a percentage calculator and got this for the answer. Wish you luck.

Answer:

Convert the decimal to a percentage by multiplying the decimal by 100

9515500%

Step-by-step explanation:

don't know if this the answer your looking for.

Eric and Shiloh each have a savings account. The ratio of Eric's account balance to Shiloh's account balance is 4:3. Together they have a total of $140 in their accounts. In the tape diagram below, how much money does each bar represent? [Type your answer as a number.]​

Answers

Answer:

20

Step-by-step explanation:

E:S

4:3

4u+3u=140

7u=140

u=20

398 divided by 344?
Please help me.

Answers

Answer:

1.15697674419

Step-by-step explanation:

Answer:

1.15697674419 is the answer

please can some one solve this for me thankyou :-)

its sudoku

Answers

 

In the .docx file is a SUDOKU that needs to be resolved.

See the solution in the attached image.

   

Help please! Could you put an explanation as well?

Answers

Answer:

y=-(4x/3) -1

Step-by-step explanation:

Slope=m= -4/3

y intercept = c = -1

now using equation;

y= mx+c

y= (-4/3)x+(-1)

y=-(4x/3) -1

30 cupcakes he spreads 1/5 mint icing and 1/2chocolate how many will have vanilla icing

Answers

Answer: 12 vanilla

Explanation:

1/5 of 30 = mint
6 = mint
1/2 of 30 - 6 = chocolate
1/2 of 24 = chocolate
12 = chocolate
30 - (12 + 6) = vanilla
30 - 18 = vanilla
12 = vanilla

what are terms
answer choices...

1. the number in front of the variable
2. a letter that represents a number
3. the individual parts of an expression
4. the number that stands Alone with no variable...

please answer ​

Answers

Answer:

3. the individual parts of an expression.

Step-by-step explanation:

an example would be 5x + 2y - 6

5x, 2y, and 6 are all terms that are separated by symbols like +,-,× etc.

Simplify and Factorise a(a + b - c) - bc

Answers

[tex] {2a}^{2} + ab - ac - bc[/tex]

Step-by-step explanation:

[tex] = a(a + ab - c) - bc[/tex]

[tex] = {a}^{2} + {a}^{2} + ab - ac - bc[/tex]

[tex] = {2a}^{2} + ab - ac - bc[/tex]

Put these substances in order of density with the most dense first and the least dense last.

Answers

Answer:

iron

rubber

cotton ball

helium

Solve

1+−=0
2 − ^2 = 4

Answers

Answer:

Both are inaccurate things.

pls help me answer this​

Answers

This picture doesn’t include all of the variables values, without it this can’t be solved. :)

can anyone help me thanks

Answers

Answer:

C

Step-by-step explanation:

We can use the vertex form of a quadratic equation, given by:

[tex]f(x)=a(x-h)^2+k[/tex]

Where a is the leading coefficient and (h, k) is the vertex.

We are given that the vertex is (-3, 1).

Hence, h = -3 and k = 1. By substitution:

[tex]f(x)=a(x-(-3))^2+(1)[/tex]

Simplify:

[tex]f(x)=a(x+3)^2+1[/tex]

With this, we can eliminate B and D.

Notice that our parabola is curving downwards.

Therefore, our leading coefficient must be negative.

The only choice that leaves us with is C.

So, our function is:

[tex]f(x)=-(x+3)^2+1[/tex]

And our final answer is C.

Linda and Rob open an online savings account that has a 2.89% annual interest rate, compounded
weekly. If they deposit $35 every week, how much will be in the account after 15 years?

Answers

Answer:

FV= $34,222.33

Step-by-step explanation:

First, we need to calculate the weekly interest rate:

Weekly interest rate= 0.0289/52= 0.00056

To calculate the future value (FV), we need to use the following formula:

FV= {A*[(1+i)^n-1]}/i

A= weekly deposit

n= 15*52= 780

A= $35

FV= {35*[(1.00056^780) - 1]} / 0.00056

FV= $34,222.33

The owner of Carlisle Construction is a little
overprotective of his brand new cement mixer,
so each night, he parks it in a storage facility
that is 120 feet long, 45 feet wide, and 45
feet high. What is the facility's volume in cubic
yards?

Answers

Answer:

The facility's volume in cubic yards is 9000

Step-by-step explanation:

The volume of the facility is given by the multiplication of it's dimensions.

We want the volume in cubic yards, so the dimensions have to be in yards.

Each feet has a third of an yard. So the dimensions are:

120 feet = 40 yards

45 feet = 15 yards

45 feet = 15 yards

What is the facility's volume in cubic yards?

[tex]V = 40*15*15 = 9000[/tex]

The facility's volume in cubic yards is 9000

27 students are learning to make balloons animals. There are 3,172 balloons to be shared equally among the students. How many balloons are left over after sharing them equally? Show all necessary work.

Answers

Answer:

you would do 3,172 divided 27 which would be 117 then subtract that by 3,172

Step-by-step explanation:

answer number 11 pls

Answers

Answer:

121.52 feet

Step-by-step explanation:

9.8+2.6 = 12.4

12.4 * 9.8 = 121.52

Afla 3 numere naturale știind ca produsul primelor doua este 54, produsul ultimelor doua este 12,iar suma dintre primul și al treilea este 11

Answers

Answer:

Cele 3 numere naturale sunt:

Primul număr = a = 9

Al doilea număr = b = 6

Al treilea număr = c = 2

Step-by-step explanation:

Fie cele 3 numere naturale reprezentate ca:

Primul număr = a

Al doilea număr = b

Al treilea număr = c

Produsul primelor două este de 54

a × b = 54

ab = 54 ...... Ecuația 1

a = 54 / b

Produsul ultimelor două este 12

b × c = 12

bc = 12 ........ Ecuația 2

c = 12 / b

Suma primului și celui de-al treilea este 11

a + c = 11 ...... Ecuația 3

Înlocuim

54 / b pentru a și 12 / b pentru c

54 / b + 12 / b = 11

54 + 12 / b = 11

Cross Multiply

66 / b = 11

11b = 66

b = 66/11

b = 6

Rezolvarea pentru un

a = 54 / b

a = 54/6

a = 9

c = 12 / b

c = 12/6

c = 2

Prin urmare, cele 3 numere naturale sunt:

Primul număr = a = 9

Al doilea număr = b = 6

Al treilea număr = c = 2

simplify the expression 12( a+ 5)

Answers

Answer:

12a+60 i think lol

Step-by-step explanation:

this is how i did it though:

12(a+b)

12a+60

I think it would be 12(a+60) because 60÷12 is five

Plsss help ASAP pls this is due at 12:00

Answers

Answer:

$74.49

(basically $74.50)

Step-by-step explanation:

hope that helps :))

please help and explain!! I got 14x +0​

Answers

Answer:

[C] 16

Explanation:

7x + 8 − 7x + 8

= 7x + 8 + −7x + 8

Combine Like Terms

= 7x + 8 + −7x + 8

= (7x + −7x) + (8 + 8)

= 16

It's 16.
It's would be 7x+8-7x+8 the sevens cancel put and you add the 8s. Also rmbr that a positive time a negative is still negative.

What is the value of the expression three less than the quotient of ten and a number, increased by six" when n = 2?

Answers

Answer:

The Answer is 8.

Step-by-step explanation:

I just took the test on Edge and got it right, hope this helps! :)

What is the value of x?

−3/4(12−8x)=5x+15−7x

Answers

Answer:

x = 3

Step-by-step explanation:

step 1: distribute -3/4 among 12 and 8x to get:  -36/4 + 6x

step 2: combine 'like terms' on right side to get -2x + 15

-9 + 6x = -2x + 15

-9 + 8x = 15

8x = 24

x = 3

How much interest is earned on a principal amount of $400 invested at an interest rate of 5% for 3 years

Answers

Answer:$63.05

Step-by-step explanation:400*1.05*1.05*1.05=463.05

463.05-400=63.05

What is the area of a rectangular cake with a length of 10 inches and width of 6 inches?

Answers

Answer:the area of the cake is 60 inches

Step-by-step explanation: length times width. hope this helps.

(18 ÷ 3) + (3² - 7) =

Answers

finish brackets first.

(6) + (9-7)

= 6+2

=8

Mike had $800. He now has $500. What is the percent decrease?​

Answers

300$ is the answer !
$200 is the answer for your question
Other Questions
pretty easy freshman math i just dont really know what the answers are Layla invests money in an account paying a simple interest of 6.4% per year. If she invests $120 and no money will be added or removed from the investment, how much will she have in one year, in dollars and cents? 35 percent as a decimal Which type of plant lives the longest? A large company states in their promotional literature that 80% of their employees have college degrees. If 5 employees are selected at random from this company, what is the probability that all 5 will have college degrees? Solving systems of linear inequalities Hi, I've noticed that a lot of people here lie about the correct answers to problems. I understand if you just really don't know and accidentally told the wrong answer but otherwise, it is unacceptable. People can fail important tests because some people thought it would be funny to joke about the answer. Does making other people fail make you happy?Do you need to push others down to make yourself feel good? Most subjects are ok but its hard to find good reliable answers for social studies. People can get bad scores that lowers their self esteem because you think that the only way to make your self feel good is to see others fail. Please be aware of this. Repost. Lets help everyone succeed, thanks! Kory and two of his friends are going to rent a 3 bedroom apartment for $960 a month. The security deposit is $400 and the pet deposit is $260. In addition to the deposits, Kory and his friends must pay first and last month's rent. If they split the cost evenly, how much will each pay to move in? Point P is the centroid of LMN. Find PN Magnetism is always present when electric charges ___________. Combine like terms to write an equivalent expression for 9y7y. Rewrite the following equation in slope-intercept form.9x 20y = 15Write your answer using integers, proper fractions, and improper fractions in simplest form. in a lever, if the fulcrum is between the effort and load, it is a ______ class lever HELP ME PLEASE IM FAILING Sally is seeking a loan with a simple interest rate of 8% per year. If she wants toborrow $5,000, then how much will she be charged in interest for 2 years. Joanna is driving 185 miles to visit her family. She drives 68 miles in the morning, stops for lunch, and then drives the rest of the distance. How many miles did she drive after lunch?Use the variable m to represent the number of miles she drove after lunch.Which equation represents this situation and its solution?A. m + 68 = 185; m = 117B. 185m = 68; m = 17C. 68m = 185; m = 17D. m + 185 = 68; m = 117 The scale of a map of Florida is 2 cm = 3 miles. If the distance between Apopka and Orlando on the map is 12 cm what is the actual distance? A soccer league has 25 sixth graders, 20 seventh graders, and 15 eighth graders. What is the ratio of 8th graders to 7th graders? ***Write your answer in FRACTION form. Solve 18 (5/6)a.13/14b.15c.18 5/6d.23/6 My shoes were dirty because I had worked/I had been working in the garden?