For dy/dt = (1 + t^2)/ (3y - y^2), the hypotheses of Theorem 2.4.2 are satisfied, and a unique solution exists in some interval around the initial point if y ≠ 0 and y ≠ 3.
The hypotheses of Theorem 2.4.2 state that for the initial value problem
dy/dt = f(t, y), y(t₀) = y₀
to have a unique solution in some interval t₀ - h < t < t₀ + h within α < t < β, provided that:
f and its partial derivative with respect to y, ∂f/∂y, are continuous in a rectangle α < t < β, γ < y < δ that contains (t₀, y₀).
To determine if the hypotheses are satisfied for the given differential equation we need to check if f and ∂f/∂y are continuous in a rectangle that contains the initial point (t₀, y₀). If they are, then the hypotheses of Theorem 2.4.2 are satisfied, and a unique solution exists in some interval around the initial point.
dy/dt = (1 + t^2)/ (3y - y^2)
dy/ dt = (1 + t^2)/ y(3 - y)
So dy/dt is not continuous at y = 0 and y = 3.
So the hypotheses of Theorem 2.4.2 are satisfied, and a unique solution exists in some interval around the initial point if y ≠ 0 and y ≠ 3.
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A conveyor belt carries bales of hay from the ground to the barn loft 24 ft above the ground. The belt makes a 60 degree angle with the ground. How far does a bale
of hay travel from one end of the conveyor belt to the other. Round your answer to the nearest foot.
Answer = 24 ÷ sin 60 = 27.71281 = 28 ft
given s/a = 4; l/a = 0.20; i/e = 0.10; a = l e and a = 100. find i/s.
The value of i/s is 0.02.
Now, According to the question:
"Information available from the question"
s/a = 4; l/a = 0.20; i/e = 0.10; a = l e and a = 100.
We have to find the i/s
We can first find the value of e, using the equation a = l + e, where l/a = 0.20 and a = 100:
e = a - (l/a) * a = 100 - (0.20 * 100) = 100 - 20 = 80
Next, we can find the value of i using the given information i/e = 0.10:
i = i/e * e = 0.10 * 80 = 8
Finally, we can find the value of i/S using the equation i/S = i / (S/a) * a = 8 / (4 * 100) = 8 / 400 = 0.02.
So, the value of i/S is 0.02.
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If an elephant grows 2 4/5 inches a day, how many inches will it grow in 4 days?
The number of inches will it grow in 4 days is 11.2 inches if If an elephant grows 2 4/5 inches a day
What is a mixed fraction ?
A fraction represented with its quotient and the rest is a mixed fraction. for instance, 2 1/3 is a blended fraction, where 2 is the quotient, 1 is the remainder. So, a combined fraction is a mixture of a whole quantity and a right fraction.
Given ,
If an elephant grows 2 4/5 inches a day,
We have to find how many inches will it grow in 4 days
So, the expression for calculating could be,
let n be number of days.
As it grows 2 4 / 5 = 10+4 / 5 = 14 /5
for n number of days = n * 14 /5
so, put n= 4
that is 4*14/ 5 = 56 / 5 = 11 . 2
Therefore, The number of inches will it grow in 4 days is 11.2 inches if If an elephant grows 2 4/5 inches a day
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Which term of the series 5+9+13+is 85
Answer:
The fourth term in the series 5+9+13+__ is 85. The series follows an arithmetic pattern, where each subsequent term is 4 greater than the previous one. Therefore, the fourth term in the series is 5+9+13+17 = 85.
Tyrants his own landscaping business he earns $30 per hour pulling weeds 25 per our raking leaves and $20 per hour cutting the grass ty want to know how much he earns each week
Tyrant earns a total of $800 per week from his landscaping business.
What is amount?Amount the term used to describe a quantity or size of something will stop it is used to refer to a number of objects items or people as well as the measure of money time distance.
He earns $600 from pulling weeds ($30 per hour for 20 hours), $250 from raking leaves ($25 per hour for 10 hours) and $150 from cutting the grass ($20 per hour for 10 hours). This adds up to a total of $800 per week. By working this amount of hours, Tyrant can make a decent amount of money and still have time to enjoy his life.
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help me with this graph transformation pls
On solving the provided question, we can say that the function is y = f(x) and (7.-6) and (7,3); nm = 3+6//-/7 => m = not defined
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
the function is
y = f(x)
and (7.-6) and (7,3)
m = 3+6//-/7
m = not defined
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A restaurant sells Thai iced teas and flatbread called roti. The scatter plot shows the relationship between the number of Thai iced teas and the number of roti sold each day for two weeks. Which line best fits the data?
A linear trend line is best fits the data.
Which line best fits the data?The theory used in this question is linear regression, which is used to identify the linear relationship between two variables.
By plotting the points from the scatter plot and fitting a line to the data, we can determine the linear trend of the data.
1. Look at the scatter plot and identify the type of data.
In this case, the data is numeric, showing the relationship between two variables: the number of Thai iced teas and the number of roti sold each day.
2. Determine the type of line that best describes the data.
A linear trend line is best for this type of data, as it shows the relationship between the two variables in a straight line.
3. Draw the line. Using the data points from the scatter plot, draw a straight line that passes through as many of the points as possible.
This line is the linear trend line.
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Find the average rate of change of the function over the given intervals.
f(x) = 10x^3 + 10; a) [1,3] b) [-6,6]
a) The average rate of change of the function f(x) = 10x^3 + 10 over the interval [1,3] is ______ (Simply your answer)
The average rate of change of the function f(x) = 10x³ + 10 over the interval [1,3] is 130, and The average rate of change of the function f(x) = 10x³ + 10 over the interval [-6,6] is 360.
The average rate of change of function f over the interval a≤x≤b is given by the expression:
f(b)−f(a)/b−a
It is a calculation of how much the function changed per unit, on average, over that interval.
It is derived from the straight-line slope connecting the interval's endpoints on the function's graph.
a) [1,3]
Here, a = 1, b = 3
⇒f(3)−f(1)/3−1
⇒[10(3)³ + 10] - [10(1)³ + 10]/2
⇒(270 + 10 - 10 - 10)/2
⇒260/2
⇒130
b) [-6,6]
Here, a = -6, b = 6
⇒f(6)−f(-6)/6+6
⇒[10(6)³ + 10] - [10(-6)³ + 10]/12
⇒(2160 + 10 + 2160 - 10)/12
⇒4320/12
⇒360
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Suppose you choose at random a number from the interval
[8,32]
with the following density function:
f(x)= 32256
3
⋅x 2
,8≤x≤32
The probability of the event
E=[10,23]
is
P(E)=
The probability of selecting a number from the interval [10,23] is 3/32256 × (23^2 - 10^2) = 0.7122. Probability of selecting number [10,23] is 0.7122, integrating density function.
The probability of selecting a number from the interval [8,32] is given by the density function f(x)= 3/32256⋅x^2, where 8 ≤ x ≤ 32. We can calculate the probability of the event E=[10,23] by integrating the density function over the interval, i.e. P(E)=∫1023f(x)dx. This can be simplified to P(E)=3/32256 × (23^2 - 10^2), which equals 0.7122. Therefore, the probability of selecting a number from the interval [10,23] is 0.7122. To calculate this, we first determined the probability density function f(x) by noting that the probability of selecting a number between 8 and 32 is 1. We then divided this probability by the size of the interval, giving us the probability density f(x)= 3/32256⋅x^2. This was used to calculate the probability of the event E=[10,23] by integrating the density function over the interval. The integral was simplified to P(E)=3/32256 × (23^2 - 10^2), which equals 0.7122. This is the probability of selecting a number from the interval [10,23].
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Is either x = 8 or x = 10 a solution to 4x<344x<34?  A. Neither is a solution.  B. They are both solutions.
For the inequality expression 4x < 34, x = 8 is a solution.
What is Linear Inequalities?Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.
Given is a linear inequality 4x < 34.
We have to solve the inequality to find the solutions.
Dividing both sides of the inequality by 4,
4x / 4 < 34 / 4
x < 8.5
That is, values of x are below 8.5.
So x = 8 is a solution and x = 10 is not a solution.
Hence x = 8 is a solution for the given inequality.
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how many yards in a foot
A yard is 36 inches or three feet long. The yard is a common way to express distance. A yard measures 3 feet.
Is a yard exactly 3 feet?36 inches or three feet make up a yard. Distances are frequently expressed using the yard. 3 feet make up a yard.
The length is determined by the yard and feet. In both the imperial and US customary systems of measuring, both units are utilized. Three feet make up one yard. The length of three feet is equal to one yard.
The yard to foot conversion factor makes 1 yard equivalent to 3 feet. Use the converter below to change the value of a yard to a foot.
The yard is an English unit of length that is equivalent to 3 feet, or 36 inches, in both the British imperial and US customary systems of measurement. It has been precisely standardized as 0.9144 meters by international agreement since 1959.
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Swathi purchased a bed for $219 and a mattress for $359. How much did she spend on these items in total?
$
Answer:578
Step-by-step explanation:
219+359=578
can someone please help me(10 points will give brainliest!!!)
x=55, if Scura produces and sell 55000 bottles of sunblock.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, Scura makes sun block and their annula revenues depends on how much they sell.
Let x be the quantity of 5 oz. bottles of sun block that they make and sell each year measured in 1000's of bottles.
Thus if x=10 then theu make and sell 10000 bottles of sun block each year. If x=25 then they make and sell 25000 bottles of sun block each year.
a) When x=50
Number of bottles = 50×1000
= 50000
b) Number of bottles are 55000
So, x= Number of bottles/1000
x= 55000/1000
x=55
Therefore, x=55, if Scura produces and sell 55000 bottles of sunblock.
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The angle bisectors of AABC are AV, B, and CV. They meet at a single point V.
(In other words, V is the incenter of AABC.)
Suppose SV = 12, CV= 15, m L SBT=92°, and m ZUAV= 24°
Find the following measures.
Note that the figure is not drawn to scale.
Answer:
m ZUAV = 24°m L SBT = 92°m L SAV = m L SBT / 2 = 92° / 2 = 46°m L CAV = 180° - m L SAV - m ZUAV = 180° - 46° - 24° = 110°m L SCV = m L CAV = 110°m L SVB = 180° - m L SAV - m L SCV = 180° - 46° - 110° = 24°m L CVB = 180° - m L CAV - m L SVB = 180° - 110° - 24° = 46°m L SVT = 180° - m L SBT = 180° - 92° = 88°To find the area of the triangleArea = (1/2) x (12)(15)sin(92)
For this exponential function,
what is the output value (y),
when the input value (x) is O?
y = 2.3x
(0, [?])
Answer:
When the input value (x) is 0, the output value (y) is also 0. In this exponential function, any value raised to the power of 0 equals 1, and 2.3 raised to the power of 0 equals 1, so 2.3x (0) = 2.3 * 1 = 2.3, and the output value is 0.
shawn and brittney rode bikes for the same amount of time. shawn traveled at 10.2 mph and brittney at 13.7 mph. if brittney traveled 8.75 miles further than shawn, how long were they both riding bikes for?
Shawn and Brittney both were riding bikes for 2.5 hours.
As per the given data, Shawn traveled at 10.2 mph and Britney traveled at 13.7 mph.
They traveled for the same amount of time.
Britney traveled 8.75 miles further than Shawn.
Let, Shawn and Britney both traveled for t hours.
Shawn traveled at 10.2 miles per hour.
Therefore for t hours, Shawn traveled is [tex]$(10.2 \times \mathrm{t})$[/tex] miles [tex]$=10.2 \mathrm{t}$[/tex] miles.
Britney traveled at 13.7 miles per hour.
Therefore for t hours, Britney traveled [tex]$(13.7 \times \mathrm{t})$[/tex] miles [tex]$=13.7 \mathrm{t}$[/tex] miles.
Brittney traveled 8.75 miles more than Shawn.
That means the distance between both of them after t hours is 8.75.
Therefore We can write,
13.7 t - 10.2 t = 8.75
3.5 t =8.75
t = [tex]$\frac{8.75}{3.5} \\[/tex]
t = 25
So we have got that they are riding the bikes for 25 hours.
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a disk 2 inches in diameter is thrown at random on a tiled floor, where each tile is a square with sides 4 inches in length. let c be the event that the disk will land entirely on one tile. in order to assign a value to p(c), consider the center of the disk. in what region must the center lie to ensure that the disk lies entirely on one tile?
The probability that the disk will land entirely on one tile is 1/4.
For, this question I have attached an image which shows that the inner red square is the area of a tile in which the centre of the disk could land and the disk would be contained entirely within the tile while the grey area is the area in which the centre of the disk would land and the disk would not be entirely contained within the tile.
Now, The area of a square is the square of side length. The inner square has an area of 2² = 4 and the entire square (red and grey regions combined) has an area of 4² = 16.
Hence, the probability that the disk's centre lands in the red zone is the area of the red zone, divided by the total area, which is
4/16 = 1/4
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$75 invested for 6 months yield simple interest of $2.00. what was the of interest ?
The rate of interest was 5.33%
What Is Simple Interest?Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest. Simple interest relates not just to certain loans. It's also the type of interest that banks pay customers on their savings accounts.
Given here: The amount invested was $75 for 6 months and S.I =$2.0
We know S.I= P×R×T / 100
2.0 =75×r×1/2 /100
r=2×100×2/75
r=400/75
r=5.33%
Hence, The rate of interest was 5.33%
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The sum of the present ages of Mark and his mother is 60 years. In 6 years, she will be twice as old as he will be. Find their present ages,
This question can be solved using 2 variables x and y.
Putting the variables in the equation according to the conditions given would give the value of the variable.
In 6 years time the age of Mark will be 18+6=24 years and his mother will be 42+6=48 years which will be twice of 24.
Let the present age of Mark be x and his mother be y.
Then according to the given conditions.
x+y= 60 ---- equation 1
y+6= 2(x+6)
y+6= 2x+12
y-6= 2x------equation2
From equation 1 the value of y is found to be
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
Answer:
Option A and Option D have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p. The equation can be rewritten as 2.3p – 14.1 = 6.4p – 4 by combining the constants and subtracting 0.01p from both sides.
Miguel bought 8 equally priced pens for $3.84
How much will 15 pens cost?
find the 12 term of the geometric sequence 10 -20 40
Answer:
the answer is 9.6
Step-by-step explanation:
–19k − –16k + 13k + –8k = –20
an someone help please
Given the problem:
–19k − –16k + 13k + –8k = –20
(I'm going to assume that is a minus sign between -19k and -16k)
(Subtracting a negative = add)
Combine all like terms:
2k=-20
Divide both sides by 2:
k=-10
please help like without guessing its important
Because we have two lines non-parallel, the system has only one solution, then the correct option is the fourth one.
Which statement is false?Remember that a system of linear equations:
y = f(x)
y = g(x)
Can have:
No solutions: if the lines are parallel.one solution: if the lines are not parallel.infinite solutions: if the two equations represent the same line.In this case we know that the lines intercept at (4, 5), so the two lines are not parallel, then the system has only one solution.
Then the correct option is the fourth one, because there aren't other points that can be the solution of the system.
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A Ferri Wheel ha a radiu of 16 feet. How far will you travel if you take a ride that goe around 5 time?
Round anwer to the nearet hundredth and for pi ue π=227
If we take a ride that goes around 5 times, we will travel for 502.86 feet. The result is obtained by using the formula for circumference.
How to find circumference?Circumference is the perimeter of a circle. It can be calculated by the following formula.
C = 2πr
Where
C = circumferencer = radius of a circleA Ferri wheel has a radius of 16 feet. If you take a ride that goes around 5 times, determine the distance you traveled!
(Round answer to the nearest hundredth and for pi use π = 22/7)
The shape of the wheel is round (a circle). The distance traveled is the circumference multiplied by the number of rounds.
We have
Radius, r = 16 feetNumber of rounds, n = 5Distance traveled
= C × n
= 2πr × 5
= 2(22/7)(16) × 5
= 502.86 feet
Hence, the distance traveled by the wheel is 502.86 feet.
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a hexagon inscribed in a circle has three consecutive sides, each of length $3$, and three consecutive sides, each of length $5$. the chord of the circle that divides the hexagon into two trapezoids, one with three sides, each of length $3$, and the other with three sides, each of length $5$, has length equal to $m/n$, where $m$ and $n$ are relatively prime positive integers. find $m n$.
The relatively prime positive integers of m+n is 409.
Since ABCD is an isosceles trapezoid
An isosceles trapezoid can be defined as a trapezoid in which non-parallel sides and base angles are of the same measure.
=>∠BAD = ∠ CDA Angles formed by the non parallel sides of an isosceles trapezoid are equal.
Given, AB = BC
Join AC
In ΔABC
∠BCA = ∠BAC Angle formed by the equal sides of and isosceles triangle
with its base are equal.
In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length
AB = BC-CD Arcs formed by same side chords on the circle are equal.
Measure of complete angle is 360 degrees.
=2θ+2θ+2θ+2Φ+2Φ+2Φ
=6θ+6Φ=360
[tex]$$& \widehat{A B}+\widehat{A F}=\widehat{B F}=120 \\[/tex]
∠CDE=120
Join FB
In ΔFAB,
By Law of Cosine:
[tex]$$\begin{aligned}& c^2=a^2+b^2-2 a b \cos C \\& \Rightarrow B F^2=3^2+5^2-2.3 \cdot 5 \cos 120 \\& \Rightarrow B F^2=3^2+5^2-30 \cos 120 \\& \Rightarrow B F^2=9+25-30 \cdot(-0.5) \\& =B F^2=34-30.5 \\& \Rightarrow B F^2=34+15 \\& \Rightarrow B F^2=49 \\& \Rightarrow B F=7\end{aligned}$$[/tex]
Laws of Sine:
⇒[tex]$ & \sin A / a=\sin B / b={Sin} C / c[/tex]
⇒[tex]& \sin \Theta=5 \sqrt{3} / 14 \ \& \sin \Phi=3 \sqrt{3} / 14 \\[/tex]
In ΔAFD,
⇒[tex]& \angle A F D=3 \Phi \ \& \angle A D F=\Theta \\[/tex]
[tex]& \Rightarrow {Sin} \Theta / 5=\sin 3 \Phi / A D \\& \Rightarrow {Sin} \Theta=5 \sqrt{3 /} / 14 \\& \Rightarrow{Sin} 3 \Phi={Sin}(\Phi+2 \Phi) \\& \Rightarrow {Sin} 3 \Phi={Sin} \Phi . {Cos} 2 \Phi+{Cos} \Phi . {Sin} 2 \Phi[/tex]
[tex]& \Rightarrow {Sin} 3 \Phi= {Sin} \Phi \cdot {Cos} 2 \Phi+{Cos} \Phi \cdot {Sin} 2 \Phi \\& \Rightarrow {Sin} 3 \Phi={Sin} \Phi \cdot\left(1-2 \sin ^2 \Phi+2 {Sin} \Phi \cdot \cos ^2 \Phi\right) \\& \left.\Rightarrow {Sin} 3 \Phi={Sin} \Phi \cdot\left(1-2 \sin ^2 \Phi\right)+2\left(1-\sin ^2 \Phi\right)\right) \\& \Rightarrow {Sin} 3 \Phi={Sin} \Phi \cdot\left(3-4 \sin ^2 \Phi\right) \\[/tex]
[tex]& \Rightarrow {Sin} 3 \Phi=3 \sqrt{3} / 14 \cdot(3-27 / 49) \\& \Rightarrow {Sin} 3 \Phi=3 \sqrt{3} / 14 \cdot(120 / 49) \\& \Rightarrow {Sin} 3 \Phi=180 \sqrt{3} / 343[/tex]
Now,
[tex]$$&{Sin} \Theta / 5={Sin} 3 \Phi / A D \\& \Rightarrow A D=5 {Sin} 3 \Phi / {Sin} \Theta \\& \Rightarrow A D=180 \sqrt{3} / 343 / 5 \sqrt{3} / 14 \\& \Rightarrow A D=180 \sqrt{3} / 343 X 14 / 5 \sqrt{3} \\& \Rightarrow A D=360 / 49 \\& m+n=360+49 \\& \Rightarrow m+n=409[/tex]
Therefore, the value of m + n is 409.
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Pls help me i’ll give brainliest
Answer:
Step-by-step explanation:
root 14= 3.7
root 15= 3.9
24/7= 3.4
so the numbers will be placed in its location accordingly
(a) Find the Riemann sum for f(x)=x3,3≤x≤14, if the partition points are 3,6,11,14 and the sample points are 4,9,12. R = (b) Find the Riemann sum if the partition points are 3,6,11,14 and the sample points are the midpoints. M =
Riemann Sum: A mathematical operation that involves splitting a region into rectangles and calculating the sum of the areas of the rectangles in order to estimate the area under a curve.
R: (3^3)(3) + (6^3)(3) + (11^3)(3) + (14^3)(3)
= 4,845 \sM: (3.5^3)(3) + (7.5^3)(3) + (11.5^3)(3) + (14.5^3)(3)
= 5,827.5
Riemann Sum is a numerical method for approximating the curve's area under the curve. To do this, the area is divided into rectangles, and the total of those areas is used. The product of the rectangle widths and the function evaluated at the sample locations is multiplied to determine the sum. The sample points may be taken at the rectangles' midpoints, right endpoints, or left endpoints.
In this instance, the partition points are at 3, 6, and 11 and we are computing the Riemann sum for f(x) = x3, 3 x 14. The Riemann total is 4,845, if the sample points are at 4, 9, and 12. The Riemann sum is 5,827.5 if the sample points are located at the midpoints of the rectangles. Because of this, the midpoint and endpoint Riemann sums are larger
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Divide using long division . -4x^2+12x^3-7x+2 by 2x^2 +1
The quotient is -2x2 + 8x3 - 7x + 2 and indeed the remainder is 0, according to the question.
What is an example of long division?We can put the division symbol "" between two integers to indicate that they have been split. As an illustration, we may write 36 6 to represent the division of 36 by 6. Additionally, we may represent it as the fraction 366.
To divide[tex]-4x^2 + 12x^3 - 7x + 2[/tex] by [tex]2x^2 + 1[/tex]using long division, we write out the division in the form:
[tex]2x^2 + 1[/tex]
[tex]-4x^2 + 12x^3 - 7x + 2[/tex]
Step 1: Divide the first term of the dividend ([tex]-4x^2[/tex]) by the first term of the divisor (2x^2). We get -2x^2.
Step 2: Multiply the entire divisor ([tex]2x^2 + 1[/tex]) by [tex]-2x^2.[/tex] This gives us[tex]-4x^4 + -2x^2.[/tex]
Step 3: Subtract this result from the dividend, updating the dividend to [tex]8x^3 - 7x + 2.[/tex]
Step 4: Repeat the process until the degree of the remainder is less than the degree of the divisor. In this case, the final remainder is non-zero, so we have:
[tex]2x^2 + 1[/tex]
[tex]-4x^2 + 12x^3 - 7x + 2[/tex]
[tex]-2x^2[/tex]
[tex]8x^3 - 7x + 2[/tex]
[tex]8x^3 - 7x + 2[/tex]
So the quotient is [tex]-2x^2 + 8x^3 - 7x + 2[/tex] and the remainder is 0.
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Where do i put the dots on the graph? Screenshot*
