Mathematics College

The drag force F on a boat varies jointly with the wet surface area A of the boat and the square of the speed s of the boat. A boat with a wet surface area of 50ft2 traveling at 7mph experiences a drag force of 98N . Find the wet surface area of a boat traveling 7.5mph and experiencing a drag force of 135N .

Answers

Answer 1

Final answer:

The wet surface area of the boat is approximately 69.7ft^2.

Explanation:

The drag force on a boat varies jointly with the wet surface area and the square of the speed of the boat. This can be represented by the equation:

F = k · A · s^2

where F is the drag force, A is the wet surface area, s is the speed, and k is a constant of variation.

To find the wet surface area of a boat traveling at 7.5mph and experiencing a drag force of 135N, we can set up the following proportion:

(98N) ÷ (50ft^2) = (135N) ÷ (x ft^2)

Cross-multiplying and solving for x, we find that the wet surface area of the boat is approximately 69.7ft^2.

Related Questions

Find the lcm of 6, 5, 3

Answers

Hello There!

6 = 6 12 18 24 30 36
5 = 5 10 15 20 25 30
3 = 3 6 9 12 15 18 21 24 27 30

It would be 30.

Hope This Helps You!
Good Luck :)
The LCM's of 6, 5, and 3. To solve this question, let's list the multiples.

6: 6, 12, 18, 24, 30
5: 5, 10, 15, 20, 25, 30
3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

As you can see, all of the three numbers have a multiple of 30. The LCM of 6, 5, and 3 is 30.

If Logx (1 / 8) = - 3 / 2, then x is equal to

A. - 4

B. 4

C. 1 / 4

D. 10

Answers

answer is C 1/4

 see attached picture, it is not exact but with rounding it comes out correct.

Which equation has no solution?

4(x + 3) + 2x = 6(x + 2)
5 + 2(3 + 2x) = x + 3(x + 1)
5(x + 3) + x = 4(x + 3) + 3
4 + 6(2 + x) = 2(3x + 8)

Answers

4(x+3)+2x=6(x+2) is the right answer

Answer:

B: 5 + 2(3 + 2x) = x + 3(x + 1)

Step-by-step explanation:

Just took it it's correct so leave a like

Janae bought wallpaper that cost $25.90 for each roll of 14 square feet. Find the unit price.

Answers

Answer:

The unit price is $1.85

Step-by-step explanation:

Janae bought a roll of wallpaper that cost = $25.90

Each roll is of = 14 square feet

Cost per square feet = [tex]\frac{25.90}{14}[/tex] = $1.85

The unit price is $1.85

Find 10-3 Write the subtraction fact two ways?

Answers

10 - 3 = 7.
Other ways to write it:
3 + 7 = 10.
7 + 3 = 10.

I hope this helps! :>

There are two ways to write the subtraction fact 10 - 3:

10 - 3 = 7

7 + 3 = 10

What are these two ways?

The first way is to simply subtract the two numbers. The second way is to add the two numbers together to get the original number.

Both ways are correct and can be used in different situations. For example, if you are trying to figure out how many apples are left if you have 10 apples and you eat 3, you would use the first way to subtract the two numbers to get 7 apples.

If you are trying to figure out how many apples you need to buy to have 10 apples if you already have 3 apples, you would use the second way to add the two numbers together to get 7 apples.

Find out more on subtraction fact here: https://brainly.com/question/1726293

#SPJ3

please help
An arithmetic sequence has this recursive formula

Answers

the explicit formula is B

93 times the sixth power of ten

Answers

93 x 6^10

93 x 60466176 = 5623354368
hope this helps

what is the value of the underlined digit? 587

Answers

There is no underlined dogit
If the line is under the 5 it's five hundreds, in the 8 eight hundreds, and the 7 seven ones.

How are the decimals .009 and .09 related?

Answers

They're related only because they are smaller than .1. They both have 9 and both have at least on zero. They're different though because .09 is a larger number than .009

Answer:

0.09 is ten times of 0.009

Step-by-step explanation:

The two decimals are 0.009 and 0.09

We can rewrite the decimals in the scientific notation.

0.009 = [tex]9\times 10^{-3}[/tex]

And 0.09 = [tex]9\times 10^{-2}[/tex]

Now we divide first decimal 0.09 by 0.009

[tex]\frac{0.09}{0.009}=\frac{9\times 10^{-2} }{9\times 10^{-3} }[/tex]

=[tex]\frac{10^{-2}}{10^{-3}}[/tex]

= [tex]\frac{10^{3} }{10^{2} }=10[/tex]

Therefore, 0.09 is ten times of 0.009

What is the equilibrium price per DVD?

Answers

The equilibrium referred to here is the dynamic equilibrium. It means that there is a change happening, but the opposite change are equal so they cancel out. So, we can determine the equilibrium price at the point where the demand and supply curve intersect. That would be at the quantity of 60 units. Therefore, the equilibrium price is $10.

Prove that 1=2 with well arranged steps and justify each step

Answers

Justification Step 1: Let a = b. Step 2: Then a^2 = ab , Step 3: a^2 + a^2 = a^2 + ab , Step 4: 2a^2=a^2 + ab, Step 5: 2a^2 - 2ab = a^2 + ab - 2ab, Step 6: and 2a^2 - 2a^b = a^2 + ab - 2ab . Step 7: This can be written as 2(a^2 - ab) = 1(a^2 - ab) , Step 8: and cancelling the (a^2 - ab) from both sides gives 1 = 2.

√32 greater or less than 5.1

Answers

The pie of 32 is 5.6 and then there's 5.1

Your answer will be greater because 5.6 is greater than 5.1.

Point Q is the midpoint of segment PR. If PQ= (15x-2) and QR= (5x+3) find the value of Q.

Answers

is that the measure or linear equation
check the picture below.

so, the distance to Q, or one can say Q's length is the same as PQ's. or QR's for that matter.

Raul and Ruth Are saving for a trip.Raul starts with $350 and saves $15 per week.Ruth starts with $200 and saves $25 per week. When will they have the same amount?

Answers

Develop two linear equations to represent the savings of these two people:
Raul:  rl=$350 + $15x
Ruth:  rh=$200 + $25x
In both cases, x represents the number of weeks elapsed.

When will these two people have saved up the same amount?  Set rl = rh and solve for x, the number of weeks elapsed:

$350 + $15x = $200 + $25x

$150 = $10x           gives us x= 15.  Their savings will be equal after 15 weeks.

Answer:

15

Step-by-step explanation:

55% of what number is 22?

Answers

55% = 55/100 = 0.55

22 : 0.55 = 40 

55% of  40 is 22
The number will be represented by the variable x.

Now convert the percent into a decimal by moving the % sign two places to the left and make the % sign into a decimal point.

55% = 0.55

In mathematics, 'of' can sometimes mean multiply.
Likewise, 'is' can sometimes mean equal.

0.55x = 22

Solve for x.

0.55x = 22
x = 40 <-- Divide both sides by 0.55.

So, the answer is 40.

Simplify the complex number i^39 as much as possible.

Answers

Answer:

-i

Step-by-step explanation:

i = [tex]\sqrt{-1}[/tex]

[tex]i^{2}[/tex] = - 1

Every [tex]i^{x}[/tex] will be equal to -1, when n is even.

Break apart [tex]i^{39}[/tex] into ([tex]i^{38}[/tex])([tex]i^{1}[/tex])

Since 38 is even, [tex]i^{38}[/tex] will be equal to -1

-1*([tex]i^{1}[/tex]) = -i

To simplify i^39, we must use the cyclical pattern of i's powers, which repeats every four. i^39 simplifies to i^3, which is equal to -i.

To simplify the complex number i^39, we should recognize the cycle of powers of i. Since i represents the square root of -1, the powers of i cycle every four powers:

i = ii^2 = -1i^3 = -ii^4 = 1

To find the equivalent of i^39, we can divide 39 by 4 to get a quotient and a remainder: 39 divided by 4 is 9 with a remainder of 3. This means that i^39 is equivalent to i^3, which is -i.

Marty wants to paint a box. He can choose to use either blue, green, yellow, or black paint. Also, he can style the paint by painting with a brush, a roller, or a sponge. How many different combinations of color and painting method can Marty choose?

Answers

Since there are 3 different ways of painting each color, we have 3+3+3+3=12 (because there are 4 different colors) ways to paint this

Answer:

12

Step-by-step explanation:

Marty can choose his paint in 4 ways and his style in 3 ways. Thus there are a total of 4x3=12 different combinations he can choose.

Prove that if d|m and d|n, then d|(m+n)

Answers

[tex]d\mid m[/tex] means to say there is some [tex]k_1[/tex] such that [tex]m=dk_1[/tex]. Similarly, [tex]d\mid n[/tex] is equivalent to saying there exists [tex]k_2[/te]x such that [tex]n=dk_2[/tex].

Now, [tex]m+n=dk_1+dk_2=d(k_1+k_2)=dk_3[/tex], i.e. there is some [tex]k_3[/tex] such that [tex]m+n[/tex] is a multiple of [tex]d[/tex], i.e. [tex]d\mid(m+n)[/tex].

Frances left a 19% tip on a meal, including the tip, it's cost was $27.37. What was the cost of the meal before the tip?

Answers

This is just multiplying and subtracting
So 19% in decimal is 0.19 
so 27.37 x 0.19 = 5.2 (If not rounded it is 5.2003)
5.2 - 27.37 = 22.17 (If not rounded 22.167)

Answer:

$22.17

Step-by-step explanation:

Please see attachment. Calculations executed in black ink. Justification explained in green ink. Solution highlighted in blue.

~~

Thank you!

how many significant digits are in 23,000

Answers

2 ,It is the numbers at the beginning the zeros dont count so you would just count the numbers above 0 

Brainiest to Response. AP Statistics Help on Hypothesis Testing! I have various AP Stats questions I'd like to check with those who completed this course or knows about p-values, Hypothesis Testing, and alphas. If you've taken the course and can help me with some AP Statistics questions, I'd appreciate it.

Answers

ill give it a shot friend.

Kendra and her horse completed the barrel racing course in 15.839 seconds. What is this number rounded to the nearest tenth? :explain how you decided

Answers

the answer is 15.84.

To find the nearest tenth, you go to the 3rd place after the decimal and decide: if the value is 5 or greater, go to the second place after the decimal and round up one. If it does not, the value of the second decimal stays the same.
15.839 rounded to the nearest tenth would be 15.8. It would be that because when you look at the number to the right when it is below five you leave the number your rounding alone, but when the number to the right is higher you would add one to the number that you are rounding. Easy. 

The difference between 4 and the product of 6x and 40

Answers

Sent a picture of the solution to the problem (s).

What decimal equivalent of 5/6

Answers

divide 5 by 6 to get0.8333 ( the 3 keeps repeating)

One fifth of the employees of Delta Industries, Inc., work in the Southeastern region. If the company employs 252 workers in that region, what is the total number of employees working for the company?

Answers

so, 252 is 1/5 of the total workforce then, the total or whole will then be 5/5 or 1 whole... well, if 252 is 1/5, what's 5/5?

[tex]\bf \begin{array}{ccll} amount&fraction\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 252&\frac{1}{5}\\\\ x&\frac{5}{5} \end{array}\implies \cfrac{252}{x}=\cfrac{\frac{1}{5}}{\frac{5}{5}}\implies \cfrac{252}{x}=\cfrac{\frac{1}{5}}{1}\implies \cfrac{252}{x}=\cfrac{1}{5} \\\\\\ \cfrac{252\cdot 5}{1}=x[/tex]
Final answer:

One fifth of the employees of Delta Industries, Inc., work in the Southeastern region. The total number of employees working for the company is 1260.

Explanation:

If one fifth of the employees of Delta Industries, Inc. work in the Southeastern region, and there are 252 workers in that region, we can find the total number of employees by multiplying 252 by 5.

5 times 252 equals 1260. Therefore, the total number of employees working for the company is 1260.

Central Middle School has 2,470 students and the ratio of students to teacher is 26:1. How many new teachers are needed to reduce this ratio to 19:1?

Answers

so, the school has 2470 students, and the ratio from students to teacher is 26:1 currently, so hmmm how many teachers are there with that ratio anyway?

[tex]\bf \cfrac{student}{teacher}\qquad 26:1\implies \cfrac{26}{1}=\cfrac{\stackrel{2470}{students}}{\stackrel{teachers}{t}}\implies \cfrac{26}{1}=\cfrac{2470}{t} \\\\\\ t=\cfrac{1\cdot 2470}{26}\implies \boxed{t=95}[/tex]

hmm alrite... what if the amount of students is kept the same, but more teachers come in, that the ratio changes and is no longer 26:1 but 19:1?

how many teachers will there be then?

[tex]\bf \cfrac{student}{teacher}\qquad 19:1\implies \cfrac{19}{1}=\cfrac{\stackrel{2470}{students}}{\stackrel{teachers}{t}}\implies \cfrac{19}{1}=\cfrac{2470}{t} \\\\\\ t=\cfrac{1\cdot 2470}{19}\implies \boxed{t=130}[/tex]

so, if there are 130 teachers and 2470 students, the ratio is 19:1.

at 26:1 is with 95 teachers.

how many more new teachers are needed? well, surely you'd know that.

Write 93 11/16 as a decimal

Answers

93 11/16 written as a decimal is 93.6875. Rounded it is approximately 93.7

I hope this helps:)

0.04 is 1\10 of what

Answers

0.04 is 1/10 of 0.4

hope this helps

Find the present value of Php 50,000.00 due in 4 years if money is invested at 12% compounded semi-annually.

Answers

In this case, Php 50,000 money invested for 4 years with 12% rates. If the rate is 12% compounded semi-annually that means it would be 6%/ 6 months. Then the amount of money after 4 years would be:

Php 50,000.00 * (100+6)%^(4 years/ 6 months)=
Php 50,000.00 * 106%^(8)= Php 79,692.40

Pre cal/cal master needed

F(x)= 2x^2 + 3x-2 and g(x)= x-2

find equation for f(g(x))

My answer : 2x^2 -8 +3x-8

True answer: 2x^2 -5x

How do we get true answer? I plugged in g(x) into the x's of F(x) but got a waaaaaay different answer.

Answers

Take x-2 and insert it into 2x^2 + 3x-2 where the x is located 
2x^2 + 3x-2
2(x-2)^2 + 3(x-2)-2

Now work out 2(x-2)^2 + 3(x-2)-2 also follow PEMDAS
2(x-2)^2 + 3(x-2)-2 
Since (x-2)^2 is an Exponent, lets work with that first and expand (x-2)^2.
(x-2)^2
(x -2)(x-2)
x^2 -4x + 4
Now Multiply that by 2 because we have that in 2(x-2)^2
(x-2)^2  =  x^2 -4x + 4
2(x-2)^2  =  2(x^2 -4x + 4)
2(x^2 -4x + 4) = 2x^2 - 8x + 8
2x^2 - 8x + 8

Now that 2(x-2)^2 is done lets move on to 3(x-2).

Use the distributive property and distribute the 3
3(x-2) = 3x - 6

All that is left is the -2 

Now lets put it all together 
2(x-2)^2 + 3(x-2)-2

2x^2 - 8x + 8 + 3x - 6 - 2

Now combine all our like terms 
2x^2 - 8x + 8 + 3x - 6 - 2
Combine:  2x^2      =  2x^2 
Combine: -8x + 3x  =  -5x
Combine:  8 - 6 - 2 =   0

So all we have left is
2x^2 - 5x





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