Answer:
Step-by-step explanation:
an open box is to be made from a two-foot by three-foot rectangular piece of metal by cutting equal squares from the corners and turning up the sides. find the volume of the largest box that can be made in this manner. round your final answer to the nearest hundredth.
The volume for the largest box will be 1.056 foot³. This can find out by application of differentiation.
What is AOD?
AOD is nothing but application of differentiation. It implies scopes where we can use differentiation to make our calculations easy.
Here, given
Length and breadth = 2,3 foot
Let us consider length of side of square = x
So, after cutting squares left sides of rectangular sheet = 2-2x , 3-2x
So, volume = (2-2x)*(3-2x)*x
v = 4x³ - 10x² + 6x
To find largest volume , [tex]\frac{dv}{dx}[/tex] = 0
[tex]\frac{dv}{dx}[/tex] = 12x² - 20x + 6
12x² - 20x + 6 = 0
x = 0.4 , 1.3
But, for 1.3 volume will be negative i.e. not possible.
So, volume = 2.2*1.2*0.4
= 1.056 foot³
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Please help.
Solve the inequality show all your work
-4x+5>37
The solution for x in the inequality expression is x < -8
How to determine the solution for x?From the question, we have the following inequality expression that can be used in our computation:
-4x+5>37
Subtract 5 from both sides of the inequality
So, we have
-4x + 5 - 5 >37 - 5
Evaluate the like terms
This gives
-4x > 32
Divide both sides by -4
x < -8
Hence, the solution is x < -8
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Please help again 10 points again to first one
Answer: it would be 18 candies that are left
Step-by-step explanation:
I did the math
an 800 g steel plate has the shape of the isosceles triangle shown in the figure(figure 1).
The x- and y-coordinates of the center of mass are; (20, 0)
What is the center of mass of an object?The center of mass is the location where the sum of the relative position of the masses in a mass distribution is zero. It is the point where force can be applied on the distributed mass without causing a rotation of the system.
The mas of the steel plate = 800 g = 0.8 kg
The base length of the isosceles triangular plate = 20 cm = 0.2 m
The height of the isosceles triangular plate = 30 cm = 0.3 m
Considering a small strip of height, dx and width, I, we get
Area of small strip, dA = I·dx
Density of the plate for a unit thickness, ρ = M/A
Density of the small strip of mass dm = dm/dA
Considering the density of the plate as uniform, we get;
[tex]\displaystyle {\frac{dm}{dA} =\frac{M}{A}[/tex]
Therefore;
[tex]\displaystyle {dm=\frac{M}{A}\times dA}[/tex]
The area of the triangular plate, A = (1/2) × 0.2 m × 0.3 m = 0.03 m²
Mass of the plate, M = 0.8 kg
Therefore;
[tex]\displaystyle {dm=\frac{0.8}{0.03}\times I\cdot dx}[/tex]
The width of the small strip, I, located at a distance x from the vertex of the triangular plate, using similar triangles, indicates;
[tex]\dfrac{I}{20} = \dfrac{x}{30}[/tex]
[tex]I=20\times \dfrac{x}{30} = \dfrac{2}{3} \cdot x[/tex]
Therefore;
[tex]\displaystyle {dm=\frac{0.8}{0.03}\times I\cdot dx} = \frac{0.8}{0.03}\times \dfrac{2}{3} \cdot x\cdot dx}[/tex]
The center of mass, [tex]x_{cm}[/tex], can be obtained with the formula; [tex]\displaystyle {x_{cm} = \dfrac{1}{M} \cdot \int\limits {x} \, dm }[/tex]
Therefore; [tex]\displaystyle {x_{cm} = \dfrac{1}{0.8} \cdot \int\limits {x} \cdot \frac{0.8}{0.03} \cdot \frac{2}{3}\cdot x\, dx }[/tex]
[tex]\displaystyle {x_{cm} = \dfrac{1}{0.8} \cdot \int\limits {x} \cdot \frac{0.8}{0.03} \cdot \frac{2}{3}\cdot x\, dx } = \dfrac{1}{0.8} \times \frac{0.8}{0.03} \times \frac{2}{3}\cdot \int\limits^3_0 {x^2} \, dx[/tex]
[tex]\displaystyle {x_{cm} = \dfrac{1}{0.8} \times \frac{0.8}{0.03} \times \frac{2}{3}\cdot \int\limits^3_0 {x^2} \, dx = \frac{200}{9} \cdot \left[\frac{x^3}{3} \right]^{0.3}_0[/tex]
[tex]\displaystyle {x_{cm} = \frac{200}{9} \cdot \left[\frac{x^3}{3} \right]^{0.3}_0=\frac{200}{9} \times \frac{0.027}{3} =0.2[/tex]
The location of the x-coordinate center of mass, [tex]x_{cm}[/tex] = 0.2 m = 20 cm from the vertex, which is the same location as the x-coordinate of the centroid of the plate of uniform density.
The plate is symmetrical about the x-axis, therefore, the y-coordinate of the center of mass is along the x-axis, which is [tex]y_{cm}[/tex] = 0
The coordinate of the center of mass = (0.2, 0)
Part of the question requires the location of the coordinate of the center of mass of the triangular plate
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You have saved $2.82 to buy a magazine that costs $7.39. Estimate how much more money you need to buy the magazine
HELPPPPPP MEEEEEEEE Ps. THIS IS DECIMALS AND STUFF
For questions 7-9, factor each polynomial completely over the set of complex
numbers.
7. a(x)=2x²-3x³-24x² +13x+12
8. b(x) = x² − 2x³ −17x² +4x+30
9. c(x)=2x³-5x² +12x-5
PLEASE SHOW WORK
Answer:
answers attached int he files below all in order
The table of values below represents inverse variation. What is the value of k?
Answer:
B) k = 30---------------------------
It is assumed the first column represents x- values and the second column represents y- values.
Inverse variation equation:
y = k/x, where k is constant.Substitute one pair of coordinates, x = 3, y = 10:
10 = k / 3k = 10*3k = 30Correct choice is B.
Answer:
b) k = 30
Step-by-step explanation:
Formula we use,
→ y = k/x
Now the value of k will be,
→ y = k/x
→ 10 = k/3 || → 6 = k/5
→ k/3 = 10 || → k/5 = 6
→ k = 10 × 3 || → k = 6 × 5
→ [ k = 30 ] || → [ k = 30 ]
Hence, the value of k is 30.
Aaron's goal is to read an average (mean) of 26 pages per day for 6 days. During the first 5 days, he reads 23 pages per day. How many pages must he read on the 6th day to reach his goal
A. 26
B. 19
Aaron has to read 41 pages on the 6th day to reach his goal.
What is the speed of reading?
Any of the many methods that promise to increase one's reading speed include speed reading. Chunking is one speed-reading technique, as is reducing subvocalization. The many available speed-reading training programs may utilize books, videos, software, and seminars.
We have,
26 pages per day for 6 days:
26×6=156,
So Aaron should read 156 pages by the 6th day to reach his goal,
During the first 5 days, he reads 23 pages per day then,
23 × 5 = 115
That’s how many pages he’s already read.
156-115=41
Hence, Aaron has to read 41 pages on the 6th day to reach his goal.
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I need help to get these answers
The quadratic function, f(x) = 3·x² + 6·x, has the following values;
1. The function has a minimum value
2. The y-intercept of the function is (0, 0)
The axis of symmetry is; x = -1
The x-coordinate of the vertex is; x = -1
3. The table of values can be presented as follows;
x [tex]{}[/tex]-2 -1 0
f(x) [tex]{}[/tex]0 -3 0
The vertex is (-1, -3)
4. Please find attached the graph of the function
What is a quadratic function?A quadratic function is a function that has 2 as the highest power of the variables.
The specified function is; f(x) = 3·x² + 6·x
1. The coefficient of x² in the specified quadratic function, which indicates the existence of a minimum or maximum value is positive, therefore, the function has a minimum value
2. The y-intercept is the value of the function when x = 0, therefore;
f(0) = 3 × 0² + 6 × 0 = 0
Therefore, at the y-intercept, x = 0, and f(x) = 0
The y-intercept is (0, 0)
The axis of symmetry is a line that passes through the vertex
A the vertex, we get, f'(x) = 6·x + 6 = 0
Therefore; 6·x + 6 = 0
6·x = -6
x = -6/6 = -1
f(-1) = 3·(-1)² + 6 × (-1) = -3
The vertex is (-1, -3)
Therefore, the axis of symmetry is the line x = -1
The x-coordinate of the vertex of the function is; x = -1
3. A table of values for the function can be presented as follows;
x [tex]{}[/tex] f(x)
-6 [tex]{}[/tex] 72
-5 [tex]{}[/tex] 45
-4 [tex]{}[/tex] 24
-3 [tex]{}[/tex] 9
-2 [tex]{}[/tex] 0
-1 [tex]{}[/tex] -3
0 [tex]{}[/tex] 0
1 [tex]{}[/tex] 9
2 [tex]{}[/tex] 24
3 [tex]{}[/tex] 45
4 [tex]{}[/tex] 72
5 [tex]{}[/tex] 105
4. . Please find attached the graph of the function created with MS Excel
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find the value of the constant c which makes fx|y (x, y) a valid conditional probability mass function.
c=1/2 which makes fx|y (x, y) a valid conditional probability mass function.
What is conditional probability?
The possibility of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability. It is determined by multiplying the likelihood of the earlier event by the increased likelihood of the later, or conditional, event.
Given that;
p(x) = [tex]c (\frac{2}{3} )^n[/tex] where x = 1,2,3,........
for getting value of c we are using the expression :
[tex]\sum_{n=1}^{\infty} c(\frac{2}{3})^n = 1[/tex]
[tex]c\sum_{n=1}^{\infty} (\frac{2}{3})^n = 1[/tex]
Since we want p(x) to be a Probability Mass Function, your approach is correct, since for any such function
fX:A→[0,1],X:S→A⊆R, it is :
[tex]\sum _{x\in A} \ fX(x)=1[/tex]
As long as you've correctly understood that condition, you can proceed with your specific exercise as follows:
[tex]\sum_{n=1}^{\infty} c(\frac{2}{3})^n = 1[/tex]
⇔ [tex]c\sum_{n=1}^{\infty} (\frac{2}{3})^n = 1[/tex]
⇔2c = 1
⇔c = 1/2
Hence c = 1/2 is the valid conditional probability mass function.
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A triangle has side lengths of n, n – 3, and 2(n − 2). If the perimeter of the triangle is at least 37 units, what is the value of n?
OA.
n> 11
OB
n> 8
O C.
n > 10. 5
OD
n > 7. 5
Answer:
A. n ≥ 11
Step-by-step explanation:
You have a triangle with sides (n), (n-3), and 2(n-2). Its perimeter is at least 37 units, and you want to know the value of n.
PerimeterThe perimeter is the sum of the side lengths:
P = (n) +(n -3) +2(n -2)
P = n + n -3 +2n -4
P = 4n -7
ConstraintThe perimeter is at least 37, so we have ...
P ≥ 37
4n -7 ≥ 37
4n ≥ 44 . . . . . . . add 7
n ≥ 11 . . . . . . . divide by 4
The value of n is at least 11.
In 1980, about 17.7 million households had cable television. This was about 25.8% of the households that had cable in 2000. How many households had cable in 2000?
In 2000, cable was available in 45683700000 homes.
What is percentage?Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.
In 1980, 17700000 = 25.8%\s1% = 4566600000
Then, in 2000, there were 45683700000 households (17 700 000 + 4566 600 000).
Comparing two amounts while rebasing the second amount to 100 is the simplest way to use percentages. Let's assume that we are interested in the proportion of employed women who are female.
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Which statement could be used to explain why f(x) = 2x – 3 has an inverse relation that is a function?The graph of f(x) passes the vertical line test.f(x) is a one-to-one function.The graph of the inverse of f(x) passes the horizontal line test.f(x) is not a function.
Answer: Choice B) f(x) is a one-to-one function
What this means is that each x input lands on a unique y output. For example, plugging x = 0 leads to y = -3. No other x value will lead to y = -3. This allows us to find the inverse.
The vertical line test is used to see if we have a function or not. The horizontal line test is used to see if an inverse is possible.
The phrasing "The graph of the inverse of f(x) passes the horizontal line test" is close, but we need to erase "the inverse of" to have choice C be useful. In other words, if choice C said "The graph of f(x) passes the horizontal line test", then it would be correct and useful.
Side note: Another term for "one-to-one" is "injective".
The mean cost of a five pound bag of shrimp is 42 dollars with a variance of 49. If a sample of 54 bags of shrimp is randomly selected, what is the probability that the sample mean would be less than 43.4 dollars? Round your answer to four decimal places.
The probability that the sample mean would be less than 43.4 dollars is 0.9292.
What is a probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true.
From the information, the mean cost of a five pound bag of shrimp is 42 dollars with a variance of 49 and a sample of 54 bags of shrimp is randomly selected.
Therefore, the probability will be:
P(x < 43.4)
Using normal distribution
= P(z < 43.4 - Mean( / 7/✓54)
= P(z < 43.4 - 42( / 7/✓54)
= P(z < 1.4697)
= 0.9292
The probability is 0.9292.
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Jorge wants to buy a drink. Which option is cheaper per ounce: one 24-ounce cup for $1.92 or two 12-ounce cups for $0.96 each?
The 24-ounce cup costs $0.08 per ounce, and the 12-ounce cups cost $0.085 per ounce. The 24-ounce cup is the cheaper option.
The 24-ounce cup costs $0.08 per ounce, and the 12-ounce cups cost $0.085 per ounce. The two 12-ounce cups are the cheaper option.
The 24-ounce cup costs $0.085 per ounce, and the 12-ounce cups cost $0.08 per ounce. The two 12-ounce cups are the cheaper option.
The cost per ounce in both options is the same.
The cost per ounce in both options is the same. Then the correct option is D.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The rate is the ratio of the amount of something to the unit.
Jorge wants to buy a drink.
Choice 1: 24-ounce cup for $1.92
Choice 2: 12-ounce cups for $0.96 each
The cost per ounce in choice 1 is calculated as,
⇒ $1.92 / 24
⇒ $0.08 per ounce
The cost per ounce in choice 2 is calculated as,
⇒ $0.96 / 12
⇒ $0.08 per ounce
The cost per ounce in both options is the same. Then the correct option is D.
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solve for x under the assumption that x >0 x-70/x<-3
x under the assumption that x >0 x-70/x<-3, x > -35
WHAT IS INEQUALITY?
Economic inequality comes in many forms, most notably wealth inequality measured by the distribution of wealth and income inequality measured by the distribution of income (the quantity of money people get paid) (the amount of wealth people own). There are significant forms of economic inequality among various groups of people in addition to economic inequality between nations or states. Wealth, income, as well as consumption are the three main focuses of significant economic measurements. There are numerous ways to gauge economic inequality, with the Gini coefficient being among the most popular. The Disparities Human Development Index is a statistic composite index which offers another type of measurement by taking inequality into account.
assuming x > 0,
(x-70/x) < 3
= x-70 < 3x = -70 < 2x
= x > -35
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What is the 200th term in this sequence: 21, 29, 37, 45, 53, ...?
A(200) =
Hence, the [tex]200th[/tex] term in the sequence is [tex]1613[/tex].
What is the sequence?
A sequence is a list of objects, typically numbers, in which order matters, repetition is allowed, and the same elements can appear multiple times at different positions in the sequence.
Here given that,
The sequence is
[tex]21,29,37,45,53,...[/tex]
The general formula is
[tex]a_n=a_1+d(n-1)[/tex]
[tex]a_1=21[/tex]
[tex]d=a_2-a_1\\d=29-21\\d=8[/tex]
Substitute it in the general formula is
[tex]a_2_0_0=21+8(200-1)\\a_2_0_0=21+8(199)\\a_2_0_0=21+1592\\a_2_0_0=1613[/tex]
Hence, the [tex]200th[/tex] term in the sequence is [tex]1613[/tex].
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Who now what is egal 8+8-8×8÷8
Answer:
8+8-8×1
8+8-8
16-8
8 Ans.
You have an urn with 6 red, 10 blue and 4 black balls.
What is the probability that you take different colours in two"picks"?
The probability that you take different colors in two"picks" is 31/45.
You could choose one red followed by one blue, one blue followed by one red, one blue followed by one black, one black followed by one blue, one black followed by one red, or one red followed by one black.
P( different colors) = P( one blue followed by one red ) +P( one red followed by one blue) + P( one blue followed by one black ) +P( one black followed by one blue) +P( one black followed by one red ) +P( one red followed by one black)
P(one blue followed by one red) = (10/20)( 6/19) = 3/19
P(one red followed by one blue) = (6/20)( 10/19) = 3/19
P(one blue followed by one black) = (10/20)( 4/19) = 2/19
P(one black followed by one blue) = (4/20)( 10/19) = 2/19
P(one red followed by one black) = (6/20)( 4/19) = 6/95
P(one black followed by one red) = (4/20)( 6/19) = 6/95
P(different colors )= 3/19 + 3/19 + 2/19 + 2/19 + 6/95 + 6/95
= 31/45
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HELP QUICKLY THANK YOU!
The values are;
⇒ F ∩ H = Ф
⇒ F ∪ H = (- ∞, 7]
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
F and H are defined as;
F = {v | v < 4 }
H = {v | v ≥ 7 }
Now,
Since, F and H are defined as;
F = {v | v < 4 }
H = {v | v ≥ 7 }
Hence, The values are;
F ∩ H = {v | v < 4 } ∩ {v | v ≥ 7 }
= Ф
And, F ∪ H = {v | v < 4 } ∪ {v | v ≥ 7 }
= (- ∞, 7]
Thus, The values are;
⇒ F ∩ H = Ф
⇒ F ∪ H = (- ∞, 7]
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HELP ME PLEASE! IM SO CONFUSED
Answer:
299,792 km599,585 km899,377 km1,199,170 km1,498,962 kmStep-by-step explanation:
You want to find the distance traveled by light in km for periods of 1–5 seconds at a speed of 299,792,458 m/s.
UnitsThe speed is given in meters per second, and the table values are wanted in kilometers. There are 1000 meters in 1 km, so it can be convenient to convert the speed to km/s before doing other calculations.
(299,792,458 m/s) / (1000 m/km) = 299,792.458 km/s
DistanceThe distance is found by multiplying the speed by time:
d = 299,792.458t
It is convenient to let a calculator do the multiplication (and rounding). The attachment shows the result of using t = {1, 2, 3, 4, 5}.
The distances are, respectively, {299792, 599585, 899377, 1199170, 1498962} km.
6. Find the length of a guy wire that makes an angle of 45 degrees with the ground if the wire is attached to the top of a tower 63 meters high. (A guy wire runs from the top
of the tower, diagonally, to the ground.
Step-by-step explanation:
see following explanation above....
Find the sum of (8 + 2 − 4) and (3 − 5).
Answer:
4
Step-by-step explanation:
(8+2-4)+(3-5)
(10-4)+(-2)
6-2
4
Hopes this helps please mark brainliest
Functions f, g, and h are defined as follows: f(x) = x − 2, g(x) = 2x^2 − 1, and h(x) =
2x^3 + 4.
(a) Find the inverse of function g(x).
(b) Find f(h(-2))
(c) Find g(f(5))
(those are NOT answer choices but different parts needed to be answered. Please show all work for brainliest)
The inverse function of g is g⁻¹(x) = √(x/2 + 1/2)
The value of f(h(x)) is -14The value of g(f(5)) is 17How to determine the inverse function of g?From the question, we have the following equations
f(x) = x - 2
g(x) = 2x² - 1
h(x) = 2x³ + 4
To determine the inverse function of g, we start by making the function f(x) as an equation
So, we have
y = 2x² - 1
Swap variables x and y
x = 2y² - 1
Add 2 to both sides
2y² = x + 1
Divide by 2
y² = x/2 + 1/2
Square root both sides
This gives
y = √(x/2 + 1/2)
So, we have
g⁻¹(x) = √(x/2 + 1/2)
How to determine f(h(x))Here, we have
f(x) = x - 2
h(x) = 2x³ + 4
This gives
f(h(x)) = h(x) - 2
So, we have
f(h(x)) = 2x³ + 4 - 2
Evaluate
f(h(x)) = 2x³ + 2
So, we have
f(h(x)) = 2(-2)³ + 2
Evaluate
f(h(x)) = -14
How to determine g(f(x))Here, we have
f(x) = x - 2
g(x) = 2x² - 1
This gives
g(f(x)) = 2(f(x))² - 1
So, we have
g(f(x)) = 2(x - 2)² - 1
So, we have
g(f(5)) = 2(5 - 2)² - 1
Evaluate
g(f(5)) = 17
Hence, the functions g(f(5)) is 17
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Answer:
a) g^-1(x) = - √2x+1, √2x+1
2 2
b) -14
c) 17
Step-by-step explanation:
a) g(x) = 2x² - 1
y= 2x² - 1 becomes x = 2y² - 1
Solve for y: x = 2y² - 1
g^-1(x) = - √2x+1, √2x+1
2 2
*answer is: -√2x+1 (over) 2 & √2x+1 (over) 2*
b) Find: f(h(-2))
h(x) = 2x³ +4
h(-2) = 2(-2)³ + 4
= - 12
f(x) = x – 2
f(-12) = (-12) – 2
= -14
c) Find: g(f(5))
f(x) = x – 2
f(5) = (5) – 2
= 3
g(x) = 2x² - 1
g(3) = 2(3)² - 1
= 17
different data sets that have a median of 13
Two different data sets that have a median of 13 are
9, 10, 13, 18, 2010, 13, 13, 18How to determine the datasets?From the question, we have the following parameter
Median =13
The median of a dataset is the number at the middle position
So, we can make use of the following dataset
9, 10, 13, 18, 20
This is so because the middle number is 13
Another possible dataset is
10, 13, 13, 18
Similarly, this is because the middle number is 13
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Parallel & perpendicular lines
Answer:Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect. Perpendicular lines are lines that intersect at a right (90 degrees) angle.
Compare 160 and 115/9 using <, >, or =.
The correct comparison between the given numbers ; √160 and 115 / 9 is; 115 / 9 > √160.
Which sign correctly compares the given numbers?It follows from the task content that the sign which correctly compares the two numbers as given in the task content be determined.
Since the given numbers in the task content can be evaluated as follows;
√160 = 12.64911064.
115 / 9 = 12.7777777778
From the results of the evaluations as represented above, since 12.7777777778 is greater than 12.64911064, it follows that the 115 / 9 > √160.
Therefore, the required correct comparison is;
115 / 9 > √160
The answer choice which is correct is as represented above.
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Tell whether the expression is positive or negative without evaluating it. -3/10 X (-8/15)
The expression -3/10 X (-8/15) is positive
Expression
Expression in mathematics has two or more variables, terms and constants. Also, arithmetic expression contains only numbers and mathematical operators and algebraic expression
The expression has negative sign and from mathematical calculation we already know the following relation:
+ x + = +
positive multiply by positive equals Positive
- x - = +
Negative multiply by Negative equals Positive
+ x - = -
Positive multiply by Negative equal Negative
hence, - [tex]\frac{3}{10}[/tex] x - [tex]\frac{8}{15}[/tex]
The negative sign multiply by -3/10 X (-8/15) sign will give positive.
Therefore, the expression -3/10 X (-8/15) is positive.
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The mean of 11 numbers is 7 one of the numbers, 13, is deleted. What is the mean of the remaining 10 numbers?.
If mean of 11 numbers is 7 one of the numbers, 13, is deleted then the mean of remaining 10 numbers is 6.4
The mean of 7 numbers = 11
We know,
Mean = Sum of the terms / Number of terms
Substitute the values in the equation
11 = Sum of the terms / 7
The sum of the terms = 11 × 7
= 77
Number 13 is deleted
Sum of the terms = 77 - 13
= 64
Number of terms = 11 - 1
= 10
The mean = Sum of the terms / Number of terms
Substitute the values in the equation
= 64 / 10
= 6.4
Hence, the mean of the remaining 10 numbers is 6.4
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chapter 17 review questions how does a b-tree differ from a b -tree? why is a b -tree usually preferred as an access structure to a data file?
The difference in b-tree and b +tree, b -tree is a self balancing tree data structure that maintains sorted data and b +tree is a modified version of b -tree.
b -tree is used to sort the data with various pieces facilities such as insertion ,deletion and search etc whereas b +tree is a modified version of b -tree providing all the functions smoothly and quickly .
In b -tree, both internal nodes and leaf nodes are used to store records and keys whereas in b +tree keys are stored in internal nodes whereas records are storing leaf nodes
In b +tree, no duplication is allowed but in b +tree duplication may occur
A b +tree usually preferred as an access structure to a data file as as the height of the tree remains balanced and less as compared to b -tree . We can assess the data stored in b +tree sequentially as well as directly . keys are used for indexing . Faster search queries as the data is stored only on a leaf nodes.
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