The general solution of dy over dx equals x times y plus 3 times x question is [tex]y=e^{\frac{x^{2} }{2} +c_{1}} -3[/tex]
What is Differential equation?A differential equation is an equation that contains one or more functions with its derivatives.
The given differential equation is dy over dx equals x times y plus 3 times x question
dy/dx=xy+3x
dy/dx=x(y+3)
dy/dx-x(y+3)=0
Solve seperable ODE
[tex]y=e^{\frac{x^{2} }{2} +c_{1}} -3[/tex]
Hence, the general solution of dy over dx equals x times y plus 3 times x question is [tex]y=e^{\frac{x^{2} }{2} +c_{1}} -3[/tex]
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Find the measures of the angles of a triangle with one angle measuring 130 and the other two measuring x.
Answer:
x = 25 degrees
Step-by-step explanation:
The sum of the angles of a triangle is always 180 degrees. Therefore, in a triangle with one angle measuring 130 degrees, the measures of the other two angles must add up to 180-130 = 50 degrees.
So, if the measures of the other two angles are x, the equation would be:
x + x = 50
This means that the measure of each angle is 50/2 = 25 degrees.
Therefore, in a triangle with one angle measuring 130 degrees, the measures of the other two angles are both 25 degrees.
At what point do the curves
r1(t) = t, 3 − t, 48 + t2 and
r2(s) = 8 − s, s − 5, s2
intersect? (x, y, z)=
AND Find their angle of intersection, θ, correct to the nearest degree.
θ =
At point, the parametric curve cross (4, 1, 32).
What are parametric functions?t functions expressed as x = f(y) = y = f(x) = (some function of the variable x) (some function of the variable y).
It is frequently more easier to view functions of two or more variables (although we'll keep it at two here) as parametric functions, particularly in physical science.
The introduction of the idea of time makes parametric functions the most simple to understand.
Imagine tracing a parabola-like function from left to right as time passes.
Then, it is simple to begin considering how the x-coordinate and the y-coordinate change as a function of time: x = f(t), y = g. (t). In this sense, time is actually referred to as the parameter.
We will investigate functions for which a point exists in this section.
Hence, At point, the parametric curves cross (4, 1, 32).
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Senor Pena found some change on the floor while cleaning a classroom. He found a total of 6 coins that consisted of quarters and nickels. If the total change was $1.30, how many of each coin did he find?
Answer:
There are 5 quarters and 1 nickel
Step-by-step explanation:
Let Q and N be the numbers of Quarters and Nickels that Senor Pena found, respectively.
The value of each coin is $0.25 for quarters and $0.05 for each nickel
The total of $1.30 would be the result of:
1) Quarters: $0.25*Q, and
2) Nickels: $0.05*N
So we can write: $0.25*Q + $0.05*N = $1.30
We also know he found 6 coins, so:
Q + N = 6
We have two equations and two unknowns. We can use substitution to find the answer.
Rearrange the second equation to isolate one of the two variables. lets isolate Q:
Q = 6-N
We can use this definition of Q in the first equation by substitution:
$0.25*Q + $0.05*N = $1.30
$0.25*(6-N) + $0.05*N = $1.30
Leaving off the $ signs for clarity:
0.25(6-N) + 0.05N = 1.30
1.5 - 0.25N + 0.05N = 1.30
-0.2N = -0.20
N = 1
There is 1 nickel
Since Q = 6-N, Q = 5
There are 5 quarters and 1 nickel
CHECK
Do 5 quarters and 1 nickel add to $1.30?
5*($0.25) + 1*($0.05) = $1.30?
$1.25 + $0.05 = $1.30 YES
20 children lineup to ride go carts.The go cart operator collects two dollars from each child in order from the first to the 20th in line. do the ordered pairs (child number, amount paid) represent a function? explain your reasoning.
Yes, the ordered pairs (child number, amount paid) represent a function.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Number of children = 20
Cost per children = $2
Now,
The ordered pairs are:
(1, 2), (2, 4), (3, 6), (4, 8), (5, 10), (6, 12), (7, 14), (8, 16), (9, 18), (10, 20),
(11, 22), (12, 24), (13, 26), (14, 28), (15, 30), (16, 32), (17, 34), (18, 36), (19, 38), (20, 40)
The ordered pairs are a function.
A function can be one-to-one or many-to-one but not one-to-many.
We see that the ordered pairs are one-to-one.
Thus,
The ordered pairs are functions.
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the figure above shows the inside dimensions, in feet, of a certain room. an architect made a scale model of the room that had a floor and four walls, but not a ceiling. what was the scale of the model, in inches per foot, if the inside of the model had a total surface area of 2,304 square inches?
The scale of the model is 0.00017 ft/in, or in inches per foot.
To determine the scale of the model, we need to find the ratio of the size of the model to the size of the real room. We can use the information provided about the total surface area of the model to find this ratio.
The total surface area of the model is given as 2,304 square inches. We can find the total surface area of the real room by multiplying the lengths of the four walls and the floor.
The inside dimensions of the room are given as 8 ft x 12 ft x 8 ft x 12 ft x 8 ft = 8 x 12 x 8 x 12 x 8 = 92,160 sq ft
Now we can find the ratio of the size of the model to the size of the real room by dividing the surface area of the model by the surface area of the real room and converting it to inches per foot.
2,304 sq in / 92,160 sq ft = 0.025 sq in/ sq ft
To convert square inches to square feet we divide by 144, so 0.025 sq in/ sq ft = 0.025/144 = 0.00017 ft/in
So, the scale of the model is 0.00017 ft/in, or in inches per foot.
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Determine the savings for each group price. Both the unit price and the group price
are given: 1 bookshelf for $14.95 or 6 for $85.00
By taking a difference, we will see that you can save $4.70 if you buy the pack.
How to find the savings on the group price?To find the savings, we need to take the difference between the cost of the 6 times the cost of 1 bookshelf, and the cost of the 6 bookshelves.
The cost of 1 bookshelf is $14.95, and the cost of 6 together is $85.00, then the savings is given by:
S = 6*$14.95 - $85.00
S = $89.70 - $85.00
S = $4.70
You save $4.70 in total if you buy the pack.
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If A and B are mutually exclusive, then P(A\capB) = 0.
A and B are independent if and only if P(A\capB) = P(A)P(B)
If A and B are two events with P(A) = 0.4, P(B) = 0.2, and P(A B) = 0.5. Find the following:
(a) P(A \cap B) (b) P(A?\cap B) (c) P(A?\cup B?) (d) P(A|B)
If A and B are independent events with P(A) = 0.4 and P(B) = 0.2. Find the
following:
(a) P(A \cap B) (b) P(A?\cap B) (c) P(A? \cup B?) (d) P(A|B)
If A and B are mutually exclusive events with P(A) = 0.4 and P(B) = 0.2. Find the following:
(a) P(A\cap B) (b) P(A?\cap B) (c) P(A? \cup B?) (d) P(A|B)
Roll a die once. The event of getting a "2" and the event of getting a "5" are (a) independent;
(b) mutually exclusive;
(c) Neither
Roll a die twice. The event of getting a "2" on the first roll and the event of getting a "5" on the second roll are
(a) independent;
(b) mutually exclusive;
(c) Neither
(A) P(AB) = P(A B) = 0.5 denotes that there is a 0.5 chance that occurrences A and B will occur simultaneously. We cannot tell whether this relationship holds true for these specific events because the provided information does not specify whether A and B are independent or mutually exclusive.
(b) P(A'B) = P(A') + P(B') - P(A'B') = 0.6 denotes that there is a 0.6 chance that events A and B will occur together.
(c) The chance that either the complement of event A or the complement of event B will occur is 0.5. P(A'B') = 1 - P(AB) = 1 - 0.5 = 0.5.
(d) P(A|B) = P(AB) / P(B) = 0.5 / 0.2 = 2.5 denotes that there is a 2.5 percent chance that event A will occur provided that event B has already occurred.
If P(A) = 0.4 and P(B) = 0.2, respectively, then A and B are independent events.
(a) P(AB) is the probability that both occurrences A and B will occur at the same time. It is calculated as P(A) * P(B) = 0.4 * 0.2 = 0.08. The likelihood that A will occur is independent of the likelihood that B will occur since the two events are unrelated.
(b) P(A'B) = P(A') * P(B) = (1-0.4) * 0.2 = 0.12 is the likelihood that events A and B will occur in complement.
(c) The probability that either the complement of event A or the complement of event B will occur, or both, is given by P(A'B') = 1 - P(A'B) = 1 - 0.08 = 0.92.
(d) P(A|B) = P(AB) / P(B) = 0.08 / 0.2 = 0.4, which represents the likelihood that event A will occur in the absence of event B.
if P(A) = 0.4 and P(B) = 0.2, respectively, and A and B are events that cannot coexist.
(a) P(AB) = 0 (by definition of mutual exclusion), indicating that there is no chance that events A and B will occur simultaneously.
(b) The probability that event A's complement, event B, will occur is P(A'B) = P(B) = 0.2.
(c) The probability that either the complement of event A or the complement of event B will occur, or both, is P(A'B') = P(A') + P(B') = 0.6.
(d) Since P(AB) = 0, the probability of event A occurring provided that event B has already occurred is undefined. P(A|B) = P(AB) / P(B) = 0 / 0.2 = undefined.
Roll a die once. The event of getting a "2" and the event of getting a "5" are mutually exclusive.
Roll a die twice. The event of getting a "2" on the first roll and the event of getting a "5" on the second roll are independent events.
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Let x equal the age, in human years, for a dog that is 2 years old or older. For each of your chosen breeds, write an expression to model its age in dog years. (Hint: Use (x - 2) in each expression.)
These are the dog years:
2yrs: 23 yrs old
3yrs: 27 yrs old
4yrs: 31 yrs old
5yrs: 35 yrs old
75 yrs: ............
find out what's the expression/answer for 75 years.
Therefore , the solution of the given problem of expression comes out to be 15 years: 75 years
what is expression ?In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.
Here,
an expression to represent a dog's age in dog years for a dog that is at least two years old in order to respond to the inquiry above. if x represents human age
then the dog is 2 years older
X = human years
x + 2 = is for the dog age
For 75 years
15 years: 75 years
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Sheleah and her family are planning a trip from Los Angeles, California to Melbourne, Australla. Whille booking her
family's plane tickets, she notices on the itinerary that the airline is offering a sixteen hour straight flight from Los
Angeles to Melbourne on a Boeing 747-8 Intercontinental Jet. In an effort to learn more about the capabilities of the Jet,
Sheleah does a little research and stumbles upon the following graph and facts about the Jet's fuel consumption.
Boeing 747-8 Intercontinental Jet
Jet Fuel Available (gallons)
70,000
60,000
50,000
40,000
30,000
20,000
10,000
63,500
2
55,562.5
3
4
47,625
39,687.5
31,750
23,812.5
9
7
8
10
Flight Time (hours)
11
12
15,875
13
14
7,937.5
15
17
The Boeing 747-8 Intercontinental Jet can carry approximately 63,500 gallons of jet fuel, making it possible for the Jet to
travel 14,430 kilometers before needing to refuel.
Create a linear model that represents the amount of fuel on the plane, In gallons, as a function of the flight time, In hours.
Show all of your work.
PLEASE HELP I NEED TO FINISH BY TONIGHT
The linear model that represents the amount of fuel on the plane is F(h) = 63,500 - 7937.50h
What is the linear function ?A linear function is a function that has a single variable raised to the power of 1. A linear function increases or decreases by a constant value . As the flight time increases , the amount of fuel declines . Thus, the linear function would be a decreasing function .
The form of the linear function is:
Total fuel left = capacity of the plane - (fuel consumed peer hour x number of hours )
Total fuel left = 63,500 - [(63500 - 55562.5) x h]
F(h) = 63,500 - 7937.50h
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Three types of beverage were served at a wedding dinner. 2 persons shared a can of beer. 3 persons shared a jar of fruit punch. 4 persons shared a bottle of wine. 78 cans of beverange were served altogether. How many guests were at the dinner?
Therefore , the solution of fraction problem is number of guests in the dinner were 72.
What is fraction with an example from real life?A fraction is referred to as the portion of a whole in mathematics. For instance, if a pizza is cut into four equal pieces, each one is represented by a quarter. Fractions make calculations quicker and easier by making it easier to distribute and judge numbers.
Here,
Given :
Let the number of guests be x,
2 persons shared a can of beer. 3 persons shared a jar of fruit punch. 4 persons shared a bottle of wine ++78
12+8x+6x 24
26x = 1872
x = 72
= 78
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twenty-six people, numbered consecutively 1 through 26, are seated equally spaced around a circular table. which numbered person is seated directly across from person number 9?
On solving the provided question, we can say that permutation will = 1/2(26) = 13 ways
what is permutation?The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order.
here,
by permutation,
1 through 26
permutation will = 1/2(26) = 13 ways
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how to graph 2x + y > -1
Answer:
Step-by-step explanation:
f(x)=-2³√x-1-2
please solve ASAP
Answer:1.233
Step-by-step explanation:
Find the length of the arc on a circle of radius r intercepted by a central angle θ. (Round your answer to two decimal places.) Radius r Central Angle θ 16 inches 240°Find the length of the arc on a circle of radius r intercepted by a central angle θ. (Round your answer to two decimal places.)Radius r Central Angle θ
16 inches 240°
The length of the arc intercepted by the central angle of 240 degrees on a circle with a radius of 16 inches would be 67 inches (rounded to two decimal places)
To find the length of an arc on a circle intercepted by a central angle, we can use the formula: arc length = (θ / 360) * (2 * π * r)
where θ is the measure of the central angle in degrees, π is approximately 3.14, and r is the radius of the circle.
In this case, we are given a circle with a radius 16 inches and a central angle of 240 degrees. Plugging these values into the formula, we get:
arc length = (240 / 360) * (2 * 3.14 * 16) = (2/3) * 100.48 = 67 inches
So the length of the arc intercepted by the central angle of 240 degrees on a circle with a radius of 16 inches would be 67 inches (rounded to two decimal places)
Therefore, the length of the arc would be 67 inches.
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Construct the following quadrilateral
Rhombus BEND
BN = 5.6 cm
DE = 6.5 cm
Answer:
Step-by-step explanation:
To construct this rhombus, we will need a compass and a straightedge.
Step 1: Using the compass, draw two arcs intersecting at point E with the radius of 5.6 cm from B and D respectively.
Step 2: With the same radius, draw two more arcs intersecting at point N from both sides of point E.
Step 3: Draw a straight line from D to E and from E to N.
Step 4: Now draw a line from B to N with the same radius used in Step 2.
The resulting shape is the rhombus BEND with side lengths of 5.6 cm and 6.5 cm.
a person jogs eight complete laps around a quarter-mile track in a total time of 12.5 min. determine the total distance in meter (1 mile
8 laps time 1/4 mile is 2 miles .
Average speed in miles per hour:
2 mi / 12.5 min * 60 min/hour = 9.6 mph
Average velocity is zero, since velocity is directional and the person jogged around a track. [I mention that in case this was set up as a trick question.]
But if we're really looking for average speed in m/s we can easily convert:
A mile is about 1.6 km, so it's about 1600 m.
(2 mi * 1600 m/mi) / (12.5 min * 60 s/min) = 1800 / 750 = 2.4 m/s
The directional speed of an item in motion, as measured by a specific unit of time and observed from a certain point of reference, is what is referred to as velocity.
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A room 9m ×7. 5 m i covered with tile. Ize of each tile i 25 cm by 20cm. Find the cot of tile at the rate of ₹45per tile
The price to tile the room is $3,240.
We must figure out how many tiles are required to cover the floor before multiplying that number by the cost per tile to get the cost of tiling the room.
To begin, we must change the room's measurements from meters to centimeters in order to make them consistent with the tile's size. Multiplying 9 by 100 and 7.5 by 100 will yield the results we need: 9m x 100cm/m = 900cm, and 7.5m x 100cm/m = 750cm
Since the room and tile dimensions are now both expressed in centimeters, we can calculate the number of tiles required to cover the space by dividing its size by the tile's area:
25 cm × 20 cm / 36000 cm / 500 cm = (900 cm x 750 cm) / 72
In order to cover the room, 72 tiles are required. We must multiply the quantity of tiles by the price per tile in order to determine the cost:
72 tiles x 45 cents each tile = 3,240
Therefore, the price to tile the room is $3,240.
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partial quotients, 5,166÷.42?
4,200
5,000
840
420
This is the answer hope you understand it
Suppose the slope of a line is positive. Describe what happens to the graph of the line as you move from left to right.
As you move the graph of the line from left to right, the output value of the function increases.
How to define a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change of the linear function.b is the intercept, representing the initial value of the linear function.The slope determines if the function is increasing or decreasing over it's domain, as follows:
Positive slope: increasing function.Negative slope: decreasing function.A positive slope means that the function increases when it moves from left to right, that is, when x increases.
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when isa travels to the usa for a holiday he leaves the uk at 1.00 pm local time and lands at 5.00 pm local time. on the return journey he leaves at 8.00 pm local time and lands at 10.00 am local time the next day. find the length of the flight in hours and the time difference between the uk and the part of the usa that isa visited
Isa took 4 hour when isa go from UK to USA and took 14 hour when she returns and time difference will be 10 hours
What is a definition distance?
the extent or amount of space between two things, points, lines, etc. the state or fact of being apart in space, as of one thing from another; remoteness
when isa travels to the usa for a holiday he leaves the uk at 1.00 pm local time and lands at 5.00 pm local time.
so isa took 4 hour
on the return journey he leaves at 8.00 pm local time and lands at 10.00 am local time the next day
isa tool 14 hour
find the length of the flight in hours and the time difference between the uk and the part of the usa that isa visited
length of flight is 18 hour
time difference will be 14-4 = 10 hour
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This is a parallelogram. y = ___
The value of y in the parallelogram is 120^o.
Properties of a parallelogram.A parallelogram is a plane figure which has opposite sides to be equal. Some of its properties are:
i. Opposite sides are equal in length
ii. It has two diagonals
iii. Sum of adjacent angles is 180^o
The value of y in the diagram can be determined as;
m<ADC + m<DCB = 180^o (sum of adjacent angles is 180^o)
(x + 8) + 3x = 180
4x = 180 - 8
= 172
x = 172/ 4
= 43
x = 43^o
So that;
m<ADC = x + 8
= 43 + 8
= 51^o
Therefore,
m<ADC + m<DAB = 180^o
51^o + (y + 9) = 180^o
y + 60 = 180
y = 180 - 60
= 120
y = 120^o
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Find m∠S in rhombus RSTU
Answer:
In a rhombus, opposite angles are equal, therefore:
m∠S = m∠U = a + 62 degrees
And
m∠R = 2a - 80 degrees
The opposite angles of a rhombus are supplementary, meaning they add up to 180 degrees. So,
m∠S + m∠R = 180 degrees
Therefore,
a + 62 + 2a - 80 = 180
Solving for a, we get:
a = 59
So,
m∠S = a + 62 = 59 + 62 = 121 degrees
Solomon has some electronics his parents said he could recycle, marcus has permission to recycle some small
household appliances, they looked online and discovered that the local recycling center offers $0.60 per pound
for the appliances and $1.50 per pound for the electronics. but there is a $27 hazardous waste fee that has to
be paid to recycle electronics, no matter how much you recycle.
The pounds that they would have to each recycle so that they earned the same amount of money from the recycle center is 30 pounds.
Equations that depict the revenue from recycling electronics and appliances are:
The following calculation can be used to calculate how much money Solomon can make by recycling appliances:
p = $0.60a
Solomon's potential earnings from recycling electronics are represented by the equation p = $1.50e - $27.
Here,
p = amount earned
a = pounds of appliances recycled
e = number of electronics recycled
The equation that depicts Solomon's earnings when he makes the same amount of money would be the same as the equation that describes his earnings when recycling gadgets.
$1.50e - $27 = $0.60e
To determine the number of pounds:
Combine and add similar terms
$1.50e - 0.60e = $27
$0.90 = $27
Dividing both sides of the equation by 0.9, we get
$27/ 0.9 = 30 pounds
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The complete question is:
"After reading about earning money by recycling, Solomon and Marcus are excited to do some recycling themselves. Solomon has some electronics his parents said he could recycle. Marcus has permission to recycle some small household appliances. They looked online and discovered that the local recycling center offers $0.60 per pound for the appliances and $1.50 per pound for the electronics. But there is a $27 hazardous waste fee that has to be paid to recycle electronics, no matter how much you recycle.
Write one equation that represents how much Solomon would earn by recycling electronics. Write another equation that represents Marcus earns from recycling appliances. How many pounds would they have to each recycle so that they earned the same amount of money from the recycle center?"
here are two plants (A and B) in an industry. To reduce pollution, the government has imposed environmental standards forcing each plant to cut emissions by 60%. At the emissions standard, the marginal social benefit of pollution for Plant A is $500 and the marginal social benefit of pollution for Plant B is $125. The same level of pollution can be achieved at a lower cost by
To achieve the same level of pollution at a lower cost, the government could adjust the environmental standards for each plant based on their respective marginal social benefits of pollution.
The government's environmental standards require Plant A and Plant B to reduce their emissions by 60%. The marginal social benefit of pollution for Plant A is $500 and the marginal social benefit of pollution for Plant B is $125. This means that the benefit of reducing one unit of pollution for Plant A is $500, while for Plant B is $125.
This information suggests that Plant A has a higher marginal social benefit of pollution than Plant B. Since the government's standards require both plants to reduce emissions by the same percentage, Plant A will have to reduce a greater amount of pollution than Plant B to reach the same level of emissions. This means that the cost of reducing pollution for Plant A will be higher than the cost of reducing pollution for Plant B.
To achieve the same level of pollution at a lower cost, the government could adjust the environmental standards for each plant based on their respective marginal social benefits of pollution. For example, if Plant A has a marginal social benefit of $500 and Plant B has a marginal social benefit of $125, the government could require Plant A to reduce its emissions by 50% and Plant B to reduce its emissions by 70%. This would achieve the same level of pollution while minimizing the cost of reducing pollution for both plants.
Thus, To achieve the same level of pollution at a lower cost, the government could adjust the environmental standards for each plant based on their respective marginal social benefits of pollution.
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Find an equation of the plane tangent to the following surface at the given point. 7xy +yz +4xz - 48 = 0; (2,2,2) The equation of the tangent plane at (2,2,2) is ... = 0.Find an equation of the plane tangent to the following surface at the given point. yze^xz + 7 = 0; (0, - 7,1) An equation of the tangent plane at (0, - 7,1) is ... = 0. Find an equation of the plane tangent to the following surface at the given point. z = 4 - 4x^2 - 2y^2; (2,3,-30) z = ...?Find an equation for the plane that is tangent to the surfacez = In (x^2 + y^3) at the point P(0,1,0). The equation of the plane is ... = 0
Therefore , the solution of the given problem of equation comes out to be x−3y−4z=0.
The equation is what?When the equals symbol (=) is used to signify equality, a mathematical equation appears to be a formula that connects two statements. In algebra, a factual assertion called an equation shows that several mathematical variables are equal. An equal sign separates the amounts doc d + 6 and 12 in the formula obd + 6 = 12, for instance. The relationship between the syllables to each side of each letter can be expression mathematically. Frequently, the symbol and the message are identical.
Here,
First, we rewrite the surface equation as
f(x, y, z) = x² - y²+2z²
y²+22=0
Thus, our role is as follows:
f(x, y, z) = x² - y²+2z²
We employ the Del, or gradients operator, to determine the normal at any given location in vector space:
Vf(x, Y, Z) = x - y + z
When partially differentiating, keep in mind that we only differentiate with respect to the variable in issue and regard the other factors as constants.
Consequently, (x)(2)+(y)(6)+(z)(2)=(1)(2)+(3)(6)+(2) (-8)
2x−6y−8z=2−18+16
2x−6y−8z=0
x−3y−4z=0
Therefore , the solution of the given problem of equation comes out to be x−3y−4z=0.
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What is a 1:2 ratio example?
A 1:2 ratio example could be 1 cup of flour and 2 cups of sugar. A ratio is a comparison of two or more numbers that shows the relationship between them. A 1:2 ratio means that for every 1 unit, there are 2 units.
A ratio is a comparison between two or more numbers. A 1:2 ratio means that for every 1 unit, there are 2 units. As an example, if you have 1 cup of flour and 2 cups of sugar, the ratio is 1:2 – 1 cup of flour and 2 cups of sugar.
A ratio is a comparison of two or more numbers that shows the relationship between them. A 1:2 ratio means that for every 1 unit, there are 2 units. For example, If you have 1 cup of flour and 2 cups of sugar, the ratio is 1:2. This means that for every 1 cup of flour, there are 2 cups of sugar. Ratios can be used to compare different items, such as ingredients in a recipe, to make sure that the proportions are correct. Ratios are an important tool when measuring and comparing different values.
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The length of a rectangle is shown below:
On a coordinate grid from negative 6 to positive 6 on the x-axis and on the y-axis, two points A and B are shown. Point A is on ordered pair 1, 3, and point B is on ordered pair negative 1, 3. A straight line joins points A and B.
If the area of the rectangle to be drawn is 10 square units, where should points C and D be located if they lie vertically below the line that connects B and A, to make this rectangle? (5 points)
( the image is attach below)
C(−1, 1), D(1, 1)
C(−1, −2), D(1, −2)
C(−1, 5), D(1, 5)
C(−1, −7), D(1, −7)
The coordinates of the points C and D are:
C = (1, -2), D = (-1, -2).
What is cartesian coordinate system?
A Cartesian coordinate system in a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates. These numerical coordinates are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length.
Given:
The coordinates of A and B are A(1, 3) and b(-1, 3).
We have to find the coordinates of point C and D.
We know that C and D are directly below A and B respectively. So the x-values must coincide.
Then we can say that:
C = (1, y)
D = (-1, y)
Now, remember that for a rectangle of length L and width W the area is:
A = W*L
In this case, the length is AB, then:
L = 1 - (-1) = 2
And the area is 10 square units, so:
10 = W*2
10/2 = W = 5
This means that:
AC = BD = 5
So the difference between the y-component of A and the y-component of C is 5 units
3 - y = 5
3 - 5 = y = -2
Hence, the coordinates of the points C and D are:
C = (1, -2), D = (-1, -2)
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trish goes to a bar with six friends to celebrate her 25th birthday. they're ready to party. each of her friends order her a 1.5 oz. shot (37% abv), and she takes all of them within half an hour. she weighs about 155 pounds. what is her bac level? should she drive?
She should not drive due to her BAC level of 0.117 percentage , which is above the legal limit in most states.
1. Calculate total amount of alcohol consumed:
1.5 oz. x 6 shots
= 9 oz.
2. Calculate amount of alcohol in grams:
9 oz. x 28.35 g/oz.
= 254.15 g
3. Calculate BAC:
(254.15 g/10,000 mL) x (155 lbs x 0.45359 kg/lbs) x (1g/1000mg) x (1.2 g/dL)
= 0.117% BAC
The amount of alcohol consumed by Trish was 9 oz. of 37% abv (alcohol by volume) liquor, which is equivalent to 254.15 g of pure alcohol. To calculate her BAC, we need to convert her weight to kilograms and then multiply the amount of alcohol consumed by her weight, taking into account that there is 1.2 g of alcohol per deciliter of blood. After doing the calculations, we can see that Trish's BAC level is 0.117%, which is above the legal limit for driving in most states, so she should not drive.
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The equation, 687.5 = 550(1 0.05t), represents the amount of money earned on a simple interest savings account. what does the value 550 represent?
The value 550 represents the initial deposit into the savings account.The equation 687.5 = 550(1 + 0.05t) is an equation in the form of A = P(1 + rt), which represents simple interest.
The equation 687.5 = 550(1 + 0.05t) is an equation in the form of A = P(1 + rt), which represents simple interest. The equation states that the amount A (687.5) is equal to the product of the initial deposit P (550) and the sum of one and the interest rate (0.05) multiplied by the time t (t is unknown). Thus, the value of 550 represents the initial deposit into the savings account.
The value 550 represents the initial deposit into the savings account.
The equation 687.5 = 550(1 + 0.05t) is an equation in the form of A = P(1 + rt), which represents simple interest.
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9.1 Exercises Listing the terms of a sequence In exercises 1-6 write the first five terms answer key
The first five terms of the sequence [tex]a_n = 3n/(n+4)[/tex] are:
3/5, 3/4, 9/7, 3/2, 15/9.
What is a sequence?
A sequence in A.P stands for "Arithmetic Progression" which is a sequence of numbers in which each term is the sum of the previous term and a constant called the common difference.
Now the given expression is
To find the first five terms of the sequence [tex]a_n = 3n/(n+4),[/tex] we need to substitute the values of n from 1 to 5 and solve for [tex]a_n[/tex].
a1 = 3*1/(1+4) = 3/5
a2 = 3*2/(2+4) = 3/4
a3 = 3*3/(3+4) = 9/7
a4 = 3*4/(4+4) = 12/8 = 3/2
a5 = 3*5/(5+4) = 15/9
Hence, the first five terms of the sequence [tex]a_n = 3n/(n+4)[/tex] are:
3/5, 3/4, 9/7, 3/2, 15/9.
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