It follows that continuity at infinity is provided by having the same limit while approaching it from either side, i.e., the limit towards + and, which makes sense based on your understanding.
When a function can be extended to P1, it is said to be "continuous at infinity" (R).
What is the limit?Calculus's idea of the limit describes how a function behaves as its input gets closer to a particular value. As long as the limit is present, the value that f(x) approaches as x moves closer to c is represented by the notation lim(x -> c) f(x), which stands for the limit of a function at the point x = c.
You must demonstrate that all three of the following conditions are true in order to prove that a function f is continuous on an interval:
Every point in the interval has f specified, and the interval has f's bound.
For each and every > 0, there is a corresponding > 0 such that |x - c| implies |f(x) - f(c)| for all x and all c in the interval.
F is considered to be continuous on the interval if these requirements are met.
To learn more about Limit, Visit
brainly.com/question/282767
#SPJ4
density dependent population growth in scetion 5.9, we introduced a model for population growth. our model predicts that a population of organisms will grow according to the differential equation:
In nature, there are various constraints on population number and expansion. Some are depending on the density, whereas others are not.
A population's per capita growth rate changes—typically declines—with rising population density due to density-dependent limiting constraints. One illustration is how individuals in a group compete for scarce food.
Independent of population density, several factors impact the per capita growth rate. Natural catastrophes like forest fires are examples.
Diverse limiting variables can combine in intricate ways to generate different patterns of population expansion. Some populations exhibit cyclical oscillations, where the population size varies cycle by cycle in a predictable manner.
To know more about equations visit: brainly.com/question/10413253
#SPJ4
how many ways are there to select 10 countries in the united nations to serve on a council if 3 is selected from a block of 52, 1 are selected from a block of 62 and 6 are selected from the remaining 75 countries?
There are 12,804,280,000 ways to select 10 countries in the United Nations to serve on a council.
UN Council Country SelectionThe number of ways to select 3 countries from a block of 52 is given by the combination formula:
C(52, 3) = 52! / (3! * (52 - 3)!) = 19600.The number of ways to select 1 country from a block of 62 is given by:C(62, 1) = 62.
The number of ways to select 6 countries from the remaining 75 countries is given by:C(75, 6) = 75! / (6! * (75 - 6)!) = 178,365.
Finally, to find the number of ways to select 10 countries in total, we multiply the number of ways to select 3, 1, and 6 countries:
19600 * 62 * 178365 = 12,804,280,000.
So there are 12,804,280,000 ways to select 10 countries in the United Nations to serve on a council.
Learn more about UN Council Country Selection here:
https://brainly.com/question/28098328
#SPJ4
what are the x-intercepts for the graph below?
Answer:
C. (-5,0) ( -2, 0)
Step-by-step explanation:
The X-intercept is when the y = 0
We see the x-intercept on the graph is located at (-5,0) and (-2,0), so the answer is C.
Which of the following notations correctly describe the end behavior of the
polynomial graphed below?
Answer:
dfgss sdffcfsgdbebgndnngsageqfetehashqrvdqhqdhtqi
Anika is on the crew to set up rides for the state fair. The crew does most of the setup on the day that the fair arrives at the fairground and then continues to work on finishing the setup for about a week to have the rides ready to go in time for the opening of the fair. The scatter plot shows Anika's setup time on different days and the linear model for the data.
(a) What is the equation of the line, written in slope-intercept form? Show how you determined the equation.
(b) Anika arrived on Day 0. Based on the linear model you created in Part A, predict how long Anika worked on Day 0.
(c) Approximately how much did her setup time decrease per day?
a) The linear function for this problem is defined as follows: y = -0.75x + 20.
b) The time that he worked on Day 0 is given as follows: 20 hours.
c) The daily decrease in the setup time is given as follows: 0.75 hours a day.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change of the output variable relative to the input variable.The intercept b represents the value of y when the graph of the function touches of crosses the y-axis.Two points from the graph are given as follows:
(8, 14) and (16,8).
When x increases by 8, y decays by 6, hence the slope m is given as follows:
m = -6/8
m = -0.75.
Hence:
y = -0.75x + b.
When x = 8, y = 14, hence the intercept b is given as follows:
14 = -0.75(8) + b
b = 14 + 0.75(8)
b = 20.
Hence the function is defined as follows:
y = -0.75x + 20.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
how many elements are in the set {7, 7, 7, 7}?
The set {7, 7, 7, 7} have only one element because we can write that set as {7}.
The empty set and the original set itself are included in the power set, which is a set that contains all other subsets as well. P is typically used to indicate it. The number of subsets that can be generated from a given set determines the cardinality of a power set.
In set theory, the set of all subsets of a Set A, including the Set itself and the null or empty set, is referred to as the power set (or power set). The Power Set of the given set will consist of 2n elements if the given set has n elements. It also symbolizes the power set's cardinality.
The set is {7, 7, 7, 7}.
We can write this set as {7}. So the element of set {7, 7, 7, 7} has one element only.
To learn more about set link is here
brainly.com/question/8053622
#SPJ4
I need help with this, can’t figure out the mistake. Basically just show me the mistake then I can take it from there.
Answer: They needed to find the hypotenuse of the triangle not the sum of the legs.
Step-by-step explanation:
use the multiplier method to increase £88 by 14 %
you must show ur workings
Please help meeeee !!!!!long division step by step
Answer:
25 r12
Step-by-step explanation:
first, u ask yourself how many times can 30 go in 7, well it can't so you do 30 can go in 76, 2 times because. 30x2 is 60 and it doesn't go over 76.
30x2 is 60 so on the first box u put 2. Then u multiply again 30x2 which is 60 so u put the 60 on the box below the 76. U subtract
Next, you would subtract it which would turn out to be 16. Since 16 can't go in 30 equally, u would drop down the 2 in the 762 now you can do 30 into 162 which is 5 times bc 30x5 is 150 and doesn't go over so u put the 5 in the box next to the 2.
30x5 is 150, u put that in the box below 162. Then u subtract 162-150 which is 12. So you have a remainder of 12.
how many planes are orthogonal to a given plane in space? explain.
There are an infinite number of planes that are orthogonal to a given plane in space, and this is due to the fact that a plane can be thought of as a flat surface that extends indefinitely in all directions.
Orthogonal Planes in Space: In three-dimensional space, a plane is said to be orthogonal to another plane if the two planes are perpendicular to each other, i.e., their normal vectors are perpendicular. Since the normal vectors of two orthogonal planes are perpendicular to each other, this means that the angle between them is equal to 90 degrees.
Given a plane in space, there are an infinite number of planes that are orthogonal to it. This is because a plane can be thought of as a flat surface that extends indefinitely in all directions.
Here you can learn more about Orthogonal Planes
https://brainly.com/question/13908858#
#SPJ11
The figure below is dilated by a factor of 3 3 centered at the origin. Plot the resulting image.
The image of the transformation is R' (-12, 3), S' (-12, 12) and T' (-6, 3)
How to determine the image of the transformation?The complete question is added as an attachment
The coordinates of the triangle are given as
R = (-4, 1)
S = (-4, 4)
T = (-2, 1)
The transformation is given as
Dilation by a scale factor of 3
Centered at the origin
The rule of the transformations is
(x, y) = 3(x, y)
So, we have
R' = 3 * (-4, 1) = (-12, 3)
S' = 3 * (-4, 4) = (-12, 12)
T' = 3 * (-2, 1)= (-6, 3)
Hence, the image of the transformation is R' (-12, 3), S' (-12, 12) and T' (-6, 3)
Learn more about image of transformation on https://brainly.com/question/11709244
#SPJ1
There are five consecutive odd integers. The sum of the three last integers is 3 more than the sum of the two greatest.
Step-by-step explanation:
x
x+2
x+4
x+6
x+8
these are the 5 consecutive odd integers.
when starting with an odd number as x, with every added 2 we get again an odd number.
the sum of the last 3 integers is 3 more than the sum of the 2 greatest :
x+4 + x+6 + x+8 = x+6 + x+8 + 3
we can subtract (x+6) abd (x+8) from both sides :
x + 4 = 3
x = -1
so, the 5 numbers are
-1
1
3
5
7
3 + 5 + 7 = 15
5 + 7 + 3 = 15
correct.
Determine if the triangles are similar by side-side-side similarity
9) △MST is not similar to △DJZ
10) △ARP is not similar to △TRY.
11) △XYZ is not similar to △RVW
12) △ADE is not similar to △ABC.
What are similar triangles?
Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.
"If in two triangles, sides of one triangle are proportional to (i.e., in the same ratio of) the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similar," states the Side-Side-Side (SSS) criterion.
The length of the sides of △MST are 16, 12, 5.
The length of the sides of △DJZ are 10, 7, 3
The ratio of sides is
16/10 ≠ 12/7 ≠ 5/3.
The length of the sides of △ARP are 15, 12, 5.
The length of the sides of △TRY are 54, 43.2, 18
The ratio of sides is
15/54 ≠ 12/43.2 ≠ 5/18.
The length of the sides of △XYZ are 17, 15, 8
The length of the sides of △RVW are 30.6, 27,4
The ratio of sides is
30.6/17 ≠ 27/15 ≠ 4/8.
The length of the sides of △ABC are 9, 8, 6.
The length of the sides of △ADE are 24, 12+8 = 20, 9+6=15
The ratio of sides is
24/9 ≠ 20/8 ≠ 15/6.
To learn more about similarity,click on the below link:
https://brainly.com/question/26407472
#SPJ1
question in image
answer choices
y= -3x + 2
y= -1/3x + 15
y = -1/3x + 2
y= -3x + 15
The correct line of best fit is y = -1/3x + 2. Option C
What is the line of best fit?A line of best fit is a line that is used to approximate the underlying pattern or relationship between two variables in a scatterplot. The line of best fit is drawn so that the number of points above the line and below the line are approximately equal (and the line passes through as many points as possible).
The line of best fit is used to make predictions about the response variable based on the predictor variable, and to understand the strength and direction of the relationship between two variables.
Learn more about line of best fit:https://brainly.com/question/14279419
#SPJ1
a town's population has been growing linearly. in 2003 the population was 21,000. the population has been growing by 1700 people each year. write an equation for the population, p, years after 2003.
An equation for the population, p, years after 2003 is 45000 + 1700t .
What is an equation for the population?The population of a town has been increasing linearly. The population was 21,000 in 2003. 1700 persons have been added to the population annually.
Locate the necessary equation:
An equation for the population, p, years after 2003.
Given: Population in 2003 was 45,000.
Additionally, annual population growth equals 1,700.
After t years, the population will expand by 1,700t because it has been rising linearly.
Population t years later = 45000 + 1700t, then.
P(t) = 45000 + 1700t is the needed equation as a result.
An equation for the population, p, years after 2003 is 45000 + 1700t .
To learn more about linearly refer to:
https://brainly.com/question/26310043
#SPJ4
35 POINTS AND BRAINLIEST
A zoologist recorded the speed of two cheetahs. Cheetah A ran 18 miles in 16 minutes. Cheetah B ran 54 miles in 50 minutes. Which statement is correct?
Cheetah A has a higher ratio of miles per minute than Cheetah B because 18 over 16 is greater than 54 over 50.
Cheetah A has a higher ratio of miles per minute than Cheetah B because 18 over 16 is less than 54 over 50.
Cheetah B has a higher ratio of miles per minute than Cheetah A because 18 over 16 is greater than 54 over 50.
Both cheetahs have the same ratio of miles per minute.
The sum of a two digit number is 11 if the digits at the tens place is increased by 5 and the digit at the once place decreased by 5. Then this number is found to be twice the Orginal two digit number when reversed. Find the number
The two digit number is 38.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Le x be the number at the ten's place and y be the number at the unit's place.
So, the number is 10x+y
The sum of digits of a two-digit number is 11.
That is, x+y=11 -------(i)
If the digit at tens place is increase by 5 and the digit at unit place is decreased by 5, the digits of the number are found to be reversed.
10(x+5(y-5)=10y+x
9x-9y=-45
x-y=-5 -------(ii)
Add equation (i) and (ii), we get
2x=6
x=3
Substitute x=3 in equation (i), we get
y=8
So, the number is 38
Therefore, the two digit number is 38.
To learn more about the linear system of an equations visit:
https://brainly.com/question/27664510.
#SPJ1
To graph the function f, we plot the points x, f(x) Correct: Your answer is correct. in a coordinate plane. To graph f(x) = x2 − 5, we plot the following points. (x, 0) (x, x − 3) (x, 2x) (x, 1) (x, x2 − 5) So the point 3, is on the graph of f. The height of the graph of f above the x-axis when x = 3 is Complete the table. x f(x) = x2 − 5 (x, y) −2 −1 0 1 2 0
The complete table for the function f(x)=x^2-2 is given below.
What is a function?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).
There are several types of functions in math. Some important types are:
Injective function or One to one function: When there is mapping for a range for each domain between two sets.
Surjective functions or Onto function: When there is more than one element mapped from domain to range.
Polynomial function: The function which consists of polynomials.
Inverse Functions: The function which can invert another function.
Now,
Given
f(x)=x^2-2
The table will be filled as
x f(x) =x^2-2 (x,y)
-2 2 (-2,2)
-1 -1 (-1,-1)
0 -2 (0,-2)
1 -1 (1,-1)
2 2 (2,2)
To know more about functions visit the link
https://brainly.com/question/12431044?referrer=searchResults
#SPJ4
Right question is in image.
find all values of for which this approximation is within of the right answer. assume for simplicity that we limit ourselves to .
The range of the values of x is
|x| [tex]\leq[/tex] 0.5304 [tex]\leq[/tex] 1
Now, According to the question:
Let us consider the polynomial function as f(x) . Hence we need to find
[tex]T_5(x)[/tex] he formula for the Taylor series is:
[tex]T_n(x) =[/tex] Σ[tex]\left \{ {{n} \atop {j=0}} \right.}[/tex] [tex]\frac{f^(^f^)(a)}{f!}[/tex]
Suppose n =5, a=0 then
[tex]T_5 (x)= \frac{f(0)}{0!}(x -0)^0 + \frac{f'(0)}{1!}(x -0)^1+ \frac{f"(0)}{2!}(x -0)^2+...+ \frac{f^(^5^)(0)}{5!}(x -0)^5[/tex]
[tex]T_5(x)=\frac{f(0)}{0!}+ \frac{f'(0)}{1!}x+\frac{f"(0)}{2!}x^{2} + \frac{f"'(0)}{3!}x^3+\frac{f""(0)}{4!}x^4+\frac{f^(^5^)(0)}{5!}x^5[/tex]
From the data:
f(x) = cos x => f(0) = cos(0) = 1
f'(x) = -sin x => f'(0) = -sin(0) = 0
f"(x) = -cos x => f"(0) = -cos(0) = -1
f"'(x) = sin x => f'"(0) = sin(0) = 0
f""(x) = cos x => f""(0) = cos0 = 1
f""'(x) = -sin x => f""'(0) = -sin(0) = 0
Substitute this data in the Taylor series:
[tex]T_5(x)=\frac{f(0)}{0!}+ \frac{f'(0)}{1!}x+\frac{f"(0)}{2!}x^{2} + \frac{f"'(0)}{3!}x^3+\frac{f""(0)}{4!}x^4+\frac{f^(^5^)(0)}{5!}x^5[/tex]
[tex]T_5(x) =\frac{1}{0!}+\frac{0}{1!}x+\frac{(-1)}{2!}x^{2} + \frac{0}{3!}x^3+\frac{1}{4!}x^4+\frac{(0)}{5!}x^5[/tex]
[tex]T_5(x) = 1 - \frac{1}{2!}x^{2} +\frac{1}{4!}x^4[/tex]
Now, the remainder of the Taylor series is Taylor series satisfies the following inequality.
[tex]|R_n(x)|\leq \frac{M}{(n +1)^1^!} (x-a)^n^+^1for|x+a|\leq d,here|f^(^n^+^1^)(x)|\leq M\\\\|x|\leq 1,a=0,n=5= > |f^(^6^)(x)|\leq 1[/tex]
Given that the approximation should be within 0.003712
Then,
[tex]\frac{1}{(6)}|x|^6\leq 0.003712\\ \\= > \frac{1}{(6)}|x|^6\leq 0.003712\\ \\= > |x|^6\leq (0.003712)^6\\\\= > |x|^6\leq 0.022272\\\\|x|\leq (0.022272)^\frac{1}{6}\\ \\|x|\leq 0.5304[/tex]
Hence, the range of the values of x is
|x| [tex]\leq[/tex] 0.5304 [tex]\leq[/tex] 1
Learn more about Taylor Series at:
https://brainly.com/question/29733106
#SPJ4
The given question is incomplete , complete question is :
Find [tex]T_5(x)[/tex], the degree 5 Taylor polynomial of the function f(x) = cos(x) at
a = 0.
Find all values of x for which this approximation is within 0.003712 of the right answer. Assume for simplicity that we limit ourselves to |x| [tex]\leq[/tex] 1
6.1/3.9 = 2.8x/x+8.1
solve for x
Answer:
0.89
Step-by-step explanation:
6.1/3.9=28/10x/x+81/10
61/39=28x(x)/10+8.1
61/39-81/10=28x(x)/10
610/390_3159/390=28x(x)/10
2469/390=28x(x)/10
2469/390=14/5x(x)
2.51=14/5x
12.55=14x
x=0.89
A computer coat $800 it loe 1/5 of it value every year after it’ purchaed complete the table after how many year will the computer be worth le than $100 _____ year write an equation repreenting the value v of the computer t year after it wa purchaed
The equation that represent the value of the computer in years is: computer cost at (n-1) year - 1/5 (n-1cost) and the computer be worth less than $100 at 10 year
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
According to the data problem,
The cost of computer = $ 800
It lost 1/5 of value every year.
The value of computer after 0 years = cost of computer = $ 800
The value after 1 year = 800 - (1/5*800) = $640
The value after 2 years = 640 - (1/5*640) = $512
The value after 3 years = 512- (1/5*512) = $409.6
Continue with the formula we have:
The value after 9 years = 134.21 - (1/5*134.21) = 107.37
The value after 10 years = 107.37 - (1/5*107.37) = 85.90
The value after n years = computer cost at (n-1) year - 1/5 (n-1cost)
Learn more about algebraic operations at: brainly.com/question/3927786
#SPJ4
A man has $215,000 invested in three properties. One earns 12%, one 10% and one 8%. His annual income from the properties is $20,600 and the amount invested at 8% is twice that invested at 12%.
Annual income = 45000 the amount invested at 8% is twice that invested at 12%. 12% property $45000 × 0.12 = 5400
10% property $8000
8% property $7200
What is annual income?The entire amount of money you make during the course of a year is your yearly income, in contrast. Along with your wage, this sum also includes earnings from other sources, such as interest on savings or rent from a home you own. Bonuses and overtime pay are other possible components of your yearly revenue.
let, x in 12%
so, 2x in 8%
and 21,5000 - 3x in 10%
so, annual income = 2x × 0.08 + ( 215000 -3x) × 0.10 + x × 0.12= 20,600
=> x = 45000
so, 2x = 90000
so, 215000 - 3x = 80000
so,
12% property $ 45000
10% property $80000
8% property $90000
b)
12% property $45000 × 0.12 = 5400
10% property $8000
8% property $7200
To know more about annual income visit:-
brainly.com/question/28352034
#SPJ4
Use the fact that
sin
38
°
≈
0
.
6157
sin
38
°
≈
0
.
6157
to solve for
m
.
m
.
cos
m
°
≈
0
.
6157
Answer:
Below
Step-by-step explanation:
Remember the trig identity sin^2 + cos^2 = 1
.6157^2 + cos ^2 = 1
cos^2 = 1 - .6157^2
cos^2 = .6209
cos = ~ ± .7879
The graph of the line m is shown.use the similar slope triangles to compare the slope of segment RT and TV
Note that from the graph given above and their slopes, it is correct to state that mRT = mTV.
What is the justification for the above assertion?First, note that the slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line.
Here, Slope RT = Δy/Δx = SR/ST = 2/4 = 1/2
Slope TV = Δy/Δx = UT/UV = 1/2
Thus, since the Slope of RT = 1/2 and the Slope of TV = 1/2 it i correct to state that mRT = mTV.
Learn more about Slopes:
https://brainly.com/question/3605446
#SPJ1
Answe pleaseeeee I really need help will give points
The circle has a radius of 15 and is centered at (-2,4).
What are the equations for circles?The general equation of a circle is [tex](x - h)^{2} + (y - k)^{2} = r^2[/tex], where (h, k) denotes the position of the circle's center and r is the radius.
What do H and K represent when they are encircled?The equation for a circle is [tex](x - h)^{2} + (y - k)^{2} = r^2[/tex], where (h, k) stands for the coordinates of the circle's center and r for the radius. A circle touches the x-axis if it is tangent to it at the coordinates (3, 0).
Equation for a circle is[tex](x+2)^2 + (y-4)=225[/tex]
(-2,4) = represents the location of the circle's center.
[tex]r^2=(15)^2[/tex]
r = 15 = its radius
To know more about circle visit:-
brainly.com/question/25469568
#SPJ1
A wire of length 66cm i bent into the hape of a circle. Find it area. If it i bent into the hape of a quare,what will be it area ?which figure encloe _________take π=22\7
The area of the circle is 346.5 cm² while the area of the square is 272.25 cm². The figure that encloses more area is the circle.
If a wire of length 66cm is bent into the shape of a circle and square, then this length will be its circumference and perimeter, respectively.
C = 66cm = 2πr
r = 10.5 cm
P = 4s = 66cm
s = 16.5 cm
The area of the circle is given by the formula
A = πr²
A = π(10.5 cm)²
A = 346.5 cm²
So, the area of the circle is 346.5 cm².
The area of the square is given by the formula
A = s²
A = (16.5 cm)²
A = 272.25 cm²
So, the area of the square is 272.25 cm².
Therefore, the figure that encloses the greater area is the circle.
The problem seems unreadable, it must have been...
"a wire of length 66 cm is bent into the shape of a circle. find its area. if the same wire is bent into the shape of a square, what will be its area? which figure enclose more area, the circle or the square? take π = 22/7."
Learn more about area here: https://brainly.com/question/25292087
#SPJ4
James lives 4.32 km from school. Megan lives 0.96 km from school. The distance James lives from school is how many times as long as the distance Megan lives from school? The distance James lives from school is ____ times, as long as the distance Megan lives from school
Answer:
4.5
Step-by-step explanation:
Distance that James has to travel = 4.32 km
Distance that Megan has to travel = 0.96 km
How many times as long
==> 4.32/0.96 = 4.5
Therefore,
The distance James lives from school is 4.5 times, as long as the distance Megan lives from school
4.5 is the answer which goes into the blank
Ruby’s model for a Fourth of July party hat is shown. The model is composed of a rectangle and 2 right triangles. What is the area of Ruby’s model for a Fourth of July party hat?
Total area of Ruby’s model for a Fourth of July party hat is 182.75 square centimeter.
What is Area of Rectangle?The area of Rectangle is length times of width.
Let us find the area of the red colour right triangle.
Area of red triangle=1/2×13.5×9
=60.75 square cm.
Area of blue triangle=1/2×8×9
=36 square cm.
Area of rectangle=Length×breadth
=(13.5+8)4
=21.5×4
=86 square cm.
The total area of Ruby’s model for a Fourth of July party hat is
60.75+36+86
182.75 square centimeter.
Hence, total area of Ruby’s model for a Fourth of July party hat is 182.75 square centimeter.
To learn more on Area of Rectangle click:
https://brainly.com/question/20693059
#SPJ1
2^5 - x = 1/16/Solve for x
The value of x is -0.03125 or - 1/32.
Solving equations involves finding the value of the unknown variables in the given equation. The condition that the two expressions are equal is satisfied by the value of the variable. Solving a linear equation in one variable results in a unique solution, solving a linear equation involving two variables gives two results.
Solving equations is computing the value of the unknown variable still balancing the equation on both sides. An equation is a condition on a variable such that two expressions in the variable have equal value.
[tex]2^{-5} - x = \frac{1}{16}[/tex]
[tex]x =2^{-5} - \frac{1}{16}[/tex]
[tex]x = \frac{1}{2^{5} } - \frac{1}{16}[/tex]
[tex]x = \frac{1}{32} } - \frac{1}{16}[/tex]
x = (16 - 32) / (16 x 32)
x = -16 / 512
x = -0.03125
0r
x = [tex]-\frac{1}{32}[/tex]
Therefore, the value of x is -0.03125 or - 1/32.
To learn more about equation solving visit : brainly.com/question/19297665
#SPJ4
What is the general equation of a plane?
Answer: a (x – x1) + b (y– y1) + c (z –z1) = 0.
Step-by-step explanation:
Recall that the general form of the equation of a straight line in two dimensions is
++=0.
This can also be written in the form
=+, where is the gradient and is the -intercept, which we can determine by knowing two points on the line.
If (,) is a point that lies on the line, we can determine from the general form as =−(+); thus, the equation of the line can be written as
+−(+)=0.
The equation of the line can also be realized as a dot product of two vectors as (,)⋅(−,−)=0.
Now, if we define the position vectors,⃑=(,),⃑
then the equation of the line can be written in vector form as⃑ ⋅⃑=⃑⋅⃑,where ⃑=(,) is called a normal vector of the line and ⃑−⃑ will lie completely on the line.
A property of the dot product states that two vectors are perpendicular to each other if their dot product is zero. This equation of the line in vector form shows that the normal vector ⃑ and the vector ⃑−⃑ are perpendicular to each other by this property.
The general equation of a plane in three-dimensional space can be represented as Ax + By + Cz = D.
What is the plane?
A plane is a two-dimensional doubly ruled surface spanned by two linearly independent vectors. The generalization of the plane to higher dimensions is called a hyperplane. The angle between two intersecting planes is known as the dihedral angle.
Where A, B, and C are coefficients and D is a constant.
The coefficients A, B, and C represent the components of the normal vector to the plane, and D represents the distance of the plane from the origin.
The equation defines a set of all points (x, y, z) in space that satisfy the equation and lie on the plane.
Hence, The general equation of a plane in three-dimensional space can be represented as Ax + By + Cz = D.
To learn more about the plane visit,
https://brainly.com/question/12227980
#SPJ4