We can find the coordinates of the point that partitions a line segment into a ratio of 1 to 5 by using the formula:
(x, y) = (x1 + r * (x2 - x1), y1 + r * (y2 - y1))
Where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment, and r is the ratio of the distance from the starting point to the point of interest, to the total distance of the line segment. In this case, r = 1/(1 + 5) = 1/6.
We know the coordinates of the two endpoints of the line segment:
(x1, y1) = (-10, 9)
(x2, y2) = (-4, 3)
So, we can substitute these values into the formula and find the coordinates of the point that partitions the line segment into a ratio of 1 to 5:
(x, y) = (-10 + (1/6) * ((-4) - (-10)), 9 + (1/6) * (3 - 9))
= (-10 + (1/6) * (-6), 9 + (1/6) * (-6))
= (-10 -1/6, 9 -1)
= (-10/6 -1/6, 3/2 -1)
= (-16/6, 3/2 -1)
= (-8/3,-1/2)
So, the coordinates of the point on the directed line segment from (-10, 9) to (-4, 3) that partitions the segment into a ratio of 1 to 5 is (-8/3,-1/2)
It is important to notice that this point is a vector and not a point in the Cartesian plane
Draw the graph of y=f(x) and y= 1/f(x) on the same axes.
f) f(x) = -(x+4)²+1
are there any specific steps to get the answers here?
Answer: To graph y = f(x) and y = 1/f(x) on the same axes, you can follow these steps:
First, graph y = f(x) by plotting a few points, such as (-5, -19), (-3, -1), (0, 1) and (5, 19), and then connecting them with a smooth curve.
Then, graph y = 1/f(x) by finding the inverse function of f(x) which will be
1/f(x) = -1/(x+4)²+1
Next, plot a few points on this new function, such as (-5, -1/19), (-3, -1), (0, 1) and (5, 1/19), and then connecting them with a smooth curve.
Finally, make sure that the same x and y scales are used for both graphs, and label the axes and the functions clearly.
It is important to note that as f(x) = -(x+4)²+1, the domain of f(x) is all real numbers but the range is (1, infinity) so the reciprocal will be defined only for the range of f(x) and the domain of 1/f(x) will be (1, infinity)
Also, the graph of y = f(x) will be a parabola opening upwards and y = 1/f(x) will be a parabola opening downwards, both with vertex (-4,1)
The graph of y = -(x+4)²+1 will be a parabola opening upwards and the graph of y = -1/(x+4)²+1 will be a parabola opening downwards.
Step-by-step explanation:
giving a test to a group of students, the grades by the two different classes are summarized below. a a b b c c total morning class 4 4 20 20 8 8 32 32 afternoon class 13 13 5 5 7 7 25 25 total 17 17 25 25 15 15 57 57 enter your answer as a fraction or as a calculation involving fractions. if one student is chosen at random, find the probability that the student got a a a given that the student was in the afternoon class.
The probability that the student got a a a given that the student was in the afternoon class is 25/57
In math the term probability is defined as based on the possible chances of something to happen
Here we have given that a test to a group of students, the grades by the two different classes are summarized.
and it can be written like the following;
a b c Total
Morning class 4 20 8 32
Evening Class 13 5 7 25
Total 17 25 15 57
Here we know that the total number of students is obtained as
=> 57
And the number of students who have been taking the afternoon class is calculated as,
=> 25
Then the probability the student got a a a given that the student was in the afternoon class is written as,
=> 25/57
To know more about Probability here.
https://brainly.com/question/11234923
#SPJ4
at a school, 20 percent of the sixth-grade students said that jazz is their favorite kind of music. if 30 sixth-grade students prefer jazz music, how many sixth-grade students are at the school? explain your reasoning.
Answer:
150 students in total
Step-by-step explanation:
30 students is 20%
20% x 5 = 100%
30 x 5 = 150 students
Two communications companies offer calling plans. With Company X, it costs 30c to connect and then 4c for each minute. With Company Y, it costs 15c to connect and then 3c for each minute. Write and simplify an expression that represents how much more Company X charges, in cents, for n minutes.
Answer:
30 + 4n
Step-by-step explanation:
Company X = 30 + 4n
Please help, I cannot figure out how to do this for the life of me -number 15
Determine whether the set S spans R2. If the set does not span R2, then give a geometric description of the subspace that it does span.
S = {(-1, 2), (2, -1), (1, 1)}
A. S spans R2.
B. S does not span R2. S spans a line in R2.
C. S does not span R2. S spans a point in R2.
A set S spans R^2 if any element of R^2 can be written as linear combination of elements of S the set S spans R2.
(a) Given that S={ (1,-1),(2,1) }
Let (x,y) be the any element in R^2.
(x,y) = C1(1,-1)+C2(2,1)
(x,y) = (c1+2c2,-c1+c2)
x = c1+2c2
y = -c1+c2
x+y = 3c2
c2= {x+y}/{3}
c1 = c2-y
= {x+y}/{3}-y
={x-2y}/{3}
So for any element (x,y) in R^{2} we have the constants c_1,c_2 so that (x,y) can be written as,
(x,y)= {(x-2y)}/{3}(1,-1) + {(x+y)}/{3}(2,1)
So S= { (1,-1),(2,1) } spans R^2.
(b) Given that S = { (1,1) }
Let (x,y) be the any element in R^2.
(x,y)=c_1(1,1)
(x,y)=(c_1,c_1)
x=c_1,y=c_1
If x,y are distinct then do not get a value of c_1 so that (x,y) = c_1(1,1).
So set S= { (1,1) } does not span R^2.
(c) Given that S= { (0,2),(1,4) }
Let (x,y) be the any element in R^2.
(x,y)=c_1(0,2)+c_2(1,4)
(x,y)=(c_2,2c_1+4c_2)
x=c_2
y=2c_1+4c_2
c_1={y-4c_2} / {2}
={y-4x} / {2}
So (x,y)= {(y-4x)}/{2}(0,2)+x(1,4)
So any element of R^2 can be written as written as linear combination of elements of Set S.
Hence set S={ (0,2),(1,4) } spans R^2.
Learn more about sets here :
https://brainly.com/question/28492445
#SPJ4
While you could use the associative property on all the following expressions, select two of the following expressions that using the associative property to write an equivalent expression that would help you calculate the value of the expression using mental math.
Group of answer choices
Answer:
A, C
Step-by-step explanation:
A)
(120 ∙ 8) ∙ 5 = 120 ∙ (8 ∙ 5)
Multiply 8 and 5 first to get 40.
Then 40 × 120 = 4800
C)
(17 + 75) + 25 = 17 + (75 + 25)
Add 75 and 25 first to get 100.
then 17 + 100 = 117
ladder is leaning against a wall so that it makes an angle of 35 degrees with the wall.
If the base of the ladder is 4 feet from the base of the wall, how long is the ladder?
The length of the ladder used in the question is; 6.974 ft
How to use trigonometric ratios?The 3 main trigonometric ratios are;
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
Now, since the ladder makes an angle of 35 degrees with the wall, it means the ladder will be the hypotenuse of the right angle triangle and the distance from the base of the wall to the base of the ladder will be labelled as h = 4 will be the opposite side of the triangle. Thus;
4/hypotenuse = sin 35
hypotenuse = 4/sin 35
hypotenuse = 4/0.5736
Hypotenuse = 6.974 ft
Read more about trigonometric ratios at; https://brainly.com/question/13276558
#SPJ1
2023 1-100 math challenge answers
Answer:
Step-by-step explanation: 1*23= 23 because anything times one is equal to itself
Two restaurants offer customers large pizzas using different measurements for diameter. Restaurant 1: One large 14-inch pizza for $12.99 Restaurant 2: One large 36.83-centimeter pizza for $12.99 If 1 inch = 2.54 centimeters, what is the length of the crust around the larger pizza, using π = 3.14?
A. 115.65 inches
B. 22.77 inches
C. 43.96 inches
D. 45.53 inches
Answer:
D. 45.53 inches
Step-by-step explanation:
Restaurant 1: diameter = 14 inches
Restaurant 2: diameter = 36.83 inches × (1 inch)/(2.54 cm) = 14.5 inches
The larger pizza is from Restaurant 2, and its diameter is 14.5 inches.
circumference = πd = 3.14 × 14.5 inches = 45.53 inches
Answer: D. 45.53 inches
Answer:it is d 45.53
Step-by-step explanation:becuase I did the test
Wenxuan, Charlene and Siti shared a box of stickers. Wenxuan took 8 more than of the total number of stickers. Charlene took 7 more than of the remaining 1 1 3 2 stickers. Siti took the last 23 stickers. How many stickers were there in the box at first?
Answer:
We can start solving the problem by using algebraic equations. Let x be the total number of stickers in the box at first.
According to the problem, Wenxuan took 8 more than of the total number of stickers, so he took x + 8 stickers.
The remaining stickers after Wenxuan took his share is x - (x+8) = x - x - 8 = -8 stickers.
Charlene took 7 more than of the remaining stickers, which is -8 + 7 = -1 stickers.
So, Charlene took x - (x+8) + 7 = -1 stickers.
Siti took the last 23 stickers, so the total number of stickers remaining is -1 - 23 = -24.
Now we can use this information to set up the equation:
x + (x+8) + (x-x-8+7) + (-1-23) = x
Solving for x we get x = 32
Therefore, there were 32 stickers in the box at first.
is the formula z =
adratic inequality
-6± √b²
2a
4ac
used to find the solutions to a quadratic equation of the form az² + bz+c= 0.
Yes, the formula z = -b± √(b²-4ac)/2a is used to find the solutions (or roots) of a quadratic equation of the form az² + bz + c = 0. This is known as the Quadratic Formula.
What is the Quadratic Equation?
A quadratic equation is a type of polynomial equation of degree 2 in one variable (x), which can be written in the form of ax² + bx + c = 0, where a, b, and c are real numbers, and a is not equal to zero. The solutions or roots of this equation can be found by using the Quadratic Formula which is z = -b ± √(b²-4ac) / 2a.
The Quadratic formula is valid for any quadratic equation in standard form (ax² + bx + c = 0), where a, b, and c are real numbers, and a is not equal to zero. The two solutions are given by the formula are the roots of the equation, and they are always real and distinct, unless the discriminant b² - 4ac is negative, in which case the roots are complex numbers.
Hence, Yes, the formula z = -b± √(b²-4ac)/2a is used to find the solutions (or roots) of a quadratic equation of the form az² + bz + c = 0. This is known as the Quadratic Formula.
To learn more about the quadratic equation, visit:
https://brainly.com/question/1214333
#SPJ1
based on the responses, which of the following is a 95 percent confidence interval for the proportion of all city residents who would respond very supportive or somewhat supportive of the proposal?
As per the given confidence interval, the proportion of all city residents who would respond very supportive or somewhat supportive of the proposal is 336 ± 0.197
The term confidence interval is defined as the statistical measure used to indicate the range of estimates within which an unknown statistical parameter is likely to fall.
Here we have given that the random sample of 1,018 city residents were asked to rate their level of support for a proposal being considered by the city council.
Here we have also know that the percent of confidence interval is 95%.
Here we also identified the following values,
Total population = 1,018
Very supportive population = 336
Somewhat supportive population = 387
Not supportive population= 295
Then the value of confidence interval is calculated as,
Proportion of positive results = P = x/N = 0.3301
Lower bound = 0.3012
Upper bound = 0.3599
Therefore, it can be written as,
=> 336 ± 0.197
Complete Question:
A random sample of 1,018 city residents were asked to rate their level of support for a proposal being considered by the city council. Based on the responses, which of the following is a 95% confidence interval for the proportion of all city residents who would respond very supportive of somewhat supportive of the proposal?
To know more about Confidence interval here.
https://brainly.com/question/24131141
#SPJ4
The admission fee at an amusement park is $1.25 for children and $7.20 for adults. On a certain day, 253 people entered the park, and the admission fees collected totaled $1060. How many children and how many adults were admitted?
There were _______ children admitted.
There were _______ adults admitted
This is a system of equations problem. We can set up the following equations:
x = number of children admitted
y = number of adults admitted
1.25x + 7.20y = 1060 (the total amount of money collected)
x + y = 253 (the total number of people admitted)
To find the number of children admitted, we can use the second equation to solve for one of the variables in terms of the other.
x + y = 253
x = 253 - y
Now we can substitute this expression into the first equation:
1.25(253 - y) + 7.20y = 1060
Solving for y we get
y = 120
So there were 120 adults admitted.
We can use the second equation to find the number of children admitted:
x + y = 253
x = 253 - y
x = 253 - 120
x = 133
So there were 133 children admitted.
Therefore,
There were 133 children admitted.
There were 120 adults admitted.
Answer:
128 children, 128 adults
Step-by-step explanation:
1.25 per child (c)
7.2 per adult (a)
a+c = 253 so c = 253-a
1.25c+7.2a=1060
2 equations 2 variables, solve
1.25 (253-a) + 7.2*a = 1.25*253 -1.25a + 7.2a =1060
sp 5.95a =1060- 1.25*253
so a =125
c = 253-125 = 128
Find the volume of the solid of revolution obtained by rotating the region bounded by the curves x=0
, y=0
The volume of the solid of revolution is 0
The volume of the solid of revolution obtained by rotating the region bounded by the curves x=0 and y=0 is zero since the area of the region is zero.
To calculate the volume of a solid of revolution, we use the formula V = ∫2dx, where r is the radius of the circle obtained by rotating the curve about the x-axis. Since the region bounded by the curves x=0 and y=0 has an area of 0, the radius r is also 0 and the integral becomes 0. Therefore, the volume of the solid obtained by rotating the region bounded by the curves x=0 and y=0 is 0.
Learn more about volume of the solid here:
https://brainly.com/question/12649605
#SPJ4
let f(x)=3x-1.then find g(x):if f(g(x))=9x the power of 2+12x+8
Answer:
3x^2 + 4x + 3
Step-by-step explanation:
we can use this information to find g(x) in terms of f(x).
substitute f(x) = 3x-1 into f(g(x)) = 9x^2 + 12x + 8, we get:
3g(x) - 1 = 9x^2 + 12x + 8
Now, we can solve for g(x) by isolating it on one side of the equation:
3g(x) = 9x^2 + 12x + 9
g(x) = 3x^2 + 4x + 3
therefore g(x) is equal to 3x^2 + 4x + 3
Select the correct answer from each drop-down menu.
Robbie wants to construct an equilateral triangle. He draws diameter AB of circle O and constructs the perpendicular bisector of
diameter AB, find the points X and Y. Then he draws the triangle AXB. What error did he make?
The first mistake Robbie made was
Submit
.He should have
Reset
The first mistake Robbie made was, take improper lengths. AB is the diameter; its length is longer than the sides AX and XB. So, the triangle formed will not be an equilateral triangle.
What is an equilateral triangle?An equilateral triangle in geometry is a triangle with equally long sides. The three angles opposing the three equal sides are equal in size because the three sides are equal.
The first mistake Robbie made was, take improper lengths. AB is the diameter; its length is longer than the sides AX and XB. So, the triangle formed will not be an equilateral triangle.
He should have, after drawing the diameter AB, construct a circle with point A as the center and AO as the radius. Mark the point of intersection as X. Then, AO, AX and OX would form an equilateral triangle.
Learn more about equilateral triangle here:
https://brainly.com/question/3461022
#SPJ1
Answer:
1. constructing the perpendicular bisector of AB
2.
Step-by-step explanation:
show that {1,2,3} under multiplication modulo 4 is not a group but that {1,2,3,4} under multiplication modulo 5 is a gruoup.
The set {1,2,3} is not a group under multiplication modulo 4, as it does not contain an identity element. However, the set {1,2,3,4} is a group under multiplication modulo 5.
A group is a set of elements which is closed under an operation and contains an identity element. In order to be a group, the set must satisfy the four group axioms: closure, associativity, identity, and invertibility. The set {1,2,3} does not satisfy the group axioms under multiplication modulo 4, since it does not contain an identity element, and thus is not a group.
On the other hand, the set {1,2,3,4} is a group under multiplication modulo 5, since it contains an identity element (1) and is closed under multiplication. The other group axioms are also satisfied, as the operation is associative, and each element has an inverse (for example, the inverse of 1 is 4). Therefore, {1,2,3,4} is a valid group under multiplication modulo 5.
Learn more about set here
https://brainly.com/question/12979762
#SPJ4
Projects that adopt agile methodology are not prone to the typical rapid changes that occur throughout the system development lifecycle.
False
True
Projects that adopt agile methodology are not prone to the typical rapid changes that occur throughout the system development lifecycle, The statement is False.
The methodology is defined as to the overarching strategy and rationale of your research project.
It involves studying the methods used in your field and the theories or principles behind them, in order to develop an approach that matches your objectives.
Agile project management methodology is commonly used for software development projects. It has greater adaptability to frequently changing scopes. Adopt Agile because they want to increase speed to market, meet customer demand, or increase team productivity.
To know more about Methodology:
https://brainly.com/question/12325081
#SPJ4
The bottom of a deep trench in an ocean is estimated to be 12,731 feet below sea level.
The corresponding integer is?
please help
Answer:
-12,731
Step-by-step explanation:
You want to know what integer would be used to represent the value 12,731 feet below sea level.
Signed valuesUsually we measure elevation up from sea level. So, distances below sea level are usually represented with negative numbers. The integer corresponding to 12,731 feet below sea level would be ...
-12,731 . . . . feet
an adventurous dog strays from home, runs five blocks east, four blocks north, five blocks east, two blocks north, and three blocks west. assuming that each block is about 100 m, how far (in m) from home and in what direction (in degrees counterclockwise from the east axis) is the dog? use a graphical method.
The distance between the Dog from the Home is 360.55 m and the direction of the Dog from Home is North-East.
In the inquiry,
The daring dog begins, let's say, at O.
He walks 300 meters east by 3 blocks.
then,
200 m / 2 blocks north
100 m East of 1 block
Block North = 100 meters.
200 m = 2 blocks west
So,
the separation between the Dog's initial location and ending position.
OE is supplied by,
By using Pythagoras' theorem to triangle OLE,
OE²=OL²+LE²
OE²=200²+300²
OE²=40000+90000
OE=360.55m
Therefore, the distance of the Dog from the Home is 360.55 m and the direction of the Dog from Home is North-East.
Know more about Pythagoras' theorem
https://brainly.com/question/343682
#SPJ4
Drag numbers to complete a function in terms of x and y for the line that contains the points (2, 4) and (6, 16). Numbers may be used once, more than once, or not at all. 12346 y = x –
The function in terms of x and y for the line that contains the points (2, 4) and (6, 16) would be; y=3x-2
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
The slope of the line is calculated as follows:
m = Δy/Δx
Given that the line that passes through the points (2, 4) and (6, 16)
To find the function of the line that passes through points (2, 4) and (6, 16)
Therefore, the slope of the line is;
m = Δy/Δx
m = 3
The equation is;
y = mx + c
y = 3x - 2
To know more about the Slope of the line here;
brainly.com/question/14511992
#SPJ1
the 1x8 vector resulting from multiplying each entry of x by 4. do this in one line! store the result as x4.
The 1x8 vector resulting from multiplying each entry of x by 4.x4 = [4*x1, 4*x2, 4*x3, 4*x4, 4*x5, 4*x6, 4*x7, 4*x8]
For example, if x = [1, 2, 3, 4, 5, 6, 7, 8], x4 would be [4, 8, 12, 16, 20, 24, 28, 32]. This can be represented mathematically as x4 = [4x1, 4x2, 4x3, 4x4, 4x5, 4x6, 4x7, 4x8] which is the same as 4*x = [4x1, 4x2, 4x3, 4x4, 4x5, 4x6, 4x7, 4x8]. By multiplying each entry of x by 4, we can create a new vector x4 with every entry multiplied by 4.Multiplying each entry of a 1x8 vector x by 4 can be expressed as multiplying the vector by the scalar 4, resulting in a 1x8 vector x4. For example, if x = [1, 2, 3, 4, 5, 6, 7, 8], then x4 = [4, 8, 12, 16, 20, 24, 28, 32].
Learn more about vector here:
https://brainly.com/question/29740341
#SPJ4
The graph of an absolute value function f(x) = a|x| includes the point (1, 12). Complete the following statements.
The value of a is 12. Therefore, the equation of the function is f(x) = 12|x|.
What is a function's absolute value?In algebra, an objective function function is one where the variables is inside the bars denoting absolute values. The absolute value is also referred to as the modulus function, and its most popular representation is f(x) = |x|, wherein x is a real number.
How can I solve a function using absolute values?Finding x values that turn the equation inside the exact amount positive or negative into a constant is how absolute value equations are solved. Plot two for the negative and positive cases that intersect at the expression's 0 to graph exact value functions.
To find the value of a, we can use the point (1, 12) to set up the equation:
a = 12/|1| = 12
To know more about absolute value function visit:
https://brainly.com/question/10664936
#SPJ1
The value of x that makes the equation true is ____
The value of x that makes the equation true is 12°. The solution has been obtained using angle sum property of triangle.
What is Angle Sum Property?
The Angle Sum Property states that the sum of the measures of the angles of a triangle is 180°. This means that if you add up all three angles of a triangle, the total measure will be 180°. This property is true for all triangles, regardless of the size or shape. It is one of the most important properties in geometry and is used to solve problems involving angles in triangles.
We are given two angles as (2x)° and (5x+18)°
Also, we are given two sides of the triangle are same.
This means that the angles opposite to the sides are also same.
Thus, the angles of the triangle are (2x)°, (5x+18)° and (5x+18)°
Using angle sum property,
⇒ (2x)° + (5x+18)° + (5x+18)° = 180°
⇒ (2x)° + 2 * (5x+18)° = 180°
⇒ (2x)° + (10x+36)° = 180°
⇒ (12x + 36)° = 180°
⇒ (12x)° = 144°
⇒ x = 12°
Hence, the value of x that makes the equation true is 12°.
Learn more about angle sum property from the given link
brainly.com/question/22262639
#SPJ1
Use a graphing calculator to graph f(x)=-x^3+3x²-2 and find the following features of the graph. Round answers to the nearest hundredth, if necessary.
The x-intercepts of this graph from least to greatest are x = -0.73, x = 1, and x = 2.73.
The local minimum of this graph is (0, -2).
The local maximum of this graph is (2, 2).
The intervals on which the function is decreasing are x < -0.73 and x > 1.
The intervals on which the function is increasing are 1 < x < 2.73.
What is the local minimum of a graph?The local minimum of a graph can be defined as the point on the graph of a function where it changes from a decreasing function to an increasing function, which is given by this ordered pair (0, -2).
Conversely, the local maximum of a graph can be defined as the point on the graph of a function where it changes from an increasing function to a decreasing function, which is given by this ordered pair (2, 2).
For any given function, y = f(x), if the output value is decreasing when the input value is increased, then, the function is referred to as a decreasing function.
In conclusion, we would use an online graphing calculator to plot the given function f(x) = x³ + 3x² - 2 in order to determine its key features.
Read more on function here: brainly.com/question/3990145
#SPJ1
What is the Domain:x > 3 , -3 ≤ x ≤ 3, all real numbers
The domain and the range of y = 12x - 36 are the set of all real numbers
How to determine the domain and the range?From the question, we have the following parameters that can be used in our computation:
y = 12x - 36
There is no restriction on the input values, x
So, the domain of y = 12x - 35 is all real numbers, since there is no restriction on the input (x).
The range of y = 12x - 35 is also all real numbers, since the output (y) can be any real value, depending on the input (x).
This can be seen by considering that for any real number x, the output y = 12x - 35 will also be a real number.
Read more about domain and range at
brainly.com/question/2264373
#SPJ1
Complete question
What is the Domain of y = 12x - 36
x > 3 ,
-3 ≤ x ≤ 3,
all real numbers
Also, determine the range
The equation p=t/3 is used to calculate the individual profit,p, made by each of three brothers operating a lemonade stand with total profit, t
The total profit as the subject of formula is t = 3p
How to make the total profit the subject of formulaFrom the question, we have the following parameters that can be used in our computation:
p = t/3
Where
Individual Profit = p
total profit = t
Recall that, we have
p = t/3
Multiply both side of the equation by 3
So, we have
3p = t
Rewrite as
t = 3p
Hence, the solution is t = 3p
Read more about subject of formula at
https://brainly.com/question/657646
#SPJ1
Complete question
The equation p=t/3 is used to calculate the individual profit,p, made by each of three brothers operating a lemonade stand with total profit, t
make t the subject
A graphing calculator is recommended. Use technology to find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. (Round your answers to five decimal places.) y = e−x2, y = 0, x = −5, x = 5. a) about x-axis. b) about y= - 1
The volume of the solid obtained by rotating the region bounded by the given curves about the specified line about x-axis is 3.93740 and y=-1 is 5.0740
We have to find the volume of given curve about x-axis
we have [tex]$\mathrm{y}=\mathrm{e}-\mathrm{x}^2,[/tex] y=0, x=-5, x=5
(a).
The volume of solid of revolution about the x-axis using disk method is evaluated as:
The disk method is the process of finding the volume of an object by dividing that object into many small cylinders/disks and then adding the volumes of these small disks together.Volume V=[tex]\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2 \mathrm{dx}$[/tex]
[tex]$$\begin{aligned}& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{x=5}\left(\mathrm{e}^{-\mathrm{x}^2}\right)^2 \mathrm{dx} \\& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{x=5} \mathrm{e}^{-2 \mathrm{x}^2} \mathrm{dx} \\& \mathrm{V}=\pi \sqrt{\frac{\pi}{2}}=3.93740 .\end{aligned}$$[/tex]
V=3.93740
we use the formula
[tex]$$\int_{-\mathrm{n}}^{\mathrm{n}} \mathrm{e}^{-\mathrm{a} \mathrm{x}^2} \mathrm{dx}=\frac{\sqrt{\pi} erf \sqrt{a} n }{\sqrt{a} }[/tex](b). The volume of solid of revolution about the y= - using washer method is:
This particular shape is called a washer, or a disk. This shape is obtained by rotating two functions around the x-axis or the y-axis. To find the volume of this shape, create slices of the shape and subtract the missing middle space after finding the total volume. This method is called the washer method.[tex]$$\begin{aligned}& \text { volume } \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2-{ }^2 \mathrm{dx} \\& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2 \quad 2 \mathrm{y}-{ }^2 \mathrm{dx} \\& \mathrm{V}=\pi \int_{\mathrm{x}=-5}^{\mathrm{x}=5} \mathrm{y}^2 2 \mathrm{ydx} \\& \mathrm{V}=\pi \int_{-5}^5 \mathrm{e}^{-2 \mathrm{x}^2} 2 \mathrm{e}^{-\mathrm{x}^2} \mathrm{dx} \\& \mathrm{V}=\pi \sqrt{\frac{\pi}{2}} .77245 \\& \mathrm{~V}=5.0740\end{aligned}$$[/tex]
Therefore, the The volume of solid of revolution about the y= - using washer method is 5.0740
For more such questions on disk method
https://brainly.com/question/28184352
#SPJ4
Solve for x. *
A. 180
B. 50
C. 130
D. 138
Answer: c) 130
Step-by-step explanation:
x+8+42=180
x=180-50
x=130