The mass of the particles that a river can transport is proportional to the fifth power of the speed of the river. A certain river normally flows at
a speed of 4 miles per hour. What must its speed be in order to transport particles that are 12 times as massive as usual? Round your
answer to the nearest hundredth.

The Mass Of The Particles That A River Can Transport Is Proportional To The Fifth Power Of The Speed

Answers

Answer 1

Answer:

6.58 miles per hour

Step-by-step explanation:

Let the mass and speed be represented by m and s respectively. So that,

m [tex]\alpha[/tex] [tex]s^{5}[/tex]

m = k[tex]s^{5}[/tex]

where k is the constant of proportionality.

For a certain river, speed = 4 miles per hour.

m = k [tex](4)^{5}[/tex]

m = 1024k ............ 1

In order to transport particles that are 12 times as massive as usual;

12m = k[tex]s^{5}[/tex]

m = [tex]\frac{ks^{5} }{12}[/tex] ............. 2

Thus,

[tex]\frac{ks^{5} }{12}[/tex] = 1024 k

[tex]s^{5}[/tex] = 12 x 1024

   = 12288

[tex]s^{5}[/tex] 12288

s = [tex]\sqrt[5]{12288}[/tex]

  = 6.5750

s = 6.58 miles per hour

Therefore, its speed must be approximately 6.58 miles per hour.


Related Questions

Example 2
Let f(x) = 3x2 - 1. Find each of the following
a. f(9)
b. f(-2)
HELP PLS

Answers

Answer:

Step-by-step explanation:

f(9) = 3(9)^2 - 1 = 242

f(-2) = 3(-2)^2 - 1 = 11

f(9) is 242 abs f(-2) is 11

Which quadrant in the coordinate plane below has positive x and negative
y values?

Answers

Answer:

2 or ii

Step-by-step explanation:

This recipe makes 8 flapjacks.
How much of each ingredient is needed to make 12 flapjacks by following this recipe?

Recipe: Makes 8 flapjacks
140 g margarine
120 g sugar
100 mL syrup
240 g oats
50 g raisins

Answers

Answer:

Margarine = 210 gram

Sugar = 180 gram

Syrup = 150 ml

Oats = 360 gram

Raisins = 75 grams

Step-by-step explanation:

Given:

Recipe for 8 flapjacks

140 g margarine

120 g sugar

100 mL syrup

240 g oats

50 g raisins

Find:

Recipe for 12 flapjacks

Computation:

Margarine = [140/8]12

Margarine = 210 gram

Sugar = [120/8]12

Sugar = 180 gram

Syrup = [100/8]12

Syrup = 150 ml

Oats = [240/8]12

Oats = 360 gram

Raisins = [50/8]12

Raisins = 75 grams

1. The distance between two cities is 150 miles. What is 60% of that distance?

HELP PLSSSSSSS

Answers

60% as a decimal is 0.60

Multiply the distance by 0.60:

150 x 0.60 = 90 miles.

Answer:

90

Step-by-step explanation:

60 percent is the same as 0.6

150 * 0.6 = 90

Danielle constructs a scale model of a building with a rectangular base. Her model is 2 inches in length and 1 inch in width. The scale on the model is 1 inch = 47 feet. What is the actual area, in square feet, of the base of the building? in ft2

Answers

Answer: The actual area of the base of the building = 4418 square feet.

Step-by-step explanation:

Dimensions of model: 2 inches in length and 1 inch in width.

The scale on the model is 1 inch = 47 feet.

Actual length = 2 x (47 feet) = 94 feet

Actual width = 1 x 47 feet = 47 feet

Actual area of base of building  = (Actual length) x (Actual width)

= 94 x 47 square feet

= 4418 square feet

Hence, the actual area of the base of the building = 4418 square feet.



Paused
At 7 pm the temp was 5°F. At 12 am the temp was -7°F. What was the change in temp?

Answers

Answer: 12°

Step-by-step explanation:

add together 7 and 5 to get the change since 7 is negative

5 to -7 is 12 units

ABCD- parallelogram, If the perimeter of Triangle CPQ is 15cm, Find the perimeter of triangle BAQ. Find the perimeter of triangle PDA. Also find x ( pls help )

Answers

Answer:

BAQ = 36 cm

PDA = 51 cm

x = 8/3 cm

Step-by-step explanation:

I've attached an image below, I'm not completely sure if im right but hope this helps!

Can I get some help please

Answers

Answer:

The three gallon container is the better buy. See below.

Step-by-step explanation:

8 pints

2 pints = 1 quart.

8 pints = 4 quarts.

4 quarts = 22.64   Divide by 4

1 quart = 5.66

3 gallons.

1 gallon = 4 quarts

3 gallons = 12 quarts.

The cost of 1 quart = 54.48/12 = 4.54

Cuánto es 187+165= porfas ayudenmeeee boran monzooooon ayudaaaaa por fas

Answers

Answer:

dont spread Spanish but 187 + 165= 352

Solve each equation mentally.
2x = 10
-3x = 21
ws
1/3x = 6
- 1/3x = -7

Answers

Answer:

5, -7, 18, 14

Step-by-step explanation:

1) x = 5

2) x = -7

3) x = 18

4) x = 14

Peter says, "If you subtract 12 from my number and multiple the difference by -7, the result is -189" what is peter's number

Answers

Answer:

-37.8

Step-by-step explanation:

Im smart lol

Answer:

The number is 39!!

Step-by-step explanation:

Can I please have Brainliest?

400-36v^2 can someone find the factor?

Answers

Answer:

-4(3v - 10)(3v + 10)

Step-by-step explanation:

You must find the factored form of 400 - 36v^2.

You can rearrange this to - 36v^2 + 400 to make it less confusing.

So you have - 36v^2 + 400.

The next step is to see what you can take out of this. You can take out a GCF, a greatest common factor. This is basically a number that goes into both 36 and 400. This number is 4.

36 / 4 = 9 and 400 / 4 = 100.

Since it is a negative 36, you need to take out a negative 4.

So you put a 4 outside parenthesis and divide - 36 / 4 and 400 / 4.

-4(9v^2 - 100).

Now you must factor the inside of the parenthesis.

9v^2 - 100.

This is the same as 9v^2 + 0v - 100.

What are 2 numbers that multiply to get -100 and add to get 0?

These numbers are -10 and +10.

2 terms that multiply together get 9v^2 are 3v and 3v.

So the answer is:

-4(3v - 10)(3v + 10).

This is the factored form.

1/2 til 2:00? = what time

Answers

Answer:

the answer is 1:30pm/am

The results favorite Nascar driver.
40% Ehrnhardt, 13% petty, 18% waltrip, 29% Gordon
(a) Order the popularity of the choices from greatest to least.
(b) It was estimated that 360 people were surveyed. If this was true, how many people would have voted for Ehrnhardt? Round to the nearest whole number. Show your work.
(c) 65 people voted for Petty. Was the estimate of total voters from Part (b) accurate? Explain.

Answers

Answer:

(a) Earnhardt (40%), Gordon (29%), Waltrip (18%), and Petty (13%)

(b) 144, work is below

(c) No

Step-by-step explanation:

(b)

convert 40% to a decimal by dividing by 100 = 0.4

360 x 0.4 = 144 people voted for Earnhardt

(c) converting Petty's percentage to a decimal, we get 0.13. 360 x 0.13 = 46.8, or 47 people, not 65.

Waltrip's percentage, 0.18 x 360 = 64.8, or 65 people.

find x=, if x-7=11 HURRY!!

Answers

Answer:

X = 18

Step-by-step explanation:

X - 7 = 11

Add 7 to both sides

X - 7 + 7 = 11+7

X = 18

x=18 because 18-7=11

can someone helpp with this

Answers

Here is my answer, hope to help you

You buy 2 pencils and 3 erasers for $4. How might this look as an equation?

Answers

Answer:

2x+3y=4 I don't know the variables so I use x and y

I need help with this question ASAP

Answers

Answer:

46

Step-by-step explanation:

180-134=46

Answer:

They're both 46 degrees

Step-by-step explanation:

Angle b and 134 are right next to each other so they're supplementary and have to equal 180 degrees.

180-134=46, and since Angle c is is a vertical angle with Angle b, it also equals 46^^

The lines represented by the equations by - x = 5 and y = { x = 1 are
are they parallel or perpendicular

Answers

Answer:

Parallel

Step-by-step explanation:

Let the required lines be y-x = 5 and y = x-1

If y-x = 5

y = x + 5

The slope m = 1

For the line y = x - 1

The slope m is also 1

Since the slope of both lines are the same, hence both liens are parallel

What is the circumference of the circle
below?

Answers

Answer:

113.1

Explanation:
C=2πr

How do you find the area of the shaded sector of the circle? The radius is 10in and the sector is 45 degrees

Answers

Given:

Radius of the circle = 10 in

Central angle of the sector = 45 degrees

To find:

The area of the sector.

Solution:

Area of a sector is

[tex]A=\dfrac{\theta}{360^\circ}\pi r^2[/tex]

Where, [tex]\theta[/tex] is the central angle in degrees.

Putting r=10 and [tex]\theta=45^\circ[/tex], we get

[tex]A=\dfrac{45^\circ}{360^\circ}\pi (10)^2[/tex]

[tex]A=\dfrac{1}{8}\pi (100)[/tex]

[tex]A=12.5\pi[/tex]

Therefore, the area of the sector is 12.5π sq. inches.

What is the slope of the line through (-1,-7), (3,9)

Answers

Answer:

The slope is 4

Step-by-step explanation:

basilly you add easy x(-1,-7) + y(3,9) = 2/2

make sure that you add x left and y right  first -1+3=2 and then -7+9=2 equal=2,2 together and just add both equal 4

Most easy just put you answer in a graht and count the squares

hope this helps ;)

Equation for slope = (y2-y1)/(x2-x1)

= (9- -7)/(3- -1) = 16/4 = 4

Paul wants to find the center and radius of the circle defined by the equation x2+y2+10x−14y+40=2

Answers

Answer:

x-intercept(s):

None

y-intercept(s):

(0,7+√11),(0,7−√11)Step-by-step explanation:

A rectangular pyramid has a volume of 216 in.
A rectangular prism has the same height as the rectangular pyramid and a base that is
congruent to the base of the rectangular pyramid.

What is the relationship between the volume of the rectangular pyramid and the rectangular prism?

The volume of a rectangular prism is 3 times the volume of a rectangular pyramid. The volume of the rectangular prismis 648 in?

The volume of a rectangular prism is 2 times the volume of a rectangular pyramid. The volume of the rectangular prism is 432 in?

The volume of a rectangular prism is 1/2 the volume of a rectangular pyramid. The volume of the rectangular prism is 108 in

The volume of a rectangular prism is 1/3 the volume of a rectangular pyramid. The volume of the rectangular prism is 72 in?

ILL GIVE BRAINLIEST HELP ASAP

Answers

Answer:

4.5x6x5.5= 148.5

Step-by-step explanation:

148.5

Answer:

148.5

Step-by-step explanation:

4.5 * 6 * 5.5

=

148.5

The triangles shown below must be congruent.
47
710
71
)47
62
7
7
O A. True
B. False

Answers

Answer:

True

(Angle-Side-Angle)

The triangles shown below must be congruent is a True Statement.

We have two Triangles in which

There are three angles Congruent in both Triangles.

Also, the side of the triangle is congreunt.

As we know that there is no Criteria which as congruency rule AAA Criteria.

So, we can take two Congruent angles and one Congruent side.

Thus, the statement is True.

Learn more about Congruency here:

https://brainly.com/question/7888063

#SPJ7

For what values of x is the rational expression below undefined?
+5
32 - 3

Answers

Answer:

29

Step-by-step explanation:

PLEASE HELP
Which equation would you use to solve the following situation?
Ms. Green has 18 pencils at her desk. Students borrow some of the pencils, and 6 pencils are left at the end of the school day. How many pencils were borrowed?

x - 6 = 18
18 - x = 6
18 + 6 = x

Answers

Answer:

18-x=6

Step-by-step explanation:

because

if you have eighteen and some were borrowed and 6 were left so it will be subtracted

Answer:

18 - x = 6

Step-by-step explanation:

In any equation x is the unkown you are trying to figure out.

In a word-problem-solving question its helpful to set out what you know and what you dont know:

You know the original number of pens = 18

You know the final number of pens = 6

You dont know how many pens were taken.

Therefore x is the difference between 18 and 6.

18 pens take away x pens is equal to 6

hence 18 - x =6

The measure of the minor arc BC is 63º. What is the measure of ZBAC?

Answers

Answer:

measure or arc BAC should be 297 degrees (with assumptions)

Step-by-step explanation:

Assumption 1: the cap Z in your question is actually an angle symbol

Assumption 2: A is the center of the circle

IF these assumptions are true, then the measure of arc BAC is 36 - 63 = 297 degrees

2x + 3y = 5x - y
Complete the missing value in the solution to the equation.
( _ , 0 )

Answers

Answer:

(4y/3, 0) or if there are no options, it's probably (0, 0)

Step-by-step explanation:

2x + 3y = 5x - y

So we are trying to find the missing value in the solution (_, 0)

We are looking for the x-intercept/root if the coordinate is in this way:  (_, 0)

So to find the root, We are solving for x

2x + 3y = 5x - y

First, subtract 5x from bth sides

2x + 3y - 5x = 5x - y - 5x

2x + 3y - 5x = -y

Add like terms

-3x + 3y = -y

Now, subtract 3y from both sides

-3x + 3y - 3y = -y - 3y

-3x = -4y

Divide both sides by -3

-3x/-3 = -4y/-3

x = -4y/-3

We are not done yet because the answer above is not quite right. A negative number divided by a negative number results in a positive number.

So x = 4y/3

Now that we found x, we can input it to the coordinate

(4y/3, 0)

I put it on Sesmos graphing calculator and the answer seems to be (0, 0)

Fill in the blank to complete the equation below.

14 + 35
= 7(2 + ___)

Answers

Answer:

5

Step-by-step explanation:

14+35=49 and we are looking for the number times 7 that gives us 49.

So, we already have 2. 2+ what times 7 gives us 49? 2 + 5 = 7 and so now our equation looks like this:

14+35 =7 (2+5)

Or

14+35= 7x7 becuase 7x7 is 49 and 14+35 is also 49.

(If you need more help, let me know!)

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