. An oil refnery is located on the north bank of a straight river that is 2 km wide. A pipeline is to be constructed from the refnery to storage tanks located on the south bank of the river 6 km east of the refnery. The cost of laying pipe is $400,000ykm over land to a point P on the north bank and $800,000ykm under the river to the tanks. To minimize the cost of the pipeline, where should P be located
Answer:
The point P should be located at 0,51 Km from point B, to minimize costs
Step-by-step explanation:
The oil refinery ( point A ) the opposite point ( B) in the south bank, and the storage tank (point C) these three points shape a right triangle. Let´s call x the distance between point A and point P ( the arriving point of the pipeline in the south bank ) then:
Cost = cost of pipeline in-ground* ( 6 - x ) + cost of pipeline in water* L
where L is the hypothenuse of the right triangle ( A , B , P )
Cost ($) = 400000 * ( 6 - x ) + 800000 * √ 2² + x²
C (x) = 400000* ( 6 - x ) + 800000* √4 + x²
C(x) = 2400000 - 400000*x + 800000* √4 + x²
Tacking derivatives on both sides of the equation
C´(x) = - 400000 + 800000* ( 2x)/√4 + x²
C´(x) = 0 - 400000 + 1600000*x / √4 + x² = 0
- 400000* (√4 + x² ) + 1600000*x = 0
- (√4 + x² ) + 4* x = 0
- (√4 + x² ) = - 4*x
Squaring both sides
4 + x² = 16*x²
15*x² = 4
x² = 4/ 15
x = ± √0,27
x = ± 0,51
We should dismiss the negative solution
x = 0,51 Km
The point P should be located at 0,51 Km from point B
Helppp plssssssssssss
Answer:
The answer is C
Step-by-step explanation:
If you plot them carefully.
Find the surface area of the following figure with the given dimension
Answer:
435 in.²
Step-by-step explanation:
Surface area of the square pyramid = area of the square base + ½(Perimeter of base)(slant height)
Area of base = s²
s = 15 in
Area = 15² = 225 in²
Perimeter of the base = 4(15) = 60 in
Slant height = 7 in
Surface Area = 225 + ½(60)(7)
= 435 in.²
if x=49 and y=160 then what is the value of z?
9514 1404 393
Answer:
z = 62°
Step-by-step explanation:
You know that ...
x = (1/2)(y -z)
So ...
2x = y - z
z = y - 2x = 160 -2(49)
z = 62 . . . . degrees
Joseph drove to his grandmother's house which is 279 miles away in 4.5 hours. If he continues at the same speed, approximately how long will it take him to drive 325 miles?
Answer:
5.24 hours
Step-by-step explanation:
I like to set these up as ratios.
279 miles/4.5 hours = 325 miles/ x hours
Then cross multiply
279x = 4.5 x 325
279x = 1462.5
divide both sides by 279
x = 5.24 hours
You can also solve 279 miles/4.5 hours to get the miles per hour driven, then divide 325 by that number:
279/4.5 = 62mph
325/62 = 5.24
if the sphere shown above has a radius of 15 units , then what is the volume of the sphere ?
Answer:
4,500 cubic units
Step-by-step explanation:
Answer:
4,500 cubic units
Have a good day.
The probability of event A is 0.42, and the probability of event B is 0.39. If A and B are independent events, what is P(A and B)?
Answer:
0.1638
Step-by-step explanation:
P(A and B) or simply the probability of both events happening is the product of their individual probabilities.
P(A and B)= (0.42×0.39)= 0.1638
jack surveyed students at his school about whether they use computers or cell phones more. He found that of the 74 seventh-graders he surveyed, 53 said they used their cell phones more. In the 8th grade, 59 students used their cell phone more, compared to 38 who used their computer more. What number should be placed in the orange box below?
Answer:
Number of student of 7th grade using computer = 21
Total number of 8th grader student surveyed = 97
Step-by-step explanation:
The complete question is attached herewith
Solution
As we can see in the table
Total number of 7th grader student = 74
Out of these 74 student, 53 use cell phone
Hence, the number of student of 7th grade using computer = 74-53 = 21
Like wise, total number of 8th grader student surveyed = 59 +38 = 97
please help im stuck on this
Answer:
Slope = -8/5
Step-by-step explanation:
Use the slope formula:
m = y2 - y1 / x2 - x1
Plug in the numbers from the ordered pairs given in the graph: (-1, 4) and (4, -4).
m = -4 - 4 / 4 - - 1
m = -8 / 5
m = -8/5
m = rise/run, meaning verticl units/horizontal units
Check your work by counting it out on the graph:
From the first black dot at (-1, 4), count 8 units down and then 5 units to the right. After counting, I ended at the second ordered pair at (4, -4) which means my slope is correct.
Anyone know how to do this people are answering the question but aren’t choosing two anwsers
Answer:
Option B and Option D are the two answers
Solve the following system of linear equations by substitution and determine whether the system has one solution, no solution, or an infinite number of solutions. If the system has one solution, find the solution.
-4x+y=12
-8x+2y=14
Answer:
no solution
Step-by-step explanation:
find the area of this parallelogram
Answer:
98 in²
Step-by-step explanation:
14x7=98
4n = 2n+6 I really need help
HELP GIVING 20 POINTS
While on vacation in Belmont, Lara went out for a dinner that cost $75. If sales tax in Belmont is 8% and Lara left a 20% tip on $75, what was the total cost of her meal?
Answer:
The total cost as $96
Step-by-step explanation:
To find the total amount find the tax amount and the tip amount
75 * 8% = 6
75 * 20% = 15
add 6 and 15 to 75 to get 96
Answer:
ok
Step-by-step
ok
Find the value of each variable using sine and cosine. Round your answers to the nearest tenth.
Answer:
r = 19.0
s = 17.7
Step-by-step explanation:
In the given right triangle ABC,
Measure of Hypotenuse (AC) = 26
m(∠CAB) = 43°
By applying sine rule in the given triangle,
sin(43)° = [tex]\frac{\text{Opposite side}}{Hypotenuse}= \frac{BC}{AC}[/tex]
sin(43)° = [tex]\frac{s}{26}[/tex]
s = 26[sin(43)°]
s = 17.73
s ≈ 17.7
Similarly, by applying cosine rule in the given triangle,
cos(43)° = [tex]\frac{\text{Opposite side}}{Hypotenuse}= \frac{AB}{AC}[/tex]
= [tex]\frac{r}{26}[/tex]
r = 26[cos(43)°]
r = 19.02
r ≈`19.0
) What is the absolute value |-5 l
Answer: 5
Step-by-step explanation:
Select the correct answer. What is the period of ? A. B. C. D.
Answer:=
2π/3
Step-by-step explanation:
plato
someone actually help me please :/ I REALLY NEED HELP AND NO ONES HELPING
Answer:
a) 8 m
Step-by-step explanation:
a) all sides of a square are equal - there's 4 sides.
4x = 32m
x = 32/4
x = 8 m
i like ur toga pfp besty :)
1. Identify the a, b, and c in the function:
f(x) = 3x² – 9x +4
A=
B=
C=
Answer:
A=3
B=-9
C=4
Hope this helps ^^
Plsss help mark brainlist
Answer:
17
Step-by-step explanation:
34 / 2 = 17
2(x+50)=16+4x
What is x?
Answer:
x=42
Step-by-step explanation:
Write the equation.
2(x+50)=16+4x
Spread the parentheses
2x+100=16+4x
Put variables on one side, numbers on the other.
2x-4x=16-100
Add/subtract/multiply/divide the variables with variables and numbers with numbers.
-2x=-84
Make x alone
-x=-42
Flip sides to make x positive
42=x
Someone please answer this
Answer:
8 m is the answer.
Step-by-step explanation:
a = ?
b (Brennan and Hannah) = 6 m
c (Jayce and Hannah) = 10 m
According to the Pythagoras theorem,
a² + b² = c²
a² + 6² = 10²
a² + 36 = 100
a² = 100 - 36
a² = 64
a = 8 m
∴ Jayce and Brennan are 8 m apart.
A company manufactures Products A, B, and C. Each product is processed in three departments: I, II, and III. The total available labor-hours per week for Departments I, II, and III are 1020, 1140, and 960, respectively. The time requirements (in hours per unit) and the profit per unit for each product are as follows. Product A Product B Product C Dept. I 2 1 2 Dept. II 3 1 2 Dept. II 2 2 1 Profit $18 $12 $15
How many units of each product should the company produce in order to maximize its profit?
Product A
Product B
Product C
What is the largest profit the company can realize?
$
Are there any resources left over? (If so, enter the amount remaining. If not, enter 0.)
labor in Dept. I
labor in Dept. II
labor in Dept. III
Answer:
a)
product A = 12O units
Product B = 220 units
product C = 280 units
b) $9000 = max/largest profit
c) No resource left
Step-by-step explanation:
Available hours
Dept. I = 1020
Dept. II = 1140
Dept. III = 960
Total available hours = 3120 hours
products produced by each department
product A Product B Product C
Dept. I 2 1 2
Dept. II 3 1 2
Dept. III 2 2 1
profits $18 $12 $15
Determine how many units of each product to be produced to attain maximum profit
let each product be represented as : x , y , z
2x + y + 2z = 1020 -------- ( department A ) --- 1
3x + y + 2z = 1140 -------- ( department B ) --- 2
2x + 2y + z = 960 --------- ( department c ) ---- 3
max profit : 18 x + 12y + 15 y
solving equation 1 from 2
x = 120
solve equation 2 from 3 simultaneously
x - y + z = 180
-y + z = 60
solve equation 1 and 3
-y + z = 60
∴ z = 60 + y
back to equation 1
2( 120 ) + y + 2( 60 + y ) = 1020
240 + y + 120 + 2y = 1020
∴ y = (1020 - 360 )/ 3 = 220
therefore ; z = 60 + 220 = 280
amount of each product to be produced to gain maximum profit
product A = 12O units
Product B = 220 units
product C = 280 units
ii) The largest profit
18 ( 120 ) + 12(220) + 15 ( 280 ) = $9000
What is the 21st term of the sequence with a1 = -7 and d = 3?
Answer:
53
Step-by-step explanation:
[tex]a + (n - 1)d \\ = - 7 + (21 - 1)3 \\ = 53[/tex]
Answer
53
Step-by-step explanation:
. Eado fime Blend buys lunch at school, the balance on her school lunch account changes
by 53. Last month, Eiend's balance changed by-536 in all. She wants to know how
many times she bought lunch last month
Which expression represents the number of times
Een bought lunch last month?
- 36 - 3
-263
No LINKS
Answer:
-36 ÷ -3
Step-by-step explanation:
Change in her school lunch account balance per lunch = -3
Total change in her school lunch balance last month = -36
Expression to show number of times Elena bought lunch last month = Total change in her school lunch balance last month ÷ Change in her school lunch account balance per lunch
= -36 ÷ -3
= -36/-3
= 12 times
Elena bought lunch 12 times last month
Solve the following word problem by creating and solving a system of linear equations. Rachel offers to go to the coffee shop to buy cappuccinos and lattes for her co-workers. She buys a total of nine drinks for $35.75. If cappuccinos cost $3.75 each and the lattes cost $4.25 each, how many of each drink did she buy? a 2 cappuccinos, 7 lattes b 6 cappuccinos, 3 lattes C 4 cappuccinos, 8 lattes d 5 cappuccinos, 4 lattes
Answer:
85
Step-by-step explanation:
Do you think the answer is A, B, C, or D.
Answer:
its A i guess
y is directly proportional to the square root of (x+2). when x =7 y=2. find y when x =98
Answer:
98/7=14
14*2=28
y=28
Step-by-step explanation:
(07.01)
What is the value of x in the equation x + 10 = 13? (4 points)
1-3
0 2 3
3) 13
4) 23
Answer:
x=3
Step-by-step explanation:
x+10=13
x=13-10
x=3
what is the markup percentage based on retail for an item with a dollar mark up of $70.00, cost of $30.00, and retail price of $100.00?
Answer:
70/100= 0.7= 70%
70%