Let f(x) = x2 + 3. Approximate the area bounded by the curve y = f(x), the x-axis, and the vertical lines x = 0 and x = 2 using a Riemann sum (right-point rule) with four rectangles. Answer: Check
Answers
The approximate area bounded by the curve y = f(x), the x-axis, and the
vertical lines x = 0 and x = 2 is 9.75 square units.
To approximate the area using a Riemann sum (right-point rule) with four
rectangles, we first need to divide the interval [0, 2] into four subintervals
of equal width. The width of each subinterval is:
Δx = (2 - 0)/4 = 0.5
So, the four subintervals are:
[0, 0.5], [0.5, 1], [1, 1.5], [1.5, 2]
Using the right-point rule, we approximate the area of each subinterval
by multiplying the width of the subinterval by the height of the function at
the right endpoint of the subinterval. That is:
For the interval [0, 0.5], we have \(f(0.5) = (0.5)^2 + 3 = 3.25\), so the area of
the first rectangle is:
A1 = Δx × f(0.5) = 0.5 × 3.25 = 1.625
For the interval [0.5, 1], we have \(f(1) = (1)^2 + 3 = 4\), so the area of the second rectangle is:
A2 = Δx × f(1) = 0.5 × 4 = 2
For the interval [1, 1.5], we have \(f(1.5) = (1.5)^2 + 3 = 5.25\), so the area of
the third rectangle is:
A3 = Δx × f(1.5) = 0.5 × 5.25 = 2.625
For the interval [1.5, 2], we have \(f(2) = (2)^2 + 3 = 7\), so the area of the
fourth rectangle is:
A4 = Δx × f(2) = 0.5 × 7 = 3.5
Therefore, the Riemann sum for the given function and intervals with four
rectangles using the right-point rule is:
R4 = A1 + A2 + A3 + A4 = 1.625 + 2 + 2.625 + 3.5 = 9.75
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Related Questions
Every morning for the past 12 days, Beth used Two-thirds of a cup of milk on her cereal. To determine how much milk she used in total, she set up the equation, Two-thirds times 12 = question mark ?. What is the total amount of milk that Beth used
Answers
Answer:
It would be 8
Step-by-step explanation:
Answer:
(c) 8 Cups
Step-by-step explanation:
The endpoints of a diameter of a circle are located at (3, -7) and (5, 7). Write the equation of the circle
a. (x + 4)² + y² = 25
c. (x - 4)2 + y² = 50
b. (x - 4)2 + y² = 25
d. (x +4)+ y2 = 50
Answers
The center of the circle is (4, 0). The radius is √50. The equation of the circle is (x - 4)² + y² = 25. The correct option is a.
To find the equation of a circle, we need the center and radius. The center of the circle is the midpoint of the diameter, which can be found by averaging the x-coordinates and the y-coordinates of the endpoints.
Midpoint formula:
Midpoint(x, y) = ((x1 + x2) / 2, (y1 + y2) / 2)
Let's calculate the midpoint using the given endpoints (3, -7) and (5, 7):
Midpoint(x, y) = ((3 + 5) / 2, (-7 + 7) / 2)
= (8 / 2, 0 / 2)
= (4, 0)
So, the center of the circle is (4, 0).
Next, we need to find the radius, which is the distance between the center and one of the endpoints. We can use the distance formula to calculate this distance.
Distance formula:
Distance = √((x2 - x1)² + (y2 - y1)²)
Using the center (4, 0) and one endpoint (3, -7):
Distance = √((3 - 4)² + (-7 - 0)²)
= √((-1)² + (-7)²)
= √(1 + 49)
= √50
So, the radius is √50.
Now we have the center (4, 0) and the radius √50. We can write the equation of the circle in the form (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.
Substituting the values, we get:
(x - 4)² + (y - 0)² = (√50)²
(x - 4)² + y² = 50
Therefore, the equation of the circle is: a. (x - 4)² + y² = 25
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pleasee help me,A train travels from station P to station Q at a speed of 90km/h in 3hours 40minutes.The train stops at station Q for 25minutes before returns to station P.The time taken from station P to station Q.Calculate the average speed,in km/h,of the whole journey of the train
Answers
I need help please lol
Answers
Answer:
48.75
Step-by-step explanation:
First, find the cost for 1 key chain if the cost is $67.50 for 150 key chains.
Answers
Each key costs 45 cents
Brainliest?
Answer:
$2.2
Step-by-step explanation:
so first you divide 250 by 67.50 whatever that is is the answer
10(x+12)=15x solve for x with how ?
Answers
Answer:
x = 24
Step-by-step explanation:
10(x+12)=15x (Given)
10x + 120 = 15x (Distributive property of equality)
-5x = -120 (Subtraction property of equality)
x = 24 (Division property of equality)
please help me on this will give you brainliest
Answers
Answer:
57.603
Step-by-step explanation:
We can separate this into two sections, using the and:
Fifty-seven - simply the whole number 57
Six hundred three thousandths - This could be intrepreted as 0.603, which is confirmed through the "3" being in the thousandths place.
Sorry that took so long! I had to think a bit about this one
Alison used a coordinate grid to show where the trees are in her backyard. She wants to put a birdbath exactly halfway between the two oak trees. What are the coordinates of this location? If each grid represents 1 foot, how far apart are the two oak trees? What is the perimeter of the triangle determined by the three trees? (Round your answer to the nearest foot)
Answers
Answer:(5,4)
Step-by-step explanation:
how far can freddy drive in 8 hours at an average speed of 50 miles per hour ?
Answers
Answer:
400 miles
Step-by-step explanation:
Distance = rate * time
Distance = 50 miles per hour * 8 hours
Distance = 400 miles
Answer:
400 miles
Step-by-step explanation:
Distance =rate×time
50miles×8hrs=400
Which of the following is equivalent to 8^(1/3)?
Option 1
Option 2
Option 3
Option 4
(look at photo for answers)
Answers
the answer is option 2....
Answer:
Option 2
Step-by-step explanation:
when the power appears as a fraction, take the root of the number based on the denominator of the fraction when numerator is equal to 1
What percent is represented by the shaded area?
Answers
because 6 out of the 20 squares are shaded so it would be 6/20 which would equal .30 or 30%
(1,6)(7,4) what is the slope
Answers
Answer:
4-6
m= ----- = -2/6 = -1/3 Therefore, the slope is -1/3.
7-1
Step-by-step explanation:
I used the slope equation. Hope this helps! Have a good day! :D
is a fraction a term? If it's not a term, why is it that we can apply the distributive property to it? the distributive property only works for either terms, or addition and subtraction. a fraction is technically division, so why does it work? Please help!!!!!
Answers
No, a fraction is not a term. The distributive property can be applied to fractions because it is a general mathematical principle.
A fraction is not considered a term in the traditional sense. It is a mathematical expression that represents division. However, the distributive property can still be applied to fractions because the property itself is a fundamental rule of arithmetic that extends beyond specific types of expressions.
The distributive property states that for any real numbers a, b, and c:
a × (b + c) = (a × b) + (a × c).
When working with fractions, we can apply the distributive property as follows:
Let's consider the expression: a × (b/c).
We can rewrite this as: (a × b)/c.
Now, let's distribute the 'a' to 'b' and 'c':
(a × b)/c = (a/c) × b.
In this step, we applied the distributive property to the fraction (a/c) by treating it as a whole.
Although fractions represent division, we can still use the distributive property because it is a general mathematical principle that allows for manipulating expressions involving addition, subtraction, multiplication, and division.
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Solve pls! Lots of points! Question down below!
Answers
Answer:1024 grid squares
Step-by-step explanation:
Let's call the side length of the original piece of graph paper "x".
Since, side length of the cut out square is then (x-2) because the cut out square has to have an integer number of grid squares, and each side of the square would take up 2 grid squares on the graph paper.
The number of grid squares in the cut out square is then (x-2)^2.
The number of grid squares left on the graph paper is 124, so we have:
x^2 - (x-2)^2 = 124
Expanding the right side:
x^2 - x^2 + 4x - 4 = 124
Simplifying:
4x = 128
therefore:
x = 32
therefore original graph paper contains 32 grids i.e 32^2 = 1024
Answer:
any of {128, 133, 140, 160, 224, 320, 380, 700, 1024}
1024 if the original grid was square
Step-by-step explanation:
You want to know how many grid squares are on a piece of graph paper if a square number of grid squares can be cut from it to leave 124 grid squares.
Square graphIf the graph is square to begin with, a square of x² can be removed from its size (x+a)² to leave 124 squares. That is ...
(x +a)² -x² = 124
(a)(2x+a) = 124
The factor pairs of 124 are ...
124 = 1·124 = 2·62 = 4·31
Of these, only 2 and 62 differ by an even number, so we have a=2 and x=30.
The graph paper could be 32 units square originally, having 1024 grid squares.
Rectangular graphThere is nothing in the problem statement that requires the original graph paper be square. If it is not necessarily square, there are 13 possible shapes it could be. Those have 9 different possibilities for numbers of grid squares.
The graph paper could have originally had this number of grid squares:
128 = 4×32 = 8×16. The square removed is 2².133 = 7×19. The square removed is 3².140 = 5×28 = 7×20 = 10×14. The square removed is 4².160 = 8×20 = 10×16. The square removed is 6².224 = 14×16. The square removed is 10².320 = 16×20. The square removed is 14².380 = 19×20. The square removed is 16².700 = 25×28. The square removed is 24².1024 = 32×32. The square removed is 30². . . . . discussed above__
Additional comment
You may notice that removing a 24×24 square from a graph that is 25×28 leaves no border on one side.
These values were found using a search script.
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Please Help!
Factor the following trinomial
\(9x^2-24x+16\)
Please show work
Answers
=> 9x² - 24x + 16
Split the middle term(term with x) in such a manner so that the product of those parts is equal to the product of term with x² and constant. Here, those parts are 12 & 12 as 12*12 = 9*16.
=> 9x² - 24x + 16
=> 9x² - (12 + 12)x + 16
=> 9x² - 12x - 12x + 16
=> 3x(3x - 4) - 4(3x - 4)
=> (3x - 4)(3x - 4)
Method 2
=> 9x² - 24x + 16
=> (3x)² - 2(3x*4) + 4²
=> (3x - 4)²
=> (3x - 4)(3x - 4)
Method 3
In case if you can't find the factors of the middle term.
Say f(x) = 0, find the zeroes using quadratic formula. Zeroes of this eqⁿ are [-(-24) ± √24²-4(9)(16)] / 2(9) = 4/3 & 4/3
Therefore, f(x) = (x - 4/3)(x - 4/3) = (3x - 4)(3x - 4)/9
Ignore the numeric constant.
f(x) = (3x - 4)(3x - 4)
Janelle is considering two options for saving money. One option earns simple interest while the other option earns interest compounded monthly. If there are no additional deposits or withdraws, how much more will Janelle earn with the compound interest option? Assume Janelle deposits $3,000 at 3% interest for 7 years for both options
Answers
Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.
The amount Janelle will earn with the compound interest option can be calculated using the formula for compound interest:
\(A = P(1 + r/n)^{(nt)}\)
Where:
A is the total amount after interest has been compounded
P is the principal amount (the initial deposit)
r is the annual interest rate (expressed as a decimal)
n is the number of times interest is compounded per year
t is the number of years
In this case, Janelle deposits 3,000 at an interest rate of 3% for 7 years. We'll compare the simple interest and compound interest options.
For the simple interest option, the interest is calculated using the formula:
I = P * r * t
Where:
I is the total interest earned
Using the given values, we can calculate the interest earned with simple interest:
I = 3000 * 0.03 * 7
I = 630
Now, let's calculate the total amount earned with the compound interest option.
Since the interest is compounded monthly, the interest rate needs to be divided by 12 and the number of years needs to be multiplied by 12:
r = 0.03/12
t = 7 * 12
Using these values, we can calculate the total amount with compound interest:
\(A = 3000 * (1 + 0.03/12)^{(7*12)}\)
A ≈ 3,729.19
To find out how much more Janelle will earn with the compound interest option, we subtract the initial deposit from the total amount with compound interest:
Difference = A - P
Difference = 3,729.19 - 3,000
Difference ≈ 729.19
Therefore, Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.
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Feri invests some money.
The rate of interest for the first year is 2.5%.
At the end of the second year the overall percentage increase of Feri's investment is 6.6%.
Find the rate of interest for the second year.
Answers
The rate of interest for 2nd year is 4.1%
How to find the interest rate for the second yearFrom the given parameters;
Rate of interest for 1st year = 2.5
As we know the formula for Simple interest is given by
=> I = (PTR)/100
We will use this formula in the following problem
Let 100 be Feri's investment
At the Rate of interest of 2.5
Interest on 100 = [(100(1)(2.5)]/100 = 2.5
Total amount at end of 1st year = 100 + 2.5 = 102.5
Let x be the rate of interest for 2nd year
At the rate of interest of x
interest on 100 = [(100(1)(x)]/100 = x
Total amount at end of 2st year = 102.5 + x
Given that, at end of the 2 years, the rate of interest becomes 6.6%
Interest on 100 at the rate of 6.6%
=> [(100(1)(6.6)]/100 = 6.6
=> total amount = 100 + 6.6 = 106.6
As we know in both cases, the amount must be equal
=> 102.5 + x = 106.6
=> x = 4.1
Therefore, The rate of interest for 2nd year = 4.1
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What are all the exasperations that are equivalent to 4y+12
Answers
There are many expressions that are equivalent to 4y + 12, which can be obtained by using algebraic operations to manipulate the expression while maintaining its value. Here are a few examples:
12 + 4y
2(2y + 6)
4(y + 3)
8y/2 + 12
4(y + 3) - 3y + y
2(2y + 6) + 2(y - 3)
4y + 9 + 3
4y - 4 + 16
These are just a few examples. There are many other expressions that are equivalent to 4y + 12, depending on what operations you apply and how you choose to represent them.
In mathematics, an expression is a combination of mathematical symbols, numbers, and/or variables, that represents a value or a relationship between values. It may include arithmetic operations such as addition, subtraction, multiplication, and division, as well as algebraic operations such as powers, roots, and logarithms.
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PLEASE ANSWER THE TEST IS TOMORROW!!
A gift box in the shape of a triangular prism height of 4 inches, and a height of 3 inches. What is the length of the base?
Answers
The length of the base of the triangular prism will be 6 inches.
Given that:
Height of triangle, h = 3 inches
Height of prism, H = 4 inches
Volume, V = 36 cubic inches
Let the prism with a base area of A and a height of H. Then the volume of the prism is given as,
V = A x H
The length of the base is calculated as,
36 = 1/2 x B x 3 x 4
12B = 72
B = 6 inches
The length of the base of the triangular prism will be 6 inches.
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The complete question is given below.
A gift box in the shape of a triangular prism has a volume of 36 cubic inches, a base height of 4 inches, and a height of 3 inches. What is the length of the base?
You are given the following information about a population:
⢠There are two alleles: C and c.
⢠C codes for green hair and c codes for white hair.
⢠C is dominant over c.
⢠The frequency of the c allele is 0.3.
⢠The population is comprised of 100 individuals.
Assuming the population is in Hardy-Weinberg equilibrium, how many individuals have green hair?
A. 9% of the population will have green hair.
B. 91% of the population will have green hair.
C. 51% of the population will have green hair.
D. 49% of the population will have green hair.
Answers
Assuming the population is in Hardy-Weinberg equilibrium, the individuals have green hair are equal to 91% .
From the data present in problem,
Hardy and Weinberg proved mathematically that in a population all dominant and recessive alleles include all alleles for a given gene. Mathematically, denoted as p + q = 1.0
Where, p = frequency of dominant alleles (C)
q = frequency of recessive alleles (c) = 0.3
Number of population individua's = 100
Hardy and Weinberg described all the possible genotypes for a gene with two alleles. The binomial expansion representing this is,
p² + 2pq + q² = 1.0
Where, p² = proportion of homozygous dominant individuals (Green)
• q² = proportion of homozygous recessive individuals (White)
2pq = proportion of heterozygotes (Green)
Since, p+ q = 1.0
=>p = 1 - q = 1 - 0.3 = 0.7
=>p = 0.7
The genotypic frequencies are as follows:
CC (p²) = (0.7) = 0.49
Cc (2pq) = 2x(0.3)(0.7) = 0.42
cc (9²) = (0.3)² = 0.09
p² + 2pq + q² = (0.49) + (0.42)+(0.09)= 1.0
The expected number for each genotype are as follows: CC (p²) = (0.49×100) = 49
Cc (2pq) = (0.42×100)= 42
cc(q²) = (0.09×100) = 9
The number of individuals have green hair is as follows: (p²)+(2pq) = 49+42= 91
Thus, required individuals percentage is 91%.
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Someone Help? I am not too sure if I am right.
Answers
Answer:
You are right.
Step-by-step explanation:
The values corresponding to x = 3 is -5.
pls help suuper simple!!
Answers
Answer: x > - 9 or x < - 26
Step-by-step explanation:
Ok, so modulus means that 0.2x + 3.5 is either greater than 1.7, or less than -1.7. Putting that in equation, we get,
0.2x + 3.5 > 1.7 or 0.2x + 3.5 < -1.7
0.2x > -1.8 or 0.2x < -5.2
x > -9 or x < -26
There u go.
pls help have to turn in soon
Answers
Answer:
The one you already have selected along with
428
Step-by-step explanation:
anything to the 0 power is itself
3. In the figure below, what is m 2 if m26 = 120°?
3\2
41
56
87
educe for classroom use.
A. 60°
B. 90°
C. 120°
D. 150°
Answers
Answer:
C. 120°
Step-by-step explanation:
\(m \angle \: 2 = m \angle 6 \\ (corresponding \: \angle s) \\ \\ \because \: m \angle 6 = 120 \degree \\ ...(given)\\ \\ \red{ \bold{\therefore \: m \angle 2 = 120 \degree }}\)
Sheily paid $3.55 for a fruit drink.she now has $25.30.How much money did she have before buying the fruit drink?
Answers
Answer:
$28.85
Step-by-step explanation:
$25.30 leftover money + $3.55 cost of drink = $28.85 Sheily had before buying the drink.
Answer: 28.85
Step-by-step explanation:
This is an addition problem so the answer is pretty straight forward, if she paid 3.55 for a drink that is how much money she already spent to have that drink. Now that she has a drink the question is simply asking how much she had BEFORE she purchased the drink. So just add 3.55 and 25.30 together and you have your answer. Hope this helped.
144 cubic meters in inches.
Answers
Answer:
I think is 8.787e+6 cubic inches.
Kathy’s father thinks she spends too much time on the phone. He wants to see how much time she spent talking last month, but he does not have the phone bill; he has only his checkbook, which tells him that her bill last month was $110. The phone company charges a monthly base fee of $50, plus ten cents per minute. How many minutes did Kathy spend on the phone last month?
Answers
Answer:
600 minutes
Step-by-step explanation:
110-50= 60
60 divided by 0.10= 600
If the circumference of a circle is 2πr, what is the perimeter of the semi-circle?
Answers
The perimeter of a semi-circle consists of the curved part (half of the circumference of a circle) and the straight diameter connecting the two ends of the curved part.
The circumference of a full circle is given by 2πr, where r is the circle radius. Since a semi-circle is half of a full circle, the curved part of the semi-circle would be half of the circumference, which is (1/2) * 2πr = πr.
To calculate the semi-circle perimeter, we need to add the straight diameter to the curved part. The diameter of the full circle is 2r, so the diameter of the half-circle is r. Therefore, the perimeter of the semi-circle is equal to the curved part (πr) plus the diameter (r), which gives a total perimeter of πr + r.
In simplified form, the semi-circle perimeter is (π + 1) * r.
Find the equation of the circle whose center and radius are given.
center ( -2, -5), radius = 1
Answers
Answer:
(x + 2)^2 + (y + 5)^2 = 1
Step-by-step explanation:
Since this circle is centered at (-2, -5), we have to add values within the squares. The standard form of a circle equation is:
(x - h)^2 + (y - k)^2 = r^2
So -2 is h and -5 is k. Substituting that in we get:
(x + 2)^2 + (y + 5)^2 = r^2
We are given the radius is 1, and one squared is one, so the final equation is:
(x + 2)^2 + (y + 5)^2 = 1
find the y intercept of y=4x-2
Answers
Answer:
y intercept: -2
Step-by-step explanation:
hope this helps :)
Answer:
Slope=4 and the intercept on the y-axis is -2
Step-by-step explanation:
Use the formula y=mx+c
m=slope
c is the intercept on the y-axis
y=4x-2 can be like this
Y=4x+(-2)
That is why slope is 4 and intercept on y-axis is -2
:)