A steamer travels 36 km upstream and 32 km downstream in 6.5 hours. The same steamer travels 4 km upstream and 40 km downstream in 180 minutes. Determine the steamer's speed in still water and the stream's speed.

Answers

Answer 1

Answer:

The streamer's speed in still water is 90.23 km/h while the stream's speed is 33.33 km/h

Step-by-step explanation:

Let v = streamer's speed in still water and v' = stream's speed. His speed upstream is V = v + v' and his speed downstream is V' = v - v'.

Since he travels 36 km upstream, the time taken is t = 36/V = 36/(v + v').

he travels 32 km downstream, the time taken is t' = 32/V' = 32/(v - v')

The total time is thus t + t' = 36/(v + v') + 32/(v - v')

Since the whole trip takes 6,5 hours,

36/(v + v') + 32/(v - v') = 6.5  (1)

Multiplying each term by (v + v')(v - v'), we have

(v + v')(v - v')36/(v + v') + (v + v')(v - v')32/(v - v') = 6.5(v + v')(v - v')  (1)

(v - v')36 + (v + v')32 = 6.5(v + v')(v - v')  (1)

36v - 36v' + 32v + 32v' = 6.5(v² + v'²)

68v - 4v' = 6.5(v² + v'²)        (2)

Also he travels 4 km upstream, the time taken is t" = 4/V = 4/(v + v').

he travels 40 km downstream, the time taken is t'" = 40/V' = 40/(v - v')

The total time is thus t" + t'" = 4/(v + v') + 40/(v - v')

Since the whole trip takes 180 minutes = 3 hours,

4/(v + v') + 40/(v - v') = 3  (3)

Multiplying each term by (v + v')(v - v'), we have

(v + v')(v - v')4/(v + v') + (v + v')(v - v')40/(v - v') = 3(v + v')(v - v')  (1)

(v - v')4 + (v + v')40 = 3(v + v')(v - v')  (1)

4v - 4v' + 40v + 40v' = 3(v² + v'²)

44v - 36v' = 3(v² + v'²)      (4)

Dividing (2) by (4), we have

(68v - 4v')/(44v - 36v') = 6.5(v² + v'²)/3(v² + v'²)      

(68v - 4v')/(44v - 36v') = 6.5/3

3(68v - 4v') = 6.5(44v - 36v')

204v - 12v' = 286v - 234v'

204v - 286v = 12v' - 234v'

-82v = -222v'

v = -222v'/82

v = 111v'/41

Substituting v into (2), we have

68v - 4v' = 6.5(v² + v'²)      

68(111v'/41) - 4v' = 6.5[(111v'/41)² + v'²]        

[68(111/41) - 4]v' = 6.5[(111/41)² + 1]v'²    

[68(111/41) - 4]v' = 6.5[(111/41)² + 1]v'²

[7548/41 - 4]v' = 6.5[12321/1681 + 1]v'²

[(7548 - 164)/41]v' = 6.5[(12321 + 1681)/1681]v'²

[7384/41]v' = 6.5[14002/1681]v'²

[7384/41]v' = [91013/1681]v'²

[91013/1681]v'² - [7384/41]v' = 0

([91013/1681]v' - [7384/41])v' = 0

⇒ v' = 0 or ([91013/1681]v' - 7384/41) = 0

⇒ v' = 0 or [91013/1681]v' - 7384/41) = 0

⇒ v' = 0 or v' =  7384/41 × 16841/91013

⇒ v' = 0 or v' =  180.097 × 0.185

⇒ v' = 0 or v' =  33.33 km/h

Since v' ≠ 0, v' = 33.33 km/h

Substituting v' into v = 111v'/41 = 111(33.33 km/h)/41 = 3699.63 km/h ÷ 41 = 90.23 km/h

So, the streamer's speed in still water is 90.23 km/h while the stream's speed is 33.33 km/h


Related Questions

For a function g(x), the difference quotient is StartFraction 6 Superscript x + h minus 3 Baseline minus 6 Superscript x + 3 Baseline Over h EndFraction. What is the average rate of change of g(x) on the interval from x = –2 to x = 1?

Answers

Answer:

The average rate of change in that interval is 1.99

Step-by-step explanation:

Here we have that the difference quotient for g(x) is:

[tex]\frac{6^{x + h} - 3 - 6^x + 3}{h}[/tex]

Remember that for a general function f(x), the difference quotient is:

[tex]\frac{f(x + h) - f(x)}{h}[/tex]

So if we look at the difference quotient for g(x), we can conclude that:

[tex]g(x) = 6^x - 3[/tex]

Also remember that the average rate of change in an interval (a, b) is just:

[tex]\frac{g(b) - g(a)}{b - a}[/tex]

So here we want the average rate of change of g(x) in the interval from x = -2 to x = 1, this is:

[tex]R = \frac{(6^1 - 3) - (6^{-2} - 3)}{1 - (-2)} = \frac{6 - 6^{-2}}{3} = 1.99[/tex]

The average rate of change in that interval is 1.99

Find f(-3) PLEASE HELP

Answers

Answer:

2

Step-by-step explanation:

When the point on the x-axis is on -3, the point on the y-axis is 2. Therefore, f(-3) is equal to 2.

If this helps please mark as brainliest

Answer: 2

Step by step explanation

five fifth-grade teachers and six fourth-grade teachers ordered 2 large pizzas all together how much will each person need to pay.

Answers

Answer:

$5.50

Step-by-step explanation:

5+6= 11

11/2

someone help!!!!!!!!

Answers

Answer:

Top right

Step-by-step explanation:

First, we have "h is increasing on the interval (3, +∞)." This means that h must be increasing for all values 3 and higher. This is shown on the top left, top right, and bottom right graphs because when x goes up on each of them, the function increases as well. However, for the bottom left graph, this is not shown because as x goes from 3 to 4, the function decreases.

Next, the statement given is "h(4)=2". This means that when the x value is 4, the y value is equal to 2. This is true for the top left and top right pictures. However, for the bottom right, as the x value is 4 on the x axis, the corresponding y value is 1, not 2.

This leaves us with the top left and top right. The final characteristic given is "The domain of h is [3, +∞). This means that the x values of said function only go from 3 to infinity. As the top left graph has values of x below 3, this leaves the top right graph as h

In the diagram below of triangle PQS, S is the midpoint of PR and T is the midpoint of QR. If ST = 5x - 22, and PQ = 3x + 19, what is the measurement of PQ?

Answers

Answer:

PQ = 46

Step-by-step explanation:

The midsegment ST is half the length of the third side PQ , that is

ST = [tex]\frac{1}{2}[/tex] PQ , so

5x - 22 = [tex]\frac{1}{2}[/tex] (3x + 19) ← multiply both sides by 2 to clear the fraction

10x - 44 = 3x + 19 ( subtract 3x from both sides )

7x - 44 = 19 ( add 44 to both sides )

7x = 63 ( divide both sides by 7 )

x = 9

Then

PQ = 3x + 19 = 3(9) + 19 = 27 + 19 = 46

" El ingreso mensual de una empresa está dado por la siguiente ecuación: (0,2) 10000(0,95) p I  , dondep es la cantidad gastada en publicidad:a) ¿Cuál es el ingreso total, cuando no se tienen gastos publicitarios?b) ¿Cuál es el valor del ingreso total, si $ 15 es el gasto mensual en promoción?"

Answers

Respuesta:

Ingresos = 9500

Ingresos = 8573,75

Explicación paso a paso:

La ecuacion:

Yo = 10000 (0,95) ^ (0,2) p

p = monto gastado en publicidad

Los ingresos totales cuando no hay gastos:

p = 0

Yo = 10000 (0,95) ^ (0,2) * 0

Yo = 10000 (0,95) ^ 0

Yo = 10000 (0,95)

Yo = 9500

Si el gasto mensual de la promoción es de $ 15

p = $ 15

Yo = 10000 (0,95) ^ (0,2) * 15

Yo = 10000 (0,95) ^ 3

Yo = 10000 (0,857375)

Yo = 8573,75

pls help in this
7.6x5.2

Answers

Answer:

39.52

Step-by-step explanation:

Answer:

Table multiplication:

7.6 times

5.2 =

15.2

38.0

—-

39.52

8/-5. + -1/2 how do you do it because I really don't know

Answers

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \frac{ - 21}{10} \:(or) \: - 2 \frac{1}{10} }}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex] \frac{8}{ - 5} + ( \frac{ - 1}{2} )[/tex]

[tex] \\= \frac{ - 8}{5} - \frac{1}{2} [/tex]

Since the denominators are unequal, we find the L.C.M (lowest common multiple) for both denominators.

The L. C. M for 5 and 2 is 10.

Now, multiply the L.C.M. with both numerator & denominator.

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

[tex] \\= \frac{ - 16}{10} - \frac{5}{10} [/tex]

Now that the denominators are equal, we can subtract the numerators.

[tex] \\= \frac{ - 16 - 5}{10} [/tex]

[tex] \\= \frac{ - 21}{10} [/tex]

[tex] \\= - 2 \frac{1}{10} [/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♨}}}}}[/tex]

Answer:

-21/10

Step-by-step explanation:

-8/5. + -1/2

2(-8/5) + (-1/2)5

-16/10 - 5/10

-21/10

Drag each tile to the correct box
Arrange the following pairs of coordinates in order from least to greatest based on the distances between the points.
(4.1) and (2, 2)
(-5. 2) and (-3, -2)
(3.-4) and (-2, 1)
(-1.-2) and (1-4)
(5.-2) and (-1, -1)

Answers

Answer:

Step-by-step explanation:

Use the formula of distance between two points (x₁, y₁) and (x₂, y₂),

Distance =  [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

1). Distance between (4, 1) and (2, 2) = [tex]\sqrt{(4-2)^2+(1-2)^2}[/tex]

                                                        = [tex]\sqrt{5}[/tex]

                                                        = 2.24

2). Distance between (-5, 2) and (-3, -2) = [tex]\sqrt{(-5+3)^2+(2+2)^2}[/tex]

                                                            = [tex]\sqrt{20}[/tex]

                                                            = 4.47

3). Distance between (3, -4) and (-2, 1) = [tex]\sqrt{(3+2)^2+(-4-1)^2}[/tex]

                                                          = [tex]\sqrt{50}[/tex]

                                                          = 7.07

4). Distance between (-1, -2) and (1, -4) = [tex]\sqrt{(1+1)^2+(-4+2)^2}[/tex]

                                                          = [tex]\sqrt{8}[/tex]

                                                          = 2.83

5). Distance between (5, -2) and (-1, -1) = [tex]\sqrt{(5+1)^2+(-2+1)^2}[/tex]

                                                           = [tex]\sqrt{37}[/tex]

                                                           = 6.08

Therefore, increasing order of the distance will be 2.24 > 2.83 > 4.47 > 6.08 > 7.07

Answer:

Use the formula of distance between two points (x₁, y₁) and (x₂, y₂),

Distance =  

1). Distance between (4, 1) and (2, 2) =

                                                       =

                                                       = 2.24

2). Distance between (-5, 2) and (-3, -2) =

                                                           =

                                                           = 4.47

3). Distance between (3, -4) and (-2, 1) =

                                                         =

                                                         = 7.07

4). Distance between (-1, -2) and (1, -4) =

                                                         =

                                                         = 2.83

5). Distance between (5, -2) and (-1, -1) =

                                                          =

                                                          = 6.08

Therefore, increasing order of the distance will be 2.24 > 2.83 > 4.47 > 6.08 > 7.07

Step-by-step explanation:

Brainiest will be given . Please help me

Answers

Answer:

If the shape of end face has n sides

Then, in total, there are n+2 faces

Using that formula

Faces in 20-sided polygon = n+2 = 20+2 = 22

Step-by-step explanation:

Pls vote as brainliest

The system of inequalities below describes the relationship between Cori's age C and Livy's age L. C + L ≥ 43 C - 4L ≤ 3 Livy could be 13 years old and Cori could be 35 years old.

Answers

Answer:

Cori could be 35 years old.

Livy could be 8 years old

Step-by-step explanation:

Given

[tex]C + L \ge 43[/tex]

[tex]C - 4L \ge 3[/tex]

Required

Possible values of C and L

Make C the subject in: [tex]C - 4L \ge 3[/tex]

[tex]C \ge 3 + 4L[/tex]

Substitute for C in [tex]C + L \ge 43[/tex]

[tex]3 + 4L + L \ge 43[/tex]

[tex]3 + 5L \ge 43[/tex]

Collect like terms

[tex]5L \ge 43-3[/tex]

[tex]5L \ge 40[/tex]

Solve for L

[tex]L \ge 8[/tex]

Solve for C

[tex]C \ge 3 + 4L[/tex]

[tex]C \ge 3 + 4 * 8[/tex]

[tex]C \ge 35[/tex]

you have five dollar bills and ten dollars bills for a total amount of $325. you have a total of 37 bills. A) write a system of linear equations that models the situation. B) how many of each type of bill do you have?

Answers

Answer:

nine $5 bills and twenty-eight $10 bills

Step-by-step explanation:

f = # of five dollar bills

t = # of ten dollar bills

system of equations:

t + f = 37

10t + 5f = 325

solve the first equation for 't' to get:

t = 37-f

substitute '37-f' to 't' in second equation to get:

10(37-f) + 5f = 325

370 - 10f + 5f = 325

-5f = -45

f = 9

t + 9 = 37

t = 28

Which number represents the probability of an event that is very likely to occur?
A. O 0.09
B. O 0.12
C. O 0.3
D. O 0.95

Answers

Answer:

D

Step-by-step explanation:

higher amount then the rest

Select the correct answer. The elevations of five points below sea level are given here. Which elevation is closest to sea level? A. -50 feet B. -68 feet C. -77 feet D. -86 feet E. -97 feet

Answers

Answer:

the answer is B i think

Step-by-step explanation:

2 to the negative 3 power times how much is 2 to the negative 1 power? Does the answer match your answer from question 3b? Why or why not?

Answers

Answer: 2^-3 = 1/8

2^-1 = 1/2

you have to multiply 2^-3 by 4 to get to 2^-1

Step-by-step explanation:

and angle is 21 more than twice its complement find it

Answers

Answer:

angle = 67°

Step-by-step explanation:

let

a = angle in degrees

(90-a) = complement

given

a = 2(90-a)+21

Solve for a

a = 180 - 2a + 21

3a = 201

a = 67°

(Find m∠IGH) m∠IGH=

Answers

Answer:

angle IGH = 50 degree

Step-by-step explanation:

triangle GHI is an isosceles triangle because it's two sides are equal.

if angle I is 50 degree then angle G is also 50 degree becasue in isosceles triangle the base angles are equal.

Jodi has two bank accounts. Her parents started Account A for her. It currently has $100 in it, and Jodi deposits $20 into it each month. Jodi's grandparents started Account B for her. It currently has $300 in it, and her grandparents deposit $40 into it each month.

Answers

Answer:

(f+g)(x) = 60x + 400

Step-by-step explanation:

Given :

Amount in account A:

f(x) = 20x + 100

Amount in account B :

g(x) = 40x + 300

Total amount in Account A and B:

f(x) + g(x) = (20x + 100) + (40x + 300)

(f+g)(x) = (20x + 40x) + (100 + 300)

(f+g)(x) = 60x + 400

2.5kg of potatoes cost $1.40 work out the cost of 4.25 kg of potatoes

Answers

Answer:

Cost of 4.25 kilogram potato = $2.38 (Approx.)

Step-by-step explanation:

Given:

Cost of 2.5 kilogram potato = $1.40

Find:

Cost of 4.25 kilogram potato

Computation:

Cost potato = Amount of potato need[Price of y potato / Amount of y potato]

Cost of 4.25 kilogram potato = [4.25][1.40 / 2.5]

Cost of 4.25 kilogram potato = [4.25][0.56]

Cost of 4.25 kilogram potato = 2.38

Cost of 4.25 kilogram potato = $2.38 (Approx.)

Name the ordered pair for point H.
25 points if answered.

Answers

Answer:

H=(1,3)

This because the x-axis position is 1, and the y-axis position is 3.

the answer is (1,3)!!!

Help





Will





Give




BRIANLIST




Answer

Answers

v = s/t => average speed = 39,1/2,06= about 19 mi/hr, i guess

Which transformations could have occurred to map
AABC to AA"B"C?
O a rotation and a reflection
O a translation and a dilation
O a reflection and a dilation
O a dilation and a rotation

Answers

The transformations that could map ABC to A"B"C" are: (d) a dilation and a rotation

From the figure, we have the following highlights:

Triangle A"B"C is smaller than triangle ABCThe side lengths of both triangles are in equivalent ratioTriangle ABC is rotated about point C to form triangle A"B"C

The above highlights mean that:

The transformations that could map ABC to A"B"C" are dilation and rotation

Hence, option (d) is true

Read more about transformations at:

https://brainly.com/question/4289712

The length of a rectangle is 18 cm and the width is 6 cm. A similar rectangle has a width of 2 cm.What is the length of the second rectangle? pls help im solving hw ._.

Answers

Given:

Two rectangles are similar.

Length of first rectangle = 18 cm

Width of first rectangle = 6 cm

Width of second rectangle = 2 cm

To find:

The length of the second rectangle.

Solution:

We know that the corresponding sides of similar triangles are proportional. So,

[tex]\dfrac{\text{Length of first rectangle}}{\text{Width of first rectangle}}=\dfrac{\text{Length of second rectangle}}{\text{Width of second rectangle}}[/tex]

Let x be the length of the second rectangle. Then,

[tex]\dfrac{18}{6}=\dfrac{x}{2}[/tex]

[tex]3=\dfrac{x}{2}[/tex]

[tex]3\times 2=x[/tex]

[tex]6=x[/tex]

Therefore, the length of the second rectangle is 6 cm.

can someone help me i dont understand​

Answers

Answer:

8900000 * 10^-3

Step-by-step explanation:

(8.9*10^-3)/(10^-6)

(8.9*10^-3)/(1/1000000)

8.9*10^-3* 1000000

8900000 * 10^-3

what is the common difference for this arthimitic sequence? -8, -13, -18, -23
a. 5
b. -5
c. -28
d. -21

Answers

b. -5 is the answerrrrrrrrrrrr

angle2 cong angle5 so A|| B

Answers

Answer:

False

Step-by-step explanation:

If angle 2 and angle 5 are equal in length, then what we have is that the two lines are not parallel

For the two lines to be parallel, these two angles should be supplementary

what this mean is that these two angles should add up to give 180 degrees

A scientist uses a submarine to study ocean life.
*She begins at sea level, which is an elevation of 0 feet.
*She descends for 91 seconds at a speed of 2.2 feet per second.
*She then ascends for 32 seconds at a speed of 0.7 feet per second.

At this point, what is her elevation, in feet?

if you anserw corectly ill give you crown and more points

Answers

Answer:

-177.8 feet below sea level.

Step-by-step explanation:

First, we know that decend means to lower. Anything lower than 0 has to be negative. It says that she decends for 91 seconds at a speed of 2.2 feet per second. So first to find out how many feet she descended in those 91 seconds, you need to multiply 91*-2.2= -200.2. Then, it says that she ascends for 32 seconds at the speed of 0.7 feet per second. It's the same thing, but ascend means to go up. So, we multiply 32*0.7=22.4. Now we add the two numbers together to get -177.8.

Hope this helps!

In the circle below, segment AB is a diameter. If the length of arc ACB is 6pi what is the length of the radius of the circle?

Answers

Answer:

12

Step-by-step explanation:

Length of the radius of the circle is equals to 6units.

What is length of the arc?

" Length of the arc is defined as the distance between two point as a part of the circumference of the given curve."

Formula used

Length of the arc = rθ

r = radius of the circle

θ = central angle

Radius = [tex]\frac{diameter}{2}[/tex]

According to the question,

Given,

Diameter = AB

Length of the arc = 6pi

Here central angle formed with diameter 'θ' = 180°

                                                                     = [tex]\pi[/tex]

Substitute the value in the length of the arc formula we get,

   [tex]6\pi = r \pi[/tex]

⇒ [tex]r = 6units[/tex]

Hence, length of the radius of the circle is equals to 6units.

Learn more about length of the arc here

https://brainly.com/question/16403495

#SPJ2

Someone help me with this please!

Answers

Answer: y=40

Step-by-step explanation: 70-30=40

HELP ME PLS- math question

Answers

Answer:

x+2x+90 =180

3x =180

x =60

x=2y

2y=60

y=30

2y +z =180

z =180-60

. z =120

Other Questions
Where is point C on the number line? About how much money do you spend on clothes a year? tan ydx - x ln xdy=0 Suppose that the first goal in a GP problem is to make 3 X1 + 4 X2 approximately equal to 36. Using the deviational variables d1 and d1+, the following constraint can be used to express this goal.3 X1 + 4 X2 + d1 d1+ = 36If we obtain a solution where X1 = 6 and X2 = 2, what values do the deviational variables assume?a. d1 = 0, d1+ = 10b. d1 = 6, d1+ = 0c. d1 = 5, d1+ = 5d. d1 = 10, d1+ = 0 In the overall equation for photosynthesis, six molecules of carbon dioxide and sixmolecules of water result in a molecule of sugar and six molecules of ayo, anyone needs help with some spanish homework? im spanish and i can easily talk on english, so, i can help with spanish stuff. angle2 cong angle5 so A|| B a free trade agreement is likely to result in What makes you happy, sad, angry, fearful and hopeful ? What is the common ratio of the sequence?-2, 6, -18, 54,...-3-238 Fertilizer grade is the relative _________ in a bag of fertilizer. Proportion Percentage GradeRatio Paraphrase the following poem: (20 points)You may write me down in historyWith your bitter, twisted lies,You may trod me in the very dirtBut still, like dust, Ill rise.Does my sassiness upset you?Why are you beset with gloom?Cause I walk like Ive got oil wellsPumping in my living room.Just like moons and like suns,With the certainty of tides,Just like hopes springing high,Still Ill rise.Did you want to see me broken?Bowed head and lowered eyes?Shoulders falling down like teardrops,Weakened by my soulful cries?Does my haughtiness offend you?Dont you take it awful hardCause I laugh like Ive got gold minesDiggin in my own backyard.You may shoot me with your words,You may cut me with your eyes,You may kill me with your hatefulness,But still, like air, Ill rise.Does my sexiness upset you?Does it come as a surpriseThat I dance like Ive got diamondsAt the meeting of my thighs?Out of the huts of historys shameI riseUp from a past thats rooted in painI riseIm a black ocean, leaping and wide,Welling and swelling I bear in the tide.Leaving behind nights of terror and fearI riseInto a daybreak thats wondrously clearI riseBringing the gifts that my ancestors gave,I am the dream and the hope of the slave.I riseI riseI rise. Which number represents the probability of an event that is very likely to occur?A. O 0.09B. O 0.12C. O 0.3D. O 0.95 PLEASE HELP ASAP! IF CORRECT I WILL ANSWER ONE OF YOUR QUESTIONS AND GIVE BRAINLIEST. How did employment conditions change for African Americans during World War II?a.Employers with government contracts could not discriminate when hiring.b.All employers were forbidden to discriminate when hiring.c.Employment of skilled African American workers declined.d.Only employers with government contracts could discriminate when hiring. b. Why is school regarded as a secondary means of socialization? organ pembiakan jantan The length of a rectangle is 18 cm and the width is 6 cm. A similar rectangle has a width of 2 cm.What is the length of the second rectangle? pls help im solving hw ._. five fifth-grade teachers and six fourth-grade teachers ordered 2 large pizzas all together how much will each person need to pay. In which states of matter will a substance have a fixed volume?O A. Liquid and solidO B. Solid and gasO C. Plasma and gasO D. Liquid and gas What are the coordinates of B if the figure is reflected across the x-axis? What is the mapping rule for finding the coordinates of a figure reflecting across A) the x-axis (x,y) ->B) the y-axis (x,y) ->