a. Trapezoidal Rule- 9.413607
b. Midpoint Rule-9.393861
c. Simpson's Rule -9.400407
a. We use n=8 for this integral, .Δt=4-0/8=0.5
Therefore the integral range is[0,0.5,1.0,1.5......3.0,3.5....4.0 ]
#For the Trapezoidal Rule:
[tex]\int\limits^a_b[/tex]∫(x)dx≈[tex]Tn=[/tex]Δr/2[∫([tex]x0[/tex])+2∫(x1)+....+∫(xn)]
=[tex]\int\limits^4_0[/tex][tex]In(2+ex[/tex])dx≈[tex]T8[/tex]
=0.5/2[[tex]In[/tex](2+[tex]e0.0[/tex])+2In(2+e0.5)+2In(2+e1.0)+....+2In(2+e3.5)+In(2+e4.0)]
=0.25[1.098612+2.588754+3.102889+3.737962+4.479090+5.304017+6.189846+7.117283+4.035976]
≈9.413607
Hence, the approximate integral value using Trapezoidal rule is 9.413607
b.For the Midpoint Rule, we calculate the integral as:
[tex]\int\limits^a_b[/tex]∫(x)dx≈[tex]Mn=[/tex]Δx[∫[tex](x1)[/tex]+∫([tex]x2)[/tex]........∫([tex]xn)}[/tex]
x1 is the midpoint of the ith interval.
From our interval ,[0,0.5,1.0,1.5....3.0,3.5,4.0]the applicable intervals are
[0.25,0.75,1.25,2.25,2.75,3.25,3.75]
We therefore have the integral value as:
=4/8[[tex]In[/tex](2+[tex]e0.25[/tex])+In(2+[tex]e0.72[/tex])+In(2+[tex]e1.25[/tex])+....+In(2+[tex]e1.75[/tex])+In(2+[tex]e2.25[/tex])[tex]In[/tex](2.75)+In(2+e0.5)+In(2+e1.0)]
Hence, the approximate integral value using the Midpoint Rule is 9.393861
c. For the Simpson's Rule, we calculate the integral rule as follows:
Hence, the approximate integral value using the Simpson's Rule is 9.400407
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Question 1 of 21
If r= 1 and 0 = 5, what is the approximate arc length?
A. 2.618 units
B. 0.883 units
C. 15.708 units
D. 3.927 units
The distance between two places along a segment of a curve is known as the arc length.
What is arc length of a circle?
The distance between two places along a segment of a curve is known as the arc length. Curve rectification is the process of measuring the length of an irregular arc section by simulating it with connected line segments.
There are a finite number of segments in the rectification of a rectifiable curve. Using the arc length formula, one may determine a circle's arc length given its radius and center angle. Arc length is equal to r, where r is the radian unit. Arc length is equal to (r/180), where r is the radius in degrees.,
Given :[tex]$r=1, \theta=5 \pi / 6$[/tex]
Now, arc length
[tex]&=\theta / 2 \pi * 2 \pi r \\[/tex]
[tex]&=(5 \pi / 6) / 2 \pi \times 2 \times 3.14 \times 1 \\[/tex]
[tex]&=5 / 12 \times 6.28 \\[/tex]
[tex]&=31.4 / 12[/tex]
=2.618 units
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Find the area of a circle
Answer: 452 cm squared
Step-by-step explanation:
Since the diameter is the radius times two, the radius of this circle is 24 divided by 2 which is 12. To find the area of a circle you multiply the radius by pi. Pi= 3.14, so 3.14(pi) times 12(radius)= 452.16 cm.
Answer:
452.16 ft²
Step-by-step explanation:
find radius
24 : 2 = 12 ft
find area (πr²)
π12² =
3.14 * 12² =
3.14 * 144 =
452.16 ft²
What is 6.25 as a fraction and decimal
a researcher could be examining what percentage of golfers buy only titleist balls, or might be looking at what percentage of high school students buy from taco bell between meals. in either case, the mean or percentage is derived from a sample, so it is:
The mean and percentage is deduced from a sample in either case, so it is: the statistic for the sample.
What is defined as the sample statistic?A sample statistic (or simply statistic) is any number calculated from the sample data. The sample median, average, sample standard deviation, as well as percentiles are some examples. Because it is based on data acquired through random sampling, a type of random experiment, a statistic is a random variable. As a result, a statistic is both known and random.For the given question,
A researcher could be looking at which percentage of golfers only use Titleist balls, or what proportion of high school students eat at Taco Bell between meals.
As a result, either in case, the mean as well as percentage is deduced from a sample, as follows: statistics from a sample.
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What is distance between (3, 8) and (5, 14)? Round to the nearest tenth if necessary (example 5.6).
Answer:
Step-by-step explanation:
1.\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}
2.\sqrt{\left(5-3\right)^2+\left(14-8\right)^2}
3.2\sqrt{10}
Stella walks down a flight of stairs to the basement. Then she walks back up the stairs and another flight of stairs to the second floor of her house. Each flight of stairs represents a change of 12 feet in height. How far is Stella above the ground
If Stella walks down a flight of stairs to the basement. Then she walks back up the stairs and another flight of stairs to the second floor of her house. How far is Stella above the ground is: 12 ft.
Height above the groundGiven:
Flight stair = 12 feet
Hence,
Let walking from down a flight of stairs to the basement = -12 f
Let walking back up the stairs = 12Ft
Now let determine Stella height above the ground.
Height = -12 feet + 12 feet + 12 feet
Height = 12 feet
Therefore we can conclude that Stella is 12 feet above the ground.
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View the image attatchment for question.
Answer: -4 only
Step-by-step explanation:
Though f(x) approaches -2 for the x-values of -5, -4, and -2, the limits for -5 and -2 don't exist because the left and right hand limits are not equal.
While in Canada, Renita bought a
souvenir that is 14.5 centimeters
long. She knows that 1 inch equals
2.54 centimeters.What is the length of the souvenir in inches
carissa is a graph of the equation 4x+3y=-7 what will the slope Of Carissa graph be
Answer:
y= [tex]-\frac{4}{3}x-\frac{7}{3}[/tex], so [tex]-\frac{4}{3}[/tex] is your slope!
Step-by-step explanation:
It's best to get this equation in slope-intercept form, meaning to solve for y.
My work is shown below, as to how I solve for y.
4x + 3y = -7
3y = -7 - 4x
Afterward, divide the other side by 3.
y = (-4/3)x (-7/3)
That's how you get the answer. Hope this helped.
As, y = mx + b, and the m stands for the slope, -4/3 is your slope.
John flipped a coin 50 times .It landed on tails 35 times .what is the ratio of the number of times the coins landed on heads to the number of flips.
Answer:
15:50
Step-by-step explanation: Out of the 50 times the coin was flipped, it landed on tails 35 times. This means it landed on heads 15 times (50-35=15). The ratio of heads to the total number of flips would be 15:50.
By visual inspection, determine the best-fitting regression model for the data plot below.
The best fitting regression model for the given data plot is A.Quadratic
The curve-shaped graph of a quadratic function is known as a parabola. On the graph, it is either the highest or lowest point. You can imagine it as the parabola's endpoint.
It is a diagram that illustrates the connection between two or more values or objects. Linear simply implies straight. Straight-line graphs called linear graphs are used to show the relationship between two quantities.
A curve that depicts an exponential function is known as an exponential graph. A curve with a horizontal asymptote and either an increasing slope or a decreasing slope is called an exponential graph. i.e., it begins as a horizontal line, increases or drops gradually, and then the growth or decay accelerates.
The given curve is Quadratic as its graph is parabolic in nature.
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need help with this asap!!!!!
Answer:
that looks hard
Step-by-step explanation:
Question content area top
Part 1
Point B has coordinates (5,1). The x-coordinate of point A is −3. The distance between point A and point B is 10 units. What are the possible coordinates of point A?
The possible coordinates of the point A is (-3, -5) and (-3, 7)
How the coordinates of point A can be calculated?The given parameters are:
Point B = (5, 1)Distance between the two points, D = 10 unitsx-coordinate of point A = −3This means that
A = (-3, y)
The distance between any two points is calculated as
D = √[(x₁ - x₂)² + (y₁ - y₂)²]
Substitute the known values in the above equation
So, we have
10 = √[(-3 - 5)² + (y - 1)²]
Evaluate the difference
10 = √[(-8)² + (y - 1)²]
Take the square of both sides
100 = (-8)² + (y - 1)²
So, we have
100 = 64 + (y - 1)²
Evaluate the like terms
(y - 1)² = 36
Take the square roots
y - 1 = ±6
This gives
y = 1 ± 6
So, we have
y = -5 and 7
Hence, the coordinates of point A is (-3, -5) and (-3, 7)
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U2 L2 solutions of a graphed equationWhich point is not a solution to the equation 4y = 167A (4, 2)C. (2, 3)D. (5, 1.5)Question 1
(4,-2) does not lie on the line
Here, we want to select the point that is not a solution to the graphed line
What we have to do is just to susbtitute the value of x and y. If by aritjmetic operation, the result is 16, then the point lies on the line
We proceed as follows;
a) (4,-2)
-2(4) -4(-2)
-8+8 = 0
This lies on the line
b) (1, -4.5)
-2(1)-4(-4.5) = -2 + 18 = 16
This is not on the line
c) (-2,-3)
-2(-2)-4(-3) = 4 + 12 = 16
d) -2(-5)-4(-1.5)
= 10 + 6 = 16
As we can see, only the first point does not lie on the line
PLEASE HELP ME IAM GROUNDED AND MY MOM IS FURIOUS BECAUSE I HAVE AN F
Answer:
k=151, g=71, m=29, h=109
Step-by-step explanation:
Vertical angles and sum theory. lmk if you want an in detail explanation
Which expression is equivalent to 8(x+3)−14(20x−56)
8(101 -34x) is the equivalent expression of 8(x+3)−14(20x−56)
What is the equivalent expression?
Equivalent expressions can be defined as expressions that are the same, even though they may look a little different. If you plug in the same variable value into equivalent expressions, they will each give you the same value when you simplify
Given 8(x+3)−14(20x−56)
By eliminating the parenthesis:
8(x+3)−14(20x−56) = ( 8(x) + 8(3) ) - ( 14(20x) - 14(56) )
= 8x + 24 - 280x + 784 Add/Subract like terms
= -272x + 808
= 8(-34x + 101)
= 8 (101 -34x)
Therefore the equivalent expression for 8(x+3)−14(20x−56) is 8(101 -34x)
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Write the point-slope form of the equation of the line given the two points.
(-1,4) and (-4,2)
will give branlest if able to Fill in the missing number from the table using the equivalent ratios in the ratio table. (hint: 4 times what value equals 5)
Group of answer choices
12
8
5
4
Answer: The answer is 8.
Step-by-step explanation:
Selecting the number of bins is an important decision when working with histograms. Are there any rules or recommendations for choosing the number or width of bins? what happens if we use too many or too few bins?.
When working with Histograms, choose from 5 to 20 bins. The greater the data collection, the more probable it is that you will require a high number of bins. For example, a collection of 12 data points may deserve 5 bins, whereas a set of 1000 numbers will most likely benefit from 20 bins. The exact number of bins is typically a matter of personal preference.
What is a Histogram?
A histogram displays numerical data by arranging it into equal-width "bins." Each bin is represented by a bar, the height of which corresponds to the number of data points in that bin. Bins are sometimes known as "intervals," "classes," or "buckets."
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what is the value of 7 p + q/3 when p=6 and q=12
Answer:
46
Step-by-step explanation:
What is the product of the complex numbers below? (4 - 21)(1 + 7) O A. 18 - 307 - OB B. -10 - 301 O C. -10 + 261 + O + D. 18 + 261
Given:
[tex](4-2i)(1+7i)[/tex]To find: The product of two complex numbers:
Explanation:
On expansion we get,
[tex](4-2i)(1+7i)=4+28i-2i-14(i^2)[/tex]As we know,
[tex]i^2=-1[/tex]So, we w
16=16r
WILL MARK BRAINILEST!!
Assuming you're trying to find the value of r...
Answer:
r = 1
Step-by-step explanation:
Take your starting equation:
16 = 16r
Since r is multiplied by 16, divide both sides by 16 to isolate r.
16 / 16 = 1
16r / 16 = r
The result is 1 = r, which can be written as:
r = 1
What x-value makes the set of ratios equivalent? Tiles 2 : 3 = 6 : x ,4 : 7 = x : 42 , 2x : 48 = 3 : 12, 12 : 15 = x : 20Pairs691624
What x-value makes the set of ratios equivalent? Tiles 2 : 3 = 6 : x ,4 : 7 = x : 42 , 2x : 48 = 3 : 12, 12 : 15 = x : 20
Part 1
we have
2 : 3 = 6 : x
value of x=9
Part 2
4 : 7 = x : 42
x=24
Part 3
2x : 48 = 3 : 12
2x=12
x=6
Part 4
12 : 15 = x : 20
x=16
Three friends ate lunch at a restaurant and divided the bill equally. They used the expression below to determine how much each person owed.
(1.75+5.95)+(2.25+4.75)+(1.09+7.95) /
3
please help mee
Each friend pay the bill 7.9133(approx.)
Given,
The expression is given :
(1.75+5.95)+(2.25+4.75)+(1.09+7.95) / 3
Three friends ate lunch at a restaurant and divided the bill equally.
Now, According to the question:
The expression is :
(1.75+5.95)+(2.25+4.75)+(1.09+7.95) / 3
Calculate the sum or difference
=(7.7 + 7 + 9.04 )/ 3
=23.74 / 3
= 7.9133 (approx.)
Hence, Each friend pay the bill 7.9133(approx.)
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isaac's favorite cereal is running a promotion that says 111-in-444 boxes of the cereal contains a prize. suppose that isaac is going to buy 666 boxes of this cereal, and let xxx represent the number of prizes he wins in these boxes. assume that these boxes represent a random sample, and assume that prizes are independent between boxes. what is the probability that he wins exactly 222 prizes in the 666 boxes? you may round your answer to the nearest hundredth.
Using the binomial distribution, there is a 0.6328 = 63.28% probability that she wins at most 1 prize.
For each box, there are only two possible outcomes, either it has a prize, or it does not. The probability of a box having a prize is independent of any other box, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
The parameters are:
x is the number of successes.
n is the number of trials.
p is the probability of a success on a single trial.
In this problem:
She buys 5 boxes, hence
1 in 4 boxes has a prize, hence
The probability is:
P ( X ≤ 1 ) =P ( X = 0 ) + P ( X = 1 )
Then ,
P ( X ≤ 1 ) = P ( X = 0 ) + P ( X = 1 )
= 0.2373 + 0.3955
= 0.6328
Thus 0.6328 = 63.28% probability that she wins at most 1 prize
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Can The intersection of two planes can be a line.
The intersection of two planes can be a line. Therefore, it's true.
What is a plane?A plane is a flat, two-dimensional surface that never ends in mathematics. A plane is a point, a line, and three-dimensional space's equivalent in two dimensions.
A line is formed by the intersection of two planes. The planes are parallel if they do not intersect. Due to the endless nature of planes, they cannot meet at a single place. In addition, because planes are flat, they cannot intersect over more than one line.
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Simplify the expression and rationalize the denominator.
36a8b4
7c
a satellite can move at 17,000 miles per hour. how many hours will it take to reach a star that is three light years away? recall that and . show your work.
Hours satellite will take to reach a star that is three light years away is 1.039 * [tex]10^{9}[/tex] hours.
Given :
satellite can move at 17,000 miles per hour.
let t be the number of hours
Convert the disance to miles
3 light years = 3 * 9.5 * [tex]10^{12}[/tex] kilometers
= 3 * 9.5 * [tex]10^{12}[/tex] * 0.62 miles
= 1.767 * [tex]10^{13}[/tex] miles
divide by the speed to get the time in hours
t = 1.767 * [tex]10^{13}[/tex] miles /17000 miles /hour
t = 1.039 * [tex]10^{9}[/tex] hours
Hence hours satellite will take to reach a star that is three light years away is 1.039 * [tex]10^{9}[/tex] hours.
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A rectangular room is
4
meters longer than it is wide, and its perimeter is
32
meters. Find the dimension of the room.
Find the length and the width.
Answer: 60 m squared dimensions
6 m width
10 m length
Step-by-step explanation:
subtract 8 from the perimeter to account for 2 sides having the extra length then divide the answer by 4 to get the length if all the sides were equal
32-8=24
24/4=6
then add the 4 m back to the answer to get the length
Deliver the equation of the parabola with a focus at (2, -1) and a directrix of y= 1/2
Answer: It will be letter c
Step-by-step explanation:
