The equivalent of the given expression ( (4 1/2)x - 3 ) + ( -2 + (1 3/4)x ) is (6 1/4)x - 5.
What is the equivalent of the given expression?Given the expression in the question;
( (4 1/2)x - 3 ) + ( -2 + (1 3/4)x )
First, convert the mixed fractions into an improper fractions.
( (4 1/2)x - 3 ) + ( -2 + (1 3/4)x )
( (4×2 + 1/2)x - 3 ) + ( -2 + (1×4 + 3/4)x )
( (8 + 1/2)x - 3 ) + ( -2 + (4 + 3/4)x )
( (9/2)x - 3 ) + ( -2 + (7/4)x )
Now, remove the parenthesis and collect like terms
(9/2)x - 3 + -2 + (7/4)x
(9/2)x + (7/4)x - 3 - 2
9x/2 + 7x/4 - 5
Now, add the two fractions containing x
(9x × 4)+(7x × 2)/8 - 5
( 36x + 14x )/8 - 5
50x/8 - 5
(50/8)x - 5
(25/4)x - 5
Convert 25/4 into an improper fraction
(6 1/4)x - 5
Therefore, the equivalent of the given expression ( (4 1/2)x - 3 ) + ( -2 + (1 3/4)x ) is (6 1/4)x - 5.
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What is the answer!???
ou want to save for a brand-new car. You put the $5,000 your Grandma gave you when you graduated in an account that pays 6% interest and is compounded monthly. How much will you have at the end of five years
An account that pays 6% interest and is compounded monthly. At the end of five years, you will have approximately $6,691.13 in the account.
To calculate the amount you will have at the end of five years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years
In this case, the principal amount (P) is $5,000, the annual interest rate (r) is 6% (or 0.06 in decimal form), the interest is compounded monthly, so the number of times compounded per year (n) is 12, and the number of years (t) is 5.
Plugging these values into the formula, we have:
A = $5,000(1 + 0.06/12)^(12*5)
Calculating the expression inside the parentheses first:
(1 + 0.06/12)^(12*5) ≈ 1.33822558
Now, substituting this value back into the formula:
A ≈ $5,000 * 1.33822558
A ≈ $6,691.13
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HELP PLEASE ONLINE SCHOOL IS HARD!!!
Answer:
27
Step-by-step explanation:
Since the exponents are negative, what we need to do is switch up the places so that it's positive.
\(\frac{3^{-9} }{3^{-12} }\)
\(\frac{3^{12} }{3^{9} }\)
Now, we can use the \(\frac{x^a}{x^b} = x^a^-^b\) rule to solve for the answer.
\(3^{12-9}\)
3³
27
can someone pls help for brainlest
Answer:
6 x 8 = 48 yd2 (square yards)
Step-by-step explanation:
Answer:
Area of triangle is 23 yd².
Step-by-step explanation:
Given :-
Base of triangle = 8 yd
Height of triangle = 6 yd
To find
Area of triangle
Solution :-
we know that,
Area of triangle = 1 / 2 × base × height
substitute the values
Area of triangle = 1/2 × 8 yd × 6 yd
multiplying the values
Area of triangle = 1/2 × 46 yd²
divide the values
Area of triangle = 46 yd ² /2 = 23 yd².
Therefore, Area of triangle is 23 yd ².
the following question is a general question. it applies to the problem above, but also to any problem. in constructing 95% confidence intervals for the difference in means, what do we expect will be true over the long run?
Over the long run, we can be confident that our interval estimates are capturing the true population difference in means 95% of the time, making it a reliable and widely used measure in statistical analyses.
About 95% confidence intervals for the difference in means.
In the long run, when constructing 95% confidence intervals for the difference in means, we expect that:
In 95% of the cases, the true population difference in means will be captured within the calculated confidence intervals.
The remaining 5% of the time, the true population difference in means will fall outside the calculated confidence intervals, indicating a lack of precision in our estimation.
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A bookshop has a sale in which paperback books are sold at a 20% discount and
hardback books are sold at a 40% discount. Lucy bought three paperbacks for
£6 each and four hardbacks for £9 each.
Answer:
Step-by-step explanation:
Given:
Paper backs 20% off, Bought 3 at $6 each.
Hardbacks 40% off, Bought 4 for $9 each.
Solution:
Paperbacks:
Cost without discount = $6 x 3
Cost without discount = $18
In order to find percent of a number, change the percent to decimal and multiply.
Discount = $18 x 20%
Discount = $18 x .2
Discount = $3.20
Amount she paid with discount = $18 - $3.20
Amount she paid with discount = $14.40
Hardbacks:
Cost without discount = $9 x 4
Cost without discount = $36
In order to find percent of a number, change the percent to decimal and multiply.
Discount = $36 x 40%
Discount = $18 x .4
Discount = $7.20
Amount she paid with discount = $36 - $7.20
Amount she paid with discount = $28.80
Totals:
Total Amount she paid with discount = $28.80 + $14.40
Total Amount she paid with discount = $43.20
A hummingbird lives in a nest that is 12 feet high in a tree.
Answer:
12
Step-by-step explanation:
Answer:
is there another part of this question or is this it?
Step-by-step explanation:
Assume that blood pressure readings are normally distributed with a mean of 116 and a standard deviation of 6.4. If 64 people are randomly selected, find the probability that their mean blood pressure will be less than 118.
The probability that the mean blood pressure of 64 randomly selected people will be less than 118 is approximately 0.9938.
You want to find the probability that the mean blood pressure of 64 randomly selected people will be less than 118, given that blood pressure readings are normally distributed with a mean of 116 and a standard deviation of 6.4.
Step 1: Calculate the standard error of the mean (SEM).
\(SEM=\frac{standard deviation}{\sqrt{sample size} }\)
\(SEM=\frac{6.4}{\sqrt{64} }\)
\(SEM=\frac{6.4}{8}\)
\(SEM = 0.8\)
Step 2: Calculate the z-score for the given value (118) using the formula:
\(z = \frac{X-mean}{SEM}\)
\(z = \frac{118-116}{0.8}\)
\(z=\frac{2}{0.8}\)
z = 2.5
Step 3: Use the z-score to find the probability (area under the curve to the left of z).
From the z-table or using an online z-score calculator, the probability for a z-score of 2.5 is approximately 0.9938.
So, the probability that the mean blood pressure of 64 randomly selected people will be less than 118 is approximately 0.9938.
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Exam
Does the equation below represent a
direct proportion? If yes, identify
the constant of proportionality.
x = 9y
A. No
B. Yes, 1/9
D. Yes, -9
C. Yes, 3
Answer:
B. 1/9 cuz it's just saying y is 1/9 of x
How many solutions does the equation 3(x-5)-7=-3x8 have
Answer:
not really good at maths. 15.33
Step-by-step explanation:
3(x-5)-7=3×8
3x-15-7=24
3x =24+15+7
3x = 46
Three will divide it's self to give you one and divide 46 to give you 15.333
(correct me if i'm wrong)
Analyze the diagram below and complete the instructions that follow.
K
B
A
гс
F
E
Given that ZCFE ZCFA, mZCFB = 68°, and mZEFD= 62°, find the measure of ZAFD.
The measure of ZAFD is 50 degrees.
Based on the given information:
ZCFE is congruent to ZCFA.
mZCFB = 68°.
mZEFD = 62°.
To find the measure of ZAFD, we can use the fact that angles in the same segment of a circle are equal.
Since ZCFE and ZCFA are congruent, angle ZCFE is equal to angle ZCFA.
Therefore, mZCFA = mZCFE.
Now, let's find the measure of angle ZCFE:
mZCFE = mZCFB + mZEFD (Angle Addition Postulate)
mZCFE = 68° + 62°
mZCFE = 130°
Since ZCFA is congruent to ZCFE, we can conclude that mZCFA is also equal to 130°.
Now, to find the measure of ZAFD, we need to consider the angles in the quadrilateral ZAFD.
The sum of the angles in a quadrilateral is always 360°.
mZAFD + mZAFB + mZBFD + mZBFA = 360°
We know that mZAFB and mZBFD are equal to 90° because they are right angles (angle AFB and angle BFD are right angles in the diagram).
Therefore, we can rewrite the equation as:
mZAFD + 90° + 90° + mZBFA = 360°
Simplifying:
mZAFD + 180° + mZBFA = 360°
Rearranging the equation:
mZAFD + mZBFA = 360° - 180°
mZAFD + mZBFA = 180°
We know that mZBFA is equal to mZCFA, which is 130°.
Substituting the known values into the equation:
mZAFD + 130° = 180°
Subtracting 130° from both sides:
mZAFD = 180° - 130°
mZAFD = 50°
Therefore, the measure of ZAFD is 50 degrees.
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A dealer sold 200 tenis rackets. Some were sold for $33 each, and the rest were sold on sale for $18 each. The total receipts from these sales were $4,800. How many rackets did the dealer sell for $18 each?
The number of tennis rackets sold by dealer for $18 is 120.
What is meant by the term linear equation?A linear equation is an equation with the highest degree of one. This means that in a linear equation, no variable has an exponent greater than 1. A linear equation's graph is always a straight line.Let "x" be the number of tennis rackets that sell for $18 each.
Then, 200 - x be the number which sell for $33 each.
The total cost is $4,800.
18x + 33(200 - x) = 4800
18x + 6600 - 33x = 4800
-15x = -1800
x = 120
Thus, the number of tennis rackets sold by dealer for $18 is 120.
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Wilma is 5 times as old as yvonne. in ten years, yvonne's age will be a third of wilma's age. how old are they now?
Using a system of equations, it is found that Wilma is 50 years old and Yvonne is 10 years old.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are given as follows:
Variable x: Wilma's age.Variable y: Yvonne's age.Wilma is 5 times as old as yvonne, hence:
x = 5y.
In ten years, yvonne's age will be a third of wilma's age, hence:
\(y + 10 = \frac{1}{3}(x + 10)\)
Since x = 5y:
\(y + 10 = \frac{1}{3}(x + 10)\)
\(y + 10 = \frac{1}{3}(5y + 10)\)
3y + 30 = 5y + 10
2y = 20.
y = 10.
Then:
x = 5y = 5 x 10 = 50.
Wilma is 50 years old and Yvonne is 10 years old.
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Graph the solution to the inequality x-6 less than or equal to 8 on a number line
The solution to the given inequality is x≤14.
What are inequalities?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Greater than (or less than or equal to), less than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
The given inequality is x-6≤8.
Add 6 to both sides of the inequality, we get
x≤14
Interval Notation: (−∞,14]
Therefore, the solution is x≤14.
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what would you have to know about the solution set of a homogeneous system of 18 linear equations in 20 variables in order to know that every associated nonhomogeneous equation has a solution
The solution set of a homogeneous system of 18 linear equations in 20 variables lies in the null space of the coefficient matrix.
To know that every associated nonhomogeneous equation has a solution, we need to ensure that the homogeneous system has a nontrivial solution.
This means that we need to know whether the rank of the coefficient matrix of the homogeneous system is less than the number of variables, i.e., whether there exist free variables.
If the rank is less than the number of variables, then there are infinitely many solutions to the homogeneous system, and thus every associated nonhomogeneous equation has a solution.
However,
We also need to ensure that the particular solution to the nonhomogeneous equation does not lie in the null space of the coefficient matrix.
This is equivalent to checking whether the null space of the coefficient matrix is orthogonal to the vector on the right-hand side of the nonhomogeneous equation.
If it is, then the nonhomogeneous equation has a solution.
So, in summary, to know that every associated nonhomogeneous equation has a solution.
We need to know whether the rank of the coefficient matrix of the homogeneous system is less than the number of variables, and we need to check whether the particular solution lies in the null space of the coefficient matrix.
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Pls help asap!!! I need to solve for x for these three questions (39 , 41 and 43) PLS ASAP!!!
Answer: 39. x= 37, 41. x=7, 43. x = 29
Step-by-step explanation:
39. 2x + 4 + 2x - 9 + x = 180
5x - 5 = 180
5x=185
185/5
x=37
41. 90 + 8x - 1 + 4x+7 =180
8x-1+4x+7=90
12x+6=90
12x=84
84/12
x=7
36+x=2x+7
36=x+7
29=x
Hope this helps.
Answer:
Hope this helps
Megan found a new knitting pattern she's been wanting to try. It makes a rainbow-striped 60-inch scarf. Last month, it took her 14 hours to knit her little sister a 30-inch scarf. If Megan plans to knit 1 hour every day, how many weeks will it take her to finish the rainbow-striped scarf?
Answer:
if it took her 14 hours to make a 30-inch scarf, we can assume it will take her to double that time to make a 60-inch scarf. 28 hours is double of 14, if she only knits one hour every day it will take her 4 weeks, 28 days is equal to exactly 4 weeks 28/7=4 weeks
Answer:
4 weeks
Step-by-step explanation:
14 hours for a 30-inch
multiply them both by 2
28 hours for 60-inch
28 divided by 7 = 4
Have a blessed and great day<3
Help me with this .identify the pairs
∠GML ≅ ∠HMJ by the Vertical Angles Congruence Theorem.
∠GMH ≅ ∠LMJ by the Vertical Angles Congruence Theorem.
∠GMK ≅ ∠JMK by the Right Angles Congruence Theorem. They form a linear pair which means they are supplementary by the Linear pair Postulate and because one is a right angle so is the other by the Subtraction Property of Equality.
What is the Vertical Angles Congruence Theorem?According to the congruence theorem of vertical angles or angles that are vertically opposing, two opposing vertical angles that are created when two lines intersect one other are always equal.
So from the figure, we can determine the vertically opposite angles,
∠GML ≅ ∠HMJ
Similarly, ∠GMH ≅ ∠LMJ
The angles ∠GMK and ∠JMK form a linear pair and are supplementary by the linear pair postulate which states that the two angles in the linear pair add up to 180°.
We know that all right angles are congruent from the Right Angle Congruence Theorem.
Hence,∠GMK ≅ ∠JMK
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what is the area under the standard normal curve between 1.03 standard deviations and 2.51 standard deviations?
The area under the standard normal curve between 1.03 standard deviations and 2.51 standard deviations is approximately 0.958 or 95.8%.
The area under the standard normal curve between 1.03 standard deviations and 2.51 standard deviations can be found using a standard normal distribution table or a calculator that can calculate probabilities for a standard normal distribution.
The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. To find the area under the standard normal curve between 1.03 standard deviations and 2.51 standard deviations, we need to find the probability of getting a value between 1.03 and 2.51 standard deviations from the mean.
Using a standard normal distribution table or calculator, we find that the probability is approximately 0.958. This means that the area under the standard normal curve between 1.03 standard deviations and 2.51 standard deviations is approximately 0.958 or 95.8%.
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find all values of for which the function =sin() satisfies the differential equation ″ 11=0. separate your answers by commas.
The required values of ω are √11 and - √11. This can be answered by the concept of differential equation.
The values of x for which the function f(x) = sin(x) satisfies the differential equation 11f''(x) = 0 are x = 0, π, 2π, 3π, 4π, ….
Given, the differential equation is y′′ + 11y = 0
Since the function is y = sin (ωt)
Therefore, the derivative of y is y′ = ω cos (ωt)
And, the second derivative of y is y′′ = −ω² sin (ωt)
Comparing the differential equation and the given function
we have−ω² sin (ωt) + 11 sin (ωt) = 0sin (ωt) [11 - ω²] = 0
Now, as sin (ωt) cannot be equal to zero for all values of ωt except 2nπ
Hence 11 - ω² = 0ω² = 11ω = ± √11
Therefore, the values of ω for which the function satisfies the given differential equation are√11 and - √11.
Hence, the required values of ω are √11 and - √11.
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20)
A single card is chosen at random from a standard deck of 52 playing cards. Which BEST describes the probability of drawing a king
from the deck?
The best description of the probability of drawing a king from the deck is 1 out of 13, or 1/13.
The probability of drawing a king from a standard deck of 52 playing cards can be determined by dividing the number of favorable outcomes (number of kings) by the total number of possible outcomes (total number of cards in the deck).
In a standard deck, there are 4 kings (one king for each suit: hearts, diamonds, clubs, and spades). Therefore, the number of favorable outcomes is 4.
The total number of possible outcomes is 52 (the total number of cards in the deck).
So, the probability of drawing a king is:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 4 / 52
Simplifying the fraction gives us:
Probability = 1 / 13
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you're in the wilderness hunting bears. you see a bear and chase it 10 miles south, 10 miles east, and 10 miles north. you wind up at the exact same point that you started. what color is the bear?
The triangle formed while chasing the bear in the given direction is an equilateral triangle and total distance covered is equal to 30 miles.
Direction while chasing bear are,
South , East , and North.
Distance covered in each direction while chasing = 10 miles.
The triangle formed by the movements of,
10 miles south, 10 miles east, and 10 miles north is an equilateral triangle.
This is because each of the three sides has a length of 10 miles.
And all three angles are 60 degrees.
To find the total distance you covered while chasing the bear,
Add up the lengths of the three sides of the equilateral triangle,
10 miles (south) + 10 miles (east) + 10 miles (north) = 30 miles
Therefore, triangle formed is an equilateral triangle and covered a total distance of 30 miles while chasing the bear.
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The given question is incomplete, I answer the question in general according to my knowledge:
You're in the wilderness hunting bears. you see a bear and chase it 10 miles south, 10 miles east, and 10 miles north. you wind up at the exact same point that you started. What type of triangle get formed and find the total distance you cover while chasing?
at state college last term, 53 of the students in a physics course earned a's, 81 earned b's, 106 got c's, 85 were issued d's, and 64 failed the course. if this grade distribution was graphed on pie chart, how many degrees would be used to indicate the a region?
Step-by-step explanation:
'a' region is 53 out of (53+81+106+85 + 64 = 389)
53/389 ths of the 360 degree circle would be the a's
53/389 * 360 = 49 degrees
The tetrahedron enclosed by the coordinate planes and the plane 2x + y + z =4
volume= 16/3, A coordinate plane is a graphing and description system for points and lines. A vertical (y) axis and a horizontal (x) axis make up the coordinate plane. There are four quadrants in the coordinate plane. The point where these lines connect is called the origin (0, 0).
limits
z= 0 to z = 4-y-2x
y= 0 to y = 4- 2x
x= 0 to x= 2
volume
v= \(\int\limits^2_0 \int\limits^4_0 \int\limits^4_0 dzdydx\)
v= \(\int\limits^2_0 \int\limits^4_0 (4-y-2x) dydx\)
v= \(\int\limits^2_0 ( 4y- y^{2} / 2 - 2xy) ^4^-^2^x _0\)
dx= \(\int\limits^2_0 [ 16-8x - 16+ 4x^2 - 16x / 2 - 8x+ 4x^2 ] dx\)
v= \(\int\limits^2_0 [ 8+ 2x^2- 8x] dx\\\)
= [ 8x + 2x^3 / 3 - 8x^2 / 2 ] ^2_0
= [16+ 16/3- 16]
v= 16/3
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Complete Question
Question: Sketch The Tetrahedron Enclosed By The Coordinate Planes And The Plane 2x+Y+Z=4. Use A Triple Integral To Find The Volume Of The tetrahedron
HELP PLEASE AS SOON AS POSSIBLE
what equivalent expression for (32 • 54)3?
Answer:
5,184 from my knowledge
1. Jason draws a rectangle in the coordinate plane at the right to represent his yard. To get from one corner of his yard to another, Jason travels 4 units down and then 6 units right. Draw arrows on the coordinate plane to show Jason’s path. Write the coordinates for his start and end points.
START:___ END:___
2. Use the coordinate plane in problem 1. What is the perimeter of rectangle YARD?
units
3. Mary models her rectangular room in the coordinate plane at the right. She plans to hang strings of lights on two perpendicular walls. What are the lengths of and ?
units units
4. Use the coordinate plane in problem 3. What is the area of Mary’s room?
square units
5. The coordinate plane at the right models the streets
of a city. The points A(3, 8), B(6, 3), and C(3, 3) are connected to form a park in the shape of a triangle. Connect the points to form the triangle. Which two sides of the park form a right angle?
and
6. Use the coordinate plane in problem 5. Tyler walks along the two sides of the park that form the right angle. How many blocks does he walk in all?
blocks
7. How can you find distances between points in a coordinate plane?
1. The coordinates are: START: (0,0) END: (6,-4), 2. The perimeter of rectangle YARD is 20 units,3. The lengths of YX and YZ are 4 units and 6 units, respectively, 4. The area of Mary's room is 24 square units,
1-To get from one corner of his yard to another, Jason travels 4 units down and then 6 units right. Starting from the origin, his starting point is (0,0). From there, he moves 4 units down to the point (0,-4), and then 6 units right to reach his endpoint, which is at (6,-4).
2-The rectangle has two sides of length 4 and two sides of length 6. The perimeter is the sum of the lengths of all sides, so it is equal to 2(4) + 2(6) = 8 + 12 = 20 units.
3-The coordinates of points Y, X, and Z are not given, so we cannot calculate the lengths directly. However, we know that the sides of a rectangle are perpendicular, so we can use the Pythagorean theorem to find the lengths. Let Y be the origin (0,0), and let X be the point (0, -4). Then YX has length 4 units. Similarly, let Z be the point (6, 0), so YZ has length 6 units.
4.To find the area of a rectangle, we can multiply the lengths of its sides. From problem 3, we know that the lengths of the sides are 4 and 6 units, so the area is 4 x 6 = 24 square units.
5. The sides AB and AC form a right angle.
To determine which sides of the triangle form a right angle, we need to find the slope of each side. The slope of AB is (3-8)/(6-3) = -5/3, and the slope of AC is (3-3)/(6-3) = 0. Since the product of the slopes of two perpendicular lines is -1, we can see that AB is perpendicular to AC. Therefore, sides AB and AC form a right angle.
6. Tyler walks 9 blocks in all.
To find the distance Tyler walks, we need to calculate the length of sides AB and AC. Using the distance formula, we can find that the length of AB is sqrt[(6-3)² + (3-8)²] =√[(34) units, and the length of AC is 3 units. Therefore, Tyler walks 3 + √[34 units along the two sides that form the right angle. This is approximately 9.4 blocks, so he walks 9 blocks in all.
7. The distance between two points in a coordinate plane can be found using the distance formula:
d = √[(x₂-x₁)² + (y₂-y₁)²]
where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points, and d is the distance between them. The formula is derived from the Pythagorean theorem, which relates the sides of a right triangle.
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Compute the left and right Riemann sums, Lo and Ro, respectively, for f(x) = 9 - (x - 3)2 on [0, 6]. (Round your answers to four decimal places.) L6 = R6 Compare their values. O Lo is less than Ro Lo and Ro are equal. O Lo is greater than Ro 6
The left and right Riemann sums are same which is equal to 35.
The given function is,
f(x) = 9 - (x - 3)²
Interval is [0, 6]
This can be divided in to 6 subintervals [0, 1], [1, 2], [2, 3], ....., [5, 6].
Δx = (6 - 0) / 6 = 1
\(x_i\) = a + Δx (i - 1), where [a, b] is the interval.
x1 = 0 + (1 × (1 - 1) = 0
x2 = 1, x3 = 2, x4 = 3, x5 = 4 and x6 = 5.
Left Riemann sum = 1. f(0) + 1. f(1) + ..... + 1. f(5)
= 0 + 5 + 8 + 9 + 8 + 5
= 35
Similarly for right Riemann sum,
\(x_i\) = a + Δx i, where [a, b] is the interval.
x1 = 1, x2 = 2, x3 = 3, x4 = 4, x5 = 5 and x6 = 6
Right Riemann sum = 1. f(1) + ..... + 1. f(5) + 1. f(6)
= 5 + 8 + 9 + 8 + 5 + 0
= 35
Hence both the sums are equal to 35.
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answers please ?!? answer if u know
Answer:
should be yellow
Step-by-step explanation:
hope this helps
Answer:
c
Step-by-step explanation:
pls give me brainliest im almost lvled up
I need help with this ASAP
Answer:
I think its Factor
Step-by-step explanation: (x-4) (x+1)
And for the equation x=4,-1