Answer:
A. underestimate
Step-by-step explanation:
it is correct on Time4learning EDGE2021 :)
hope i helped
T20 overestimates the exact value of the integral. so, the correct answer is (A).
What is integral?In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus, the other being differentiation.
here, we have,
To determine if T20 overestimates or underestimates the exact value of the integral, we need to compare the value of T20 with the exact value of the integral.
Using the formula for the trapezoidal rule with N = 20, we have:
T20 = [f(0) + f(6)]/2 + ∑(i=1 to 19) f(ih)
where h = (6-0)/20 = 0.3 and f(x) = 2e^(-x/4).
Evaluating T20 using these values, we get:
T20 = [f(0) + f(6)]/2 + ∑(i=1 to 19) f(ih)
= [2 + 2e^(-1.5)]/2 + ∑(i=1 to 19) 2e^(-ih/4)
≈ 9.149
To find the exact value of the integral, we can use integration by substitution:
∫2e^(-x/4)dx = -8e^(-x/4) + C
where C is a constant of integration. Evaluating this expression from x = 0 to x = 6, we get:
∫2e^(-x/4)dx from 0 to 6 = [-8e^(-6/4) + 8] - [-8e^(-0/4) + 2]
= 8 - 6e^(-3/2)
≈ 8.042
Since T20 ≈ 9.149 > 8.042, the exact value of the integral, we can conclude that T20 overestimates the exact value.
Next, we need to find the error bound for T20 using the formula:
Error(TN) ≤ M(b-a)^3 / (12N^2)
where M is the least upper bound for all absolute values of the second derivatives of the function 2e^(-x/4) on the interval [a,b].
The second derivative of f(x) = 2e^(-x/4) is:
f''(x) = (1/8)e^(-x/4)
To find the least upper bound M for f''(x) on the interval [0,6], we can find the maximum value of |f''(x)|:
|f''(x)| = (1/8)e^(-x/4) ≤ (1/8)e^(-0/4) = 1/8
So, M = 1/8.
Plugging in the values of M, a, b, and N into the error formula, we get:
Error(T20) ≤ M(b-a)^3 / (12N^2)
= (1/8)(6-0)^3 / (12*20^2)
= 0.00028125
Therefore, the error in the approximation T20 is guaranteed to be less than or equal to 0.00028125. So, option (A) is correct.
To know more about integral:
brainly.com/question/30714582
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Complete question:
Consider the integral approximation T20 of ∫90^3−4. does T20 overestimate or underestimate the exact value?
A. overestimates B. underestimates
Need help on the picture i attached
Answer:
1.) Standard form -
2.) Center (1,-3)
3.) Radius r=4
4.) Diameter d=8
5.) Circumference 25.12
6.) Area 50.24
7.) Graph
Step-by-step explanation:
What are the zeros for y = x squared - 4
Answer:
zeros are ±2
Step-by-step explanation:
y = x² - 4
this can be factored into (x+2)(x-2)
if you then set each factor equal to zero you will get zeros of ±2
7,16,30,49,73,?
find next number in series
Let A be the first sequence, and denote by [tex]a_n[/tex] the n-th term in A.
Consider the forward differences of A :
16 - 7 = 9
30 - 16 = 14
49 - 30 = 19
73 - 49 = 24
Call this sequence of first differences B, so that for n ≥ 1,
[tex]b_n=a_{n+1}-a_n[/tex]
where [tex]b_n[/tex] is the n-th term of B.
Now consider the forward differences of B, which is another sequence we'll call C :
14 - 9 = 5
19 - 14 = 5
24 - 19 = 5
Then if [tex]c_n[/tex] is the n-th term of C, we have for all n ≥ 1,
[tex]c_n=b_{n+1}-b_n=5[/tex]
which gives
[tex]b_{n+1} = b_n+5[/tex]
This tells us B is an arithmetic sequence - the first term is 9 and the difference between consecutive terms is 5, so we have for n ≥ 1,
[tex]b_n = 9 + 5(n-1) = 5n + 4[/tex]
Plug this into the recurrence for A :
[tex]a_{n+1} = a_n + b_n = a_n + 5n + 4[/tex]
We don't need to solve for [tex]a_n[/tex], fortunately; we just want the next term, which would be
[tex]a_6 = a_5 + 5^2 + 4 = 73 + 25 + 4 = \boxed{102}[/tex]
PLEASE HELP ILL GIVE BRAINLIEST
Answer:
1 and 2 is The first one and 3 and 5 is the second one
You have $10. If you and 3 of your friends want to go to the movies, what does the ticket price need to be for you to be able to buy all 4 tickets?
Answer:
$2.50
Step-by-step explanation:
$10/4 = $2.50
which statement is TRUE of function 1 and function 2?
Answer:
D. function 1 has a greater rate of change because the slope of function 1 is 3 and the slope of function 2 is -4
Answer:
D. function 1 has a greater rate of change because the slope of function 1 is 3 and the slope of function 2 is -4
What are the roots of this quadratic equation?
3x^2 + 10=4x
Plsss help. giving extra points if correct.
Answer:
B. ACB AND ACD
Step-by-step explanation:
since you need to prove, you need to show that the figure can work on any 2 triangles… hope it helps.
I need help on number 10 plz
Answer:
12 inches
Step-by-step explanation:
3 feet = 1 yard
1/3 yard = 1 foot
1 foot = 12 inches
Please helppppppppppppppppppppppp
Answer:
u got the right answer in the picture
How is finding the volume of prisms a bit like slicing a loaf of bread?
Answer:
To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.
Two angles of a quadrilateral measure 305° and 30°. The other two angles are in a ratio of
2:3. What are the measures of those two angles?
Answer:
10 and 15
Step-by-step explanation:
A quadrilateral will measure a total of 360 degrees. We already know that the measurements of other angles were 305 and 30. That's a total of 335 degrees. Subtract that from 360 to find out how many are left in the shape.
360 - 335 = 25. The other two angles are in a ratio 2:3. So you need to find numbers that add up to 25 in a ratio of 2:3
If you multiply that ratio by 5, you get 10:15. 10 and 15 add up to 25, so those are your other angles.
Brad is cutting logs. He has 4 logs. Brad will cut each log by 12
If Brad cuts each log by 12 he will have 48 pieces of cut logs. I hope this helps you, have a great day!
Answer:
48
Step-by-step explanation:
4x12=48
What is the product of the polynomials below?
(6 - 5x^2)(x4-x^3)
Answer:
-5x^6+5x^5+6x^4-6x^3Step-by-step explanation:
[tex]\left(6-5x^2\right)\left(x^4-x^3\right)\\\\\mathrm{Apply\:FOIL\:method}:\\\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd\\\\a=6,\:b=-5x^2,\:c=x^4,\:d=-x^3\\\\=6x^4+6\left(-x^3\right)+\left(-5x^2\right)x^4+\left(-5x^2\right)\left(-x^3\right)\\\\\mathrm{Apply\:minus-plus\:rules}\\+\left(-a\right)=-a,\:\:\left(-a\right)\left(-b\right)=ab\\\\=6x^4-6x^3-5x^4x^2+5x^3x^2\\\\Simplify\\\\=-5x^6+5x^5+6x^4-6x^3[/tex]
5th grade math. correct answer will be marked brainliest
Answer:
5280
Step-by-step explanation:
Hope this helps!
Please look at the image
Answer:
the pic is block
Step-by-step explanation:
Answer:
Jack's age =a
Matt's age= 2a+6
a+2a+6 =90
3a +6. =90
3a= 90-6
3a=84
a=28
Find the missing lengths.
Answer:
that angle is 45°
so y = 5√3
and × = √2×y
x= √2 × 5√3
x=5√6
PLSSS HELP PANICKING
The sum of Alex and John's money is $48. Alex has $3 more than twice the amount John has. How much money do they each have?
Answer:
John has $15 and Alex has $33Step-by-step explanation:
a systems of equations can be made from the information on the problem
x+y=48
x=2y+3
since x= 2y+3 substitute 2y+3 in the firat equation to get:
(2y+3)+y=48 -> 3y+3=48 -> 3y=45 -> y=15
plug in 15 for y in the second equation to solve for x
x+15 =48 --> x=33
Identify the domain of the function shown in the graph.
10-
8
8
4
2
-8-8-4
-2
-2-
2
4
8
8
10 12
4
-B
-8
-10
Answer:
domain means x- component I hope you you can identify the domain
whats 2+2 UnU thats a hard one ToT
Answer:
4
MARK ME BRAINLIEST CUZ IM DA SMARTEST :))
the answer to that is 4
f(n)=2n+1
g(n)=3n
Find f(n)+g(n)
Answer:
5n + 1
Step-by-step explanation:
f(n) + g(n) is just 2n + 1 + 3n , adding the two functions together!
Those expressions combine to 5n + 1 :)
A teaspoon of salt has a mass of 6 grams what is its mass in milligrams
Answer:
6000 milligrams
Step-by-step explanation:
trust
Find the volume of the cone.
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi.
Right circular cone
Solve for volume
V≈37.7r Radius
2h Height
9V=πr2h
3=π·22·9
3≈37.69911
Answer:
37.7
Step-by-step explanation:
3 toys cost x kobo. How many toys can be bought with #3.00?
Answer:
ok so you say I don't know for 10000000000 year's the end. :)
If f(1)=1, f(2)=4 and f(n)=3f(n-1)-f(n-2) then find the value of f(4).
Answer:
29
Step-by-step explanation:
f(3)=3f(2)-f(1)=3x4-1=11
f(4)=3f(3)-f(2)=3x11-4=29
please help brainliest
Answer:
area = 186.984
Step-by-step explanation:
The 3 rectangular surfaces are simply L * W of each so
left surface = 5.5 * 6.2 = 34.1
right surface = 5.5 * 8.5 = 46.75
bottom surface = 5.5 * 9.8 = 53.9
The front and back are the same so
front = 1/2 base * heigth = 1/2 * 9.8 * 5.33 = 26.117
front + back = 2 * 26.117 = 52.234
total = sum them all up = 34.1 + 46.75 + 53.9 + 52.234 = 186.984
do it and I give 100 points
a^2 is correct
my past answer was incorrect but this 100 percent is correct
Oscar wants to rent a car for 5 days, and he's interested in the collision
damage waiver but not the loss damage waiver. If the daily rate is $54 and
CDW is $50, what is his total rental cost?
A. $270
B. $304
C. $320
D. $520
Howto solve for x in X+10=30
Answer:
20
Step-by-step explanation:
x+10=30
x=30-10
x=20
HOPE IT HELPEDStep-by-step explanation:
=>x+10=30=>x+10-10=30-10 ten(+10) will be cancelled by negative ten(-10)=>x=20check
20+10=30
The rectangle below has an area of zº +82 + 15 square meters and a width of 2 + 3 meters.
What expression represents the length of the rectangle?
Length
2 +3
2° +8x + 15
Length
meters
Answer:
(x+5) metres
Step-by-step explanation:
correct question
The rectangle below has an area of x^2+8x+15 square meters and a width of x+3 meters. What expression represents the length of the rectangle?
Area of the rectangle = Length * width
Factorize the area
A(x) = x^2+8x+15
A(x) = x^2+3x+5x+15
A(x) = x(x+3) + 5(x+3)
A(x) = (x+3)(x+5)
Since the width is x+3, the length of the rectangle will be (x+5) metres