Estimate the area under the curve f(x) = x^2 from x = 1 to x = 5 by using four inscribed (under the curve) rectangles. Answer to the nearest integer.
Answer:
30 square units
Step-by-step explanation:
For a rectangle to be described as "inscribed" in the context of estimating the area under a curve, the entire rectangle should be positioned underneath the curve.
Therefore, as the curve of f(x) = x² is convex (concave up) in the interval [1, 5], to estimate the area under the curve by using inscribed rectangles, we can use the Left Riemann Sum.
The Left Riemann Sum is a numerical approximation method used to estimate the definite integral of a function over a given interval by dividing the interval into subintervals. It approximates the area under the curve of a function by using rectangles, where the left side of each rectangle touches the curve at the left endpoint of each subinterval.
[tex]\boxed{\begin{minipage}{11cm}\underline{Left Riemann Sum}\\\\$\displaystyle \int^b_a f(x)\; \text{d}x \approx \Delta x \left(f(x_0)+f(x_1)+f(x_2)+...+f(x_{n-2})+f(x_{n-1})\right)$\\\\$\text{where}\; \Delta x=\dfrac{b-a}{n}$\\\end{minipage}}[/tex]
The number of subintervals, n, is the number of rectangles used, and the interval is [a, b].
As the interval is [1, 5], this means that a = 1 and b = 5.
As the number of rectangles to use is 4, then n = 4.
Calculate the value of Δx:
[tex]\Delta x=\dfrac{b-a}{n}=\dfrac{5-1}{4}=\dfrac{4}{4}=1[/tex]
The given partition divides the interval [1, 5] into 4 subintervals where the width of each subinterval is one. Therefore, the left endpoints are:
[tex]x_0=1[/tex][tex]x_1=2[/tex][tex]x_2=3[/tex][tex]x_3=4[/tex]Substitute everything into the formula and solve:
[tex]\begin{aligned}\displaystyle \int^5_1 x^2\; \text{d}x &\approx 1\cdot \left(f(1)+f(2)+f(3)+f(4))\right)\\\\&=(1)^2+(2)^2+(3)^2+(4)^2\\\\&=1+4+9+16\\\\&=30\end{aligned}[/tex]
Therefore, the estimation of the area under the curve f(x) = x² from x = 1 to x = 5 using four inscribed rectangles is 30 square units.
What is the measure of an angle whose sine is√3/2 ? 60 45 30
Jamarcus's employer pays 80 percent of his medical insurance. If the insurance costs Jamarcus $20 a week, how much is his employer paying?
Answer:
$80
Step-by-step explanation:
The total amount of his medical insurance is 100%. As such if Jamarcus's employer pays 80 percent , then the amount he pays would be equivalent to 20%.
As such, if the insurance costs Jamarcus $20 a week and the total amount is Y
then,
20% of Y = $20
0.2Y = $20
Y = $100
His employer will be paying
= 80% of $100
= $80
Jenny is 65 years old, retired, and good health, and likes to travel to wor Jenny is 65 years old, retired, and good health, and likes to travel to world. Which lifestage best describes her?
Jenny is at the life stage of Mature Adulthood, this is the stage of where an adult has established their goals in life such as that involve in work, or anything that they have contributed in their life. They were able to raise a family and has learned things that happened in his or her life.
Which of the following best describes the algebraic expression 15x + 8? A. the sum of fifteen times a number and eight B. the product of fifteen plus a number and eight C. fifteen times the sum of a number and eight D. fifteen times the quantity of a number plus 8
Answer: A. [tex]\text{the sum of fifteen times a number and eight }[/tex]
Step-by-step explanation:
The given algebraic expression : [tex]15x + 8[/tex]
We can see that the constant term here is [tex]8[/tex].
The variable term is [tex]15x[/tex].
The operation used here = Addition
To convert any algebraic expression into a statement we represent the variable i.e. x by word "number".
Then the variable term is represented as : Fifteen times a number
Therefore, the best describes the given algebraic expression will be :-
"[tex]\text{the sum of fifteen times a number and eight }[/tex]"
I need help with starring the answer in mixed fraction
what is a skew line?
Skew lines are non-coplanar lines that do not intersect. For example, take a look at the image provided below. Lines m and n in the diagram do not lie on the same plane and they don't intersect. Therefore, we can say that line m is skew to line n.
How many elements does each of these sets have where a and b are distinct elements?
a.p({a,b,{a,b}})
b.p({∅,a,{a},{{a}}})?
After a researcher adds 5 points to every score in a sample, the standard deviation is found to be s = 10. the original sample had a standard deviation of s = 5.
a. True
b. False
Dan is using tiles to add –8 + 6. He begins with the tiles shown below.
mc006-1.jpg
What is the sum of –8 + 6?
–14
–2
2
14
Answer:
Step-by-step explanation:
Alright, lets get started.
The given expression is : [tex]-8+6[/tex]
-8 can be written as [tex]-6-2[/tex]
So, the expression will be = [tex]-6-2+6[/tex]
The plus six and minus six will be cancelled. so,
-2 will be remaining.
So the answer is -2 : Answer
Hope it will help :)
Answer:
-2
Step-by-step explanation:
If two ants are walking in straight lines but in different directions their paths cannot cross more than once. Write the postulate that justifies this statement.
In a public opinion poll 624, people from a sample of 1100 indicate they would vote for a specific candidate. How many votes can the candidate expect to revive from a Population of 40,000
To solve this problem the best way is
624/1100 = x/40000
x = 624*40000/1100
x = 24960000/1100
x = 22690 votes
Around 22690 votes can be expected to revive from a Population of 40,000 by taking the same ratio.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Let's say x votes can be expected to revive from a Population of 40,000.
Now,
By taking the same ratio;
x/40000 = 624/1100
x = 22690.9090 which can be counted as 22690.
Hence " Around 22690 votes can be expected to revive from a Population of 40,000 by taking the same ratio".
For more information about ratio and proportion,
brainly.com/question/26974513
#SPJ2
When adding two numbers, such as 123 and 423, care is taken to first line them up and then add like digits. How does expanding this expression to [(1 × 10^2 ) + (2 × 10^1 ) + (3 × 10^0 )] + [(4 × 10^2 ) + (2 × 10^1 ) + (3 × 10^0 )] make the operation more like a polynomial addition problem?
The volume of a cube is 27n^27 cubic units. What is the length of one side of the cube?
3n^3 units
3n^9 units
27n^3g units
27n^9 units
Answer:
3n^9
this is answer peace
Please help! Which direction would the graph y= Ix-4I+3 open? a) left b) up c) right d) down
In the diagram below de is parallel to xy what is the value of y?
Answer:
C. 75.
Step-by-step explanation:
We have been given a diagram of two parallel lines and we are asked to find the value of y.
We can see from our given diagram that angle y and the angle that measures 105 degrees is formed inside the parallel lines and on the same side of transversal.
Since the the angles formed on the same side of transversal and inside parallel lines are called consecutive interior angles and they add up-to 180 degrees, so we can set an equation as:
[tex]y^o+105^o=180^o[/tex]
[tex]y^o+105^o-105^o=180^o-105^o[/tex]
[tex]y^o=75^o[/tex]
Therefore, the value of y is 75 degrees and option C is the correct choice.
I need help!
Step 1 ?
Step 2 ?
Step 3 ?
Step 4 ?
Triangle FGH is an isosceles right triangle with a hypotenuse that measures 16 units. An altitude, GJ, is drawn from the right angle to the hypotenuse.
What is the length of GJ?
A. 2 units
B. 4 units
C. 6 units
D. 8 units
The value of the length GJ for the given triangle will be 8 units thus option (D) is correct.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
As per the given isosceles triangle which has two equal sides so suppose the length of those sides is x unit.
By Pythagoras' theorem,
⇒ x² + x² = 16²
⇒ 2x² = 256
⇒ x² = 128
The area of a triangle is given as,
⇒ (1/2) × x × x
⇒ (1/2) x²
⇒(1/2) × 128
⇒ 64 units²
The area of the triangle will also be given as,
A = (1/2) × 16 × (GJ)
Compare both areas as
64 = (1/2) × 16 × GJ
GJ = 8 units
Hence"For the provided triangle, the length GJ value will be 8 units".
For more about triangles,
https://brainly.com/question/2773823
#SPJ2
Three more than twice the sum of 7 and a number is 25 find the number
Answer:
the number is 4
Step-by-step explanation:
Hello,I think I can help you with this
Step 1
convert into mathematical terms
let x the unknown number
three more: 3 +
twice the sum of 7 and a number:2(7+x)
is 25:=25
Hence
3+2(7+x)=25
Step 2
Now, solve for x
3+14+2x=25
17+2x=25
2x=25-17
2x=8
x=8/2
x=4
the number is 4
Do not hesitate to ask me if you have any concerns
Have a great day.
There are seven vegetables. Two are squash. Two are cucumbers. The rest are carrots. You randomly choose a vegetable. Find P(cucumber). A. 1/7 B. 1/4 C. 2/7 D. 1/2
Which of the following statements is true about the triangles below?
triangleABC ≅ triangleABD by SSS
triangleABC ≅ triangleABD by ASA
triangleABC ≅ triangleABD by SAS
triangleABC ≅ triangleABD by AAA
Answer:
triangleABC ≅ triangleABD by ASA
Step-by-step explanation:
Took the test and it was correct
Rose likes to water ski on her sister's boat. the boat takes 3 gallons of gas each hour to run. gas costs $5 per gallon, how much money will she spend on gas to ski for 4 hours?
The Volume of a cube is 343ft cubed. What is the length of one side
What is a mathematical phrase that contains numbers, variables, or operators, but no equal sign?
What is the max number of slices of pizza can you get out out of 6 cuts?
Stephanie read 72 page on sundy and 83 pages on monday about haw many pages did stephanie read during the two days
Fiona is serving iced tea and lemonade at a picnic. She has only 44 cups in which to serve the drinks. If x represents the number of glasses of iced tea and y represents the number of glasses of lemonade, which equation represents the number of glasses of iced tea she can serve?
Answer:
[tex]x=44-y[/tex]
Step-by-step explanation:
Let x represents the number of glasses of iced tea and y represents the number of glasses of lemonade.
We have been given that Fiona is serving iced tea and lemonade at a picnic. She has only 44 cups in which to serve the drinks. We can represent this information in an equation as:
[tex]x+y=44[/tex]
Since x represents the number of glasses of iced tea, so we will solve for x by subtracting y from both sides of our equation.
[tex]x+y-y=44-y[/tex]
[tex]x=44-y[/tex]
Therefore, the equation [tex]x=44-y[/tex] represents the number of glasses of iced tea Fiona can serve.
the area of a rectangular field is 6603 meter squared. if the width of the field is 71 m what is it’s length
Area of rectangular field is 6603m². Given width 71m, length is 93m (6603 ÷ 71).
To find the length of the rectangular field, you can use the formula for the area of a rectangle:
[tex]\[ \text{Area} = \text{Length} \times \text{Width} \][/tex]
Given that the area is [tex]\( 6603 \, \text{m}^2 \)[/tex] and the width is [tex]\( 71 \, \text{m} \)[/tex], you can rearrange the formula to solve for the length:
[tex]\[ \text{Length} = \frac{\text{Area}}{\text{Width}} \][/tex]
Substitute the given values:
[tex]\[ \text{Length} = \frac{6603 \, \text{m}^2}{71 \, \text{m}} \][/tex]
[tex]\[ \text{Length} = 93 \, \text{m} \][/tex]
So, the length of the rectangular field is [tex]\( 93 \, \text{m} \).[/tex]
Describe the possible values for x and y when ∣x − y ∣ > 0. What does it mean when ∣x − y ∣ = 0? Can ∣x − y ∣ < 0? Explain your reasoning.
The absolute value |x−y|>0 when x and y are different, |x−y|=0 when x and y are the same, and |x−y| cannot be < 0 because absolute values cannot be negative.
Explanation:The question is about absolute value, which refers to the distance of a number from zero on a number line. The notation |x−y| represents the absolute value of (x-y).
When |x−y|>0, it means that x and y are distinct from each other. For example, if x = 2 and y = 1, |x-y| equals |2-1|=1, which is indeed greater than 0. There are infinite such values for x and y as long as they are not the same.
When |x−y|=0, it implies that x and y are the same. The only way the absolute value of a number can be zero is when the number itself is zero. Therefore, this can only happen if x = y. If x and y are both 2, for example, |x-y| equals |2-2|=0.
|x−y| cannot be less than 0. The absolute value of a number can never be negative, because it represents the distance a number is from zero and distance cannot be negative.
Learn more about Absolute Values here:https://brainly.com/question/4691050
#SPJ2
Marcus bought a shirt that was marked $28, but it was on sale for 15% off the marked price. what was the price of the shirt after the discount
Final answer:
To find the sale price of the shirt after a 15% discount on the marked price of $28, calculate the discount, subtract it from the original price, resulting in a sale price of $23.80.
Explanation:
Marcus bought a shirt that was marked $28, but it was on sale for 15% off the marked price. To calculate the price of the shirt after the discount, you first need to determine the amount of the discount. To do this, convert the percentage to a decimal by dividing by 100 (15% = 0.15) and then multiply this by the original price.
Discount amount = Original price × Discount rate
= $28 × 0.15
= $4.20.
Subtract the discount amount from the original price to find the sale price of the shirt:
Sale Price = Original price - Discount amount
= $28 - $4.20
= $23.80.
Therefore, the price of the shirt after the 15% discount is $23.80.