Baba Yaga lost her broom somewhere between her hut and Bald Mountain, and wants to get it back. She calculates that with a tailwind of 2 km/h, she can fly from her hut to Bald Mountain in 6 hours. Baba Yaga starts her trip, finds her broom 40 km before Bald Mountain, and turns around and flies home. The entire journey takes 9 hours. Find the speed Baba Yaga flies in quiet weather (with no tailwind or headwind).

Answers

Answer 1

Answer:

The speed with which Baba Yaga flies in quiet weather (with no tailwind or headwind) is approximately 2.9 km/h

Step-by-step explanation:

In the question, we have;

The speed of the tailwind = 2 km/h

The time it takes Baba Yaga to the Bald Mountain = 6 hours

The location where Baba Yaga finds her broom = 40 km before Bald Mountain

The duration of the entire journey = 9 hours

Let 'v' represent the speed with which Baba Yaga flies in quiet weather (with no tailwind or headwind), we get;

(v + 2) × t = (v - 2) × (t - 9)

v·t + 2·t = v·t - 9·v - 2·t + 18

2·t = 18 - 9·v - 2·t

4·t = 18 - 9·v

t = 4.5 - 2.25·v

(v + 2) × 6 = (v - 2) × (t - 9) + 40

6·v + 12 = (v - 2) × (4.5 - 2.25·v - 9) + 40

6·v + 12 = (v - 2) × (-2.25·v - 4.5) + 40

With a graphing calculator, we have;

6·v + 12 + 2.5·v² - 0.5·v - 9 - 40 = 0

5·v² + 11·v - 74 = 0

Using the quadratic formula

v = (-11 ± √(11² - 4·5×(-74)))/(2·5)

v ≈ 2.9, or v ≈ -5.1

Therefore;

The speed with which Baba Yaga flies in quiet weather (with no tailwind or headwind), v ≈ 2.9 km/h


Related Questions

Find the volume of a right circular cone that has a height of 2.7 ft and a base with a diameter of 14.4 ft. Round your answer to the nearest tenth of a cubic foot.

Answers

Answer:

20.4 cubic feet

Step-by-step explanation:

formula for the volume of a cone is (r^2xhxpi)/3

so, r= 14.4/2

(7.2x2.7xpi)/3

The volume of a right circular cone is 146.49 cubic foot.

What is the volume of a right circular cone?

The Volume of Right Circular Cone formula is defined as The volume of a cone is one-third of the product of the area of the base and the height of the cone.

The volume of a right circular cone is given by;

[tex]\rm Volume=\dfrac{1}{3}\pi r^h\\\\r = radius, \ h = height\\[/tex]

The volume of a right circular cone that has a height of 2.7 ft and a base with a diameter of 14.4 ft.

The radius of the cone is;

[tex]\rm Radius=\dfrac{diameter}{2}\\\\ Radius=\dfrac{14.4}{2}\\\\ Radius=7.2[/tex]

The volume of a right circular cone is;

[tex]\rm Volume=\dfrac{1}{3}\pi r^h\\\\ Volume=\dfrac{1}{3}\times 3.14 \times (7.2)^2\times 2.7\\\\Volume=146.49[/tex]

Hence, the volume of a right circular cone is 146.49 cubic foot.

Learn more about circular cone here;

https://brainly.com/question/14735698

#SPJ2

Given the vertex form of a parabola​

Answers

It’s C. You’re welcome

PL Z HELP 30 points brainliest

Kenneth sold $26,000 worth of computers in eight days. At this rate, how many dollars worth of computers can he sell in 10 days?

Answers

Answer:

$32500

Step-by-step explanation:

26,000/8=3250

325010x10=32500

Josiah had 128 toy cars. If he organizes them into groups of 7 , how many cars will be in the final group?

Answers

Answer:

2

Step-by-step explanation:

128divided by 7 = 126

11. What is the value of x?
X
X-
2
x + 5
x + 1

Answers

da - x+5

Explicación

cualquier expresión multiplicada por 1 es igual a si mismo

x-2x+s

agrupe los términos semejantes

-x+5

PLEASE PLEASE HELP!!!!

Answers

Answer:

I think acute

Step-by-step explanation:

Write the following expression using symbolic language.
1) Five less than the product of seven and a number x
2) The difference of nine times a number y and eighteen
3) Half a number n increased by four times the number
4) Twice the sum of a number w cubed and twenty-three

Answers

Answer:

             1)   7x - 5              2)   9y - 18              3)   0.5n + 4n              4)  2(w³+23) Step-by-step explanation:

1)

The product of seven and a number x:   7·x = 7x

Five less than the product of seven and a number x:

7x - 5

2)

nine times a number y:  9·y = 9y

The difference of nine times a number y and eighteen:

9y - 18

3)

half a number n:   0.5n

four times the number:   4·n = 4n

Half a number n increased by four times the number:

0.5n + 4n

4)

a number w cubed:  

the sum of a number w cubed and twenty-three:  w³+23

Twice the sum of a number w cubed and twenty-three:

2(w³+23)

Is it the first one the second one the third one the fourth one ??not to be rude but please hurry !!! 20 points !!!

Answers

Answer:

5/6 ÷ 1/12 = 10

Step-by-step explanation:

5/6 ÷ 1/12     =      5/6 x 12/1 = 60/6 = 10

Proof:

5/6 tank = 10/12 tank

If each trip takes 1/12 tank, then 10 ÷ 1 = 10 trips

Which numbers are solutions of the inequality?

x > –5; –7, –5, –1


–7 and –5

–1

–5 and –1

–5

Answers

Answer:

—1 ...........................

what would happen to a mounthly payment if the interest rate decreased

Answers

What is the payment you start with?

Jamil has $62.67 in his saving account. His grandma gave him $5.00 for mowing the lawn and $.75 for taking out the garbage. How much money does Jamil have altogether?

Answers

$62.67+$5.00+$0.75=68.42
Workup in photo below

The Bower family and the Jones family went to a restaurant and ordered food.
• Each burger cost the same, and each drink cost the same.
• The Bowers ordered 3 burgers and 2 drinks for a total of $13.50.
• The Joneses ordered 5 burgers and 4 drinks for a total of $23.50.
Which system of equations can be used to determine the cost of each burger, m, and each drink, p?

Answers

Answer:

right now in Bonny

Step-by-step explanation:

am so sorry for your prayers

hope it helps

I need help in the answer it’s math

Answers

E

Step-by-step explanation:

lolkyuhgt5jjnnnnnnneeeee

2 EASY QUESTIONS HELP

Answers

Answer:

what are the questions

Step-by-step explanation:

what is the question

Avery is going to invest $270 and leave it in an account for 20 years. Assuming the interest is compounded continuously, what interest rate, to the nearest hundredth of a percent, would be required in order for Avery to end up with $600?

Answers

Answer:

50

Step-by-step explanation:

hhh

Answer:

3.99%

Step-by-step explanation:

A grocer wants to mix two kinds of coffee. One kind sells for $1.00 per pound, and the other sells for $2.55 per pound. He wants to mix a total of 28 pounds and sell it for $1.35 per pound. How many pounds of each kind should he use in the new mix? (Round off the answers to the nearest hundredth.)

Answers

21.68 of the dollar coffee
6.32 of the expensive coffee

solve for x
4x=30
give your answer as an improper fraction in its simplest form​

Answers

Answer:

x=15/2

Step-by-step explanation:

given:-4x=304x/4=30/4x=7.5 when we convert to improper fraction=75/10=15/2

Solve for k:
k over 6.12 = 8.7

1. k = 53.244
2. k = 1.42
3. k = 2.58

Answers

Answer:

1. k=53.244 or k=13311/250



1. By what factor did the medicine decrease in the first hour and a half? Explain how you know.

Answers

Answer:

4/9

Step-by-step explanation:

At t = 0 ; volume = 270

At t = 1.5 ; volume = 80

y = P(1 - r)^t

y =ab^x (exponential)

a = initial amout at t = 0

y = final amount

t = 1.5

80 = 270b^t

80/270 = b^t

8/27 = b^1.5

8/27 = b^3/2

b^3/2*2/3 = (8/27)^2/3

Cube root of 8/27 = 2/3

Square of 2/3 = (2/3)^2 = 4/9

HELP!!! Will give brainliest:) What shapes have all sides that are congruent?

Answers

Answer:

A square has all sides congruent. SIDE A, B, C and D would be congruent in size to one another, and the angles would also be equal to one another. However, most any polygon can be drawn with all sides and angles equal. For instance, an equilateral triangle has all sides and all angles equal, and that is the definition of a polygon. Polygons with more sides are described as "regular" e.g., a stop sign or an equilateral octagon is also a shape that has all sides congruent. A rectangle, however, would not, since only two sides would be congruent to one another.

( I hope this was helpful) >;D

You deposit $400 in an account . The account earns $ 16 simple interest in years . What is the annual interest rate? year

Answers

Answer:

The correct answer is 25.

Step-by-step explanation:

deposit- 400

interest- 16

Rate= deposit divided by interest

400 divided by 16 = 25

hiii please help i’ll give brainliest thanks

Answers

Answer:

0

Step-by-step explanation:

Welcome To Brainly!

Evaluate using PEMDAS

Parenthesis - None

Exponents 2^3

2x2 = 4

4x2 =8

now we have

72/9 - 1 x 8

Multiplication and Division

Going left to right

72/9=8

-1x8=-8

now we have 8 - 8

our last step is to subtract

8 - 8 = 0

the answer is 0

Find the interest
earned:
$26,000 for 36 months
at 7.5% annual
compound interest

Answers

Answer:

Interest = $6,300 (Approx.)

Step-by-step explanation:

Given:

Amount deposit (P) = $26,000

Number of month = 36 month

Number of year (n) = 36 / 12 = 3 year

Rate of interest (r) = 7.5% = 0.075  

Find:

Interest  earned

Computation:

Interest = p[(1+r)ⁿ-1]

Interest = 26,000[(1+0.075)³-1]

Interest = 26,000[(1.075)³-1]

Interest = 6,299.71

Interest = $6,300 (Approx.)

You are making lemonade. The amount of sugar you need depends on the amount of lemonade mix you use. Cups of sugar \dfrac13 3 1 ​ start fraction, 1, divided by, 3, end fraction 111 333 Packets of lemonade mix 111 333 999 Is the amount of sugar you need proportional to the amount of lemonade mix you use?

Answers

Answer:

Yes, the amount of sugar you need proportional to the amount of lemonade mix you use.

Step-by-step explanation:

You are making lemonade. The amount of sugar you need depends on the amount of lemonade mix you use. Cups of sugar

1/3

1

3

Packets of lemonade mix

1

3

9

Is the amount of sugar you need proportional to the amount of lemonade mix you use?

Cups of sugar ∝ Number of packets

C ∝ N

C = k/N

k = C/N

a) For

1/3 cups of sugar and 1 packet of Lemonade mix

1/3 ∝ 1

1/3 = 1k

k = 1/3/1

k = 1/3

b) For

1 cups of sugar and 3 packets of Lemonade mix

1 ∝ 3

1 = 3k

k = 1/3

k = 1/3

c) For

3 cups of sugar and 9 packets of Lemonade mix

3 ∝ 9

3= 9k

k = 3/9

k = 1/3

Therefore, Yes, the amount of sugar you need proportional to the amount of lemonade mix you use. This is because the value is k is the same

Answer:

yes

Step-by-step explanation:

HELP PLS!!

If the sequence 4, 8, 12, 16 continues, what will be the 7th
term?

Answers

Answer:

28

Step-by-step explanation:

In order to find the seventh term in this arithmetic function, you need to find its function; in order to do this, you must first identify the common difference by finding the difference between two consecutive terms:

16 - 12 = 4; the common difference is 4

Now, you need to find the 0th term, which is the 1st term minus the common difference:

4 - 4 = 0

At this point, you can write out the function (where f(n) = [0th term] + [common difference]n:

f(n) = 4n

Finally, you can plug 7 into this function:

f(n) = 4(7)

f(n) = 28, so the 7th term is 28

The total cost of a pair of shoes and a hoodie is $150 the hoodie cost $100 more than the pair of shoes how much does each item cost?

Answers

x + y = 150

x = y + 100

2y + 100 = 150

2y = 50

y = 25

shoes are 25 hoodie is 125

Answer:

shoes = $25

hoodie = $125

Step-by-step explanation:

total cost = $150

hoodie = x + 100

shoes = x

x + x + 100 = 150

2x = 150 - 100

x = 50/2

x = 25

shoes = $25

hoodie = $125

add them up and u get the price of the shoe 125+25= $150

Help me please !!!!!!!!

Answers

Step-by-step explanation:

[tex] \tan(45) = \frac{x}{13} \\ 1 = \frac{x}{13} \\ x = 13[/tex]

[tex] \cos(45) = \frac{13}{y} \\ 2 \sqrt{2} = \frac{13}{y} \\ 2y \sqrt{2} = 13 \\ y = \frac{13}{2 \sqrt{2} } [/tex]

If a printer can print 68 lines in per minute how many lines can it print in an hour? (hint: 1 hour=60 minutes)

Answers

Answer:

4080

Step-by-step explanation:

You are just multiplying 68 x 60= 4080

Use the simple interest formula to find the interest earned and the ending balance. I = Prt

1. $270 at 9% for 3 years

Answers

Answer:

$72.90 is the interest earned

Step-by-step explanation:

The appropriate formula is i = prt, where r is the annual interest rate expressed as a decimal fraction.

Here, i = ($270)(0.09)(3 yr) = $72.90 is the interest earned

Nine times the sum of a number and 2 is 8. Use the variable x for the unknown number

Answers

The equation will look like this …9(x + 2)=8
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