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:
[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]
Related Questions
Which shape shows a reflection?
I’m scared to answer because I’m at 90 and I know if I get it wrong I’ll drop again
Answers
Answer:
B! Can I plz have Brainliest!!!!
Step-by-step explanation:
I've never gotten one before!
Which inequality is not true if Y equals -5?
Answers
Answer:
Can you post a picture of the problems? Or type them out?
Step-by-step explanation:
y = x - 4. 2x + 3y = -17 substitution method
Answers
Answer:
x = -1
y = -5
Step-by-step explanation:
y = x - 4 y = x - 4
2x + 3y = -17 y = (-1) - 4
2x + 3(x - 4) = -17 y = -1 - 4
2x + 3x - 12 = -17 y = -5
5x - 12 = -17
5x - 12 + 12 = -17 + 12 Check
5x = -5 2x + 3y = -17
5x/5 = -5/5 2(-1) + 3(-5) = -17
x = -1 -2 + -15 = -17
-17 = -17
The temperature was -12°F at 6:00 a.m. The temperature rose 3°F every hour
until 6:00 p.m. At what time did the temperature reach 9°F?
Answers
i need help on 12 times x."
Answers
Answer: 12x
Step-by-step explanation:
12 times x = 12x
Hope it helped u,
pls mark as the brainliest
^_^
A junior college charges $7,391 per year for tuition, $8,244 for room and board, $1,280 for books, and $730 for miscellaneous fees. What is the cost of attending this school for 2 years?
Answers
17645x2= $35290 for 2 years
Please help me with 1,2 give me the answers and show me how you get it do not send me link please just write it right here please I really need help
Answers
1.)
c^2=a^2+b^2
c^2=10^2+24^2
c^2=100+576
c^2=676
c= √676
c=26 in
2.)
c^2=7^2+14^2
c^2=49+196
c^2=245
c= √245
c~15.65 cm
Find the sum which becomes 19,320 on increasing by 15% (Percentage)
Answers
Answer:
Step-by-step explanation:
100-15=85
85 % of x=19,320
x=19,320 ×100/85≈22729.41
Annalisa is ordering a sandwich. What are the possible independent variables involved in the cost of a sandwich?
Answers
Answer:
Step-by-step explanation:
Independent variables may be referred to as one or more single or standalone variables which affects the outcome or output variable, which is the dependent or response variable. To determine the cost of sandwich (this will be the response variable), this will be affected or dictated by the independent variables, which includes ; the size of sandwich, the type of bread roll used (hard roll, soft bun, hero, slice bread). Also, the tyoe of sandwich filling which may be (cheese, Ham salad, Ham and cheese, Egg mayonnaise and so on). Therefore, these variables are independent and the combination of each of these predictor variables will dictate the dependent variable, Cost.
Given the point (3, 4) and the slope of 6, find y when x = 27.
a. 122
b. 14
c. 141
d. 148
Answers
Answer:
The answer is D. 148
144= y-4
A submarine was in a resting position 400 m below sea level. It rose 225 m. Determine its new depth?
Answers
Answer:
175 meters, since its below sea level it would be- -400m - (-225m), subtracting with negative # and negative # is the equivalent of getting closer to zero, just figure out 400 - 225, and put a - symbol at the beginning of the number
What is the length of K Street and D Street?
Answers
Answer:
775 ft
Step-by-step explanation:
1000/800= K/620
800K = 620,000
K = 775 ft
If 4 × 8 = 32, then 32 divided by 8 must equal
Answers
Answer:
Step-by-step explanation:
If 4 x 8 = 32
32 / 8 must equal 4
They are a fact family with only 32, 8, and 4 in it. I hope that's clear!
Hope that helps!
Answer:
yes!
Step-by-step explanation:
If a × b = c Then, c ÷ b = a
Therefore it is equal
Which three criteria do binomial experiments meet?
Answers
Answer:
Each of the n tests must have two success p or failure q results, they are mutually exclusive. The probability of success p of an event is fixed or constant, likewise for the probability of failure q. The tests are independent.
Step-by-step explanation:
i need to know which one is an expression, equation, and inequality
Answers
Answer/Step-by-step explanation:
An expression is a series of number without any signs so expression would be the first one.
Inequality would be when they do a sign like > or <, etc. so it would be the 2nd one.
Equation would be when they have an equal sign which would be the 3rd one.
Simple Ex.
Expression : 2 + 66 / 11 - 3 x 2
Inequality : g + h > f
Expression : 4j - 3 = j
Hope this helps :)
The Maplewood Symphony Orchestra sold 146 tickets and
collected a total of $1036 in ticket sales. Admission was $5 for
children, x, and $8 for adults, y. How many children
tickets were sold?
Answers
Answer:
44 children tickets
Step-by-step explanation:
This is a system of equations. I solved for y, the amount of adult tickets sold which equals 102. To get the amount of children's tickets, subtract 102 from 146 to get 44.
hello, i need help.
find m∠bae
Answers
Answer:
125
Step-by-step explanation:
180-55=125
Family Video charges $10 for
a monthly membership and
$2.50 per movie. Babe's
Movies charges a $12
membership and $2 per
movie. How many movies
must be rented before the
price is the same at both
stores? What is the cost?
Answers
Answer:
4 movies, $20
Step-by-step explanation:
Given data
Family Video
charges $10 for a monthly membership and
$2.50 per movie
let the number of movies be x
and the charge for x movies be y
y= 10+2.5x----------1
Babe's Movies
charges a $12
membership and $2 per
movie.
let the number of movies be x
and the charge for x movies be y
y= 12+2x----------2
equate 1 and 2
10+2.5x= 12+2x
collect like terms
12-10= 2.5x-2x
2= 0.5x
x= 2/0.5
x= 4 movies
put x= 4 in equation 1 or 2
y= 12+2x----------2
y= 12+2*4
y= 12+8
y= $20
Convierte o expresa en forma decimal y fraccionaria.
Fracción
Decimal
a) 5.2%
b) 62.8%
c) 52.4%
d) 0.4%
Answers
Answer:
c.
Step-by-step explanation:
what’s 6.305082126 rounded to the nearest degree (No decimals)
Answers
Answer:
6
Step-by-step explanation:
3 is smaller that 5 so round down
PLEASE ANSWER
What is the area of the parallelogram?
13.4 in
7.5 in
Answers
Answer:
area = 100.5 in²
Step-by-step explanation:
area = 13.4 x 7.5 = 100.5 in²
what is the value of x?
Answers
Answer:
36
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
72° and 3x are adjacent angles and are supplementary , that is
72° + 3x = 180° ( subtract 72° from both sides )
3x = 108° ( divide both sides by 3 )
x = 36° → C
some pls help I have a couple min left plzz
Answers
Find < ABD (6x-7) (8x-22)
Answers
Answer:
Look at the picture
Step-by-step explanation:
Hi I need help please
Answers
Answer:
x = 9
Step-by-step explanation:
8x - 10 = 62
8x = 72
x = 9
solve for x
8x=62+10
8x=72
x=72/8
x=9
Part 1: What is the rate of rice to quarts of water for this recipe that uses 4 pounds of rice and 5 quarts of boiling water?
Answers
Given:
A recipe uses 4 pounds of rice and 5 quarts of boiling water.
To find:
The rate of rice to quarts of water for this recipe.
Solution:
We need to divide the amount of rice by amount of water to get the rate of rice to quarts of water for this recipe.
[tex]\text{Required rate}=\dfrac{\text{Rice in pounds}}{\text{Water in quarts}}[/tex]
[tex]\text{Required rate}=\dfrac{4}{5}[/tex]
[tex]\text{Required rate}=0.8[/tex]
Therefore, the rate of rice to quarts of water for this recipe is 0.8.
The triangles below are similar.
10
y
22
33
12
y = [?]
Answers
Answer:
y=15
Step-by-step explanation:
Since the triangles are similar you take 22/33 and 10/y then cross multiply and get 330=22y now divide 330 by 22 and you get 15
The value of x is 26.4 unit and y is 15 units,
What is Similarity?Two triangles are said to be comparable if their two sides are in the same ratio as the two sides of another triangle and their two sides' angles inscribed in both triangles are equal.
Given:
As, the two triangles are similar then the ratio of their corresponding sides and angles are equal.
So, 22/ 10 = 33/ y
22y = 330
y = 330/22
y = 15
and, 22/10 = x/ 12
264 = 10 x
x= 26.4
Hence, the value of x is 26.4 unit and y is 15 units,
Learn more about Similarity here:
https://brainly.com/question/26451866
#SPJ2
Find the perimeter of the rectangle in yards.
Answers
Can someone pleaseeee help me with this!!
Answers
Answer:
I can't it's just too difficult
Using the figure below, define and name two pairs of corresponding angles.
It's due today please help
Answers
Answer:
There are no corresponding angles shown in the figure.
They are all pairs of supplementary angles.
Step-by-step explanation:
corresponding angles add up to 90°
supplementary angles add up to 180°