(a) approximate the definite integral ∫31f(x)ⅆx using a midpoint riemann sum with the subintervals [1,1.6], [1.6,2], and [2,3]. show the work that leads to your answer.
Answers
To approximate the definite integral ∫(1 to 3) f(x) dx using a midpoint Riemann sum with the subintervals [1,1.6], [1.6,2], and [2,3], you will first find the midpoint of each subinterval and then evaluate the function at those midpoints. Finally, multiply the function values by the width of the subintervals and sum them up.
1. Find the midpoints:
m1 = (1 + 1.6) / 2 = 1.3
m2 = (1.6 + 2) / 2 = 1.8
m3 = (2 + 3) / 2 = 2.5
2. Evaluate the function at the midpoints:
f(m1) = f(1.3)
f(m2) = f(1.8)
f(m3) = f(2.5)
3. Multiply the function values by the width of the subintervals:
Δx1 = 1.6 - 1 = 0.6
Δx2 = 2 - 1.6 = 0.4
Δx3 = 3 - 2 = 1
4. Sum the products:
Approximate integral = (f(1.3) * 0.6) + (f(1.8) * 0.4) + (f(2.5) * 1)
Without knowing the actual function f(x), this is the most simplified form of the midpoint Riemann sum for the given problem.
To approximate the definite integral ∫31f(x)ⅆx using a midpoint Riemann sum with the subintervals [1,1.6], [1.6,2], and [2,3], we can use the following formula:
∑(i=1 to n) f(mi)Δx
where n is the number of subintervals, f(mi) is the value of f(x) at the midpoint of the i-th subinterval, and Δx is the width of each subinterval.
In this case, n=3, Δx=0.6, and the midpoints are 1.3, 1.8, and 2.5. So we have:
∑(i=1 to 3) f(mi)Δx
= f(1.3)0.6 + f(1.8)0.6 + f(2.5)0.6
= 0.6[f(1.3) + f(1.8) + f(2.5)]
To find the values of f(1.3), f(1.8), and f(2.5), we need to evaluate the function f(x) at those points. Since we don't know the actual function f(x), we can use the given subintervals to estimate its values using the left endpoints:
f(1) = 1, f(1.6) = 2, f(2) = 4, f(3) = 9
Then, using the midpoint formula, we have:
f(1.3) = f((1+1.6)/2) = f(1.3) ≈ f(1) = 1
f(1.8) = f((1.6+2)/2) = f(1.8) ≈ f(1.6) = 2
f(2.5) = f((2+3)/2) = f(2.5) ≈ f(2) = 4
Substituting these values into the Riemann sum formula, we get:
∑(i=1 to 3) f(mi)Δx
= 0.6[f(1.3) + f(1.8) + f(2.5)]
≈ 0.6[1 + 2 + 4]
= 4.2
Therefore, the approximate value of the definite integral ∫31f(x)ⅆx using a midpoint Riemann sum with the subintervals [1,1.6], [1.6,2], and [2,3] is 4.2.
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Related Questions
2 Gallons of Juice for $4.50. How much per Gallon?
Answers
4.50 divided by 2 is 2.25
Answer: 2.25 per gallon
Step-by-step explanation:
4.50 divided by 2 = 2.25
Mia sells tickets for a football game. A kids ticket cost $2 and a adult cost $4. She sold 43 tickets. How many kids ticket and adult tickets did she sell?
Answers
Answer:
not enough information to answer
Step-by-step explanation:
A garden center is running a special on houseplants. A selection of any 2 plants cost $7. If a designer buys 22 plants for new homes, how much does the designer spend on plants?
Answers
Answer:
77
Step-by-step explanation:
*WILL GIVE BRAINLIEST*
What is surface area?
Question 5 options:
A: The sum of all the areas of all the faces of a 3D object (think: wrapping paper)
B: The measure of space inside a 2D object
C: The measure of space inside a 3D object
D: The measure around a 2D shape (Think: a fence)
Answers
Answer:
The answer is A.
Step-by-step explanation:
I learned it before.
Hope this helps.
Answer:
A
Step-by-step explanation:
Answer is A
Thanks for Brainliest, dude.
Middle School
Mathematics
Find x.
A. 8
B. 12
Answers
Answer:
17²=15²+x²
289=225+x²
288-225=x²
64=x²
x=6
Answer:
8
Step-by-step explanation:
By Pythagoras theorem,
(hypotenuse)² = (altitude)² + (base)²
(17)² = x² + (15)²
(17)² - (15)² = x²
289 - 225 = x²
x² = 64
x = √64
x = 8
hope this helps you!
What is the image point of (1,0) after a translation right 1 unit and up 4 units?
Answers
Answer:
(2,4)
Step-by-step explanation:
hope this helps :)
Answer:
(1,0) + 4 up and + 1 right
The answer is (2,4)
"Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by y = 0, y = sin(x), and 0 < x < π about the line y = -2. Please also provide a sketch of the region and the line of rotation."
Answers
The integral for the volume generated is V = ∫[0, π] 2π(x + 2) [sin(x)] dx
How to set up the integral for the volume generatedFrom the question, we have the following parameters that can be used in our computation:
y = 0 and y = sin(x)
Also, we have
The line u = -2
Set the equations to each other
So, we have
sin(x) = 0
When evaluated, we have
x = 0 and x = π
For the volume generated from the rotation around the region bounded by the curves, we have
V = ∫[a, b] 2π(x + 2) [g(x) - f(x)] dx
This gives
V = ∫[0, π] 2π(x + 2) [sin(x) - 0] dx
So, we have
V = ∫[0, π] 2π(x + 2) [sin(x)] dx
Hence, the integral for the volume generated is V = ∫[0, π] 2π(x + 2) [sin(x)] dx
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10.Which of these operations should be completed firstwhen solving an equation?a. xb. +c. ()d. +
Answers
Given the list of symbols:
x, +, ( ), ÷
Let's determine the operations that should be completed first when solving an equation.
To solve an equation, we are always required to apply the PEMDAS theorem.
PEMDAS is an acronym for:
0. P,arentheses
,1. E,xponents
,2. M,ultiplication
,3. D,ivision
,4. A,ddition
,5. S,ubtraction.
This shows the order in which the operations in an equation should be solved.
We can see that the first operation which is to be completed is the parenthesis.
Therefore, using the PEMDAS theorem, the operation that should be first completed when solving an equation is the parenthesis ().
ANSWER:
C. ( )
There are 2 students in James' class. How many students remain if 3 go outside?
Answers
Answer:
-1
Step-by-step explanation:
A circle has a radius of 7cm. Which of these is closest to its circumference?
Answers
Answer:
You didn't list the answers but it's 43.98 so close to 44 I'm guessing
Step-by-step explanation:
circumference=2*pi*r
2*3.14*7=about 44
Answer:
Approximately 22 or 7πcm
Step-by-step explanation:
The ratio between the circumference of a circle and its diameter is π. We commonly write c=2πr, using the radius instead and doubling.
In the given example, we are told that the diameter is
7 cm. So using the common approximation π≈\(\frac{22}{7}\) we find that the circumference is approximate:
\(\frac{22}{7} * 7cm= 22 cm\)
if m<4=35 degrees, find m<2 and m<3
Answers
35, ∠2 and ∠4 are alternate interior angles, so m∠2 = m∠4.
What is alternate interior angles?
Two angles that are on the interior of and, but on different sides of the transversal, are said to be alternate interior angles. The alternate interior angles theorem states that the alternate interior angles must be congruent if two parallel lines are cut by a transversal.Given
m∠4=35
From the image given, angle 2 and angle 4 lie on opposite side of the line that intercepts the two parallel lines, AB and CD. Angle 2 and angle 4 both lie within the parallel lines.
Therefore, ∠2 and ∠4 are alternate interior angles.
Thus,
m ∠2 = m∠4 (alternate interior angles theorem)
since m∠4 = 35°
therefore m∠2 = 35°
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Solve tan^2 theta + 1 = -2 tan theta on the interval 0° ≤ θ ≤ 360°.
Answers
Answer:
Step-by-step explanation:
\(tan^2 \theta+1=-2 \tan \theta \\tan^2 \theta +2 tan \theta +1=0\\(tan \theta+1)^2=0\\tan \theta=-1=-tan 45=tan (360-45)=tan 315\\\theta =315 ^\circ\)
How forgot how to do this problem. I will give brainliest!
Answers
Answers
2x+3y=4
A=2 , B=3 , C=4
step by step:
2x+3y=2 the slope is -2/3
3y=-2x+2
y=-2/3 x+2
parallel line have the same slope: -2/3
the equation of parallel line that passes through point (2,0) y=mx+b
find b
2(2)+3(0)=b
4+0=b
b=4
the equation will be
2x+3y=4
to check : graph the equations:
Gerard concluded that the triangle with sides feet, 8 feet, and cannot be used as a building frame support on the house because it is not a right triangle. How did gerard come to that conclusion? explain.
Answers
Gerard concluded that triangle with given sides cannot be used as building-frame support because it is not right triangle, he come to this conclusion because the Pythagoras-theorem is not satisfied.
In order to check if a triangle is "right-triangle", Gerard used the Pythagorean theorem. According to this theorem, in right triangle, the square of length of hypotenuse (the side opposite the right angle) is equal to sum of squares of other two sides,
So, the squares of the given sides are :
Square of √95 feet = (√95)² = 95 feet
Square of 8 feet = 8² = 64 feet
Square of √150 feet = (√150)² = 150 feet
We see that, 95 feet + 64 feet = 159 feet ≠ 150 feet,
Since the square of the longest side (√150) is not equal to the sum of the squares of the other two sides (√95 and 8), the Pythagorean-theorem is not satisfied.
Therefore, Gerard concluded that the triangle with sides √95 feet, 8 feet, and √150 feet is not a right triangle.
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The given question is incomplete, the complete question is
Gerard concluded that the triangle with sides √95 feet, 8 feet, and √150 cannot be used as a building frame support on the house because it is not a right triangle. How did Gerard come to that conclusion? explain.
1 - sin + cos/sin + cos - 1 = 1 + cos/sin
Answers
Step-by-step explanation:
it is answer of this question.
pls help!
and a reason.
Answers
Answer:
\(\angle BDA = 72^{\circ}\)
\(\angle DAB = 36^{\circ}\)
\(\angle BDC = 108^{\circ}\)
\(\angle BCD = 36^{\circ}\)
\(\angle DBC = 36^{\circ}\)
Step-by-step explanation:
Given
\(\angle ABD = 72^{\circ}\)
Required
Determine the missing angles
Since AB = AD, then:
\(\angle ABD = \angle BDA\) --- Base angles of an isosceles triangle
Hence:
\(\angle ABD = \angle BDA = 72^{\circ}\)
\(\angle ABD + \angle BDA + \angle DAB = 180^{\circ}\) --- angles in a triangle
\(72^{\circ} + 72^{\circ} + \angle DAB = 180^{\circ}\)
\(144^{\circ} + \angle DAB = 180^{\circ}\)
Collect Like Terms
\(\angle DAB = 180^{\circ} - 144^{\circ}\)
\(\angle DAB = 36^{\circ}\)
\(\angle BDA + \angle BDC = 180^{\circ}\) --- angle on a straight line
\(72^{\circ} + \angle BDC = 180^{\circ}\)
\(\angle BDC = 180^{\circ} - 72^{\circ}\)
\(\angle BDC = 108^{\circ}\)
Since ABC is isosceles, then:
\(\angle DAB = \angle BCD = 36^{\circ}\) --- base angle of isosceles
\(\angle BCD = 36^{\circ}\)
Lastly:
\(\angle BCD + \angle BDC + \angle DBC = 180^{\circ}\)
\(36^{\circ} + 108^{\circ} + \angle DBC = 180^{\circ}\)
\(\angle DBC = 180^{\circ} - 36^{\circ} - 108^{\circ}\)
\(\angle DBC = 36^{\circ}\)
See attachment
Exercise 2. Asymptotic analysis a. Solve the recurrence T(n) = 3T(n/4)+O(√n). What is the general k-th term in this case? And what value of k should be plugged in to get the answer?
Answers
a) T(n) is O\(n^{0.793}\)
b) The general k-th term in this case is T(k) = \(3^kT(1)\) + O(k√k).c)
The value of k that should be plugged in to get the answer is k= 1
How is this so?a. The recurrence T(n) = \(3T(n/4)+O(\sqrt n)\) can be solved using the master theorem.
The master theorem states that if T(n) = aT(n/b)+f(n), where a > 1, b > 1, and f(n) is \(O(n^c)\) for some constant c, then \(T(n) is O(n^log_ba^c).\)
In this case, a = 3, b = 4, and c = -1/2.
Therefore,T(n) is \(O(n^{(log_43)}^{-1/2)} = O(n^{0.793).\)
b. The general k-th term, in this case, is T(k) = 3^k*T(1) + O(k*√k).c.
The value of k that should be plugged in to get the answer is k = 1.
This is because the asymptotic analysis of T(n) is only valid for large values of n. For small values of n, the asymptotic analysis may not be accurate.
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6. Find x.
a. x² = 25
Answers
Take the square root of each side.
\(\sf \sqrt{x^{2} } =\sqrt{25} \\\\\\ x=\± 5\)
A car rental agency has 4 minivans and 8 other vehicles available. What is the probability that a randomly selected vehicle will be a minivan? Write your answer as a fraction or whole number
Answers
The probability that a randomly selected vehicle will be a minivan is 1/2.
WE know that Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
Given that the car rental agency has 4 minivans and 8 other vehicles available.
P (minivan) = number of minivans / total number of vehicles
We have 4 minivans and 8 vehicles
P (minivan) = 4/8
P (minivan) = 1/2
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Sydney has a bag of stuffed animals containing, 1 elephant, 4 bears, 3 cats, and 2 dogs. If she randomly selects 1 stuffed animal from the bag, places it on her bed and then selects another animal. What is the probability that she chooses a bear both times?
Answers
Answer:
2/15
Step-by-step explanation:
Step one:
given data
sample space
1 elephant,
4 bears,
3 cats, and
2 dogs.
sample size= 1+4+3+2= 10
Required:
By selecting without replacement, the probability that she chooses a bear both times
Step two:
the first event= Pr(bear)= 4/10= 2/5
the second event, the sample size is now 9 and the number of bears is now 3
Pr(bear)= 3/9= 1/3
Hence, the probability that she chooses a bear both times
= 2/5*1/3
=2/15
Construct a 4th-degree polynomial which has downward end behavior on both the lett and right, and has exactly three x-intercepts: (−5,0),(1,0), and (4,0). Draw a sketch of this function, and provide its equation.
Answers
The sketch of the function will exhibit a downward trend on both sides and intersect the x-axis at -5, 1, and 4. The exact values of a and b can be chosen to achieve the desired end behavior.
To construct the desired polynomial, we know that since it has downward end behavior on both sides, the leading coefficient must be negative. Moreover, since there are three x-intercepts, the polynomial must have three linear factors corresponding to those intercepts.
Let's denote the polynomial as f(x). Since it has x-intercepts at -5, 1, and 4, the factors of the polynomial can be written as (x + 5), (x - 1), and (x - 4). To ensure downward end behavior, we need to multiply these factors by two additional linear factors. We can choose (x - a) and (x - b), where a and b are large positive values.
Therefore, the equation of the 4th-degree polynomial satisfying the given conditions is:
f(x) = -(x + 5)(x - 1)(x - 4)(x - a)(x - b)
The sketch of the function will exhibit a downward trend on both sides and intersect the x-axis at -5, 1, and 4. The exact values of a and b can be chosen to achieve the desired end behavior.
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3. (05.06 MC)
Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions:
y > 3x + 10
y<-
Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution area. (6 points)
Part B: Is the point (8, 10) included in the solution area for the system? Justify your answer mathematically. (4 points)
(10 points)
Answers
Answer:
Step-by-step explanation:
y > 3x + 10
y < -3x - 1
Part A:You'd graph the given systems of linear inequalities the same way as you graph the linear equations.
To graph y > 3x + 10, plot the y-intercept, (0, 10), then use the slope, m = 3 (rise 3, run 1), to plot other points on the graph. Use a dashed line (because of the ">" symbol).
Follow the same steps for the other linear inequality. Plot the y-intercept, (0, -1), then use the slope, m = -3 (down 3, run 1) to plot other points. Use a dashed line (because of the "<" symbol).
Pick a test point on either side of the boundary line and plug it into the original problem. This will help determine which side of the boundary line is the solution. Plug in a test point that is not on the boundary line.
Use the point of origin, (0, 0) as the test point. Plug in these values into the given systems of linear inequalities to see whether it will provide a true statement.
y > 3x + 10
0 > 3(0) + 10
0 > 0 + 10
0 > 10 (False statement).
y < -3x - 1
0 < -3(0) - 1
0 < 0 - 1
0 < -1 (false statement).
Since the point of origin provided a false statement to the given systems of linear inequalities, you must shade the half-plane region where it doesn't contain the test point.
Part B:
You'll do the same process as what I've done for the test point. Plug in the values of (8, 10) into the given systems of linear inequalities. If it provides a false statement, then it means that it is not a solution to the system.
y > 3x + 10
10 > 3(8) + 10
10 > 24 + 10
10 > 34 (False statement).
y < -3x - 1
10 < -3(8) - 1
10 < -24 - 1
10 < -25 (false statement).
Therefore, (8, 10) is not a solution to the system.
What is the solution set of |-x| = -10?
(10)
7-10)
{-10, 10)
no solution
Answers
Answer:
{-10, 10)
Step-by-step explanation:
| | - means to only take the number inside, not the sign
x=-10 or 10
Answer:
i dont understand what you want me to answer
Step-by-step explanation:
The weight of 2apple i 400 gram. I ate one apple of 150 gram. Find the weight of the other apple
Answers
The weight of the other apple is 250 grams.
As per the given data:
The weight of 2 apples is 400 gram.
The weight of 1 apple is 150 grams which I ate.
We have to determine the weight of the other apple.
Subtract the weight of 1 apple from weight of 2 apples
Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers
One value is 400 and the other value is 150.
Means subtract 150 from 400.
The weight of the other apple = Weight of 2 apples - The weight of 1 apple
= 400 - 150
= 250 grams
Therefore the answer is 250 grams.
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Can someone help me with this pls. I’ll give brainliest
Answers
Answer:
26
Step-by-step explanation:
a triangle is 180 degrees add 120 + 34 to get 154
180 -154 = 26
Please helpppppp
Given m
11
n, find the value of x and y.
(9x+1)
m
jo
(7x+13)
n
Answers
2x+1=13
2x=12
x=6
7(6)+13
42+13
55
180-55
125
y= 125°
Answer:
x = 6
y° = 125°
Step-by-step explanation:
9x + 1 and 7x + 13 are alternate angles and has same measurement
9x + 1 = 7x + 13
9x - 7x = 13 - 1
2x = 12
x = 6
y° and 7x + 13 are supplementary angles so their sum is 180°
7x + 13 ➡ 7×6 + 13 = 55°
55 + y° = 180 subtract 55 from both sides
y° = 125°
Segment GH underwent a sequence of two rotations around the same center. The original length of GH is 7 meters. What is the length of the segment after the sequence of rotations?
Answers
Answer:
\(GH = 7\ meters\)
Step-by-step explanation:
Given
\(GH = 7\ meters\)
Required
Length of GH after two rotations
In transformations, when a point, shape, line or line segment is rotated; the orientation and location of the point, shape, line or line segment change.
However, the length of the point, shape, line or line segment remains the same.
This is to say that:
After line segment GH is rotated twice, its length will remain unchanged.
Hence:
\(GH = 7\ meters\)
I WILL MARK BRAINLIEST
Answers
Answer:
21.5
Step-by-step explanation:
19+24=43
43/2=21.5
15+25+16+19+24+23+29+21=172
172/8=21.5
Which phrase describes the solution set for this function?
f(x) = 2(x - 1)2 + 4
A.
one real solution and one complex solution
B.
two complex solutions
O C.
two real solutions
D.
one real solution
Answers
Note: The function is not an equation. I will form and solve an equation to answer the question.
Answer:
C. Two real solutions
Step-by-step explanation:
We have the following function:
f(x)=2(x-1)^2+4
It does not form an equation to solve, and therefore, there are no 'solutions'. We must equate the function to something to set a condition and solve it. We'll complete the equation.
Solve for x when:
f(x)=12
Substituting the function:
2(x-1)^2+4=12
Subtracting 4:
2(x-1)^2=8
Dividing by 2:
(x-1)^2=4
Taking square root:
x-1=\pm\sqrt{4}
Solving:
x=1\pm2
We have two real solutions x=3 and x=-1
Note if we had equated to 4, then the equation would have had only one real solution, and if we had equated to 0, we would have two complex solutions.
The solution of equation f(x) = 2x² - 4x + 6 is two complex solutions. Then the correct option is B.
What is the discriminant?The discriminant of a quadratic is a number that depends on the components and allows some characteristics of the roots to be deduced without calculating them.
The quadratic equation is ax² + bx + c = 0. Then the discriminant is given as,
D = b² - 4ac
If D > 0, then the roots are real and distinct root.If D = 0, then the roots are real and equal roots.If D < 0, then the roots are imaginary roots.The equation is given below.
f(x) = 2(x - 1)² + 4
f(x) = 2x² - 4x + 2 + 4
f(x) = 2x² - 4x + 6
The discriminant is given as,
D = (-4)² - 4×2×6
D = 16 - 48
D = - 32
D < 0
The roots are complex root.
The solution of equation f(x) = 2x² - 4x + 6 is two complex solutions. Then the correct option is B.
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What is the scale factor in the dilation?
One-sixth
One-third
3
6
Answers
The scale factor of the preimage to image is 3. Then the correct option is C.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.
The picture rectangle has points on coordinates (0, 0), (0, 8), (9, 8), and (9, 0). The pre-image has points (0, 0), (0, 2.5), (3, 2.5), and (3, 0).
The scale factor is given as,
SF = 9 / 3
SF = 3
The scale factor of the preimage to image is 3. Then the correct option is C.
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The complete question is given below.
What is the scale factor in the dilation?
On a coordinate plane, the image rectangle has points (0, 0), (0, 8), (9, 8), and (8, 0). The pre-image has points (0, 0), (0, 2.5), (3, 2.5), and (3, 0).
a) One-sixth
b) One-third
c) 3
d) 6
Answer:
Step-by-step explanation: C !!!!!! / 3
Edge 2023
1/6
1/3
3 <--------------- correct
6