Approximate the area under the curve y = x^2 from x = 0 to x = 3 using a Right Endpoint approximation with 6 subdivisions.
Will mark brainliest
Answers
Subdivide the interval [0, 3] into 6 subintervals of equal length, ∆x = (3 - 0)/6 = 1/2. Then the partition is
[tex]\left[0,\dfrac12\right] \cup \left[\dfrac12,1\right] \cup \left[1,\dfrac32\right] \cup \cdots \cup \left[\dfrac52,3\right][/tex]
The right endpoint of the [tex]i[/tex]-th subinterval is
[tex]r_i = \dfrac12 + (i-1)\times\dfrac12 = \dfrac i2[/tex]
with [tex]i\in\{1,2,3,\ldots,6\}[/tex].
Then the area under the [tex]y=x^2[/tex] on the interval [0, 3] is approximately
[tex]\displaystyle \int_0^3 x^2 \, dx \approx \sum_{i=1}^6 (r_i)^2 \Delta x = \frac18 \sum_{i=1}^6 i^2[/tex]
Recall that
[tex]\displaystyle \sum_{n=1}^N n^2 = \frac{N(N+1)(2N+1)}6[/tex]
Then the approximate value of the area is
[tex]\displaystyle \int_0^3 x^2 \, dx \approx \frac{6\times7\times13}{48} = \boxed{\frac{91}8}[/tex]
The actual value of the area is 9, so this approximation is an overestimation, as is always the case when using a right endpoint sum for an increasing function.
Related Questions
Find the inverse of the radical function.
Enter the correct answer in the box.
Answers
The inverse of the given function is y = x³ + 2
Finding inverse of a radical functionGiven the radical function below expressed as;
f(x) = ∛x-2
This can be written as;
y = ∛x-2
Replace y with x
x = ∛y-2
Take the cube of both sides
x³ =y - 2
y = x³ + 2
Hence the inverse of the given function is y = x³ + 2
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Answer:
[tex]f^{-1} (x)=x^{3} +2[/tex]
Step-by-step explanation:
from plato
When given
Slope= -6/5
Y-intercept= 2
What is this in Point-Slope form?
Answers
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{y - 2 = -6/5(x - 0)}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{Slope = -6/5, Goes through (0, 2)}[/tex]
Find: [tex]\textsf{The equation in point-slope form}[/tex]
Solution: We need to take the values that were given to us and plug them into the point-slope form. It doesn't seem like the problem is asking for anything more than that so we will leave it at that.
Plug in the values
[tex]\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}[/tex][tex]\textsf{y - 2 = -6/5(x - 0)}[/tex]Since the problem is just asking for the equation in point-slope form the final expression would be y - 2 = -6/5(x - 0).
Answer:
[tex]\sf y - 2 = -\dfrac{6}{5}(x - 0)[/tex]
Step-by-step explanation:
[tex]\sf \large \underline{\textsf{Given:}}\ \textsf{a line with a slope of $-\dfrac{6}{5}$, and a y-intercept of $2$}[/tex]
We're given a y-intercept of 2, but using the slope-intercept form, we can immediately determine that x = 0. Hence, the given point is (0, 2).
Then, we substitute these values into the Point-Slope Form to find the equation.
Here are both forms for future reference:
⇒ Slope-Intercept Form: y = mx + b
[ Where: m is the slope, and b is the y-intercept (when x = 0). ]
⇒ Point-Slope Form: y - y₁ = m(x - x₁)
[ Where: m is the slope, and (x₁, y₁) is a given point. ]
Substitute the values into the Point-Slope Form:
[tex]\sf\\\implies y - y_1 = m(x - x_1)\\\\\implies y - 2 = -\dfrac{6}{5}(x - 0)[/tex]
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What is the length of the hypotenuse? If necessary, round to the nearest tenth.
Answers
Answer:
c = 37 mi
Step-by-step explanation:
Pythagorean theorem:To find 'c' use Pythagorean theorem.
[tex]\sf \boxed{\bf hypotenuse^2 = base^2 + altitude^2}[/tex]
c² = 35² + 12²
=1225 + 144
= 1369
[tex]\sf c = \sqrt{1369}\\\\ c = \sqrt{37*37}\\\\ \boxed{\bf c = 37 \ mi}[/tex]
The average hourly salary of workers in a warehouse is $14.50 with a standard deviation of $1.75. the shaded area of which curve represents the probability of the hourly salary being between $11 and $16.25?
Answers
Answer:
where is the question Skidoo
this is just a statement
If you vertically stretch the cubic parent function, f(x) = x3, what is the
equation of the new function?
Answers
Helen wants to have cake for her party. She needs 1 cake for every 8 people. Which expression helps her decide how many cakes to buy if p represents the number of people?
A. 8p
B. 1/8p
C. 8 + p
D. p-8
Answers
The midpoint of AB is M(-2, -1) If the coordinates of AA are (-7, 2) what are the coordinates of B?
Answers
Answer:
(3,-4)
Step-by-step explanation:
Please help as soon as possible!!
Answers
Answer:
A) 144 feet
[tex]\textsf{B)} \quad h(t)=16t(6-t)[/tex]
Step-by-step explanation:
Part A
Given polynomial:
[tex]h(t)=96t-16t^2[/tex]
where:
h(t) is the height of the debris (in feet).t is the time (in seconds) after the explosion.To find the height of the debris 3 seconds after the explosion, substitute t = 3 into the polynomial and solve:
[tex]\begin{aligned}\implies h(3)& = 96(3)-16(3)^2\\ & = 288 - 16(9)\\ & =288-144\\ & =144 \sf \:\: ft\end{aligned}[/tex]
Part B
To factor the polynomial, rewrite 96 as 6 × 16:
[tex]\implies h(t)=6 \cdot 16t-16t^2[/tex]
Rewrite t² as t × t:
[tex]\implies h(t)=6 \cdot 16t-16t \cdot t[/tex]
Factor out the common term 16t:
[tex]\implies h(t)=16t(6-t)[/tex]
Check
Substitute t = 3 into the factored expression:
[tex]\begin{aligned}h(3) & = 16(3)(6-3)\\& = 16(3)(3)\\& = 48(3)\\& = 144\:\: \sf ft \end{aligned}[/tex]
As the height is 144 ft when t = 3 is substituted into the original polynomial and the factored polynomial, this confirms that the factorization is correct.
Given: ΔABC
Prove: m∠ZAB = m∠ACB + m∠CBA
Triangle A C B is shown with its exterior angles. Line A B extends through point X. Line A C extends through point Y. Line C A extends through point X.
We start with triangle ABC and see that angle ZAB is an exterior angle created by the extension of side AC. Angles ZAB and CAB are a linear pair by definition.
We know that m∠ZAB + m∠CAB = 180° by the
.
We also know m∠CAB + m∠ACB + m∠CBA = 180° because
.
Using substitution, we have m∠ZAB + m∠CAB = m∠CAB + m∠ACB + m∠CBA.
Therefore, we conclude m∠ZAB = m∠ACB + m∠CBA using the
.
Answers
m∠ZAB + m∠CAB = 180° by the angle addition postulate
m∠CAB + m∠ACB + m∠CBA = 180° because of the triangle angle sum theorem
m∠ZAB = m∠ACB + m∠CBA using the subtraction property
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
m∠ZAB + m∠CAB = 180° by the angle addition postulate
m∠CAB + m∠ACB + m∠CBA = 180° because of the triangle angle sum theorem
m∠ZAB = m∠ACB + m∠CBA using the subtraction property
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Answer:
We start with triangle ABC and see that angle ZAB is an exterior angle created by the extension of side AC. Angles ZAB and CAB are a linear pair by definition.
We know that m∠ZAB + m∠CAB = 180° by the
✔ angle addition postulate
.
We also know m∠CAB + m∠ACB + m∠CBA = 180° because
✔ of the triangle angle sum theorem
.
Using substitution, we have m∠ZAB + m∠CAB = m∠CAB + m∠ACB + m∠CBA.
Therefore, we conclude m∠ZAB = m∠ACB + m∠CBA using the
✔ subtraction property
.
Step-by-step explanation:
two number cubes are rolled. Deterimine the number of ways that you could get a sum that is less than 5. The number cube is out of 6
Answers
Answer: six ways
Step-by-step explanation: The pairs when the cube is rolled that are less than five would be; (1,1), (1,2), (1,3), (2,1), (2,2), (3,1) since each cube is out of six.
Tawny wrote an expression to represent “the quotient of 82 and a number, decreased by 26.” She then evaluated the expression when n = 2. Which statements are true about the expression and its value? Check all that apply.
The correct expression is 82 minus StartFraction 24 Over n EndFraction.
To evaluate the expression, subtract 26 from the quotient.
To evaluate the expression, subtract the quotient from 82.
The correct expression is StartFraction 82 Over n EndFraction minus 26.
The operations include division and subtraction.
To evaluate, substitute 24 for the variable in the equation.
The value of the expression is 15.
Answers
The value of the expression (82/n – 26) at n = 2 will be 15. Then the correct options are B, D, E, and G.
What is division?Division means the separation of something into different parts, sharing of something among different people, places, etc.
Tawny wrote an expression to represent “the quotient of 82 and a number, decreased by 26.”
She then evaluated the expression when n = 2.
Then the expression will be
⇒ 82 / n – 26
If the value of n is 2, then the value of the expression will be
⇒ 82 / 2 – 26
⇒ 41 – 26
⇒ 15
Then the correct options are B, D, E, and G.
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The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5cm². calculate correct to 3 Significant figures, the base radius, r ,height h Volume of the cone [take π 22/7]
Answers
The volume of the cone is V = 381.15 cu.cm
What is the Curved Surface Area of the cone ?The curved surface area of the cone is given by
A = πrl
The slant height given in the question is
l = 10.5 cm
A = 115.5 sq.cm
radius = ?
Height = ?
Volume = ?
Using the Curved Surface Area Formula
115.5 = π * r * 10.5
taking π = 22/7
r = 3.5 cm
The slant height is given by
[tex]\rm l = \sqrt{ r^2 + h^2}[/tex]
Therefore the height is
[tex]\rm h = \sqrt{ 10.5^2 -3.5^2}[/tex]
h = 9.9 cm
The volume of the cone is
V = π r²h
V = (22/7) * 3.5 * 3.5 * 9.9
V = 381.15 cu.cm
The volume of the cone is V = 381.15 cu.cm
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Here are three studies:
a: june asks eight of her friends if they plan on buying a school lunch that day.
b: sam selects a random sample of coins from his coin bank to see how many of them are older than 1982.
c: peyton randomly selects six eggs from a carton. she randomly assigns three of them to be boiled for 10 minutes and the other three are boiled for 15 minutes. after they have cooled she compares how easy they are to peel.
for which of these studies can we draw conclusions of cause and effect?
a
b
c
none of them
Answers
Answer:
The answer is C
Step-by-step explanation:
Just got it.
(y ^ 4 * y ^ n)/(y ^ 2) = y ^ - 3 Find the value of n. (2 marks)
Answers
Answer:
n = -5
Step-by-step explanation:
Given:
[tex]\dfrac{y^4 \cdot y^n}{y^2}=y^{-3}[/tex]
Multiply both sides by y²:
[tex]\implies \dfrac{y^4 \cdot y^n}{\diagup \!\!\!\!\!y^2} \cdot \diagup \!\!\!\!\!y^2=y^{-3}\cdot y^2[/tex]
[tex]\implies y^4 \cdot y^n=y^{-3} \cdot y^2[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies y^{4+n}=y^{-3+2}[/tex]
[tex]\implies y^{4+n}=y^{-1}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]
[tex]\implies 4+n=-1[/tex]
Solve for n by subtracting 4 from both sides:
[tex]\implies 4+n-4=-1-4[/tex]
[tex]\implies n=-5[/tex]
Answer:
n = - 5
===========
Given equation:
[tex]\dfrac{y^4*y^n}{y^2} =y^{-3}[/tex]Solve it for n:
[tex]y^{4+n-2}=y^{-3}[/tex] [tex]y^{2+n}=y^{-3}[/tex][tex]2+n=-3[/tex][tex]n=-3-2[/tex][tex]n=-5[/tex]===========
Used properties:
[tex]a^b*a^c=a^{b+c}[/tex] product of exponents with same base[tex]a^b/a^c=a^{b-c}[/tex] division of exponents with same baseIf [tex]a^b=a^c[/tex] then [tex]b = c[/tex] equal exponents with same baseWhich of the following is a secant on the circle below?
A. SU
B. RT
C. SU
D. UT
Answers
The secant of circle is SU and RT.
What is Secant of the Circle?A straight line that intersects a circle in two points is called a secant line.
From the given diagram,
The line which intersects the circle at two points or an extended chord is SU and RT.
Hence, secant is SU and RT.
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Which ordered pair could not be the coordinates for a clockwise rotation of the point W (-3, 4)?
(-4, -3)
(3, -4)
(-4, 3)
(4, 3)
Answers
Answer:
(-4, -3)
(-4,3)
(4,3)
The clock wise rotation of the coordinate will be
(3,4)
(3,-4)
(-3,-4)
(-3,4)
Answer:
(-4,3)
Step-by-step explanation:
starting at -3 , 4
rotate clockwise 90° this will change (x,y ) to (y ,-x)
doing this 3 times results in
4,3 then 3, -4 then -4,-3 so the answer is (-4,3)
Rhonda gave the cashier $20 to pay for 3 pairs of socks. The cashier gave her $5.12. Each pair of socks cost the same amount. What is the cost in dollars and cents for each pair of socks?
Answers
Answer:
4.96 dollars
Step-by-step explanation:
20-5.12=14.88
14.88/3= 4.96 dollars
so each pair of socks costs 4.96$
Determine the period.
Answers
Match each expression with its value 2,-9,-1, or undefined
G(-0.0001)
G(0)
G(0.0001)
G(9)
Answers
By looking at the graph of the piecewise function, we can see that:
G(-0.001) = -9G(0) = -1G(0.0001) = -1G(9) is not defined.How to evaluate the piecewise function?
On the graph, we have a piecewise function, which we want to evaluate in some different values.
First we have x = -0.0001
This value belongs to the interval (-5, 0), and by looking at the graph, you can see that the function on that interval is equal to -9, then:
G(-0.0001) = -9
x = 0
x = 0 belongs to the interval [0, 9). On that interval the function values -1. (x = 0 belongs to that interval because we have a closed dot). Then we conclude
G(0) = -1
x = 0.0001
This value also belongs to the interval [0, 9)
Then G(0.0001) = -1
Finally, x = 9.
If you look at the domain of the function, you can see that there is an open dot at x = 9.
This means that x = 9 does not belong to that domain, so:
G(9) is not defined.
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8. A group of teenagers were surveyed to find out whether they like to drink coffee or tea. The result is shown below. •21 teenagers like to drink coffee or tea •3 teenagers like to drink coffee and tea. •2 teenagers do not like to drink coffee or tea. Based on the information, calculate (a) the total number of teenagers in the group. (b) the number of teenagers who like to drink coffee only or tea only.
Answers
a) 26 teenagers are in the group. 21+3+2=26
b) 21 like to drink coffee or tea only. (3 like both and 2 like neither, so 21 enjoy one or the other)
Lila and mick have pets. lila's pet has 6.73 toy bones. mick's pet has 5 times the many toy bones lila has. how many bones does mick's pet have?
Answers
Answer:33.65
Step-by-step explanation:
6.73 x 5= 33.65
Pls give me answer
Initially, a box contains three white and five red balls. Balls
are drawn at random from the box. Whenever a red ball is drawn, it is placed
back into the box together with one extra red ball. Whenever a white ball is
drawn, it is placed back into the box together with two extra white balls. What
is the probability that the first three balls are drawn out of the box alternated
in colour?
Answers
Using it's concept, it is found that the probability that the first three balls are drawn out of the box alternated in colour is of 0.1541 = 15.41%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Considering the situation described, the ways that alternate colored balls can be taken, and their probabilities, are given as follows:
R(5/8) - W(3/9) - R(5/11).W(3/8) - R(5/10) - W(5/11).Hence the probability is given by:
[tex]p = \frac{5}{11} \times \frac{3}{9} \times \frac{5}{11} + \frac{3}{8} \times \frac{5}{10} \times \frac{5}{11} = 0.0689 + 0.0852 = 0.1541[/tex]
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What is the midpoint of the segment (-6.-9)(16.5)
Answers
Answer:
M=(11,−2)
Step-by-step explanation:
Find the midpoint for [tex]P = \left(6, -9\right)P=(6,-9) \text{and} Q = \left(16, 5\right)Q=(16,5).[/tex]
The midpoint for two points P and Q is a point M whose coordinates is the half-sum of the corresponding coordinates of the two points.
Thus, [tex]M = \left(\frac{6 + 16}{2}, \frac{-9 + 5}{2}\right) = \left(11, -2\right)[/tex]
M=(11,−2)
If m || k and m || , then
k
m
3
2
Please help
Answers
Answer: [tex]k \parallel l[/tex]
Step-by-step explanation:
Lines that are parallel to the same line are parallel.
i need a little help please i am so bad with exponents right now -
Answers
Answer:
the answer is -1/8
Step-by-step explanation:
find the positive square root of 217.05 and 100.2001......with division method
Answers
The square root of 217.05 is 14.73 and the square root of 100.2001 is 10.01.
How to depict the square root?It should be noted that square root is factor of a number that when multiplied by itself will give the original number.
In this case, the square root of 217.05 is 14.73 and the square root of 100.2001 is 10.01.
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The marketing manager of a cell-phone company wants to determine which cell phone model most of her customers prefer. She separates a list of her customers into three age groups and then randomly selects a sample from each group proportional to the number of customers in each group.
What sampling method did she use?
A. Simple random sampling
B. Stratified random sampling
C. Systematic random sampling
D. Non-random sampling
Answers
Answer:
C
Step-by-step explanation:
I guess it is the answer because the manager separates the customers into 3 ange groups and randomly selects a sample from each group
Answer:
B. Stratified random sampling
Step-by-step explanation:
Calculate the middle number in the middle of 12.7 and 21.2.
Answers
The middle number is 16.95
What is Number system?The collection of numbers is called the number system. These numbers are of different types such as natural numbers, whole numbers, integers, rational numbers and irrational numbers.
Given:
Numbers are 12.7 and 21.2
Difference between number
= 21.2-12.7
=8.5
middle number
= 12.7+ 8.5/2
= 12.7+ 4.25
= 16.95
Hence, the middle number is 16.95.
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For an each situation, it begin with the square field, measuring X centimetres by X centimetres. The dimensions of this square are to be changed. How do you write an expression for the area of the new square field, and then expand, and simplify? :/
A). The length of a side is being increased by 8 cm.
B). The length is being increased by 12 cm and the width is being decreased by 7 cm.
Answers
#A
New side
X+8Area
(x+8)²x²+16x+64 cm²#2
Now it has turned rectangle
Sides
x+12 and x-7
Area
(x+12)(x-7)Answer:
A) (x + 8)² cm² = (x² + 16x + 64) cm²
B) (x + 12)(x + 7) cm² = (x² + 19x + 84) cm²
Step-by-step explanation:
Formula
Area of a square = s² (where s is the side length)
Given side length of square field:
x cm⇒ Area of field = x² cm²
Part A
If the side length of the square field is increased by 8 cm then:
⇒ new side length = (x + 8) cm
Substitute the new side length into the formula for the area of a square:
⇒ Area of field = (x + 8)² cm²
Expand and simplify:
⇒ Area = (x + 8)²
⇒ Area = (x + 8)(x + 8)
⇒ Area = x(x + 8) + 8(x + 8)
⇒ Area = x² + 8x + 8x + 64
⇒ Area = (x² + 16x + 64) cm²
Part B
If the side length of the square field is increased by 12 cm and the width is decreased by 7 cm then:
⇒ new side length a = (x + 12) cm
⇒ new side length b = (x - 7) cm
Substitute the side lengths into the formula for area of a square:
⇒ Area of a square = s × s
⇒ Area of a square = a × b
⇒ Area of the field = (x + 12)(x + 7) cm²
Expand and simplify:
⇒ Area = (x + 12)(x + 7)
⇒ Area = x(x + 7) + 12(x + 7)
⇒ Area = x² + 7x + 12x + 84
⇒ Area = (x² + 19x + 84) cm²
What is the value of x?
to
x = [? ]°
36°
Enter
I will give you 25 pts
Answers
The vale of x is 54°.
What is tangent?The tangent is defined as a line touching circles or an ellipse at only one point.
We have,
As, the tangent is perpendicular to the radius of the circle.
So, using Angle sum property in a triangle
x+90+36= 180
x+126 = 180
x= 54°
Hence, the value of x is 54°
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