An environmental landscaping company wishes to run a pipeline from a pumping platform (R) located 15 miles offshore to a terminal (B) 18miles down the coast. It costs $170,000 per mile to lay the pipeline underwater and $80,000 per mile to lay the pipeline over land. Determine how many miles from the terminal the two types of pipe should meet (P) so that the total cost is minimized. Enter the exact answer or round to the nearest hundredth.
Answers
After completing these steps, you'll find that x ≈ 6.14 miles, which is the optimal point to meet the two types of pipes to minimize the total cost.
The company should meet the two types of pipes approximately 6.14 miles from the terminal (P) to minimize the total cost.
To determine this, we'll use the following steps:
1. Draw a right triangle with vertices R, B, and P, where R is offshore, B is the terminal, and P is the meeting point.
2. Let x be the distance BP. Then, the distance RP is (18-x) miles.
3. Use the Pythagorean theorem: RP² = RBP² - BP² = 225 - x².
4. Calculate the cost function: C(x) = 170,000 * √(225 - x²) + 80,000 * x.
5. Find the derivative of C(x) with respect to x: dC/dx.
6. Set dC/dx = 0 and solve for x.
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Related Questions
The area of sector AOB is 210.25 cm². What is the exact area of the shaded region?
До
0 29 cm
B
OA. (210.25 -420.5) cm²
OB. (210.25-841) cm²
OC. (210.25 -420.5√√2) cm²
OD. (210.25-841 √2) cm²
Answers
The area of the segment is 210.25π - 420.5
What is area of segment?A segment is an interior region of a circle. It is the space between a chord and an arc.
The area of segment is expressed as;
area of segment = area of sector - area of triangle
The shaded part is a segment.
A sector is a region between two radii and an arc.
Area of triangle = 1/2 × 29 × 29
= 841/2
= 420.5
The area of the sector is given as 210.25
Therefore the area of the segment = 210.25π - 420.5
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help with question 1 plssssss
Answers
its answer comes in point
Step-by-step explanation:
3a+5a+12=90
8a=90-12
8a=78
a=78/8
a=9.75
if it is wrong than tell me plzzz
Between 11 P.M. and 8:10 A.M., the water level in a swimming pool decreased by 5/24 in. Assuming that the water decreased at a constant rate, how much did the water drop each hour?
Answers
Answer:
1/44 inches per hour
Step-by-step explanation:
there are 9 hours and 10 minutes during which water decreased by 5/24"
9 hrs, 10 min can be converted to 9 1/6 hours (10 min is 1/6 of 60 min)
5/24 ÷ 9 1/6 = 5/24 x 55/6
5/24 x 6/55 = 1/44
On 1 July 2005 Neil Chen purchased a block of land (1004 m2) with a 3 bed-room house on it for $820,000. The house was rented out immediately since 1 July 2005 till June 2018. As the relevant information was not available to him, Neil did not claim deductions for capital works under ITAA97 Div 43 for the income years in which the property was used to produce assessable income. Neil also did not obtain a building cost estimate from a quantity surveyor as he did not want to incur the expense. During July 2018, Neil decided to demolish the existing house and the vacant land was subdivided into two equal-sized blocks on 1 November 2018. Construction of two new dwellings was completed on 1 October 2019 at a total cost of $900,000 ( $450,000 for each house). Neil used both dwellings as investment properties and each of them was rented out on 1 October 2019. Neil claimed deductions for capital works under ITAA97 Div 43 for the income years for both dwellings. Due to Covid19, financial difficulties caused him to sell one of the dwellings. On 30 May 2021 he entered into a contract for sale and the tenants were moved out on 30 June 2021. The sale price was $1,050,000 with settlement on 30 June 2021. Selling costs, i.e., agent commission amounted to $12,000. Required Calculate the net capital gain(s). Neil also had $31,500 capital losses from previous years. ($21,500 loss from sale of BHP Shares and $10,000 loss from sale of Stamps).
Answers
The net capital gain is $19,500. To calculate the net capital gain(s) for Neil Chen, we need to consider the relevant transactions and deductions. Neil purchased a block of land with a house in 2005, rented it out until June 2018, and then demolished the house and subdivided the land into two blocks.
He constructed two new dwellings and rented them out starting from October 2019. Neil sold one of the dwellings in May 2021 and incurred selling costs. Additionally, he had capital losses from previous years. Based on these details, we can determine the net capital gain(s) by subtracting the total capital losses and selling costs from the capital gain from the sale.
To calculate the net capital gain(s), we need to consider the following components:
1. Calculate the capital gain from the sale: The capital gain is the difference between the sale price and the cost base. In this case, the sale price is $1,050,000, and the cost base includes the original purchase price ($820,000), construction costs ($450,000), and any other relevant costs associated with the property.
2. Deduct selling costs: Selling costs, such as agent commission, should be subtracted from the capital gain. In this case, the selling costs are $12,000.
3. Consider previous capital losses: Neil had capital losses from previous years totaling $31,500.
To calculate the net capital gain(s), subtract the total capital losses ($31,500) and selling costs ($12,000) from the capital gain from the sale. The resulting amount will represent the net capital gain(s) for Neil that is $19,500
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a list of 20182018 positive integers has a unique mode, which occurs exactly 1010 times. what is the least number of distinct values that can occur in the list?
Answers
The least number of distinct values that can occur in the list is 225.
what is mode?The value that appears the most frequently in a data collection when it is unique is known as the mode, and like the median and mean, it can be used to measure central tendency. However, occasionally there is either no mode or more than one mode. When every observed value occurs exactly once in a data collection, there is no mode.
The mode appears 10 times. That leaves 2008 numbers.
The least number of distinct values will occur if all but one of the remaining values appears 9 times
= 2008/9
=223 1/9.
So, The list can include a maximum of 225 distinct values, with the mode appearing 10 times, 223 other values nine times, and the last value once.
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Finding Angle Measures When Parallel Lines Are Cut By a Transversal
Answers
The measures of the following angles are:
∠6 = 124°, ∠2 =124°, ∠3 = 124° ∠5 = 56°, ∠7 = 124° ∠1 = 56°
What are corresponding angles?Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line (i.e. the transversal).
∠4 = 56° ( corresponding angles are equal)
∠1 =∠4 ( vertically opposite angles are equal)
∠1 = 56°
∠7 + 56° = 180 ( angles on a straight line sum up to 180°)
∠7 = 180 - 56
∠7 = 124°
∠7 = ∠6 ( vertically opposite angle are equal)
∠6 = 124°
∠3 = ∠6 ( alternate angles are equal)
∠3 = 124°
∠2 = ∠3 ( vertically opposite angle)
∠2 = 124°
∠5 = 56° ( vertically opposite angles)
The unknown angles are: ∠1 = 56° ∠2 = 124°, ∠3 = 124°, ∠4 = 56°, ∠5 = 56°, ∠6 = 124° ∠7 = 124°
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Celia bought a bag of 12 goldfish for $3 what is the cost of 1 goldfish?
Answers
Answer:
$0.25 per goldfish
Step-by-step explanation:
To figure this out, do 3 ÷ 12
We divide in this order because we are trying to figure out the cost per goldfish. We divide 12 and 3 by 12 to get 1 goldfish for $0.25.
Answer:
1 Goldfish would cost 25 cents.
Step-by-step explanation:
12 Divide by 3 = 0.25 cents
Have a good day!
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A senator wants to know her approval rating among the constituents in her state. She has her staff obtain 1000 responses to a telephone survey of
registered voters in her state
O Simple Random Sample
O Systematic
O Self-Selected
Convenience
O Stratefied
Answers
Answer:B
Step-by-step explanation:
Help me rn pleasee !!
Answers
Answer:
There are two solutions for x;
x = 0
x = \(-\frac{3}{2}\)
Step-by-step explanation:
Answer:
x = 0 or -3/2
Step-by-step explanation:
( 2 x + 3 ) ^2 − 6 x − 9 = 0 ---> distribute
4x^2 + 6x + 6x + 9 - 6x - 9 = 0 --> add the 9's together
4x^2 + 12x - 6x = 0 --> combine like terms
4x^2 + 6x = 0 --> common factor
2(2x^2 + 3x) = 0 --> divide by 2 on both sides
2x^2 + 3x = 0
then you should use the quadratic formula (can't add here or the explanation would take too long)
Delaney pays her internet provider a monthly fee of $14.95 plus $5.75 for each gigabyte of data she stores in the cloud. If Delaney paid $60.95 for the month of January, how many gigabytes of data did she use that month?
Answers
Answer: 11.3 or 11 if you are to round to nearest whole number.
Step-by-step explanation:
Take the problem step by step.
You know she has the monthly fee and a fee for each gigabyte of data she stores in her house.
Take how much she paid and Subtract the monthly fee from it since it has been a month.
$60.95 - $14.95 = $36
Now take that answer and divide it by the cost of each gigabyte to see how many she used that month.
$65 / $5.75 = 11.30434743, which rounds to 11.3 or 11 if you are to round to nearest whole number.
If sin⁶A + cos⁶A +3sin²Ф·cos²Ф+4=k, then find the value of k.
Answers
Answer:
K=5
Step-by-step explanation:
what is 140 divided by 8
Answers
Answer:
17.5
Step-by-step explanation:
Answer:
17.5 is your answer
Step-by-step explanation:
140/8
17.5
Hope this helps?
Amanda is building a soft triangular kennel for her dog. she has four wooden planks of lengths 2 feet, 3 feet, 5 feet, and 6 feet. determine which planks amanda should use to build the triangular-shaped kennel. enter the lengths from least to greatest. a triangular kennel made of carpet-covered planks
Answers
Amanda would use 3 planks of lengths 3 feet, 5 feet, and 6 feet.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.To determine which planks Amanda should use to build the triangular-shaped kennel:
To build a kennel for dog, we would try to make it the largest possible with what we have.So, we would go with the 3 longest planks: 3ft, 5ft, and 6ft.By looking at the length, we see that we could make something very close to a right triangle since we could use the 6ft as a hypotenuse, and have the two other sides as 3ft and 5 ft (6² is almost 3²+5², which equals 34).That means our corner angle would be slightly over 90 degrees.Therefore, Amanda would use 3 planks of lengths 3 feet, 5 feet, and 6 feet.
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HELP ME AGAIN BTW ITS FRACTIONS USER = or=/
Answers
Answer: < > > =
Step-by-step explanation:
Calculate the volume of a metal sphere of radius 15 cm and show that it rounds to 14140 cm^3,correct to 4 significant figures.
Answers
103,670 cm3 is the amount of water needed to fill the tank.
∴ The cylindrical tank's empty volume, "", is given as follows:
= (25 cm)2 x (60 cm)2 x (11780.972451 cm3)
The formula for the amount of water needed to full total tank only with sphere of volume "V" inside is: = V + = - V
which gives us: 103,670 cm3 - 103,669.72451 cm3 = 117809.72451 cm3 - 14,140 cm3
103,670 cm3 is the amount of water needed to fill the tank.
Describe the cylindrical tank:
In order to unite machined or formed assemblies, cylindrical tanks commonly require end closures that are either spherical or obliquely shaped.
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Cooper obtains an experimental functions of the stream function and the velocity potential for a particular flow type which are given by ψ=2xy and φ=x
2
−y
2
. Show that the conditions for continuity and irrotational flow are satisfied.
Answers
The given functions ψ = 2xy and φ = x^2 - y^2 satisfy the conditions for continuity and irrotational flow.
To show continuity, we need to verify that the partial derivatives of ψ and φ with respect to x and y are equal. Let's calculate these partial derivatives:
∂ψ/∂x = 2y
∂ψ/∂y = 2x
∂φ/∂x = 2x
∂φ/∂y = -2y
From the above calculations, we can see that the partial derivatives of ψ and φ with respect to x and y are equal. Therefore, the condition for continuity, which requires the equality of partial derivatives, is satisfied.
To show irrotational flow, we need to verify that the curl of the velocity vector is zero. The velocity vector can be obtained from the stream function ψ and velocity potential φ as follows:
V = ∇φ x ∇ψ
Taking the curl of V:
∇ x V = ∇ x (∇φ x ∇ψ)
Using vector calculus identities and simplifying the expression, we find:
∇ x V = 0
Since the curl of the velocity vector is zero, the condition for irrotational flow is satisfied.
Therefore, based on the calculations and verifications, we can conclude that the given functions ψ = 2xy and φ = x^2 - y^2 satisfy the conditions for continuity and irrotational flow.
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Question 9
Which of the following distributions has a mean that varies?
I. The population distribution
II. The distribution of sample data
III. The sampling distribution of the sample mean
a. Il only
b. Ill only
c. I only
d. all three distributions
e. Il and III
Answers
Distribution has a mean that has varies is II the distribution of sample data. The correct "option is A"
What is means ?Mean refers to the average of a set of values. The mean can be computed in a number of ways including the simple arithmetic mean add up the numbers and divide the total by the number of observations the geometric mean and the harmonic mean. mean can obtained dividing the sum of all values in a data set by the number of values.
Therefore distribution has a mean that has varies is II the distribution of sample data. The correct "option is A"
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HELP FOR BRAINLIEST & 100
please
Answers
Answer:
Hi,
Step-by-step explanation:
1) PC=PD since PC*PA=PD*PB
2)25 since PO²=PA²+r² PO=14.5, PB=14.5+10.5=25
3)
6²=3*x==> x=12
3.8 x 10^2 +1.7 x10^3
Answers
Answer:
2080
Step-by-step explanation:
that's the answer i think Good luck :)
someone PLSSSS HELPPP !! fast pls please
Answers
Answer:
A. i think
Step-by-step explanation:
Answer:
4, -16, 64, -256
the common ratio is -4
Step-by-step explanation:
a binary tree is a structure in which each node is capable of having successor nodes, called .
Answers
A binary tree is a structure in which each node is capable of having two successor nodes, called "left child" and "right child."
In a binary tree, each node can have at most two successor nodes, known as the left child and the right child. These successor nodes branch out from the parent node, forming two distinct paths or branches. The left child represents the left branch, and the right child represents the right branch. This hierarchical structure allows for efficient organization and traversal of data, as each node can connect to two other nodes, creating a branching pattern throughout the tree. The concept of left and right children enables various operations and algorithms to be performed on the binary tree, such as insertion, deletion, searching, and sorting.
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Diane got a prepaid debit card with $25 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 13 cents per yard. If after that purchase there was $18.76 left on the card, how many yards of ribbon did Diane buy?
Answers
Answer:
48 yards
Step-by-step explanation:
So you Subtract 25 - 18.76 when you get 6.24 which is how much you spent and then you divide that by .13 and you will get your answer of 48 yards.
Hope this helps pls give me brainlist
Diane bought 48 yards of ribbon.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
Diane got a prepaid debit card with $25 on it.
For her first purchase with the card, she bought some bulk ribbon at a craft store.
The price of the ribbon was 13 cents per yard.
If after that purchase, there was $18.76 left on the card,
number of yards of ribbon = (25 - 18.76)/0.13
= 6.24 / 0.13
= 48 yards.
Therefore, the ribbon is 48 yards.
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The radius of a circle is 12 mm what is the circles area
Answers
Answer:
Step-by-step explanation:
area of a circle = pi*r^2
pi = 3.14
r = 12 mm
area = 3.14 * (12)^2
area = 3.14 * 144mm
area = 452.16 mm^2 or 45.216 cm^2
Hi student, let me help you out! :)
...........................................................................................................................................
We are asked to find the area of the circle.
\(\triangle~\fbox{\bf{KEY:}}\)
Use the formula:\(\dag~\mathtt{A=\pi r^2}\)
Where:
A=Area
π=pi
r=radius (12 mm)
Have you noticed the \(~^2\) next to r? This tells us to multiply the radius times itself.
So, we substitute the values:
\(\mathtt{A=\pi (12)^2}\)
Square 12 first, then multiply:
\(\mathtt{A=144\pi }\)
Upon simplifying,
\(\dag~\underline{\mathtt{A=452.16\:mm^2}}\)
Hope it helps you out! :D
Ask in comments if any queries arise.
#StudyWithBrainly
~Just a smiley person helping fellow students :)
\(\overline{\underline{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~}}\)
a newborn kitten weights about 1/4 pound. There are 0.45 kilograms in 1 pound. If a mother cat has a litter of 6 kitten. What is the approximate total weight of the litter of 6 kittens in kilograms.
Answers
The approximate total of weight of the litter of 6 kittens 0.675kg
What is Weight ?
The force exerted on an object by gravity is known as its weight. The gravitational force acting on the item is referred to as weight in several common textbooks. Some people refer to weight as a scalar quantity that measures the gravitational force's strength.
Given,
The weight of one newborn kitten = 1/4 pounds
The value of pound in kilograms = 1pound = 0.45kg
convert the weight from pound to kilograms = 1/4 x 0.45
= 0.1125kg
Now, to find out total weight of litter of 6 kitten in kilograms
= 0.1125 x 6
= 0.675kg
Hence, The approximate total weight of the litter of 6 kittens in kilograms is 0.657kg
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−56z+28minus, 56, z, plus, 28?
Answers
Answer-
Not quite sure what your asking but the if I understood correctly the answer is -122z+56
Answer:
−112z+56
Step-by-step explanation:
−56z+28−56z+28
Combine −56z and −56z to get −112z.
−112z+28+28
Add 28 and 28 to get 56.
−112z+56
Three years ago, Daniel bought a baseball card for $20. The baseball card gains a value of $10 each year for the next three years. A friend offers to buy the baseball card foe twice the value, how much would the friend pay?
Answers
Answer:
The friend would pay $100
Step-by-step explanation:
The price of the card was $20 when Daniel bought it, it gained a value of $10 every year,
since Daniel bought it 3 years ago we will add $30 to $20 as the value increased by $10/year
so the price becomes $50, but his friend says he'll pay twice the value so,
$50×2= $100
Which set of side lengths forms a right triangle? A) 5 cm, 6 cm,7 cm B) 2 cm, 4 cm, 6 cm C) 8 cm, 9 cm, 11 cm D) 8 cm, 15 cm, 17 cm
Answers
you’re welcome
5. Which of the following transformations maps Figure A onto Figure B?
A) Translate Figure A 3 units right, and then reflect it across the x-axis.
B) Reflect Figure A across the x-axis, and then translate it 3 units left.
C) Reflect Figure A across the y-axis, and then translate it 3 units right.
D) Translate Figure A 3 units right and 2 units down.
-7654321
2
Figure A
123456
Figure B
Answers
Answer:
A)
Step-by-step explanation:
just look at the picture.
what must have happened to figure A to turn into figure B ?
is B more to the right or to the left of A ?
well, right. isn't it obvious ?
and when you look at the coordinates of a vertex, it is 3 units to the right of A.
and if the shift to the right had not happened - the 2 figures would be a mirrored image of each other with the x-axis being the mirror.
that is why A) is the right answer.
#14-Review
1) Find m/BML if m/NML = 178°
and m/NMB = 99⁰.
M N
+++
B
Answers
Step-by-step explanation:
BML is one part of NML, NMB is the second part.
so,
BML + NMB = NML
BML + 99 = 178°
BML = 79°
y=(x+5)²-4
Vertex:
Axis of Symmetry:
x-intercepts:
y-intercept:
Is the vertex a maximum or minimum?