Finite approximation method of estimating the area under the curve of the
given function makes use of rectangular approximation of the area.
The correct responses are;
i) The estimated area using a lower sum with two rectangles of equal width is 1,715 square units.
ii) The estimated area using a lower sum with four rectangles of equal width is 3,001.25 square units.
iii) The estimated area using an upper sum with two rectangles of equal width is 8,575 square units.
iv) The estimated area using a upper sum with four rectangles of equal width is 6,431.25 square units.
Reasons:
The given function is f(x) = 5·x²
The given domain is x₀ to x₁₄
i) Estimate using lower sum with two rectangles of equal width;
[tex]Let \ \Delta x = \dfrac{14}{2} = 7 \ we \ get;[/tex]
f(0) = 0
f(7) = 5 × 7² = 245
A = 0 × 7 + 245 × 7 = 1,715
The estimated area using a lower sum with two rectangles of equal width
is 1,715 square units.
ii) Estimate using lower sum with four rectangles of equal width;
[tex]Let \ \Delta x = \dfrac{14}{4} = 3.5 \ we \ get;[/tex]
f(0) = 0
f(3.5) = 5 × 3.5² = 61.25
f(7) = 5 × 7² = 245
f(10.5) = 5 × 10.5² = 551.25
A = 0 × 3.5 + 61.25 × 3.5 + 245 × 3.5 + 551.25 × 3.5 = 3,001.25
The estimated area using a lower sum with four rectangles of equal width is 3,001.25 square units.
iii) Estimate using an upper sum with two rectangles of equal width;
[tex]Let \ \Delta x = \dfrac{14}{2} = 7 \ we \ get;[/tex]
f(7) = 5 × 7² = 245
f(14) = 5 × 14² = 980
A = 245 × 7 + 980 × 7 = 8575
The estimated area using an upper sum with two rectangles of equal width
is 8,575 square units.
iv) Estimate using an upper sum with four rectangles of equal width;
[tex]Let \ \Delta x = \dfrac{14}{4} = 3.5 \ we \ get;[/tex]
f(3.5) = 5 × 3.5² = 61.25
f(7) = 5 × 7² = 245
f(10.5) = 5 × 10.5² = 551.25
f(14) = 5 × 14² = 980
A = 61.25 × 3.5 + 245 × 3.5 + 551.25 × 3.5 + 980 × 3.5 = 6,431.25
The estimated area using a upper sum with four rectangles of equal width
is 6,431.25 square units.
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Stefan's family raises honey bees and sells the honey at the farmers' market. To get ready for market day, Stefan fills 24 equal sized jars with honey. He brings a total of 16 cups of honey to sell at the farmers' market.
Answer:
Have you ever wondered how a tiny little insect like a bee could ever fill a jar of honey? If it were just down to one bee it would be a mighty task but the work is shared by many thousands of bees and is a great example of what can be achieved by a co-ordinated effort. Think of it in terms of humans creating something like a pyramid.
A jar of honey weighs 454 grammes and a bee can carry about 0.04 grammes of nectar. But nectar is only about 40% sugar and honey needs to be about 80% sugar so the bee actually only carries about 0.02 grammes of honey on each trip.
Step-by-step explanation:
There are 18 students in sir Sam 4th PE class. Each student will be given 2 1/2 minutes to explain how to solve his word problem with fractions. How long it will take for all 18 students to explain their answers? (Show solutions)
Answer:
44
Step-by-step explanation:
18 * 2.5 = 44
Cual es el ángulo que equivale a 4 ángulos rectos?
ayus lng ako hahaha hshshs
. . .Factor 2x2 + x - 1
Answer:
(2−1)(+1)
Step-by-step explanation:
22+−12x^{2}+{\color{#c92786}{x}}-12x2+x−122+2−−1
Prove that the difference between 9th square number and 5th square number is a multiple of 8?
Answer:
Step-by-step explanation:
9th square number = 81
5th square number=25
81-25=56
56 is a multiple of 8 as 8 x 7=56
Consider the following functions. f1(x) = x, f2(x) = x2, f3(x) = 2x − 4x2 g(x) = c1f1(x) + c2f2(x) + c3f3(x) Solve for c1, c2, and c3 so that g(x) = 0 on the interval (−[infinity], [infinity]). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution {0, 0, 0}.) {c1, c2, c3} = $$ Correct: Your answer is correct. Determine whether f1, f2, f3 are linearly independent on the interval (−[infinity], [infinity]).
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Answer:
(c1, c2, c3) = (-2t, 4t, t) . . . . for any value of tNOT linearly independentStep-by-step explanation:
We want ...
c1·f1(x) +c2·f2(x) +c3·f3(x) = g(x) ≡ 0
Substituting for the fn function values, we have ...
c1·x +c2·x² +c3·(2x -4x²) ≡ 0
This resolves to two equations:
x(c1 +2c3) = 0
x²(c2 -4c3) = 0
These have an infinite set of solutions:
c1 = -2c3
c2 = 4c3
Then for any parameter t, including the "trivial" t=0, ...
(c1, c2, c3) = (-2t, 4t, t)
__
f1, f2, f3 are NOT linearly independent. (If they were, there would be only one solution making g(x) ≡ 0.)
Which equation matches the graph?
Answer:
Option C): f(x) = 3x - 4.
Step-by-step Explanation:
What is a Linear Function in Slope-intercept Form?A linear function in slope-intercept form is given by f(x) = mx + b where:
"m" represents the slope, which is the measure of steepness and orientation of a nonvertical line. "b" represents the y-coordinate of the y-intercept, (0, b). The y-intercept is the point on the graph where the line intersects the y-axis. It is also the point where the x-coordinate equals to zero.How to solve for the slope?We can solve for the slope by using the following formula:
[tex]\displaystyle\mathsf{Slope\:(m)\:=\:\frac{Rise}{Run}\:=\Bigg(\frac{y_2-y_1}{x_2 - x_1}\Bigg)}[/tex]
Choose two points from the graph and substitute their values into the slope formula.
(x₁, y₁) = (2, 2)(x₂, y₂) = (0,-4)[tex]\displaystyle\mathsf{Slope\:(m)\:=\Bigg(\frac{y_2-y_1}{x_2 - x_1}\Bigg)\:=\:\Bigg(\frac{2-(-4)}{2-0}\Bigg)\:=\:\Bigg(\frac{2+4}{2}\Bigg)\:=\:\frac{6}{2}\:\:=\:3}[/tex]
Therefore, the slope of the line is 3.
How to find the y-intercept (b)?As defined in the previous section of this post, the y-intercept (0, b) is the point on the graph where it crosses the y-axis. We can see that the line intersects the y-axis at point (0, -4). This means that the value of our y-intercept, b, is -4.
Finding the y-intercept algebraically.Alternatively, we can solve for the y-intercept (b) by choosing a point on the graph and substitute its values into the slope-intercept form.
We will use and substitute the values of (x₁, y₁) and the slope into the function to solve for b.
(x₁, y₁) = (2, 2)Slope (m ) = 3f(x) = mx + b
⇒ 2 = 3(2) + b
⇒ 2 = 6 + b
⇒ 2 - 6 = 6 - 6 + b
⇒ -4 = 0 + b
⇒ - 4 = b
Hence, the value of the y-intercept is: b = 4.
Final Answer:Based from our calculations, we can infer that the linear function that matches the graph is Option C: f(x) = 3x - 4.
__________________________Keywords:Linear functions
Linear equations
Slope-intercept form
_______________________________
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Answer:
f(x)=3x-4
Step-by-step explanation:
Patty is ordering vests for her scout troop to wear in the Veterans Day parade. She ordered 12 vests from the Festive Features clothing shop. Since this was a bulk order, Festive Features reduced the price of each vest by $6. The total came to $132. Which equation can you use to find the amount, v, Festive Features normally charges for a vest?
Algebraic equations are equations that have coefficients and unknown variables in them.
The equation that you can use to find the amount "v" Festive features normally charges for a vest is: 12(v - 6) = 132
The current cost per vest was v - $6
Where v = Initial cost of the vest
The total cost of 12 vests after price reduction was:
$132.
Hence, our equation is given as:
$132 = 12(v - $6)
12(v - 6) = 132
$132 = 12v - 72
Add 72 to both sides
$132 + 72 = 12V
204 = 12v
v = 204/12
v = $17
Thus: The amount v, Festive Features normally charges for a vest is $17
Therefore, the equation to find the amount Festive Features normally charges for a vest is 12(v - 6) = 132
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You have been asked to build a tree house with a floor that is twice as long as it is wide. You have only a certain amount of wood you can use. Which of these strategies would you be most likely to use while planning the tree
house?
A. Work backward.
B. Draw a diagram.
C. Find a pattern.
D. Act it out.
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Answer:
B. Draw a diagram.
Step-by-step explanation:
Most construction starts with a diagram.
_____
Additional comment
You may actually start by finding a pattern you like, then figuring the material required to construct the pattern, then working backward to determine the dimensions you need to use to stay within your material budget. You will probably draw a diagram at many points in the planning process.
A plumber has a fixed call out rate of $80 and has an hourly rate of $60
Answer:
do FYI kkkkkkjjj ghost oh go j
The expression for the total cost will be y = 80 + 60x.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that a plumber has a fixed call-out rate of $80 and an hourly rate of $60.
The expression will be formed by assuming the hourly rate to be x dollars. The expression will be written as below:-
y = 80 + 60x
Here y is the total cost 80 is the fixed cost and x is the hourly rate.
Therefore, the expression for the total cost will be y = 80 + 60x.
The complete question is given below:-
A plumber has a fixed call-out rate of $80 and an hourly rate of $60. Write an expression for the total cost.
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without using a calculator or mathematical table sove 187²-87²
Many casinos have a game called the Big Six Money Wheel, which has 54 slots in which are displayed a Joker, the casino logo, and various dollar amounts, as shown in the table at the top of the next column. Players may bet on the Joker, the casino logo, or one or more dollar denominations. The wheel is spun and if the wheel stops on the same place as the player's bet, the player wins that amount for each dollar bet.
If a player bets $2 on the $5 denomination, find the player's expectation. (Round your answer to two decimal places.)
Creating a discrete probability distribution table based on the possible outcomes of the game. The player's expectation is $8.44
Player's bet number = $5 Bet amount = $2 Winning = $2 × $5 = $10Probability that wheel stops on $5:
Probability = required outcome / Total possible outcomesP(stops on $5) = 7/54 =
Hence, probability of not winning = 1 - 7/54 = 47/54
X :____ - 2 _____ 10
P(X) : _ 47/54 ___ 7/54
Expectation or Expected value :
E(X) = (-2 × 7/54) + (10 × 47/54)
E(X) = $8.44
Therefore, the player's expectation is $8.44
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solve this i dont know how to graph it pls tell
ASAP and i will give brainliest
Answer:
straight line through (0,4) and (2,0), shade everything above it
Step-by-step explanation:
First solve the equality, which will give you a straight line.
Then check if the inequality (the > sign) means you have to shade the area above or below it.
2x + y = 4 can easily be solved by first taking x=0, then you find y=4, hence (0,4) is a solution.
Then take y=0, then you find 2x = 4 so x=2, hence (2,0) is a solution.
Plot these two points and draw a line through them.
Now, since 2x+y has to be larger than 4, all the points to the right and above the line are valid. So that's the area you have to shade.
An amusement park sells child and adult tickets at a ratio of 8:1. On Saturday, they sold 147 more child tickets than adult tickets. How many tickets did the amusement park sell on Saturday?
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Answer:
189
Step-by-step explanation:
The difference between the ratio units is 8 -1 = 7.
The difference between child and adult ticket sales was 147 tickets, so each ratio unit stands for 147/7 = 21 tickets.
The total of the ratio units is 8+1 = 9, so 9 × 21 = 189 tickets were sold on Saturday.
__
That was 168 child tickets and 21 adult tickets.
Determine the axis of symmetry of a parabola whose graph is given below. Give your answer in the form X equals H
Answer:
x = -3
Step-by-step explanation:
The axis of symmetry of a parabola, in the form of x = h is x = -3, where the value of h is -3.
A surface curve formed by the intersection of a cone and a plane parallel to a straight line is called as parabola.
An imaginary straight line that divides a shape into two identical halves is called as axis of symmetry.
In the given figure, the graph intersects the x-axis at x = -3.
So, the axis of symmetry of a parabola in the form of x is -3.
Thus, the value of h is -3.
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Find the quotient when (21x2 -52x + 32) is divided by (7x - 8).
1:3x + 3
2:3x + 4
3:3x + 2
4:3x - 4
Answer:
4:3x-4
Step-by-step explanation:
if A=(-2,-4) and B=(-8, 4) what is the length of AB?
the length of AB is 10 cm..........
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Length of AB is equal to :
[tex]10 \: \: units[/tex]Refer to the attachment for solution ~
The product of the Roots of the quadratic equation 2x² + 5x - 7 = 0 is
Product of roots
[tex]\\ \sf \longmapsto \dfrac{c}{a}[/tex]
[tex]\\ \sf \longmapsto \dfrac{-7}{2}[/tex]
What is the length of the diagonal of the square shown below? 5 45° 5 5 90° 5 O A. 5
B. 10
C. 5
D. 5/5
E. 5.2
F. 25
The length of the diagonal of the square is d = 5√2.
Given that, the measure of the side of the square is 5.
We need to find the length of the diagonal of the square.
How to find the length of the diagonal of the square?The diagonal of a square formula is d = a√2; where 'd' is the diagonal and 'a' is the side of the square.
Now, d = 5√2
Therefore, the length of the diagonal of the square is d = 5√2.
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Find the range of the data set : -5, -6, -1, -3, 6, 10
Work Shown:
range = max - min = 10 - (-6) = 10 + 6 = 16
The range is the distance from the smallest item to the largest. Use of a number line might help sort out the values to see which is the smallest and largest.
The tickets for a figure skating performance sold out in 4 hours. If there were 40,000 tickets sold, solve the equation 40,000−4x=0 to find the number of tickets sold per hour.
Answer: look it up
Step-by-step explanation:
fay has a lemonade stand. She spends £25 on ingredients. She sells each glass of lemonade for £1.50. If she sells 40 glasses of lemonade, what is her total profit?
What is the median number of this data set 15,33,51,75,51?
Answer:
51
Step-by-step explanation:
1. The median of a data set is the quantity that's in the middle of the data points. Before looking what number is in the middle, you have to order them from least to greatest.
15, 33, 51, 51, 752. Now, when crossing from left to right then left to right again, you end up with 51 in the middle.
Therefore, the median number is 51.
Sonya buys a baseball jersey for her brother on sale for 20% off. If the price she paid was $6 lower than the regular price, what was the original price of the jersey?
Answer:
$30
Step-by-step explanation:
20%=6
5x20%=100%
so
5x6=30
Hope this helps! Thanks.
Help help please math math please
Answer:
n = 6
Step-by-step explanation:
6÷4 = 9÷n
6n = 9*4
6n = 36
n = 6
Essay buys 3 apples, 5 bananas, and 7 peaches from a market. What is the ration of bananas to total fruit in simplest form?
Answer:
5:15 or 1:3
Step-by-step explanation:
Answer:
1 : 3
Step-by-step explanation:
Number of bananas = 5
Total fruits = 15 (3 + 5 + 7)
Ratio = 5 : 15
Simplified form = 1 : 3
m
+ 4 = 7
Step One:
Step Two:
Step Three:
Step Four:
ma9
m/3+4+4+7+4
m/3-7
m=21
m/3+4-47-4
m/3*3+4=743
m/3-3
ma17
m/3+4-3=7-3
m/3*3=3*3
m/3+7=4
m=3
m/3+8=11
m/314-4=7
m+4=21
Answer:
9
Step-by-step explanation:
1. m/3+4-4=7-4
2. m/3=3
3. m/3*3 = 3*3
4. m=9
Answer:
m=9
Step-by-step explanation:
m/3+4-4=7-4
m/3=3
m/3*3=3*3
m=9
help me asap!!!!!!!!
Answer:
the last option
Step-by-step explanation:
If 6 spiders can spin 6 webs in 6 minutes how long will it take 100 spiders to spin 200 webs
Answer:
200 minutes
Step-by-step explanation:
if six spiders can spin 6 webs in 6 min then 100 spiders can spin 100 webs in 100 min then multipy by 2 and you get 200
The amount of time that 100 spiders can spin 200 webs will be 12 minutes.
What is Algebra?Algebra is the study of graphic formulas, while logic is the manipulation of those signs.
Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction is referred to as the PEMDAS rule. To answer the problem properly and accurately, this rule is applied.
If 6 spiders can spin 6 webs in 6 minutes. Then the 1 spider can sin one web in six minutes. So, the 100 spiders can spin 100 webs in 6 minutes.
Then the 100 spiders can spin 200 webs in 12 minutes.
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y-3(2y-7)=76 quick and with steps
Answer:
y = -11.
Step-by-step explanation:
Y-3(2y-7)=76
Y-6y+21=76
-5y+21=76
-5y=55
y=-11.
Answer:
Step-by-step explanation:
⇔y-6y+21=76⇔-5y+21=76⇔-5y = 76 -21⇔-5y=55 ⇔y= 55:(-5) ⇔y= -11