a motorboat travels a distance of one pier to another pier in 4 hrs and the way back in 5 hrs. What is the speed of the boat in still water if it travels 70 km with the current in 3.5 hrs?

Answers

Answer 1

let's recall that d = rt, namely distance = rate * time.

d = distance from one pier to another

c = speed of the current

b = speed of the boat

now, let's notice something, on the way over the boat travelled "d" kilometers in 4 hrs, and back the same "d" kilometers in 5 hours.

when going with the current, the boat is not really going at "b" km/s, is really going faster, at "b + c" km/s, because the current is adding to it.

now, when going against the current, the boat is not really going "b" fast, is really going slower, at "b - c", because the current is subtracting from it.

from the above, we can conclude that the 4hrs trip was with the current, since it took less time, and the 5hrs trip was against the current, and we also know that the boat does 70 km with the current in 3.5 hrs, ok hmmm let's put all that in a table.

[tex]\begin{array}{lcccl} &\stackrel{km}{distance}&\stackrel{km/h}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \textit{on the way over}&d&b+c&4\\ \textit{on the way back}&d&b-c&5\\\cline{1-4} \textit{we also know}&70&b+c&3.5 \end{array}~\hfill \begin{cases} d=(b+c)4\\\\ d = (b-c)5 \end{cases} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{(b+c)4~~ = ~~(b-c)5}\implies 4b+4c=5b-5c \\\\\\ 4c=b-5c\implies \boxed{9c=b} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{we know that}}{70~~ = ~~(b+c)3.5}\implies 70=(b+c)\cfrac{7}{2}\implies \stackrel{\textit{substituting "b"}}{70=(9c+c)\cfrac{7}{2}} \\\\\\ 70=10c\cdot \cfrac{7}{2}\implies 70=\cfrac{70c}{2}\implies 140=70c\implies \cfrac{140}{70}=c\implies \blacktriangleright 2=c \blacktriangleleft \\\\\\ \stackrel{\textit{the speed of the boat in still water is then}}{9c=b\implies 9(2)=b}\implies \blacktriangleright 18=b\blacktriangleleft[/tex]


Related Questions

Please help me with this please and thank you

Answers

Answer:

L bozo

Step-by-step explanation:

bc ur an L. ur whole life is an L

What is ED?

Enter your answer in the box.


units

Answers

Answer:

x=4

Step-by-step explanation:

There

The following box plot shows the class scores on a particular math test:
10
20
30
70
80
90
100
40 50 60
Percent
Which of the following data sets is represented in the box plot?
{40, 50, 50, 77, 77, 100)
{0.50, 60, 75, 85, 100)
{50, 60, 60, 75, 75, 85, 85, 100)
[60, 65, 70, 75, 85, 85, 85)

Answers

Answer:

maybe the third one and i would also like to see the box plot

Step-by-step explanation:

Find the median of the data set without the outlier.
Then, find the median of the data set with the outlier.

Answers

Answer:

Median without the outlier: 9

Median with the outlier: 9

Step-by-step explanation:

The outlier here is 1, because it's smaller than most of the values in the data set.

Median: the middle value of a data set

Median without the outlier: 9

7, 8, 8, 9, 9, 10, 10, 10, 10

Median with the outlier: 9

1, 7, 8, 8, 9, 9, 10, 10, 10, 10

9 + 9 = 18

18/2 = 9

Hope this helps!

Answer:

the without the outlier 9

set with with the outlier 9

Step-by-step explanation:

help me if you can please?? and thanks! :)))​

Answers

Answer:

0.0095

Step-by-step explanation:

= 0.009455 ( as they are bigger than 4 )

= 0.0095

Find the surface area (Leave your answer in terms of π) of a sphere with a radius of 12. Use 4πr² to solve.

76π

576π

48π

580π

Answers

The answer is 576π. Break down the formula: 4πr²=4*π*r(12)². 12² or 12*12 is 144. You still have 4 and π. So multiply 144 by the 4 to get 576 and finally multiply that by pi to get you the final answer of 576π.

Answer:

576π

Step-by-step explanation:

Surface Area of a Sphere

4πr²

Given

r = 12

Solving

S.A. = 4 x π x (12)²S.A. = 4 x 144 x πS.A. = 576π

Help me please it’s algebra

Answers

Answer:

80 degrees

Step-by-step explanation:

To convert radians to degrees, multiply by 180π since a full circle is 360° or 2π radians. Cancel the common factor of π. Factor π π out of 4π 4 π.

hope this helps.

The cost of a flat of strawberries to a grocery store is $7.60 and the store marks the strawberries
up 125%. Find the selling price

Answers

Answer:

7.60+9.50 = 17.10

Step-by-step explanation:

7.60 * 125% = 9.50

9.50+7.60 = 17.10

graph the linear equation. find three points that solve the equation, then plot them on the graph. 5x-4y=-18

Answers

Hhhhhhhbhiggbxdhnbfd

What is the volume of this container?

Answers

Answer:

1,253 in³

Step-by-step explanation:

The container can be split into two rectangular prisms. Adding their volumes together will give us the volume of the container.

The formula for the volume of a rectangular prism is length×width×height or base×height

Let's substitute!

(l×w×h)+(l×w×h)

=(7×5×5)+(11×14×7)

=175+1078

=1,253 in³

Hope this helps!

You ran 4 1/2 times around a quarter-mile track how far did you run

Answers

Answer:

1,809 meters. (1 & 1/8 of a mile)

Step-by-step explanation:

quarter of a mile = 402 meters
402 * 4.5 = 1,809 meters = 1 1/8 mile

SHADOWS A rectangular billboard casts a shadow on the ground in the shape of a parallelogram. What is the area of the ground covered by the shadow? Round your answer to the nearest tenth.

Answers

Answer:

Its still a rectangle, just move the triangles, you get 450

Step-by-step explanation:

If you think of it like a triangle, you can use the base, the 90 degree angle, and the hypotenuse to get the area, do it twice since there are two, and your result is 225 for one triangle, 450 for both.

given data 4,x,9,5,2,7 find x if the mode is 4

Answers

Answer:

x = 4

Step-by-step explanation:

This is because the definition of mode is the number that appears the most or is the popular of the numbers in the data set.

This could be any number since each number is listed once, but the requirements/directions say the mode is 4 so you need another 4 in order to have a mode of 4.

The group thought there was enough food for all 5 group members to
complete the trip, with each person getting the required 5600 calories per
day. However, they discover that they are missing 28,800 calories.
Using the map, create a plan a for the rest of the trip that includes taking as
many group members as possible to the South Pole, while sending the rest of
the group members directly back to base camp. Remember that each person
must have 5600 calories of food per day until he or she gets back to base
camp.
Be sure to explain how you came up with your plan. Include all work
necessary to support your answer.

Answers

To create a work plan for the food intake of each person in the group, there needs to be the required 5600 calories and there needs to be a replacement for the caloric deficit.

What is a Work Plan?

This refers to the formal roadmap that is created for a project for the purposes of streamlining it.

Based on the fact that a map was not provided, there is insufficient data to solve the problem, so a general overview will be given about a work plan.

Because the group is 28,800 calories short and needs to complete the trip with their five members, then they need to ration their supplies.

Read more about work plans here:

https://brainly.com/question/7274240

#SPJ1

what is the total price of a $20,000 car plus 8.5% sales tax ?

Answers

8.5% of 20,000 is 1,700
20,000+1,700=21,700

What is the area of the composite figure? (6π 4) cm2 (6π 16) cm2 (12π 4) cm2 (12π 16) cm2

Answers

The area of the considered composite figure is given by: Option: 6π + 16 cm²

How to calculate the surface area of a composite figure?

Surface area are derived for some standard shapes like circle, triangle, parallelogram, rectangle, trapezoid, etc.

When some shape comes which isn't standard figure, then we find its area by slicing it (virtually, like by drawing lines) in standard shapes. Then we calculate those composing shapes' area and sum them all.

Thus, we have:

[tex]\text{Area of composite figure} = \sum (\text{Area of composing figures})[/tex]

That ∑ sign shows "sum"

For this case, the missing image is attached below.

As visible, the area of the figure = Sum of area of those 3 semi circles + Area of that square(its square because it has 4 equal sides in which adjacent sides are perpendicular) in between.

The side of the square is of 2+2=4 cm( as half of its side is 2 cm), thus, Area of that square = 4² = 16 cm²

All those 3 semicircles has radius = 2 cm

Since radius is same, so area of those 3 semicircle is same = [tex]\dfrac{\pi r^2}{2} = \dfrac{\pi (2)^2}{2} = 2 \pi\: \rm cm^2[/tex]

Thus, we get:

Area of the composite figure = [tex]2 \pi +2 \pi +2 \pi + 16 \: \rm cm^2 = 6 \pi+ 16 \: \rm cm^2[/tex]

Learn more about area of a composite figure here:

https://brainly.com/question/10254615

What is the area of the beach ball with a diameter of 14 in. ?

Answers

Answer:

The answer is 675.75 square Inches

Step-by-step explanation:

Given;Diameter (d) = 14 in.To Find;Area of beach ball = ?Formula;Area = 4πr²

Now,

Radius (r) = diameter ÷ 2

r = 14/2 in.

r = 7 in.

Now,

A = 4πr²

A = 4 × 22/7 × (7)² in.

A = 4 × 22 × 7 in.

A = 615.75 square in.

Thus, The area of the beach ball with a diameter of 14 in. is 615.75 square in.

Answer:

  615.8 in²

Step-by-step explanation:

The area of a sphere is given by the formula ...

  A = 4πr² . . . . . sphere of radius r

In terms of diameter, the area is ...

  A = 4π(d/2)² = πd²

__

For a diameter of 14 inches, the area of the beach ball is ...

  A = π(14 in)² = 196π in² ≈ 615.8 in²

The area of the ball is about 615.8 square inches.

I guessed Supplementary, but I think I'm just not understanding, help

Answers

exterior angles? if that’s an option

Tell whether each number is rational or irrational.0.121121112....

Answers

A rational number is any whole number or fraction that ends or repeats. An irrational number is a number that cannot be turned into a fraction.


It’s kind of hard to read the numbers because they’re to close but I hope that that helped you a little

In pensacola in june, high tide was at noon. the water level at high tide was 12 feet and 2 feet at low tide. assuming the next high tide is exactly 12 hours later and that the height of the water can be modeled by a cosine curve, find an equation for water level in june for pensacola as a function of time (t). f(t) = 12 cospi over 2t 5 f(t) = 5 cospi over 2t 12 f(t) = 5 cospi over 6t 7 f(t) = 7 cospi over 6t 12

Answers

An equation for water level in june for pensacola as a function of time (t) is f(t) = 5 cos pi/6 t + 7.

Which equation of cos show period amplitude ?

The equation given below show aplitude and period

[tex]y = A cos bx + c[/tex]

where A = amplitude,

b = 2 pi/Period,

Period = 12 hrs,

c = midline,

x = t and y = f(t)

We have to find the amplitude

What is the formula for the amplitude?

[tex]A = 1/2 (Xmax - Xmin)[/tex]

[tex]12 - 2 / 2 = 10/2 = 5[/tex]

[tex]b = 2 pi / 12 = pi/6[/tex]

[tex]c = 1/2 (Xmax + Xmin)[/tex]

[tex]12+2/2 = 7[/tex]

Therefore, the an equation for water level in june for pensacola as a function of time (t)

[tex]f(t) = 5 cos pi/6 t + 7[/tex]

To learn more about the function of time visit:

https://brainly.com/question/24872445

Which decimal is the best approximation of √26?

5.1

5.5

5.9

I don't know.

Answers

Answer:

5.1

Step-by-step explanation:

√26 = 5.099

5.099 is approximately 5.1

Answer:

5.1

Step-by-step explanation:

k12 quiz :)

How can a cruise ship float despite its mass (This is science)

Answers

A cruise ships floats despites it mass because it is boyanty and experiences and upthrust

Achimedes Principle of Floation

This principle states that "When a body is partially or totally imersed in a fluid, it experiences an upward force (Upthrust) which is equal to the volume of the fluid displaced"

Learn more about floation here:

https://brainly.com/question/17759399

questions in the picture below​

Answers

Answer:

Answer is

a) 50%

b) 20%

c) 40%

Step-by-step explanation:


Ex. 1 Write an equation in slope-intercept form for the line that passes through (3, 8) and is
perpendicular to the line with equation y = -1/3x+8

Answers

Answer:

Step-by-step explanation:

The line perpendicual to a reference line will have a slope that is the negative inverse of the reference line.  In this case, the reference line is y= -(1/3)X+8, with a slope of -(1/3).  The negative inverse would be 3.  So the new line would have the form:

y = 3x + b

To find b, the y-intercept, use the given point and solve for b:

y = 3x + b

or 8 = 3*3 + b for the point (3,8)

8=9+b

b= -1

Thje equation of the line perpendicualr to the reference line and going through point (3,8) is:

y = 3x - 1

See attached graph.

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

Answers

Answer:

mode = 1

Step-by-step explanation:

the mode is the value that occurs most often in the data set.

1 occurs 3 times and is therefore the mode

What is the Evaluate 5^3+6x3

Answers

Answer:

33 Is your answer :)

Step-by-step explanation:

Always do P.E.M.D.A.S ( always go in order it gives you) parenthesis, exponets, multiply/divide, and add/subtract

5^3+6*3=

15+18= 33

Match the value to the correct image. Not all values will be used.
Find the approximate surface area of each right regular prism.

Answers

The approximate surface areas of corresponding prisms are listed below:

A = 108 units²A = 229 units²A = 454 units²

How to match given surface areas with given figures

The surface area of the each figure ([tex]A[/tex]), in square units, is equal to the sum of the surface area of the two bases ([tex]A_{b}[/tex]), in square units, and the surface areas of the lateral sides ([tex]A_{l}[/tex]), in square units. Since bases are regular polygons, base surface area can be determined by this expression:

[tex]A_{b} = \frac{l^{2}\cdot n }{4\cdot \tan \frac{180}{n} }[/tex]  (1)

Where:

l - Side length, in unitsn - Number of sides

The area of one lateral side is expressed by this expression:

[tex]A_{l} =h\cdot l[/tex]   (2)

Where h is the height of the rectangle, in units.

The total surface area is defined by the following formula:

[tex]A = 2\cdot A_{b} + n\cdot A_{l}[/tex]   (3)

Now we proceed to calculate each surface area:

Case I ([tex]l = 2[/tex], [tex]n = 6[/tex], [tex]h = 9[/tex])

[tex]A = 2\cdot \left[\frac{2^{2}\cdot (6)}{4\cdot \tan \left(\frac{180}{6} \right)} \right]+6\cdot (2)\cdot (9)[/tex]

A = 108.136 units²

Case II ([tex]l = 4\sqrt{3}[/tex], [tex]n = 3[/tex], [tex]h = 9[/tex])

[tex]A = 2\cdot \left[\frac{(4\sqrt{3})^{2}\cdot (3)}{4\cdot \tan \left(\frac{180}{3} \right)} \right]+3\cdot (4\sqrt{3})\cdot (9)[/tex]

A = 228.631 units²

Case III ([tex]l = 6[/tex], [tex]n = 5[/tex], [tex]h = 11[/tex])

[tex]A = 2\cdot \left[\frac{6^{2}\cdot (5)}{4\cdot \tan \left(\frac{180}{5} \right)} \right]+5\cdot (6)\cdot (11)[/tex]

A = 453.874 units²

The approximate surface areas of corresponding prisms are listed below:

A = 108 units²A = 229 units²A = 454 units²

To learn more on surface areas, we kindly invite to check this verified question: https://brainly.com/question/2835293

Answer:

Look at the picture                

Each passenger on an airplane can take two suitcases, and each suitcase can
weigh no more than 50 pounds. If there are 120 passengers and each passenger
takes the maximum weight of luggage allowed, how many tons of luggage will
there be on the plane?

Answers

Answer:

6 tons

Step-by-step explanation:

So we know there are 120 passengers. If they all take the limit, which is 50 pounds each, we can multiply the 2 figures to get 120*50=6000 pounds. Since the question is asking us to answer in tons, we must convert 6000 pounds into tons. We can do this by using the convertion factor of 2000 lbs = 1 ton. With this logic, 6000 pounds equals 3 tons. But remember, each passenger can take 2 luggages. So just multiply by 2 to get 6 tons!

I hope this helped!

Please mark brainliest! I really need it. It would be very much appreciated.

Depending on whether they’ll take one or two suitcases.
The minimum weight: 50 (one suitcase per person) x 120 (total amount of people) = 6000 pounds (3 tons)
The maximum weight: 100 (two suitcases) x 120 (total amount of people) = 12000 (6 tons)

So the answer could be 6 tons because it makes more sense to the fact that they’re taking maximum weight.

Which is more, 662 feet or
1
8
of a mile?

Answers

Answer:

the answer is 662 feet

Step-by-step explanation:

becuase one eighth of a mile is 660 feet

If 2x - 3y = 14 and -x + 2y = -8
what is the value of x+y?

Answers

answer = 4 does it is correct

Other Questions
Please help . 50 points and brainliest. Hunter has a collection of 140 coins. How many coins represent 5% of his collection? Divide/scale down to solve for the missing percent. You have learned that invasive species are plants, animals, and organisms that encroach on and ultimately take over the habitat of native species. Search invasive species in the United States and choose one species from the results. Find information on the invasive species you choose, including when, where, and how it was introduced into the United States and what dangers it might pose. Should these dangers be addressed? Are attempts being made to stop the spread of this species? If not, should anything be done to stop the spread of the species?Respond to the prompt. Support your opinions with explanations and evidence.If you can you make it about the Burmese Python. One way in which the reality of communism in the Soviet Union differed from Karl Marxs theory was thata.the society created was completely classless.b.workers did not benefit from communism, but rather suffered.c.religion was eliminated.d.none of the above. 1. Consider global movements that impacted the human rights of people during the interwar years. (a) What was one movement that resulted in the advancement of human rights?(b) What was one movement that resulted in the limitation of human rights?(c) What was different about these movements? (d) How did these movements reflect the changing times between the world wars?2. What is most to blame for the start of World War I: militarism, imperialism, nationalism, or the alliance system? Defend your choice with two specific examples. 3. How did postwar negotiations at the end of World War I ultimately contribute to the start of World War II? In your response, explain the role of the Treaty of Versailles, the Great Depression, and totalitarianism Select the correct answer. a patient has a history of poor nutrition. he has skin rashes, bleeding gums, and a cut that hasnt healed in a long time. what vitamin deficiency most likely caused these symptoms? a. vitamin a b. vitamin b6 c. vitamin b12 d. vitamin c e. vitamin e The first three terms of a geometric sequence are as follows. PLEASE HELP I'LL GIVE YOU ANYTHING YOU WANTAn unsaturated air parcel has a temperature of 25C at the ground level. The surrounding environmental temperature at the ground level is 24C. Meanwhile, the dew point temperature is 9C and the environmental lapse rate is 15C/1000m. Can the air parcel rise to 2000 meters and form clouds when rising? Why or why not? If yes, at what elevation does the cloud start to form? (DALR = 10C/1000m, MALR = 6C/1000m) Transform the table below given that g(x) = 2 f(6x).+ 8. Enter your answers as reduced fractions if necessary. Make sure your answers line up vertically with the corresponding x and f(x) values. As a hint, you can consider y f(x) to be the base graph of g(x). The chemical combination of atom a and atom b would result in Read the excerpt from "The Gift of the Magi." Where she stopped the sign read: "Mme. Sofronie. Hair Goods of All Kinds." One flight up Della ran, and collected herself, panting. Madame, large, too white, chilly, hardly looked the "Sofronie." "Will you buy my hair?" asked Della. "I buy hair," said Madame. "Take yer hat off and lets have a sight at the looks of it." Down rippled the brown cascade. "Twenty dollars," said Madame, lifting the mass with a practised hand. Madame Sofronies character is most developed through direct characterization, using her words and feelings. indirect characterization, using her thoughts and action. direct characterization, describing her physical appearance. indirect characterization, describing her personality. How many particles are there in 3 moles of Ag? How does war shape the development of civilizations? i need this with the steps how do you recognize an exponential equation What material was used for nun gudas book of homilies? a. ink on vellum b. ink on parchment c. paint on parchment d. paint on vellum Which sentence is the clearest example of alliteration? Based on the following data, what is the I-I bond energy?[tex]\frac{1}{2}[/tex]H2(g) + [tex]\frac{1}{2}[/tex]I2(g) HI(g); H = 26.36 kJBond Bond Energy (kJ/mol)H-H 435H-I 295A) 208 kJ/molB) 155 kJ/molC) 365 kJ/molD) -208 kJ/molE) -155 kJ/mol How many degrees Fahrenheit is -3C? Help please Tanslate the sentence into an equationThe sum of 4 times a number and 8 is 5.Use the variable for the unknown number