Estimate the area under the graph of f(x) = 1/x from x = 1 to x = 2 using two approximating rectangles and midpoints. Sketch the graph and the rectangles. Show detailed work.
Answers
The estimated area under the graph of f(x) = 1/x from x = 1 to x = 2, using two approximating rectangles and midpoints, is approximately 0.6857.
How did we get the value?To estimate the area under the graph of f(x) = 1/x from x = 1 to x = 2 using two approximating rectangles and midpoints, divide the interval [1, 2] into two equal subintervals and calculate the area of each rectangle.
First, let's sketch the graph of f(x) = 1/x and mark the interval [1, 2]: check the attached graph.
Next, divide the interval [1, 2] into two subintervals of equal width: check the attached graph
Now, let's find the midpoint of each subinterval and evaluate f(x) at those points:
For the first subinterval [1, 1.5]:
Midpoint = (1 + 1.5) / 2 = 1.25
f(1.25) = 1 / 1.25 = 0.8
For the second subinterval [1.5, 2]:
Midpoint = (1.5 + 2) / 2 = 1.75
f(1.75) = 1 / 1.75 ≈ 0.5714
Next, let's calculate the width and height of each rectangle:
For the first rectangle:
Width = 1.5 - 1 = 0.5
Height = f(1.25) = 0.8
For the second rectangle:
Width = 2 - 1.5 = 0.5
Height = f(1.75) ≈ 0.5714
Now, calculate the area of each rectangle:
Area of the first rectangle = Width × Height = 0.5 × 0.8 = 0.4
Area of the second rectangle = Width × Height = 0.5 × 0.5714 ≈ 0.2857
Finally, add the areas of both rectangles to get the estimated area under the graph:
Estimated area = Area of the first rectangle + Area of the second rectangle
= 0.4 + 0.2857
≈ 0.6857
Therefore, the estimated area under the graph of f(x) = 1/x from x = 1 to x = 2, using two approximating rectangles and midpoints, is approximately 0.6857.
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Related Questions
Help please .....................
Answers
Answer:
70
Step-by-step explanation:
well you know that angles in the same segment are equal so angle VWZ also= 38
triangle VWZ is a triangle so the sum of interior angles sums to 180
180-72-38=70
Find the volume of the solid that is formed when the area bounded by xy=1, y=0, x=1, and x=2 is rotated about the line x=-1.
Answers
The volume of the solid that is formed when the area bounded by x y=1, y=0, x=1, and x=2 is rotated about the line x=-1 is (14π/3) cubic units.
The solid that is formed when the area bounded by
xy=1, y=0, x=1, and
x=2 is rotated about the line
x=-1 is given by the disk method.
To find the volume of the solid, we integrate the area of each disk slice taken perpendicular to the axis of revolution,
which in this case is the line x=-1.
The area of each disk slice is given by the formula π(r^2)δx
where r is the radius of the disk and δx is its thickness.
To find the radius r of each disk slice, we consider that the distance between the line
x=-1 and the line
x=1 is 2 units.
Hence,
the radius of the disk is r=2-x.
Hence, the volume of the solid is given by:
V= ∫1^2 π(2-x)^2 dx
= π ∫1^2 (x^2-4x+4) dx
= π[(x^3/3)-(2x^2)+4x]
evaluated between
x=1 and
x=2= π [8/3-8+4-1/3+2-4]
= (14π/3) cubic units
Therefore, the volume of the solid that is formed when the area bounded by x y=1,
y=0,
x=1, and
x=2 is rotated about the line
x=-1 is (14π/3) cubic units.
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A rental car company charges $48 per day to rent a car and $0.08 for every mile
driven. Bilquis wants to rent a car, knowing that:
. She plans to drive 175 miles.
. She has at most $110 to spend.
Write and solve an inequality which can be used to determine x, the number of days Bilquis can afford to rent while staying within her budget.
Answers
The number of days Bilquis can afford to rent while staying within her budget is 2 days.
How to solve the inequalityThe question has the following data
amount charged = $48
Rent per mile = $0.08
The mile to drive = 175 miles.
Amount to spend = 110 dollars
The inequality would be written as
48x + 0.08(175) ≤ 110
we are to solve for the value of x
this would be
48x + 14 ≤ 110
48x ≤ 110 - 14
48x ≤ 96
We have to divide through by 48
x ≤ 96 / 48
x ≤ 2
Hence we can say that the number of days Bilquis can afford to rent while staying within her budget is 2 days.
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Sara will use 7 cups of apples to make 4 batches of applesauce. Choose all of the expressions that show the number of cups of apples in one batch.
Answers
To make 4 batches of applesauce, 7 cups of apples are needed.
So the number of cups, of apples in one batch is calculated as by taking the ratio as 4:7 to 1:x . Here xis the number of cups for 1 batch.
\(\begin{gathered} \frac{4}{7}=\frac{1}{x} \\ 4x=7 \\ x=\frac{7}{4} \end{gathered}\)So, from the expressions, we can see that,
(A) is correct option,
(B) is correct option,
(E) is correct option
(F) is correct option
As these all corresponds to "7/4"
a coin is flipped, where each flip comes up as either heads or tails. how many possible outcomes contain at least three heads if the coin is flipped 9 times?
Answers
There are 87 possible outcomes that contain at least three heads when a coin is flipped 9 times.
When a coin is flipped nine times, there are 512 possible outcomes, or 29. Using the equation:
P (At least one head) = 1 - 0.5n,
where n is the total number of flips, we can determine the number of outcomes that contain at least three heads.
Therefore, P (At least three heads) = 1 - P (No heads) - P (One head) - P (Two heads)
= 1 - (0.5)⁹ - 9(0.5)⁹ + 36(0.5)⁹
= 0.1718751.
The formula used to calculate the number of possible outcomes that contain at least three heads is C(9,3) + C(9,4) + C(9,5) + C(9,6) + C(9,7) + C(9,8) + C(9,9),
where C(n,r) denotes the variety of options for selecting item(s) r from a set of item(s) n.
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-4/5 / 2 i still cant find the answer
Answers
Answer:
-2.25
Step-by-step explanation:
you gotta divide -4/5 by 2
6(x + 3) = 48 solve for x and give me a number form explanation: 1+1=2
Answers
X+3=8
X=8-3
=5
Answer:
x is 5
Step-by-step explanation:
6(x+3) =48
(6*x)+(6*3)=48
6x+18=48
-18 -18
6x=30
/6 /6
x=5
If you spend $50,000 on new furniture and it is depreciating about 20% per year, how much will it be worth by its third year?
Answers
Answer:
$25,600
Step-by-step explanation:
Given: P = $50,000, r = 20% & t = 3 yearsFormula for depreciation is given as:\(A(t) = P\bigg(1-\frac{r}{100}\bigg)^t\)Plugging the values of P, r and t in the above formula, we find:\(A(3) = 50,000\bigg(1-\frac{20}{100}\bigg)^3\)\(\implies A(3) = 50,000\bigg(1-\frac{1}{5}\bigg)^3\)\(\implies A(3) = 50,000\bigg(\frac{4}{5}\bigg)^3\)\(\implies A(3) = 50,000\times\frac{64}{125}\)\(\implies A(3) =\$ 25,600\)So, after third year it will be worth by $25,600.Plzz help!! Please explain.! Will choose BRAINLIEST!!!
Answers
Answer: 3
Step-by-step explanation:
A simple way to calculate the distance between numbers on a number line is to count every number between them. A faster way is to find the distance by taking the absolute value of the difference of those numbers. We have to find PQ. TAking the difference we have 94-91= 3.
Answer:
\(3\)
Step-by-step explanation:
You can find the length by subtracting.
\(Q-P\)
\(94-91\)
\(=3\)
You can also find the length by counting the units of the distance covered between the points.
What is the domain of f(x)=(1/2)^x
Answers
Answer:
x is greater than zero c is correct
Plz, answer this question plz!
Answers
How many different letter arrangements can be made from the letters (a) Fluke? (b) Propose? (c) Mississippi? (d) Arrange? A child has 12 blocks, of which 6 are black, 4 are red, 1 is white, and 1 is blue. If the child puts the blocks in a line, how many arrangements are possible?
Answers
a) Fluke has 5 letters. b) Propose has 7 letters. c) Mississippi has 11 letters d) Arrange has 7 letters
We have been given that child has 12 blocks, of which 6 are black, 4 are red, 1 is white, and 1 is blue.
Since, the number of different letter arrangements can be made from the letters Fluke is 5! = 120.
b) the number of different letter arrangements that can be made from the letters Propose is 7! = 5040.
Therefore, Propose has 7 letters.
c) the number of different letter arrangements can be made from the letters Mississippi is
11!/(4!4!) = 34650.
Thus Mississippi has 11 letters, and it has 4 S's and 4 I's
d) the number of different letter arrangements that can be made from the letters Arrange,
7!/(2!2!) = 1260.
Thus Arrange has 7 letters, and it has two Rs and two Es.
Then, the number of arrangements that can be made is; 12!/[(6!)(4!)(1!)(1!)] = 27720 arrangements.
Therefore, the child can make 27720 arrangements with 12 blocks.
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Can you make the graph with the points plotted with x being 1, 2, 3, 4, and 5.
Answers
Answer:
oh if x is 1,2,3,4,5,
it will be a vertical line at each of these points if there are different graphs
The most concise notation to use to define function parameters x and y as double is __________. Group of answer choices
Answers
e. a 20 foot by 10 foot rectangular pool has been built. if 50 cubic feet of water is pumped into the pool per hour, write the water-level height (feet) as a function of time (hours).
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To find the water-level height (feet) as a function of time (hours), we need to know the volume of the pool and how much water is being pumped in per hour.
The volume of the rectangular pool can be found by multiplying its length, width, and height:
Volume = Length x Width x Height
Since we know the dimensions of the pool are 20 feet by 10 feet, we can assume the height is 5 feet (half the length of the pool).
Volume = 20 ft x 10 ft x 5 ft = 1000 cubic feet
This means the pool can hold 1000 cubic feet of water.
If 50 cubic feet of water is pumped into the pool per hour, we can write the water-level height (h) as a function of time (t) as follows:
h(t) = (50t) / 1000
where t is the time in hours.
For example, after 1 hour, the water-level height would be:
h(1) = (50 x 1) / 1000 = 0.05 feet
After 2 hours, the water-level height would be:
h(2) = (50 x 2) / 1000 = 0.1 feet
And so on.
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The two line plots below show the times that Marco and Antonio ran in ten trials of the 40-yard dash.
antonio's:4.5,4.5,4.6,4.6,4.6,4.8,4.8,5.2,5.2,5.3,5.5
Marcos's:4.8,4.8,4.9,4.9,4.9,4.9,5.0,5.0,5.0,5.1
Which of the following can be inferred from the data?
A. Antonio runs the race faster than Marco on average.
B. Marco always runs a better time than Antonio.
C. Marco is more likely than Antonio to improve after a poor race.
D. Antonio's average time is about 5.1 seconds,
Answers
Step-by-step explanation:
The answer is A
Bcz In a race runs faster whoever does it in less time
A group of students are going on a field trip. If the group takes 3 vans and 1 car, 22 students can be transported. If the group takes 2 vans and 4 cars, 28 students can be transported. How many students can fit in each van?
Answers
Answer:
4 cars fit for 12 students. and
2 vans fit for 16 students.
Answer:
6 students in each van.
Step-by-step explanation:
Having van as x variable and car as y variable.
3x + y = 22
2x + 4y = 28
Step 1: Solve for y in 3x + y =22
y = 22 - 3x
Step 2: Substitute y = 22 - 3x into 2x + 4y =28
2x + 4(22-3x) = 28
2x + 88 - 12x = 28
=> -10x + 88 = 28
Step 3: Solve for x (which is one van) in -10x + 88 = 28,
-10x = 28 - 88
-10x = -60
=> x = 6
Thus, we have 6 students that can fit in each van.
For the data in the table, does y vary directly with x? If it does, write variation, 1. X 2 y 18 36 54 4 6 a. no; y does not vary directly with x c. yes; y = 4.5x d. yes; y = 9x b. yes; y = 18x
Answers
The answer is (a) no; y does not vary directly with x.
Find whether y varies directly with x?To determine whether y varies directly with x, we need to check if the ratio of y to x is constant. That is, if we divide any y value by its corresponding x value, we should get the same result for all pairs of values. Let's calculate these ratios for the given data:
For x = 18, y/x = 36/18 = 2
For x = 54, y/x = a/54
For x = 2, y/x = 6/2 = 3
Since the ratio of y to x is not constant, we can conclude that y does not vary directly with x. Therefore, the answer is (a) no; y does not vary directly with x.
Note that if y did vary directly with x, we would expect the ratio of y to x to be constant for all pairs of values. In that case, we could write an equation of the form y = kx, where k is the constant of variation. However, since the ratio of y to x is not constant in this case, we cannot write such an equation.
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Based on your calculations so far, how many cubic meters of water did the hull of the titanic have to displace to stay afloat?
Answers
The cubic meters of water did the hull of the titanic have to displace to stay afloat is known to be about 52,310 tons that is 51843.918 m³ of water.
What is the titanic calculations about?The RMS Titanic is known to be a ship that is said to be owned by the White Star Line.
This is known to be the biggest British passenger liner that was said to have sank when it was on its maiden voyage in the year 1912 in the North Atlantic Ocean.
Note that it sank because it was said to have hit an iceberg on Sunday, 14 April 1912.
The Titanic was said to be about 46,328 gross register tons and was known to have displaced about 52,310 tons of water.
So, 1 ton (displacement) ≈ 0.99109 cubic meters (m³)
Therefore, 52,310 tons
= 52,310 × 0.99109 m³
≈ 51843.918 m³
Therefore, The cubic meters of water did the hull of the titanic have to displace to stay afloat is known to be about 52,310 tons that is 51843.918 m³ of water.
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pls help me and explain how to do this
Answers
The slope of the line is -3/4.
What is a line?
A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things. The term "line" can also be used to describe a line segment in daily life that contains two locations that serve as its ends.
The points on the line are (-4, 5), (0,2), (4, -1).
The slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).
The slope of the line is
(2 - 5)/(0 - (-4)) = -3/4
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A- 63
B- 125
C-44
D-45
Answers
Answer:
So, the sum of the 3 angles in a triangle is 180.
What you would do is:
180= 73+6x-4+7x+7.
Then, you add the common coefficients:
180=76+13x
Then you subtract:
104=13x
Then you divide:
x=8.
Then substitute the x value into the A value to get 44, meaning that C is the correct answer.
Write each as an algebraic expression
Answers
Answer:
4^3
11>6
y>2
13-x
Step-by-step explanation:
4 is to the third power
11 is greater than 6 which means u use this sign >
y is greater than 2
13 subtract x
Find the length of BC. (Decimal Answer)
Answers
Answer:
the answer is 9 1/3 i think the decimal would be 3 repeating
Step-by-step explanation:
Can anyone help please?
Answers
Answer:
A'(-3, 12)B'(9, 6)C'(-6, -6)Step-by-step explanation:
Dilation about the origin multiplies each coordinate value by the dilation factor.
For dilation factor k, the new coordinates are ...
(x, y) ⇒ (kx, ky)
Your dilation factor is 3, so the transformation is ...
(x, y) ⇒ (3x, 3y)
A(-1, 4) ⇒ A'(-3, 12)
B(3, 2) ⇒ B'(9, 6)
C(-2, -2) ⇒ C'(-6, -6)
Show that x=0 is a regular singular point of the given differential equation
b. Find the exponents at the singular point x=0.
c. Find the first three nonzero terms in each of two solutions(not multiples of each other) about x=0.
xy'' + y = 0
Answers
The first three nonzero terms of two linearly independent solutions about x = 0 can be obtained by Taylor expanding the solutions in terms of the exponent r and truncating the series to the desired order.
To determine if x = 0 is a regular singular point of the differential equation xy'' + y = 0, we substitute y = x^r into the equation and solve for the exponent r. Differentiating y twice with respect to x, we have y'' = r(r - 1)x^(r - 2). Substituting these expressions into the differential equation, we get \(x(x^r)(r(r - 1)x^(r - 2)) + x^r = 0\). Simplifying, we obtain r(r - 1) + 1 = 0, which yields r^2 - r + 1 = 0. Solving this quadratic equation, we find that the exponents at the singular point x = 0 are complex and given by r = (1 ± i√3)/2.
To find the first three nonzero terms of two linearly independent solutions about x = 0, we can use the Taylor series expansion. Let's consider the solution y1(x) corresponding to the exponent r = (1 + i√3)/2. Expanding y1(x) as a series around x = 0, we have y1(x) =\(x^r = x^((1 +\)i√3)/2) = x^(1/2) *\(x^(i√3/2\)). Using the binomial series expansion and Euler's formula, we can write \(x^(1/2) and x^(i√3/2)\) as infinite series.
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Please help me with this question
Answers
Answer:
Either 36.35 or 16.00173
Step-by-step explanation:
the reason im saying its either is due to not remembering whether do divide by inverse cosine to get on other side of equal sign or to just divide the cosine as is.
IF you are supposed to use inverse cosine:
16.00173
IF NOT:
36.35182
What is the coefficient of y in the expression 2x4+3y
Answers
Answer:
3
Step-by-step explanation:
Las dos ruedas traseras de un tractor tienen un perímetro 90 cm mayor que las delanteras. En un camino de 230 metros, las ruedas traseras giran 36 veces menos que las ruedas delanteras. ¿Cuál es el perímetro de las ruedas?
Answers
Sabemos que en un camino de 230 metros, las ruedas delanteras giran 36 veces más que las traseras. Esto significa que la distancia recorrida por las ruedas delanteras es 36 veces mayor que la distancia recorrida por las traseras en ese camino. Por lo tanto:
36(x + 90) = 23000
Resolviendo para x, obtenemos:
x + 90 = 23000/36
x + 90 = 638.89
x = 548.89
Por lo tanto, el perímetro de las ruedas delanteras es de 548.89 cm, y el perímetro de las ruedas traseras es x + 90 = 638.89 cm.
Is 59 a prime number?
Answers
Answer: Yes, 59 is a prime number
Step-by-step explanation: 59 is a prime number, it has only two factors, such as one and the number itself. Hence, the factors of 59 are 1 and 59.
Yes, 59 is a prime number.
What is a prime number?
Any natural number greater than 1 that is not the sum of two smaller natural numbers is referred to as a prime number. A composite number is a natural number greater than one that is not prime.
In other terms, prime numbers are positive integers greater than one that only has the number itself and 1 as factors. 2, 3, 5, 7, 11, 13, and other prime numbers are just a few examples. Never forget that 1 is neither a prime number nor a composite. Apart from 1, the other numbers can all be categorised as prime and composite numbers. Except for 2, which is the smallest prime number and the only even prime number, all prime numbers are odd.
The number in question, which is 59, has only two factors: 1 and 59.
Therefore 59 is a prime number.
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Find the area of the shaded region
Answers
Answer:
Area = 28.43 cm²
Step-by-step explanation:
area of square = 11.5 x 11.5 = 132.25 cm²
area of circle = πr² = (3.14)(5.75²) = 103.82 cm²
Area= 132.25 - 103.82 = 28.43 cm²
Answer:
28.38 cm²
Step-by-step explanation:
Area of square
a = 11.5^2
a = 132.25
The corners are 4 quarter circle
which makes a complte circle
a = πr^2
a = π(11.5/2)^2
a = 103.8689071093
Area shaded
a = 132.25 - 103.8689071093
a = 28.3810928907
Rounded
a = 28.38 cm²