We can use the distance formula to find the distance between two points in a coordinate plane:
d = √[(x2 - x1)² + (y2 - y1)²]
where (x1, y1) and (x2, y2) are the coordinates of the two points, and d is the distance between them.
Using the given coordinates of the two points, we have:
x1 = -2, y1 = 7
x2 = -5, y2 = 9
Substituting these values into the distance formula, we get:
d = √[(-5 - (-2))² + (9 - 7)²]
d = √[(-3)² + 2²]
d = √(9 + 4)
d = √13
Therefore, the distance between the points (-2, 7) and (-5, 9) is approximately √13 units. We can also approximate this value as 3.61 units (rounded to two decimal places).
The faces of a rectangular prism have areas of 9, 9, 25, 25, 49, and 49 square meters. Find the volume of the rectangular prism, in cubic meters
The volume of the rectangular prism is 105 cubic meters.
To find the volume of the rectangular prism, we can use the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height.
Since there are three pairs of congruent faces, we can deduce that the areas of the three pairs of faces represent the three dimensions of the rectangular prism. The areas are 9, 25, and 49 square meters, which are the squares of the sides' lengths.
Take the square root of each area to find the corresponding side lengths:
√9 = 3 meters
√25 = 5 meters
√49 = 7 meters
Now, apply the formula to find the volume:
V = lwh = 3 × 5 × 7 = 105 cubic meters.
The volume of the rectangular prism is 105 cubic meters.
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Josh wants to simplify the expression (-8)(10+(-5)+(-8))
Therefore, the simplified expression is 24.
To simplify the expression (-8)(10+(-5)+(-8)), you first need to solve the parentheses, following the order of operations, which requires solving the addition and subtraction within the parentheses before multiplying.
So, you have (-8)(10-5-8), which becomes (-8)(-3) after solving the parentheses. Finally, you can solve the multiplication by multiplying -8 by -3, resulting in 24.
It's important to remember the order of operations when simplifying expressions, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
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в
20°
C
62°
D
E please help with this I don’t know how to solve
The value of the arc is approximately 14.3 cm.
We are given that;
The angle = 62, 20
Now,
To find the value of arc if angle is 82 degrees
Step 1: Convert the angle from degrees to radians
Angle in radians = Angle in degrees x π/180 Angle in radians = 82 x π/180 Angle in radians ≈ 1.43
Step 2: Multiply the angle by the radius
Arc length = Angle x Radius Arc length = 1.43 x 10 Arc length ≈ 14.3 cm
Therefore, by the arc length the answer will be approximately 14.3 cm.
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out of 500 people , 200 likes summer season only , 150 like winter only , if the number of people who donot like both , the seasons is twice the people who like both the season , find summer season winter season , at most one season with venn diagram
Answer:
250 people like the summer season, 200 people like the winter season, and 50 people like both seasons.
Step-by-step explanation:
Let's assume that the number of people who like both summer and winter is "x". We know that:
- 200 people like summer only
- 150 people like winter only
- The number of people who don't like either season is twice the number of people who like both seasons
To find the value of "x", we can use the fact that the total number of people who don't like either season is twice the number of people who like both seasons:
150 - 2x = 2x
Solving for "x", we get:
x = 50
150 people like the winter season, 200 people like the summer season.
The number of people who don't like summer and winter is twice the number of people who like both seasons.
The number of people who like both the seasons= x
The number of people like summer 200
The number of people who like winter 150
The number of people who don't like summer and winter is twice the number of people who like both seasons.
To find the value of x, we can use the equation:
150-x= 2x
150= 3x
x= 50
The number of people who like both seasons is 50
The number of people who don't like both seasons is 100
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Select the correct answer. The Richter scale measures the magnitude, M, of an earthquake as a function of its intensity, I, and the intensity of a reference earthquake, IO. M = log(I/log) Which equation calculates the magnitude of an earthquake with an intensity 10,000 times that of the reference earthquake? OA. M = log(10,000) OB. M = log(10,000/Io) OC. M = log(1/10,000) OD. M = log(I/10,000)
OD. M = log(I/10,000)
How can the magnitude of an earthquake be calculated when its intensity is 10,000 times that of the reference earthquake?
The correct equation that calculates the magnitude, M, of an earthquake with an intensity 10,000 times that of the reference earthquake is option B: M = log(10,000/Io).
In the given equation M = log(I/IO), I represents the intensity of the earthquake being measured, and IO represents the intensity of the reference earthquake. Since the intensity of the earthquake in question is 10,000 times that of the reference earthquake, we substitute I with 10,000 times IO.
Therefore, the equation becomes M = log(10,000/Io), which is option B. This equation allows us to calculate the magnitude of the earthquake based on the relative intensity compared to the reference earthquake.
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How do I do this step by step
Answer:
Step-by-step explanation:
Let's call the total volume of the container "V".
We know that the container was originally 15% full, so the amount of water in the container was 0.15V.
When 48 litres of water was added, the new volume of water in the container became 0.15V + 48.
We also know that the container is now 75% full, so the new volume of water in the container must be 0.75V.
We can set up an equation to solve for V:
0.15V + 48 = 0.75V
Subtracting 0.15V from both sides:
48 = 0.6V
Dividing both sides by 0.6:
V = 80
So the container can hold 80 litres of water when it is full.
Find the area of the shaded region.
round to the nearest tenth.
1230
18.6 m
area = [ ? ] m2
The area of the shaded region is 422.8 m², rounded to the nearest tenth.
To find the area of the shaded region, we first need to determine the areas of the two shapes that make up the region. The first shape is a rectangle with dimensions of 18.6 m by 30 m, which has an area of:
Area of rectangle = length x width = 18.6 m x 30 m = 558 m²
The second shape is a semi-circle with a diameter of 18.6 m, which has a radius of 9.3 m. The area of a semi-circle is half the area of a full circle, so we can use the formula for the area of a circle to find the area of the semi-circle:
Area of semi-circle = (1/2) x π x r² = (1/2) x π x 9.3² = 135.2 m²
To find the area of the shaded region, we need to subtract the area of the semi-circle from the area of the rectangle:
Area of shaded region = Area of rectangle - Area of semi-circle
Area of shaded region = 558 m² - 135.2 m²
Area of shaded region = 422.8 m²
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The smaller of two similar rectangles has dimensions 4 and 6. Find the dimensions of the larger rectangle if the ratio of
the perimeters is 2 to 3.
O 6 by 9
2/3
by 4
12 by 12
O8 by 18
Answer:
The smaller rectangle has perimeter
2(4 + 6) = 2(10) = 20, so the larger rectangle will have perimeter 30. The dimensions of the larger rectangle are 6 by 9 since 2(6 + 9) = 2(15) = 30.
A person stands on level ground 60 m from the nearest point of a cylindrical tank of radius length 20 m. Calculate:
a- the circumference of the tank
b the percentage of the circumference that is visible to the person
The circumference of the tank is is 125.66m and the percentage of the circumference that is visible to the person is 10.24%.
a) To calculate the circumference of the cylindrical tank, using the formula C = 2πr, where C is the circumference and r is the radius of the tank. In this case, r = 20 m, so:
C = 2π(20 m) ≈ 125.66 m
b) To determine the percentage of the circumference visible to the person, we first need to calculate the angle (in degrees) that subtends the visible arc. This can be done using the inverse tangent function:
angle = atan(opposite/adjacent) = atan(20 m/60 m)
angle ≈ 18.43°
Since the visible arc is symmetrical on both sides, the total angle of the visible arc is twice the calculated angle:
total angle ≈ 36.86°
Now, calculate the percentage of the circumference that is visible by dividing the total angle by 360° and multiplying by 100%:
percentage = (36.86°/360°) × 100% ≈ 10.24%
So, the visible percentage of the circumference to the person is approximately 10.24%.
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help pls i need help on ,ath i jave a g
Answer: B
Step-by-step explanation:
What is the answer to this
The temperature are the times indicated are:
T( 0) = 5.800°
T( 0.22) = -4.9094 °
T (0.44) = -2.6792 °
T(0.66) = 2.3244°
T(0.88) = 4.8184°
T(1.1) = -4.1686 °
How did we get the above ?To solve the above, we need to use the formuala that we given which is T(x) = 5.8cos(3.8πx)
Entering the various values of x, can can obtain
T(0) = 5.8 cos (3.8π (0) ) = 5.8cos(0) = 5.800
T(0.22) = 5.8 cos (3.8 π(0.22)) ≈ -4.9094
T(0.44) = 5.8cos (3.8π (0.44) ) ≈ - 2.6792
T(0.66) = 5.8cos(3.8π (0.66)) ≈ 2.3244
T(0.88) = 5.8cos(3.8π(0.88)) ≈ 4.8184
T(1.1) = 5.8 cos(3.8π(1.1 )) ≈ -4.1686
So the above answers are correct.
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Solutions of Two-Variable Linear Inequalities
-40
5
-5
40
X
Select all of the following ordered pairs that are in
the solution set of the inequality shown.
(-10,-10)
0
0
0
(0.
(0, 10)
(10,0)
(20, 0)
(100, 100)
Answer: -403
Step-by-step explanation:
Square $ABCD$ has side length 7. What is the length of the diagonal $AC?$ (its a square also)
The length of the diagonal AC in square ABCD is approximately 9.899 units.
To find the length of the diagonal AC, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In our case, since ABCD is a square, angle ABC is a right angle. Therefore, triangle ABC is a right-angled triangle with sides AB and BC both equal to 7 units. We can apply the Pythagorean theorem to find the length of diagonal AC (the hypotenuse):
AC² = AB² + BC²
Plugging in the side lengths:
AC² = 7² + 7² = 49 + 49 = 98
Now, we take the square root of both sides to find the length of AC:
AC = √98 ≈ 9.899
So, the length of the diagonal AC in square ABCD is approximately 9.899 units.
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Antonio, a professional wrestler, went on a very strict liquid diet for 26 weeks to lose weight. When he
began the diet, he weighed in at a healthy 235 pounds and during the diet, he consistently lost 1. 5% of his
body weight each week. His weight loss can be modeled by the function W (t) = 235(0. 985)' where Wis
his weight in pounds and t is the time in weeks that he has been on the diet.
What was his weight in pounds after 5 weeks?
How long did it take(in weeks) him to weigh in at 161. 05 pounds?
Antonio's weight after 5 weeks was 202.34 pounds, and it took him 19 weeks to weigh in at 161.05 pounds.
To find Antonio's weight after 5 weeks, we can simply substitute t = 5 into the given exponential function:
W(5) = 235(0.985)⁵
W(5) ≈ 209.88 pounds
So his weight after 5 weeks was approximately 209.88 pounds. To find how long it took him to weigh in at 161.05 pounds, we can set the function equal to 161.05 and solve for t:
161.05 = 235(0.985)ᵗ
0.685106383 ≈ 0.985ᵗ
t ≈ 25.5 weeks
So it took him approximately 25.5 weeks to weigh in at 161.05 pounds
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Complete question - Antonio, a professional wrestler, went on a very strict liquid diet for 26 weeks to lose weight. When he began the diet, he weighed in at a healthy 235 pounds and during the diet, he consistently lost 1. 5% of his body weight each week. His weight loss can be modeled by the function W (t) = 235(0. 985)ᵗ where W is his weight in pounds and t is the time in weeks that he has been on the diet. What was his weight in pounds after 5 weeks? How long did it take(in weeks) him to weigh in at 161. 05 pounds?
A farmer sell 7. 9 kilograms of pears and apples at the farmers market. 3/5 of this wieght is pears,and the rest is apples. How many apples did she sell at the farmers market?
The farmer sold 3.16 kilograms of apples at the farmers market.
What is division?
A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many total groups will be established, for instance, if 20 students need to be separated into groups of five for a sporting event? The division operation makes it simple to tackle such issues. Divide 20 by 5 in this case. 20 x 5 = 4 will be the outcome. There will therefore be 4 groups with 5 students each. By multiplying 4 by 5 and receiving the result 20, you may confirm this value.
Let's start by finding out the weight of pears the farmer sold.
Weight of pears = 3/5 x 7.9 kg = 4.74 kg
To find the weight of apples, we can subtract the weight of pears from the total weight:
Weight of apples = Total weight - Weight of pears
Weight of apples = 7.9 kg - 4.74 kg
Weight of apples = 3.16 kg
Therefore, the farmer sold 3.16 kilograms of apples at the farmers market.
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I'm board so before this gets reported what's your fav show(s) on netflix
Mine is:
Lucifer
On my block
First few seasons of flash
To gather information about the elk population, biologist marked 75 elk. later, they flew over the region and counted 250 elk, of
which 15 were marked. what is the best estimate for the elk population?
es -))
a)
1,200
b)
1,250
c)
1,300
d)
1,350
The best estimate for the elk population is b) 1,250.
To estimate the elk population, you can use the mark and recapture method. The proportion of marked elk to the total marked population should be equal to the proportion of marked elk observed in the sample to the total observed population.
So, (marked elk / total marked population) = (marked elk observed / total observed population)
In this case: (75 / total population) = (15 / 250)
Now, solve for the total population:
75 / total population = 15 / 250
Cross-multiply:
15 * total population = 75 * 250
total population = (75 * 250) / 15
total population = 18,750 / 15
total population = 1,250
The best estimate for the elk population is 1,250 (option b).
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RAFFLE The Harvest Fair sold 967 raffle tickets for a chance to win a new TV. Copy and complete the table to find each probability of not winning the TV with the given number of tickets
When all 967 tickets are purchased, the probability of not winning is 0 (or 0%).
What is probability?The probability of an event occurring is defined by probability. There are numerous real-life scenarios in which we must forecast the outcome of an occurrence.
To find the probability of not winning the TV with a given number of tickets, we need to calculate the ratio of the number of losing tickets to the total number of tickets. The completed table is as follows:
Number of Tickets | Number of Losing Tickets | Probability of Not Winning
-----------------|-------------------------|----------------------------
0 | 967 | 1.000
1 | 966 | 0.999
10 | 957 | 0.990
50 | 917 | 0.948
100 | 867 | 0.897
200 | 767 | 0.793
300 | 667 | 0.690
400 | 567 | 0.587
500 | 467 | 0.483
600 | 367 | 0.380
700 | 267 | 0.277
800 | 167 | 0.173
900 | 67 | 0.069
967 | 0 | 0.000
As the number of tickets purchased increases, the probability of not winning the TV decreases. When no tickets are purchased, the probability of not winning is 1 (or 100%). When all 967 tickets are purchased, the probability of not winning is 0 (or 0%).
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An object moving vertically is at the given heights at the specified times. Find the position equation s = 1/2 at^2 + v0t + s0 for the object.
At t = 1 second, s = 136 feet
At t = 2 seconds, s = 104 feet
At t = 3 seconds, s = 40 feet
The position equation for the object is: s = -80t^2 + 208t + 88, where s is the position of the object (in feet) at time t (in seconds).
We can use the position equation s = 1/2 at^2 + v0t + s0 to solve for the unknowns a, v0, and s0.
At t = 1 second, s = 136 feet gives us the equation:
136 = 1/2 a(1)^2 + v0(1) + s0
136 = 1/2 a + v0 + s0 ----(1)
At t = 2 seconds, s = 104 feet gives us the equation:
104 = 1/2 a(2)^2 + v0(2) + s0
104 = 2a + 2v0 + s0 ----(2)
At t = 3 seconds, s = 40 feet gives us the equation:
40 = 1/2 a(3)^2 + v0(3) + s0
40 = 9/2 a + 3v0 + s0 ----(3)
We now have a system of three equations with three unknowns (a, v0, s0). We can solve this system by eliminating one of the variables. We will eliminate s0 by subtracting equation (1) from equation (2) and equation (3):
104 - 136 = 2a + 2v0 + s0 - (1/2 a + v0 + s0)
-32 = 3/2 a + v0 ----(4)
40 - 136 = 9/2 a + 3v0 + s0 - (1/2 a + v0 + s0)
-96 = 4a + 2v0 ----(5)
Now we can solve for one of the variables in terms of the others. Solving equation (4) for v0, we get:
v0 = -3/2 a - 32
Substituting this into equation (5), we get:
-96 = 4a + 2(-3/2 a - 32)
-96 = 4a - 3a - 64
a = -160
Substituting this value of a into equation (4), we get:
-32 = 3/2(-160) + v0
v0 = 208
Finally, substituting these values of a and v0 into equation (1), we get:
136 = 1/2(-160)(1)^2 + 208(1) + s0
s0 = 88
Therefore, the position equation for the object is:
s = -80t^2 + 208t + 88
where s is the position of the object (in feet) at time t (in seconds).
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Calcula dos numeros cuya suma sea 191 y su diferencia 67
The two numbers are 129 and 62, which satisfy the given conditions: their sum is 191 and their difference is 67 .
You are asked to find two numbers whose sum is 191 and whose difference is 67. Let's use the variables x and y to represent these two numbers.
We can establish the following two equations under the given conditions: 1) x + y = 191 2) x - y = 67
Now we can solve this system of linear equations to find the values of x and y.
We can start by adding both equations:
(x + y) + (x - y) = 191 + 67
2x = 258
Then we'll divide by 2 to find the value of x:
x = 129
Now, we can plug x into Equation 1 to find the value of y:
129 + y = 191
y = 191 - 129
y = 62
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A rectangle is changing in such a manner that its length is increasing 5 ft/sec and its width is decreasing 2 ft/sec. at what rate is the area changing at the instant when the length equals 10 feet and the width equals 8 feet
The area of the rectangle is changing at a rate of 20 ft²/sec when the length equals 10 feet and the width equals 8 feet.
How to find the length and width?Let L and W be the length and width of the rectangle, respectively, and let A be the area of the rectangle. Then we have:
L = 10 ft (given)W = 8 ft (given)dL/dt = 5 ft/sec (length is increasing)dW/dt = -2 ft/sec (width is decreasing)We want to find dA/dt, the rate of change of the area A with respect to time t, when L = 10 ft and W = 8 ft.
We know that:
A = L*W
Taking the derivative of both sides with respect to time t, we get:
dA/dt = d/dt (L*W)
Using the product rule of differentiation, we get:
dA/dt = dL/dt * W + L * dW/dt
Substituting the given values, we get:
dA/dt = 5 ft/sec * 8 ft + 10 ft * (-2 ft/sec)
Simplifying, we get:
dA/dt = 40 - 20 = 20 ft²/sec
Therefore, the area of the rectangle is changing at a rate of 20 ft^2/sec when the length equals 10 feet and the width equals 8 feet.
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A pair of dice is tossed. Find the probability that the sum on the 2 dice is 4, given that doubles are rolled. (Enter your probability as a fraction.)
Answer:
1/6
Step-by-step explanation:
You spin the spinner and flip a coin. How many outcomes are possible? 5 4 6 3 Submit 1 2 Cosenz. bit JETS & AMICIS
Total outcomes when we spin the spinner and flip a coin = 12
In the figure
In spinner the labelled number are from 1 to 6
And for a coin there are two outcomes head and tail
Therefore,
total number of outcomes for spinner = 6
total number of outcomes for a coin = 2
Then the number of outcomes when both are performed once
= 6x2
= 12
Hence total outcomes = 12
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Geographers use satellites in order to:
A. Capture detailed images of a location from space?
B. Collect and store digital information about a location?
C. Track the location of moving objects on Earth?
D. Organize and represent data for a location?
Answer:
Step-by-step explanation:
Geographers use satellites primarily to capture detailed images of a location from space (option A). These images can provide valuable information about the landscape, climate, and natural resources of an area, among other things. Additionally, satellites can be used in combination with other technologies to collect and store digital information about a location (option B), such as mapping the distribution of vegetation or tracking changes in land use over time. While satellites can be used to track the location of moving objects on Earth (option C), this is not typically their primary function. Finally, organizing and representing data for a location (option D) is more closely associated with Geographic Information Systems (GIS) than with satellite technology specifically.
Answer:
A. Capture detailed images of a location from space.
Step-by-step explanation:
Geographers use satellites to capture high-resolution images of the Earth's surface from space. This enables them to study and analyze different aspects of the Earth, such as its topography, land use patterns, and weather systems. These images are also used in cartography, the science of map-making, to create accurate and up-to-date maps of the Earth's surface.
expanded form 6.27x10 4
Answer:62700
Step-by-step explanation:
You take your original value and move the decimal point 4 times to the right as it is a positive power.
PLEASE HELP I NEED THIS QUICK!!!
The number of ways to travel the route is given as follows:
18 ways.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are m ways to do one thing and n ways to do another, then there are m x n ways to do both.
This can be extended to more than two events, where the number of ways to do all the events is the product of the number of ways to do each individual event, according to the equation presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
The options for this problem are given as follows:
Providence to Boston: 3 ways.Boston to Syracuse: 3 ways.Syracuse to Pittsburgh: 2 ways.Hence the total number of ways is given as follows:
3 x 3 x 2 = 18 ways.
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Rewrite the expression in the form a^na
n
a, start superscript, n, end superscript.
\dfrac{a^{-13}}{a^{-6}}=
a
−6
a
−13
=start fraction, a, start superscript, minus, 13, end superscript, divided by, a, start superscript, minus, 6, end superscript, end fraction, equals
The expression a⁻¹³/a⁻⁶ can be written as a⁻⁷ in aⁿ form.
We have been given the expression
a⁻¹³/a⁻⁶
We know that whenever there is a minus sign in the power, we need to consider a reciprocal of the number
Hence,
a⁻¹³ will become 1/a¹ and a⁻⁶ will become 1/a⁶
Hence the numerator and denominator will interchange to get
a⁶/a¹³
Now, we know that when a number is broght from denominator to the numerator, there is a minus sign added to the power. Hence we will get
a⁶ X a⁻¹³
Since the two numbers have the same base- a, we can add the powers up as there is multiplication sign in between to get
a⁶ ⁺ ⁽⁻¹³⁾
= a⁶ ⁻ ¹³
= a⁻⁷
Hence, the expression a⁻¹³/a⁻⁶ can be written as a⁻⁷ in aⁿ form.
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given g(x)=-4x-4, find g(-2)
Answer:
g(-2) = 4.
Step-by-step explanation:
To find g(-2), we simply need to substitute -2 for x in the function g(x) and simplify:
g(-2) = -4(-2) - 4
g(-2) = 8 - 4
g(-2) = 4
Therefore, g(-2) = 4.
the perimeter of an isosceles triangle is 12x^2-5x +4 cm find the length of one of its equal sides
Answer:
4x² - x + 2--------------------------
Let the equal sides be both marked as ?
Use the perimeter formula to determine one of the equal sides.
P = 2(?) + x(4x - 3)Substitute the expression for the perimeter and find the value of ?
12x² - 5x + 4 = 2(?) + x(4x - 3)12x² - 5x + 4 = 2(?) + 4x² - 3x2(?) = 12x² - 5x + 4 - 4x² + 3x2(?) = 8x² - 2x + 4? = 4x² - x + 2Hence the length of each of equal sides is 4x² - x + 2.
(1 point) Write an equivalent integral with the order of integration reversed g(y) I hope F(x,y) dydt = F(x,y) dedy f(y) a = b= f(y) = g(y) =
The missing values are:
a = 0b = 1c = 1f(y) = yg(y) = 2 - yh(y) = 0k(y) = yGiven Integral:
[tex]\int\limits^1_0 \int\limits^{2-x}_x {F(x,y)} \, dydx = \int\limits^b_a \int\limits^{g(y)}_{f(y)} {F(x,y)} \ dxdy + \int\limits^c_b \int\limits^{h(y)}_{k(y)} {F(x,y)} \ dxdy \\[/tex]
To write the equivalent integral with the order of integration reversed, express the limits of integration and functions appropriately.
Reversed integral:
[tex]\int\limits^b_a \int\limits^{g(y)}_{f(y)} {F(x,y)} \ dxdy + \int\limits^c_b \int\limits^{h(y)}_{k(y)} {F(x,y)} \ dxdy \\[/tex]
Now, let's determine the values of the variables:
a = 0: The lower limit of the outer integral remains the same as the original integral.
b = 1: The upper limit of the outer integral also remains the same as the original integral.
c = 1: The upper limit of the second inner integral is determined by the limits of integration of the original integral, which is 1.
f(y) = y: The lower limit of the first inner integral is the same as the original integral, which is y = x.
g(y) = 2 - y: The upper limit of the first inner integral is determined by the limits of integration of the original integral, which is 2 - x.
h(y) = 0: The lower limit of the second inner integral remains the same as the original integral.
k(y) = y: The upper limit of the second inner integral remains the same as the original integral.
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