An offshore oil well is 1 mile off the coast. The oil refinery is 4 miles down the coast. Laying pipe in the ocean is twice as expensive as laying it on land. Find x, and consider how finding x helps determine the most economical path for the pipe from the well to the oil refinery.

Answers

Answer 1

Answer:

[tex]x = \frac{\sqrt 3}{ 3}[/tex]

Step-by-step explanation:

Given

See attachment for complete question

First, we calculate the water pipe length (AC):

[tex]AC^2 = AB^2 + BC^2[/tex]

[tex]AC^2 = 1^2 + x^2[/tex]

[tex]AC^2 = 1 + x^2[/tex]

[tex]AC = \sqrt{1 + x^2[/tex]

The cost of laying across water is twice (2 times) laying on land.

So, the total cost (C) is:

[tex]C = 2 * \sqrt{1 + x^2} + 1 * (4 - x)[/tex]

[tex]C = 2 \sqrt{1 + x^2} + (4 - x)[/tex]

Differentiate

[tex]C' = \frac{2x}{\sqrt{1 + x^2}} - 1[/tex]

To find the most economical cost, we simply minimize C' by equating C' to 0

[tex]C' = 0[/tex]

[tex]\frac{2x}{ \sqrt{1 + x^2}}-1 = 0\\[/tex]

[tex]\frac{2x}{ \sqrt{1 + x^2}}=1[/tex]

Cross multiply

[tex]2x= \sqrt{1 + x^2}[/tex]

Take square of both sides

[tex]4x^2 = 1+x^2[/tex]

Collect like terms

[tex]4x^2 -x^2= 1[/tex]

[tex]3x^2= 1[/tex]

Solve for [tex]x^2[/tex]

[tex]x^2 = \frac{1}{3}[/tex]

Solve for x

[tex]x = \sqrt{\frac{1}{3}}[/tex]

[tex]x = \frac{1}{\sqrt 3}[/tex]

Rationalize:

[tex]x = \frac{1}{\sqrt 3} * \frac{\sqrt 3}{\sqrt 3}[/tex]

[tex]x = \frac{\sqrt 3}{ 3}[/tex]

An Offshore Oil Well Is 1 Mile Off The Coast. The Oil Refinery Is 4 Miles Down The Coast. Laying Pipe

Related Questions

The Pythagorean Theorem is
c² = g²-6²
False
O True
O No answer text provided.
O No answer text provided.

Answers

Answer:

            False

Step-by-step explanation:

It depends on the triangle.

If a is the longest side then it's true, but usually when we talk about Pythagorean theorem we mean that c is the longest side of the right triangle. So:

              c² = a² + b²

Help plz helpppppppppppppp ​

Answers

Answer:

A = 45 cm²

Step-by-step explanation:

The area (A) of a trapezium is calculated as

A = [tex]\frac{1}{2}[/tex] h( b₁ + b₂)

where h is the height and b₁, b₂ the parallel bases

Here h = 5, b₁ = 10 and b₂ = 8 , then

A = 0.5 × 5 × (10 + 8) = 0.5 × 5 × 18 = 45 cm²

The points M( 10,3) and P(-4,"8) are graphed on the coordinate plane. To the nearest
tenth of a unit, what is the distance between points Mand P? Round to the nearest
tenth.

Answers

You can make a triangle with the hypotenuse being the distance between the two points. First, find the absolute value of the change in y and change in x which would be 5 and 14. Next, solve using pythagorean theorem. 5^2 + 14^2 = c^2 —> c = 14.866

Answer: 12.5

Step-by-step explanation:

It is around 12.5 units

If cos (A+B) = cosAcos B – sinAsin B , find the value of cos 75

Answers

Answer:

Step-by-step explanation:

Cos 75 = Cos ( 30 + 45)  {Use Cos (A + B) identity}

            = Cos 30*cos 45 - Sin 30 Sin 45

            [tex]= \frac{\sqrt{3}}{2}*\frac{1}{\sqrt{2}}-\frac{1}{2}*\frac{1}{\sqrt{2}}\\\\= \frac{\sqrt{3}}{2\sqrt{2}}-\frac{1}{2\sqrt{2}}\\\\=\frac{\sqrt{3}-1}{2\sqrt{2}}\\\\=\frac{(\sqrt{3}-1)*\sqrt{2}}{2\sqrt{2}*\sqrt{2}}\\\\=\frac{\sqrt{3}*\sqrt{2}-\sqrt{2}}{2*2}\\\\=\frac{\sqrt{6}-\sqrt{2}}{4}[/tex]

Hiiiooo! Can someone please help me❤️❤️❤️ :D

Answers

Answer:

wassup baby, whas the insta?

What is the value of 19-7-15+14

Answers

Answer: the answer is 11 :)

Step-by-step explanation: I hope this helped!

Answer:

11

Step-by-step explanation:

19 - 7 = 12 - 15 = -3 + 14 = 11

or, if your brain likes it better, add the positives, then add the negatives, then subtract:

19 + 14 = 33

-7 -15 = -22

33 - 22 = 11

Rafael and his sister bought snacks for movie night.
Rafael got 3 boxed candies and 1 bag of chips for $6.99.
His sister got 2 bags of chips and 1 boxed candy for $5.98.
Find the cost for 1 of each of these items in dollars.
1 boxed candy costs $?
1 bag of chips costs $?

Answers

Answer:

1. $2.33

2. $2.99

Step-by-step explanation:

Answer:

bag of chips is 2.19

boxed candy is 1.60

Step-by-step explanation:

Desmos Calculator

Firas and Nabil are comparing their bank accounts. "I have four times more money than
you" , Firas says. "Anyway, I have only $240 less than you" , Nabil answers .
How much money does each one of them have in his account ?
should be solved as a system​

Answers

Answer:

Firas = $320

Nabil = $80

Step-by-step explanation:

Firas = 4x

Nabil = x

x + 240 = 4x

3x = 240

x = $80

Firas = $240 + $80 OR $80 x 3 = $320

Nabil = $80

Hope that helps!

what is n if the equation is
n - 2 divided by -3 = -6
Please help me I am having a lot of trouble, thank you

Answers

n - 2 / - 3 = - 6 (1) multiply both sides by -3 to get n - 2 alone
n - 2 = 18 (2) add 2 to both sides; 2 on left side gets cancelled so we can now have n all alone
n = 20

OMG PLZZZZZZ HELP ME I REALLY NEED HELP :'( EVERYONE WHO HELPS ME GETS IT WRONG PLZZZ HELP ME IM BEGGING YOU

Answers

Answer:

1st Picture: d = -16

2nd Picture: g = -13.8

Step-by-step explanation:

1st Picture: Divide both sides by -11 to balance both sides and get the answer.

2nd Picture: Subtract 1.2 from both sides.

Answer:

Question 6:

We have -12.6 = g + 1.2, so we move the 1.2 to the left side to get -13.8 = g because when you move a number you are essentially minusing that number so 1.2 becomes -1.2 .

Question 7:

We have 176 = -11d so we divide by -11 to get -16 = d.

Hope this helped!

HELPPP PLEASE!! I NEED AN ANSWER. what expressions are equal to 18 x 13?

Answers

6x39
9x26
hopes this helps

18×13 is equal to 234

Step-by-step explanation:

18×13=234

Find the equation of a line that passes through the point (-2, -1) and is
perpendicular to the line with equation y=-2x+8.

Answers

Answer:

2y-x=0

Step-by-step explanation:

Please mark as brainliest

Please, I need this done!

Answers

I don’t know if it counts as 2 but the 16x-20 is just a simplified version of the 6x+8x-30+2x+10


HELP PLS HELP PLS HELP PLS HELP PLS HELP PLS HELP PLS TY TY TY

Answers

Answer:-5+x<-1

Step-by-step explanation:

Answer:

H. -5 + x < -1

Step-by-step explanation:

Okay so let's first look at our little graph thing. What is it saying? It's telling us that what ever x is, it is NOT 4 (because the circle is not filled in) and it is less than 4 (because it's all shaded in before 4). Now that we know this, lets look at our possible answers.

F. x - 3 < 7

Now, for all of these possible answers, we can solve them exactly like normal equations (like x - 3 = 7).

x - 3 < 7

[add 3 to both sides to leave the x by itself]

x < 10

Whoa, that's not right! We don't even have 10 on our graph, so F is out of the running.

G. x + 6 [tex]\leq[/tex] 10

Okay, let's work smarter, not harder here. So we can see that there is a greater than or equal to sign there. So even if we solve it and we get 4 as the answer, our graph doesn't include 4. So we can throw this answer out right away.

H. -5 + x < -1

Solve like a normal equation in the first one.

-5 + x < -1

[add 5 to both sides to leave the x by itself]

x < 4

Hey! We got something! So let's read this with words. So whatever x is, it does not include 4, and is less than 4. So now looking back on our first brainstorm of the graph, this is in line with what we want.

So this is the answer! Yay!

Just for fun let's look at the last possible answer.

I. x - 8 > -4

Again, solve like a normal equation.

x - 8 > -4

[add 8 to both sides to leave x by itself]

x > 4

Oh! Another 4! But this time the sign is different. Let's read it again with words. So whatever x is, it does not include 4 (ok, good), and is greater than 4 (oh, not good). Our graph showed us that x is less than 4. So this answer is not the answer.

So again, we keep H. as our correct answer.

Please help!!

Choose whether the sampling is biased or unbiased

Questions are asked of randomly chosen workers at one of ten workplaces

1. Unbiased
2. Biased

The question asked is, “What do you think about the prison system in this state?”

1. Unbiased
2. Biased

The question asked is, “What do you think about the horrible prison system in this state?”

1. Unbiased
2. Biased

Answers

1. biased

2.unbiased

2. biased prisoners should be treated equally and the system is messed up

help? please and thank you​

Answers

Answer:

first one

relationship between base and perpendicular is

given by tan angle

tan x=P/h

remember perpendicular is opposite side of taken angle

tan x=13/8

<x=tàn-¹(13/8)=58.39°

for second one

relationship between base and hypotenuse is given by cos angle

cos G=b/h

cos G=24/32

<G=cos-¹(24/32)=41.4 is your answer

Plz plz help I’m failing math and need help

Answers

Answer:

5 sweat shirts- $100

8 sweat shirts- $160

9 sweat shirts- $180

12 sweat shirts- $240

Step-by-step explanation:

Each sweat shirt costs $20

Colin buys a tv for £800. It depreciates at a rate of 4% per year. How much will it be worth in 3 years? Give your answer to the nearest penny where appropriate

Answers

Answer:

£707.8

Step-by-step explanation:

Given data

Price=  £800

Rate= 4%

Time= 3 years

Let us apply the compounding formula

A=P(1-r)^r-------------Note the negative sign is because of depreciation

substitute

A= 800(1-0.04)^3

A= 800(0.96)^3

A=800*0.884736

A=  £707.8

Hence the value will be £707.8

how to calculate the Triangle Proportionality Theorem

Answers

Step-by-step explanation:

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

Simplify (y+1)+4
Help

Answers

Answer:

y+5

Step-by-step explanation:

Answer: y+5

Step-by-step explanation:hope this help

Miguel has a garden that has an area of 300 square feet. If the corn in his garden covers 160 square feet, what percent of the garden is corn?

Im not sure of my answer but I got 5.33 and the 3 repeats

Answers

Answer:

Im sorry if I'm wrong but I think it's 300+160=460

Answer:

yes your correct  but wrong

Step-by-step explanation:

To find  the area that's covered in corn you need to first write your fraction.

160/300

After you do that you have to turn it into a decimal.

.53333...

After that you need to turn it into a percent so your final answer will be....

53.333...%

BTW try looking to see if you need to round, normally it tells you to do that

What has an absolute value of 9?

Answers

Answer:

the first one 9 or -9

Step-by-step explanation:

they both have absolute values of 9

hope this helps :)

Answer:

Your answer would be 9 or -9.

Step-by-step explanation:

The absolute value of a number means the distance from 0. -9 is 9 units away from 0, as well as 9 itself. Hope this helps; have a great day!

Walmart sells shirts for $8.00 and hats for $12.
Tony is shopping and can spend no more than $50.
Which inequality represents the number of shirts, s and number of hats, h
that Tony can buy without going over budget.


help :/

Answers

Answer:

Step-by-step explanation:

8s+12h≤50

The width of a rectangle measures (8.1g-6.5)(8.1g−6.5) centimeters, and its length measures (4.7g-9.2)(4.7g−9.2) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

Answers

Answer:

P = (25.6g - 31.4)

Step-by-step explanation:

Given that,

The width of a rectangle = (8.1g−6.5) cm

The length of a rectangle, = (4.7g−9.2)

We know that,

The perimeter of a rectangle is given by :

P = 2(l+b)

Substitute all the values,

P = 2(8.1g−6.5+4.7g−9.2)

= 2(12.8g-15.7)

= 25.6g - 31.4

So, the perimeter of the rectangle is equal to (25.6g - 31.4).

Jeremy buys 1,045 ceramic tiles. He can take 25 tiles to his truck at a time in his shopping cart. What is the minimum number of trips Jeremy must make to get all the tiles to his truck?

Answers

Answer:

42

Step-by-step explanation:

its 41.8, but you cant take 41.8 trips, so you have to round it

Answer:

1020

P.S: I think this answer is right may be not

we want to find the zeros for this polynomial: p(x) = 5x^3 - 5x^2 - 10x

Answers

Answer:

x= 0, 2, -1

Step-by-step explanation:

solve the system of equations y=5x y=x^2+4
answer:(1,5) and (4, 20)

Answers

The answer is (1,5) and (4,20) they make both of the equations true

What is the length of the hypotenuse of the triangle when x = 11?
The length of the hypotenuse is about
(Round to the nearest tenth as needed.)
Helppppp

Answers

Answer:

6(11)+4=70

5(11)=55

70²+55²

=7259

square root if 7259=85.20

and that's your answer

Goodnight

Kayla goes for a long walk. This graph shows her time and distance traveled throughout the walk.​

Answers

The answer is 2.5 mph

somebody please answer only 11. and 13. ANSWER QUICKLY

Answers

11. y=x+4
13. y=1/4x +1

Answer:

Step-by-step explanation:

y=mx+b where m is the slope and b is the y intercept, value of y when x=0

11.

Since we are given the point (0,4) we already know that b=4

slope is m=(y2-y1)/(x2-x1), using our two points (0,4)(-1,3) we have

m=(3-4)/(-1-0)

m=-1/-1=1 so the line is

y=x+4

12.

Again they gave us point (0,1) so we know b=1, from points (0,1)(4,2) we find

m=(2-1)/(4-0)

m=1/4 so our line is

y=x/4+1 (or more neatly)

y=(x+4)/4

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