Two friends can paddle a canoe at a rate of 6 km/h in still water. It takes them 1 h in total to paddle 2 km up a river and another 2 km back. Find the speed of the current, rounded to the nearest tenth.

Answers

Answer 1

Answer: The speed of the current is 3.5 km/h.

Step-by-step explanation:

When they move in the river, the speed of the canoe is:

Sc is the speed of the canoe and Sr is the speed of the current.

Sc + Sr (when they move in the same direction as the current)

Sc - Sr (when they move in the opposite direction as the current)

So we have that in one hour, they moved 2km and then they returned other 2km.

Now, using the relation:

Velocity*time = distance

we can write 1hour = T1 + T2 such that:

(Sc + Sr)*T1 = 2km

(Sc - Sr)*T2 = 2km

T1 + T2 = 1hour -------> T2 = 1h - T1

Sc = 6km/h.

So we can write this as two equations:

(6km/h + Sr)*T1 = 2km

(6km/h - Sr)*(1h - T1) = 2km.

Now, the first step will be isolate one of the variables in one equation, we can get:

T1 = 2km/(6km/h + Sr)

and replace it in the second equation:

(6km/h - Sr)*(1h -2km/(6km/h + Sr)) = 2km.

Now we solve this for Sr, i will ignore the units, so it is easier to read the math.

(6 - Sr) - 2*(6 - Sr)/(6 + Sr) = 2

(6 - Sr)*(6 + Sr) - 2*(6 - Sr) = 2*(6 + Sr)

6^2 - Sr^2 - 12 + 2*Sr - 12 - 2*Sr = 0

-Sr^2 + 36 -12 -12 = 0

-Sr^2 + 12 = 0

Sr = √12 = 3.5km/h

(where we take the positive value of the square root)

Answer 2

The speed of the current is 3.5 km/h

Speed is the ratio of distance travelled to time taken. It is given by:

Speed = distance / time

Let a represent the speed of the current and t₁ represent the time spent paddling up and t₂ represent the time spent paddling back. Hence:

(6 - a)(t₁) = 2 km

t₁ = 2 / (6 - a)      (1)

(6 + a)(t₂) = 2 km

t₂ = 2 / (6 + a)   (2)

t₁ + t₂ = 1 hour

[2 / (6 - a)] + [2 / (6 + a)] = 1

12 + 2a + 12 - 2a = 36 - a²

a² - 12 = 0

a = 3.5 km/h

The speed of the current is 3.5 km/h

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Related Questions

Triangle A B C is shown. Angle B C A is a right angle. The length of hypotenuse A B is 26, the length of A C is 10, and the length of B C is 24. Given right triangle ABC, what is the value of tan(A)? Five-thirteenths Twelve-thirteenths Twelve-fifths Thirteen-twelfths

Answers

Answer:

The right option is twelve-fifths

Step-by-step explanation:

Given a right angle triangle ABC as shown in the diagram. If ∠BCA = 90°, the hypotenuse AB = 26, AC = 10 and BC = 24.

Using the SOH, CAH, TOA trigonometry identity, SInce we are to find tanA, we will use TOA. According to TOA;

Tan (A) = opp/adj

Taken BC as opposite side since it is facing angle A directly and AC as the adjacent;

tan(A) = BC/AC

tan(A) = 24/10

tan(A) = 12/5

The right option is therefore twelve-fifths

Answer:

The correct answer is option C. 12/5

Step-by-step explanation:

Hope this helps!

Brainliest would be greatly appreciated :D

an elevator moves at a rate of -5.8 feet per second from a height of
300 feet above the ground. the elevator takes 3 seconds to make its first stop.
how many feet above the ground is the elevator now?

Answers

Answer:

282.6 ft

Step-by-step explanation:

First you must figure out how far the elevator drops in three seconds.

To do so you multiply how far it falls per second (5.8 ft) by how long it falls for (3 seconds). 5.8 * 3 = 17.4

now you subtract 17.4 from 300 to get 282.6 ft

Can you please help

Answers

Pyramid
B=36
h=4
(36*4)/3=48

Prism
B=144
h=3
V= (bh)= 432

answer= 432+48 =480

6. A wire Il om long has a mass of 187 g. What is the mass of 7 cm of this wire?

Step by step explansion​

Answers

Answer:

119 g.

Step-by-step explanation:

11 cm has a mass of 187 g

So 1 cm has a mass of 187/11 g

7 cm ...............................  (187/11) * 7

= 17 * 7

=  119 g.

Given the points (-2,-4) and (-3,-5) what is the slope

Answers

Answer:

1/1

Step-by-step explanation:

Subtract 4x4 + 2x² +5 from the sum of 2x4 - 4x2–3 and 3x4 - 3x² +9.

Answers

Answer:

x^4-9x²+1

Work:

Wanda jumped rope 25 times every minute. What is the algebraic equation to express the function of the total number of times Wanda jumped rope? A. m = 25j B. m + j=25 C. 25 = j - m D. j = 25m

Answers

The answer is a m=25j

Answer:

I think it's A) bro,

Step-by-step explanation:

on the test write now soooo...

i need help pls asap!!

Answers

Answer:

No, Electric Pole is 40 ft

Step-by-step explanation:

tan 66.8° = [tex]\frac{x}{15}[/tex]

x = 35

but that is from the top of Danny, so you need to add 5 (his height)

Electric Pole is 40 ft

What is 2 with an exponent of -2 equal to?

Answers

Answer:

1/4

Step-by-step explanation:

Answer:

[tex] \boxed{\frac{1}{4} } [/tex]

Step-by-step explanation:

[tex]{2}^{ - 2} = \frac{1}{ {2}^{2} } \\ \\ \: \: \: \: \: \: \: \: \: = \frac{1}{4} [/tex]

[tex] Negative \: exponent \\ \\ = > {a}^{-x} = \frac{1}{{a}^{x}} [/tex]

A ramp into a building forms a 6° angle with the ground. If the ramp is 8 feet long, how far away from the building is the entry point of the ramp? Round the solution to the nearest hundredth.

Answers

Answer:

7.96 ft

Step-by-step explanation:

Given;

Length of ramp L = 8 ft

Angle with the horizontal (ground) = 6°

Applying trigonometry;

With the length of ramp as the hypothenuse,

The horizontal distance d as the adjacent to angle 6°

Since we want to calculate the adjacent and we have the hypothenuse and the angle. We can apply cosine;

Cosθ = adjacent/hypothenuse

Substituting the values;

Cos6° = d/8

d = 8cos6°

d = 7.956175162946

d = 7.96 ft

The building is 7.96ft away from the entry point of the ramp.

a rectangular inflatable swimming pool is 2 [tex]\frac{4}{5}[/tex] yards long, 2 yards wide, and [tex]\frac{3}{5}[/tex] yard tall. What is the volume of the pool? Round to the nearest tenth

Answers

Answer:

3.4 yd^3

Step-by-step explanation:

The volume is

V = l*w*h

V = 2 4/5 * 2 * 3/5

Changing the mixed number to an improper fraction

2 4/5 = ( 5*2+4)/5 = 14/5

V =  14/5 * 2 * 3/5

  = 84/25

Changing back to a mixed number

3*25 = 75 with 9 left over

3 9/25

3.36 yd^3

To the nearest tenth

3.4 yd^3

Answer: 3.4 yards cubed, after rounding.

Step-by-step explanation:

To find the volume of a rectangular prism, use the following formula:

[tex]V = wlh[/tex], where w is the width, l is the length, and h is the height

Substitute the values given to you into the formula:

[tex]V = 2 * \frac{3}{5} * 2\frac{4}{5}[/tex]

Simplify the mixed number by multiplying both the numerator and denominator of 2/1 by 5 to get 10/5 and add it to the fraction to get 14/5.

[tex]V = \frac{2}{1} * \frac{3}{5} * \frac{14}{5}[/tex]

Now, multiply the numerators and denominators of the fractions and simplify:

[tex]V = \frac{2 * 3 * 14}{5 * 5}\\\\V = \frac{84}{25}\\\\\\V = 3.36[/tex]

The volume is 3.36 yards cubed. Round to the nearest tenth to get 3.4 yards cubed.

IThe first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
72, 24, 8, ...
Find the 8th term.

Answers

Answer: the eight term is 8/243

Step-by-step explanation:

Each term in this geometric sequence is equal to the previous term, divided by 3.

72,24, 8

a = 72, r = 1/3

a = first term, r is common ratio

tn = ar^n-1

t8 = 72÷ 3^8–1

t8 = 72÷ 3^7

= 72/ 3^7

= 8/243

Please help ASAP! Which ordered pair is a solution of this
equation?
-5x - 9y = -8
Click on the correct answer
A.
(2,-1)

B.
(-1,2)

C.
(-22)

D.
(2,-2)

Answers

Answer: Choice C.  (-2,2)

========================================================

Explanation:

For each possible answer choice, you'll plug in the given coordinates to see which results in a true equation or not.

If we try choice A, then we plug in x = 2 and y = -1 to get

-5x-9y = -8

-5(2)-9(-1) = -8

-10+9 = -8

-1 = -8 which is false

So (x,y) = (2,-1) is not a solution. We can cross choice A off the list.

You'll find a similar situation happens with choices B and D. They don't work either.

-------

Choice C works because...

-5x-9y = -8

-5(-2)-9(2) = -8 .... replaced x with -2, replaced y with 2

10-18 = -8

-8 = -8

We get a true equation. So (-2,2) has been confirmed to be a solution.

what is the quotient of x^2-9x+14/x-7

Answers

x-2 is the quotient!

Write an integer that represents this scenario:

18-point gain

Answers

Answer:

+18

Step-by-step explanation:

A gain is a positive number

+18

Answer:

+18

Step-by-step explanation:

Neg = Drop

Pos = Gain

Gain so +

+18

Please answer correctly !!!!!! Will mark brainliest answer !!!!!!!!!!!

Answers

Answer:

0, 1

Step-by-step explanation:

The discriminant is b² - 4ac where we have ax² + bx + c, in this case a = -4, b = 12, c = -9 so D = 12² - 4(-4)(-9) = 0.

Because the discriminant is 0 that means that f(x) only has one solution for x meaning that it has only 1 x-intercept.

please answer asap! A couple plans to have 5 children. The gender of each child is equally likely. Design a simulation involving 125 trials that you can use to model the genders of the children. Write your answers as numbers.

Answers

Step-by-step explanation:

The gender of a child which is either a boy or a girl is determined by the XX-chromosomes, or XY-chromosomes.

Since the couple plan to have 5 children, the chance of a child being a boy is equal to the chance of it being a girl - the chances are 50/50.

What we do to achieve our aim is to run a simulation that would add an X or Y to an X for all 5 children.

Doing this 125 times, we obtain the number of trials we desire.

For each trial, we get for each child, C:

C1: X + (X or Y)

C2: X + (X or Y)

C3: X + (X or Y)

C4: X + (X or Y)

C5: X + (X or Y)

Since the chance of having an X is equal to the chance of having a Y, they equal probability, which is 0.5 for each.

Find the slope of the line y=5x+4

Answers

Answer:

Slope = 5

Step-by-step explanation:

y = mx + b

m = slope

Slope = 5

Answer:

5

Step-by-step explanation:

Since this is written in slop-intercept form (y = mx + b where m is slope and b is y-int.) the slope is 5.

The bar graph shows the results of rolling a number cube (a die) 50 times. What is the probability of rolling an odd number? How does this compare with the theoretical probability of rolling an odd number?


Experimental Probability. Theoretical Probability

P(odd) = % P(odd) = %

Answers

Answer:

[tex]\fbox{\begin{minipage}{12em}52 percent and 50 percent \end{minipage}}[/tex]

Step-by-step explanation:

Given (as shown in graph):

The results of rolling a number cube (a die) 50 times.

Rolling 1: 10 times

Rolling 2: 4 times

Rolling 3: 8 times

Rolling 4: 11 times

Rolling 5: 8 times

Rolling 6: 9 times

Solve for:

The probability of rolling an odd number (1, 3, 5).

Solution:

Step 1: Define the formula for calculating the probability

P = number of elements/total number of elements

Step 2: Perform the calculation

1) Theoretically, a fair die of 6 sides would give the equal chance to obtain 1, 2, 3, 4, 5, 6.

According to the formula in step 1, the number of elements in both cases are the same (odd: 1, 3, 5 => 3 elements, even: 2, 4, 6 => 3 elements, the total element is 1, 2, 3, 4, 5, 6 => 6 elements).

=> P(obtain odd number theoretically) = P(obtain even number theoretically) = 50%

2) Experimentally, apply the formula in step 1, we have:

The number of elements = Times of rolling 1 + Times of rolling 3 + Time of rolling 5 = 10 + 8 + 8 = 26

The total number of rolling: 50

=> P(obtain odd number in experiment) = 26/50 = 0.52 = 52%

Hope this helps!

:)

Answer:

^ That is correct guys

Step-by-step explanation:

GOOD LUCK


Which shows the fractions in order from greatest to least?

A.5/10,1/4,3/4,5/7
B. 3/4,5/7,5/10, 1/4
C. 5/10,5/7,3/4,1/4
D.1/4, 3/4, 5/7,5/10

Answers

Answer:

Step-by-step explanation:

D

Help please this is due in a couple minutes!!!! Anyone know the answer??!!!?

Answers

Answer:

the second one

Step-by-step explanation:

correct me if it is wrong

Over the past ten years, the town's population doubled in size. The population is currently 12,000. What was the population ten years ago? Which of the following represents the given word problem if "P" represents the population ten years ago? 2(P + 10) = 12,000 2P = 12,000 P = 2(12,000)

Answers

Answer:

2p=12,000

Step-by-step explanation:

Answer ASAP, please!!!!!! Will mark brainliest!!!!! 25 points!!!!!
Explain how the Distributive Property can be used to expand the expression on the left side of the equation.
3(x + 4) = 36.
A. Add 3 to each term inside the parentheses.
B. Subtract 3 from each term inside the parentheses.
C. Multiply each term inside the parentheses by 3.
D. Divide both terms inside the parentheses by 3.

Answers

Answer:

C

Step-by-step explanation:

The 3 is directly outside the parentheses, meaning you need to distribute the 3 to the x and the 4 because they are inside the parentheses. There is no addition, subtraction, or division involved in this so C is correct.

Answer:

C

Step-by-step explanation:

i took the test

find the value of each trigonometric ratio part 3​

Answers

Answer:

hope this helps you

Which notations accurately represent the range?
Check all that apply.
(-∞ 2) U (2, ∞)
(-∞, -2) U (-2, ∞)
{yly E R, Y ≠ -2}
{yly E R Y≠2}
y<2 or y> 2
Y<-2 or y> -2

Answers

Answer:

y < 2 or y > 2 and {y|y ∈ R, y ≠ 2}, (–∞, 2) U (2, ∞)

Step-by-step explanation:

these are the answers i got it right

5+(8×5)+72÷8 !? what is the answer please ​

Answers

Answer:

54 is the answer

Step-by-step explanation:

5+(8x5)+72/8

5+40+9

54

5 + 40 + 72\8

5 + 40 + 9

45 + 9

54

ill mark u brainliest please help me!

Answers

Answer:

C

Step-by-step explanation:

Line AC is equal to line DF.

Answer: The answer is C

Step-by-step explanation:

The way it is written is very important

it goes

AB is to DE

BC is to EF

AC is to DF

Can someone plz help me out! With this problem I really need help ASAP! I will mark you as brainiest! Help help ASAP!

Answers

Answer:

John = 82 Billy = 82 Gregg = 80 Bob = 55

Step-by-step explanation:

John = (3x38)+(2x0)-(2x8)-(2x8)

Billy = (3x30)+(2x4)-(2x3)-(2x5)

Gregg = (3x30)+(2x3)-(2x4)-(2x4)

Bob = (3x25)+(2x6)-(2x9)-(2x7)

Please help me I need to finish today!

Answers

Answer:

C

Step-by-step explanation:

For Youfang, the time spent running is equal to 15 times the week

pleaseee help me w dis!!! marking brainiest!!!

Answers

Answer:

x = -8  x=1

Step-by-step explanation:

x^2 +7x = 8

Subtract 8 from each side

x^2 +7x -8 =0

Factor

What 2 numbers multiply to -8 and add to 7

8*-1 = -8

8+-1 = 7

(x+8)(x-1) =0

Using the zero product property

x+8 =0  x-1 =0

x = -8  x=1

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