Use the Trapezoidal Rule with n = 4 to approximate
0.3523
0.7048
0.2456
0.4913
Answers
Answer:
0.7048
Step-by-step explanation:
∫₂⁴ 1 / (x − 1)² dx
n = 4, so we divide the interval into 4 regions. The width of the regions is:
(4 − 2) / 4 = 0.5
So the intervals are (2, 2.5), (2.5, 3), (3, 3.5) and (3.5, 4).
Evaluate f(x) at the ends of each interval.
f(2) = 1
f(2.5) = 4/9
f(3) = 1/4
f(3.5) = 4/25
f(4) = 1/9
Find the area of each trapezoid:
A₁ = ½ (2.5 − 2) (1 + 4/9) = 13/36
A₂ = ½ (3 − 2.5) (4/9 + 1/4) = 25/144
A₃ = ½ (3.5 − 3) (1/4 + 4/25) = 41/400
A₄ = ½ (4 − 3.5) (4/25 + 1/9) = 61/900
So the total approximate area is:
A = 0.705
Closest answer is 0.7048.
The value of expression is,
⇒ 0.7048
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
⇒ ∫₂⁴ 1 / (x − 1)² dx
Now, For n = 4, we divide the interval into 4 regions.
Hence, The width of the regions is:
= (4 − 2) / 4
= 0.5
Thus, the intervals are,
⇒ (2, 2.5), (2.5, 3), (3, 3.5) and (3.5, 4).
Thus, We can evaluate f(x) at the ends of each interval as,
f(2) = 1
f(2.5) = 4/9
f(3) = 1/4
f(3.5) = 4/25
f(4) = 1/9
Hence, the area of each trapezoid are,
A₁ = 1/2 (2.5 − 2) (1 + 4/9) = 13/36
A₂ = 1/2 (3 − 2.5) (4/9 + 1/4) = 25/144
A₃ = 1/2 (3.5 − 3) (1/4 + 4/25) = 41/400
A₄ = 1/2 (4 − 3.5) (4/25 + 1/9) = 61/900
Therefore, the total approximate area is:
A = A₁ + A₂ + A₃ + A₄
A = 0.7048
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Related Questions
Margo can purchase tile at a store for $0.89 per tile and rent a tile saw for $45. At another store she can borrow the tile saw for free if she buys tiles there for $1.39 per tile. How many tiles must she buy for the cost to be the same at both stores?
Margo must buy ____ tiles for the cost to be the same at both stores.
Answers
Answer:
She must buy 90 tiles for the cost to be the same at both stores
Step-by-step explanation:
Let x be the no. of tiles bought for the cost to be the same at both stores
Margo can purchase tile at a store for $0.89 per tile at shop 1
Cost of x tiles =0.89x
She rent a tile saw for $45.
So, total cost at Store 1 = 0.89x+45
At another store she can borrow the tile saw for free if she buys tiles there for $1.39 per tile.
So, cost of 1 tile = 1.39
Cost of x tiles = 1.39x
ATQ
0.89x+45=1.39x
45=1.39x-0.89x
45=0.5x
[tex]\frac{45}{0.5}=x[/tex]
90=x
Hence She must buy 90 tiles for the cost to be the same at both stores
EMERGENCY!!!! EXTRA POINTS! I HAVE POSTED THIS QUESTION 5 TIMES AND HAD TO REPORT ALL RESPONSES! I ACTUALLY NEED HELP!
The amusement park in Riverdale charges a $10 entrance fee plus $1 per ride. The amusement park in Esterdamb charges a $5 entrance fee and $2 per ride. For how many rides will the cost be the same for both amusement parks? x= # of rides
Number of rides_____?
Cost_____?
Answers
Answer:
the price will be the same for either amusement park
Step-by-step explanation:
10+1(x)=?
5+2(x)=?
ex; x=5
10+1(5)= 5+2(5)=
10+5= 5+10=
15 15
Answer:
5 rides, cost of $15
Step-by-step explanation:
With the information given we have two expressions:
10 + 1x and 5 + 2x
Using these expressions we can create this equation:
10 + 1x = 5 + 2x
Knowing some information we can can simply analyze some information:
The closest number each of these equations could equal is 15,
1(5) is 5 + 10 = 15, and 2(5) is 10 + 5 = 15
15 = 15 this is a true statement, so we know this is answer
Hope this helps! Have a good day!
how much money does ron have each month
Answers
Answer:
after paying all expenses Ron will have $10 leftover each month.
Answer:
10 on edge
Step-by-step explanation:
Divya’s recipe calls for 3.25 pounds of beef, 0.65 pounds of onions, 0.2
pounds of potatoes, 0.15 pounds of tomatoes, and 0.33 pounds of asparagus.
How much will Divya pay for all the ingredients in the recipe? Show your work.
Answers
The beef price is $10.65
Onions price is $2.49
Potatoes are $3.29
Tomatoes are $8.45
Asparagus is $4.99
3.25 pounds of beef is 3.25 * 10.65 = 34.61
0.65 pounds of onions is 0.65 * 2.49 = 1.62
0.2 pounds of potatoes is 0.2 * 3.29 = 0.66
0.15 pounds of tomatoes is 0.15 * 8.45 = 1.27
0.33 pounds of asparagus is 0.33 * 4.99 = 1.65
Adding these up we get 34.61 + 1.62 + 0.66 + 1.27 + 1.65
This is equal to 39.81
A recipe is mixture of ingredients.
Divya will pay $39.81 for all the ingredients in the recipe.
The beef price is $10.65 per pound
So, price of 3.25 pounds of beef is , [tex]3.25 * 10.65 = 34.61[/tex]
Onions price is $2.49 per pound
So, price of 0.65 pounds of onions is, [tex]0.65 * 2.49 = 1.62[/tex]
Potatoes are $3.29 per pound
So, price of 0.2 pounds of potatoes is , [tex]0.2 * 3.29 = 0.66[/tex]
Tomatoes price are $8.45 per pound.
So, price of 0.15 pounds of tomatoes is , [tex]0.15 * 8.45 = 1.27[/tex]
Asparagus price is $4.99 per pound.
So, price 0.33 pounds of asparagus is , [tex]0.33 * 4.99 = 1.65[/tex]
Hence, total amount paid by Divya is,
[tex]=34.61 + 1.62 + 0.66 + 1.27 + 1.65=39.81[/tex]
Thus, Divya will pay $39.81 for all the ingredients in the recipe.
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The ratio of the leg opposite to an angle to the leg adjacent to the angle in a right
triangle is called the ___ of the angle.
A. sine
B. tangent
C. cotangent
D. secant
Answers
Answer:
the answer is b. tangent
Step-by-step explanation:
The ratio of the leg opposite to an angle to the leg adjacent to the angle in a right triangle is called the tangent of the angle.
On which triangle can we apply trigonometric ratios?The trigonometric ratio can be defined in terms of ratios of perpendicular, bases, and hypotenuse.
Trigonometric ratios for a right-angled triangle are from the perspective of a particular non-right angle.
In a right-angled triangle, two such angles are there which are not right-angled(not of 90 degrees).
The slanted side is called the hypotenuse.
From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called the base.
The tangent of the angle is
[tex]\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}[/tex]
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please Help it’s urgent
Answers
Answer:
Angle IAJ
Step-by-step explanation:
X idea again. They are opposite to each other in the immediate area around them.
At the beginning of the month, Tim has $50. He mows 2 lawns and washes 1 car. Then, he buys two video games that cost $15 each and a sweatshirt that costs $35. How much money does Tim have left? (please put just your answer with the $)
Answers
Answer:
Tim has $50. 15+15=30-35=5
Tim has $5 left
Find the value of e/a. Just read the variables and numbers.
(50 points)
Answers
Answer:
35
Step-by-step explanation:
What is the correct answer?
Answers
Answer:45
Step-by-step explanation:
Sin^-1= 5÷7
What is the radius and diameter of the following circle?
111 cm
Radius
cm
Diameter =
cm
Answers
Answer:
Diameter = 212 cm
Step-by-step explanation:
D= 2r
pls helllllllllllllp
Answers
Answer:
40
Step-by-step explanation:
24 divided by = 8
8 times 5 = 40
can i have brainliest please
Answer:
40
Step-by-step explanation:
there is a 5 to 3 ratio for ice cream cones to brownies
ice cream: brownies
5:3
x:24
three times eight is 24
five times eight is 40
Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -36 and 2304, respectively.
Answer Choices:
A) an = 9 • 4n
B) an = 9 • (-4)n + 1
C) an = 9 • 4n - 1
D) an = 9 • (-4)n - 1
Answers
i need help asap! anyone know this?
Answers
Answer:
1 = 0
12x12 = 4
100=1
I think the last one is also 1
Step-by-step explanation:
The 8 in both sides gets cancelled out.
x=0
100^x=100
The hundred in both sides gets cancelled out.
x=1
12^x times 12^4=12^8
When the bases (numbers) are same and are multiplied together, you add the powers together.
12^x+4=12^8
The 12 in both sides get cancelled out.
x+4=8
x=8-4
x=4
(7^2)^9=7^3)^x
When there are powers both inside and outside the brackets, they’re multiplied with each other.
7^18=7^3x
The seven in both sides gets cancelled out.
18=3x
3x=18
x=18/3
x=6
What is the distance between points A(13, 2) and B(7, 10)
Answers
Answer:
distance = sqrt((x2-x1)^2 + (y2-y1))
distance = sqrt((7-13)^2 + (10-2)^2)
distance = sqrt( -6^2 + 8^2)
distance = sqrt(36+64)
distance = 10
Step-by-step explanation:
Answer:
10 units
Step-by-step explanation:
d = [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]
d = [tex]\sqrt{(13 - 7)^2 + (2 - 10)^2}[/tex]
d = [tex]\sqrt{(6)^2 + (-8)^2}[/tex]
d = [tex]\sqrt{36 + 64}[/tex]
d = [tex]\sqrt{100}[/tex]
d = 10 units
What is the slope of the line ?
Answers
Answer:
-3
Step-by-step explanation:
Find the volume of the figure
Answers
Answer:
450
Step-by-step explanation:
Determine if the question posed is a statistical question (yes) or not (no). What is 2 plus 2?
Answers
Answer:yes?
Step-by-step explanation:
it has #s in it lol
Answer:
no it isnt
Step-by-step explanation:
Given that x+1 is a factor of 2x^3-3x^2-8x-3 , solve 2x^3-3x^2-8x-3=0. This means find all the roots for the function.
Answers
Answer:
x=-1, -1/2, 3
Step-by-step explanation:
I need help with these plzzz
Answers
Answer:
1. C 2. B
Step-by-step explanation:
1. find the total circumference, d times pi, then put 42 over 360 and multiply them to get that section
2. The actual value of x is 33.2
So I plugged in that value for all of them
Compare the ordered pairs of the pre-image to the
image to answer these questions.
Is the dilation an enlargement or reduction?
The point of dilation is about what coordinate?
What is the scale factor?
Pre-image
Answers
Answer: Reduction
(0,0)
1/3
Step-by-step explanation:
Answer:
1-reduction
2-(0,0)
3-1/3
Step-by-step explanation:
Two gongs strike at intervals of 24 and 40minutes respectively. At twist time will they strike together again if they start simultaneously at 12 noon? Hint: 60 minutes = 1 hour
Answers
Answer:
They will sound together at 2pm
Step-by-step explanation:
Now, the first thing we need to calculate is , in how many minutes will the two gongs strike together.
To be able to do this, we need to calculate the least common multiple of the two numbers 24 and 40
The lowest common multiple between both is 120
This means that the two gongs will sound together at exactly 120 minutes
Now since 1 hour is 60 minutes, this means that 120 minutes will be = 120/60 = 2 hours
Since they both sounded together at 12 noon and the next time they will be sounding is next two hours, their sounding time will thus be 12 noon + 2 hours = 2 pm
solve the equation 18=n-18
n=_____
Answers
Answer:
36
Step-by-step explanation:
BE5-3 Cha Company buys merchandise on account from Wirtz Company. The selling price of the goods is $780, and the cost of the goods is $470. Both companies use perpetual inventory systems. Journalize the transaction on the books of both companies.
Answers
Answer:
In the books of Wirtz, the selling party, the required entries are
Debit Accounts receivable $780
Credit Revenue $780
Being entries to recognize sales revenue on account
Debit Cost of sales $470
Credit Inventory $470
Being entries to recognize the cost of items sold
In the books of Cha Company
Debit Inventory $780
Credit Accounts payable $780
Being entries to record cost of inventory purchased
Step-by-step explanation:
When a company makes a sale, the effect of such sale is dual in the books of the company being that the company would first recognize revenue and then recognize the cost of items sold.
To recognize revenue,
Debit Cash/Accounts receivable
Credit Revenue
To record the cost of the item sold
Debit Cost of sales
Credit Inventory
For the party that makes the purchase
Debit Inventory
Credit Cash/Accounts payable
what is the answer for this question below
7 (4u – 2v + w)
Answers
Answer:
28u-14v+7w
Step-by-step explanation:
Answer: 28u−14v+7w
Step-by-step explanation:
Hope that helps
Secant TQ and tangent TR intersect at point T. Chord SR and chord PQ intersect at point V. Find the values of x and y. If necessary, round to the nearest tenth.
Answers
Answer:
x=4, y=9.6
Step-by-step explanation:
Using Theorem of Intersecting Secant and Tangent
[tex]TP X TQ=TR^2[/tex]
[tex]9(9+12+x)=15^2\\9(21+x)=225\\189+9x=225\\9x=225-189\\9x=36\\x=4[/tex]
Next, we apply Theorem of Intersecting Chords
SV X VR=PV X VQ
5 X y = x X 12
Recall: x=4
5y=4 X 12
5y=48
y=48/5=9.6
Therefore: x=4, y=9.6
The leaning Tower of Pisa was completed in 1372 and makes 86 degree angle with the ground. The tower is 50 meters tall, measured vertically from the ground to the highest point. If you were to climb to the top then accidentally drop your keys, where would you start looking for them?
How far from the base of the tower would they land?
I made having no luck in figuring this out.
Answers
Answer:
The distance where the keys would drop from the base is 3.5m
Step-by-step explanation:
Height of the tower = 50m
Angle it makes to the ground = 86°
To solve this question, you have to understand that the tower isn't vertically upright and the height of the tower is different from the distance from the top of the tower to the ground.
The tower makes an angle 86° to the ground and that makes it not vertically straight because a vertically straight building is at 90° to the ground.
See attached document for better illustration.
The distance from where the keys drop to the base of the tower can be calculated using SOHCAHTOA
We have to use cosθ = adjacent / hypothenus
θ = 86°
Adjacent = ? = x
Hypothenus = 50m
Cos θ = x / hyp
Cos 86 = x / 50
X = 50 × cos 86
X = 50 × 0.06976
X = 3.488 = 3.5m
The distance where the keys would drop from the base of the tower is approximately 3.5m
Georgianna wants to use the linear model associated with the data in the table to make a prediction.
A 2-column table with 5 rows. The first column is labeled time (minutes) with entries 0, 5, 10, 15, 30. The second column is labeled distance (miles) with entries 0, 4, 9, 13, 18.
Which range of time values describes the entire interval over which she would be interpolating?
0 to 5 minutes
0 to 18 minutes
0 to 30 minutes
18 to 30 minutes
Answers
Answer:
0 to 30 minutes on edg.
Step-by-step explanation:
Answer:
c on e 2020
Step-by-step explanation:
Jamal and Cleo mow lawns together, Jamal can mow an average lawn in 60 minutes by
himself. Cleo would take 90 minutes for the same job. How long would it take both of
them together to mow one (1) lawn
Answers
Hope this helps
Please help me now I will mark you brainliest
Answers
Answer:
Out side the circle
Step-by-step explanation:
This is because the center is 0 and if the point 6, square root seven is on the circle that mean that as far as the circle goes on each side.
HELP - WILL MAKE BRAINLIEST IF CORRECT - a chunk of lava flies out of a volcano from a height of 12,447 feet a velocity of 608 feet per second. Find the highest point the lava reaches and how long it takes to reach it using the equation y= -16t^2 + 608t + 12,447.
Answers
Answer:
18,223 feet
Step-by-step explanation:
y= -16t^2 + 608t + 12,447.
y = -16(t² - 38t) + 12447
y = -16[t² - 2(t)(19) + 19² - 19²] + 12447
y = -16(t - 19)² - 16(-19²) + 12447
y = -16(t - 19)² + 18223
Vertex: (19, 18223)
Max height is 18,223 at t = 19
The parabolas are:
a = -16
b = 608
c = 12,447
x_v = -b/2a
t_v = -608/2(-16)
t_v = -608/-32
t_v = 19
Plug in t_v = 19 to find y_v
y = -16(19)^2 + 608(19) + 12,447
y = -16(361) + 11,552 + 12,477
y = -5,776 + 11,552 + 12,477
y = 18,253
We have the point (19, 18,253)
The max height is at 18,253 when t = 19
Best of Luck!
