By using Trapezoid Rule to approximate the value of the definite integral is 7.0313.
closest option to this answer is C. 7.0313.
To use the Trapezoid Rule to approximate the definite integral:
[tex]\int _0^2 x^4 dx[/tex]
with n = 4, we first need to partition the interval [0, 2] into subintervals of equal width:
[0, 0.5], [0.5, 1], [1, 1.5], [1.5, 2]
The width of each subinterval is:
Δx = (2 - 0) / 4 = 0.5
Next, we use the formula for the Trapezoid Rule:
[tex]\int _a^b f(x) dx \approx \Delta x/2 * [f(a) + 2f(a+ \Delta x) + 2f(a+2 \Delta x) + ... + 2f(b- \Delta x) + f(b)][/tex]
Plugging in the values, we get:
[tex]\int _0^2 x^4 dx \approx 0.5/2 * [f(0) + 2f(0.5) + 2f(1) + 2f(1.5) + f(2)][/tex]
where[tex]f(x) = x^4[/tex]
[tex]f(0) = 0^4 = 0[/tex]
[tex]f(0.5) = (0.5)^4 = 0.0625[/tex]
[tex]f(1) = 1^4 = 1[/tex]
[tex]f(1.5) = (1.5)^4 = 5.0625[/tex]
[tex]f(2) = 2^4 = 16[/tex]
Plugging these values into the formula, we get:
[tex]\int _0^2 x^4 dx \approx 0.5/2 \times [0 + 2(0.0625) + 2(1) + 2(5.0625) + 16][/tex]
[tex]\int _0^2 x^4 dx \approx 7.03125[/tex]
Rounding to four decimal places, we get:
7.0313
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To use the Trapezoid Rule to approximate the definite integral integral^2_0 x^4 dx with n = 4, we first need to divide the interval [0,2] into n subintervals of equal width. The approximation of the definite integral using the Trapezoid Rule with n = 4 is 6.5625 (option D).
[0, 0.5], [0.5, 1], [1, 1.5], [1.5, 2]
The width of each subinterval is h = (2-0)/4 = 0.5.
Next, we need to approximate the area under the curve in each subinterval using trapezoids. The formula for the area of a trapezoid is:
Area = (base1 + base2) * height / 2
Using this formula, we can calculate the area of each trapezoid:
Area1 = (f(0) + f(0.5)) * h / 2 = (0^4 + 0.5^4) * 0.5 / 2 = 0.01953
Area2 = (f(0.5) + f(1)) * h / 2 = (0.5^4 + 1^4) * 0.5 / 2 = 0.16406
Area3 = (f(1) + f(1.5)) * h / 2 = (1^4 + 1.5^4) * 0.5 / 2 = 0.64063
Area4 = (f(1.5) + f(2)) * h / 2 = (1.5^4 + 2^4) * 0.5 / 2 = 4.65625
Note that we are using the function f(x) = x^4 to calculate the values of f at the endpoints of each subinterval.
Finally, we can add up the areas of all the trapezoids to get an approximation of the definite integral:
Approximation = Area1 + Area2 + Area3 + Area4 = 0.01953 + 0.16406 + 0.64063 + 4.65625 = 5.48047
Rounding this to four decimal places gives us the answer B. 5.7813.
To use the Trapezoid Rule to approximate the value of the definite integral integral^2_0 x^4 dx with n = 4 and round your answer to four decimal places, follow these steps:
1. Divide the interval [0, 2] into 4 equal parts: Δx = (2 - 0)/4 = 0.5.
2. Calculate the function values at each endpoint: f(0), f(0.5), f(1), f(1.5), and f(2).
3. Apply the Trapezoid Rule formula: (Δx/2) * [f(0) + 2f(0.5) + 2f(1) + 2f(1.5) + f(2)].
Plugging in the function values, we get:
(0.5/2) * [0 + 2(0.5^4) + 2(1^4) + 2(1.5^4) + (2^4)] ≈ 6.5625.
So, the approximation of the definite integral using the Trapezoid Rule with n = 4 is 6.5625 (option D).
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Jorge builds a rectangular prism that has a volume of 42 cubic inches. Which of the following could be Jorge’s prism? (4 points)
Group of answer choices
A rectangular prism with a height of five inches, length of five inches, and a width of five inches.
A rectangular prism with a height of five inches, length of four inches, and a width of four inches.
A rectangular prism with a height of two inches, length of seven inches, and a width of three inches.
A rectangular prism with a height of six inches, length of three inches, and a width of two inches.
Answer: A rectangular prism with a height of two inches, length of seven inches, and a width of three inches.
Step-by-step explanation:
Multiply the dimensions given, then select the one that matches Jorge's required 42 in³
5×5×5 = 125
5×4×4 = 80
2×7×3 = 42
6×3×2 = 36
Answer:
A
Step-by-step explanation:
PLS HELP! i rly need help on this. it’s hard for me.
1: what is the name of that figure??
2: what would be the cross section from a vertical slice of the figure??
Answer:
The 3D solid shown in the image is a hexagonal pyramid. If we made a cross section with a vertical slice (top to bottom), we would have an isosceles triangle.
Useful Extra Knowledge:
However—and this isn't a question here, but just useful knowledge—if we made a cross section with a horizontal slice (left to right or right to left), we would have a regular hexagon. If it were a diagonal cross section, we would have an irregular hexagon.
Step-by-step explanation:
First, what's the difference between a sphere, a cylinder, a pyramid, a cone, and a prism? These are all 3D solids, but in your case, an explanation of what they are may be a good refresher:
A sphere is a 3D solid where every point is equidistant from the center point. Basically, it's a 3D circle. It's completely round.A prism is a 3D solid with straight, parallel sides and a polygonal base.A cylinder is a 3D solid with straight, parallel sides and a circular baseA pyramid is a 3D solid with sides that converge at a common vertex and a polygonal base.A cone is a 3D solid with sides that converge at a common vertex and a circular base.We definitely know this shape can't be a sphere! It's not completely round! Actually, take a closer look: there's no hint of a circle anywhere in the figure. It can't be a cylinder nor a cone.
This means it's either a pyramid or a prism. But, going back to the definitions above, let's redefine the difference between the two: pyramids have only one base and only triangular faces, while prisms have two bases and rectangular faces.
How many bases does this figure have? It has one base. And what shape are its faces? They're all triangles! This means we have to be looking at a pyramid.
So, you may think, that solves it. We're looking at a pyramid.
Sorry, buddy. It's not that easy. We can classify this figure even further. How do we do this? We use its base! And what type of polygon is the base? When we count the sides of the base, we find six sides, which means this shape is a hexagon. So this is a hexagonal pyramid, right?
Actually, there's one more specification we could give this. That hexagon has sides that are all equal to each other. That may not seem special to you, but there's a special term given to polygons who have equal sides and equal inner angles: they are called regular polygons.
That description matches the base of our shape, right? So, now we have the name of the figure: it's a regular hexagonal pyramid.
Now, what about the cross section? This means we're taking a piece of that solid, like cutting into a cake with a knife. Who likes cake here?
I digress. This piece, the cross section of the 3D solid, becomes a 2D shape. Now, the question asks for the shape of a vertical cross section, which means up and down, like the y-axis on the coordinate plane/Cartesian plane.
So, imagine taking a butter knife and slicing right down the middle of that bad boy. If you get the middle point exactly, you'll have two equal halves which would look like triangles with two equal sides: an isosceles triangle.
That's assuming you look straight on at them. If you veered to the side a little, you'd find a scalene triangle (a triangle with no equal sides).
But, should you miss the center a little, you'd get a trapezoid instead, because part of the top would be missing.
But I'm assuming the question is asking about a vertical slice exactly down the middle and viewed straight on. In that case, your answer is an isosceles triangle.
I droned on for a bit, I know. But hopefully this helps you understand the concept better! Have a great day!
You are renting a car for the day. There is a daily fee of $25 and a charge of $0.10 per mile. Your budget allows a maximum total cost of $50. How many miles can you travel on this budget?
Answer:
250 miles
Step-by-step explanation:
daily charge: $25
per mile: $0.10
budget: $50
50-25=25
25 divided by 0.10 = 250
you can travel 250 miles on this budget
Which term has the definition "The value that is half way between the minimum and the median
Find the height of a cone that has a radius of 3 in and a volume of 96.91 in.
Answer:
thank you lil shawty
Step-by-step explanation:
I WILL MARK BRAINIEST PLEASE HELP
Answer: do you still need help
Step-by-step explanation:
one answer question
Answer:
c is the answer you will get you answer as a rational number (hope I'm not wrong)
Business woman Maya spends 1⁄4 hours a day on her cell phone. Her husband Larry spends 3⁄16 hours a day on his cell phone. What is the total time spent on the phone between the couple per day?
Answer:
45 minutes, or 3/4 hours
Answer:
the 3/4 is wrong this is how it was explained in the answer screen
Step-by-step explanation:
The correct answer is:
Create Equal Denominators
1⁄4 × 4⁄4 = 4⁄16
Total Time Spent
4⁄16 + 3⁄16 = 7⁄16 hours in a day
ZPRS and ZSRQ are supplementary angles.
85
Р
R
Q
What is the measure of ZSRQ?
O 5
O 15
O 95
O 105
Answer: 95
Step-by-step explanation: All supplementary angles always have to equal 180 degrees which means that you have to only do 180-85 and boom- 95- that is ur answer. Plz mark Brainliest:).
f(x)=6, what is x? HELP ANSWER FAST!!!!!!
Answer:
x = 6 / f
Step-by-step explanation:
yooooo please help lol
Answer:
You first want to divide 210 by 50 2/3. once you do that you will get 35/251 or 0.13944
Now you should be able to make about $44 dollars
Step-by-step explanation:
how to find LCM of 58??
Answer:
Find the prime factorization of 58. 58 = 2 × 29.
Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM: LCM = 2 × 2 × 2 × 2 × 2 × 2 × 29.
LCM = 1856.
Step-by-step explanation:
It’s sad when I help people because they don’t do the same thing to so please please please... answer me once :((((((((((((((((((((((((((((((((((((((((((((((
Step-by-step explanation:
Equation = 4m=16
Answer= 4m=16
m=16/4 = 4
So Tyrone has 4 model planes.
Don't know if its correct
Mr. Lowe had to replace the fluid in his tractor tire. The tire needed 73
gallons of fluid at $1.95 per gallon. About what did it cost to replace the
needed fluid? *
Answer:
$142.35
Step-by-step explanation:
he equation shows the relationship between x and y:
y = −7x + 9
What is the slope of the equation?
−7
−2
7
9
Answer:
-7
Step-by-step explanation:
y=-7x+9
y=mx+b
m=slope
y=y-intercept
please answer correctly and quickly all question
Answer:
Step-by-step explanation:
1. 8=2x+4
8-4=2x
4=2x
x=2
2. 2x+3=9
2x=9-3
2x=6
x=3
3. 6y=54
y=54/6
y=9
5. 3= x/2
x=6
Answer:
8=2x+4
4=2x
2=x
2x+3=9
2x=6
x=3
6y=54
I'm not sure about question #4
3=x/2
6=x
What is the interest rate in A = 12,000(1 + 0.07/4)^(4)(4)
Jonathan had $40 in his bank account. He withdrew $12 and deposited $4. How much is in his bank account now?
Answer:
he 32 is what he got in bank now an hope this help.
Step-by-step explanation:
One number exceeds another by 5. The sum of the numbers is 89. What are the numbers ?
Answer:
42
Step-by-step explanation:
89-5=84
84÷2=42
and reverse it to check
(42+5)+(42)=89
Which of the following angles DO NOT have equal measure when a pair of parallel lines is crossed by a transversal?
Suppose we know that the birth weight of babies is Normally distributed with a mean 3500g and a standard deviation of 500g. What is the probability that a baby is born that weighs less than 3100g?
Answer:
0.21186
Step-by-step explanation:
We solve the above question using the z score formula.
z = (x-μ)/σ, where
x is the raw score = 3100g
μ is the population mean = 3500g
σ is the population standard deviation = 500g
z = 3100 - 3500/500
z = -0.8
Probability value from Z-Table:
P(x<3100) = 0.21186
The probability that a baby is born that weighs less than 3100g is 0.21186
10.
Describe the graph of the equation x = 7. Is the equation a function?
horizontal line; no
horizontal line; yes
vertical line; yes
vertical line; no
Answer:
The answer is Vertical Line; Yes
Step-by-step explanation:
The answer is Vertical Line; Yes. This is because all equations that are "X =" will always be vertical.
x=7 represents the equation of a function which is a vertical line
I need help my brain is too small to answer this
Answer:
5/6 or 0.83
Step-by-step explanation:
5 ÷ 6 = 0.83 or 5/6
is 14.16 or 14.6 the higher number
Answer:
14.6 because 14.6 is equivalent to 14.60
Step-by-step explanation:
Answer:
14.6
Step-by-step explanation:
It would be 14.6 because 14.6 is basically 14.60
So you would compare 14.16 to 14.60
How do i learn this subject easily?
Answer:
try to download app that can help you, watch videos on how to do the problems or ask help with someone you know or just take notes that makes you understand better
Step-by-step explanation:
Factor completely
1/25-25z^2
Answer:
1/25(1-25z)(1+25z)
Step-by-step explanation:
your welcome : )
The difference of a number and seven
Answer: x-7
Step-by-step explanation:
Answer:
x -- 7
Step-by-step explanation:
HELP HELP ME PLSS!! Please I really need help....
The sum of the measures of the interior angles of a decagon (10 sided polygon) is 1,440
Greg invested $6000 in a bond with a yearly interest of 4%. His total interest on his investment was $1200. What was the length of the investment
Answer:
5 years
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 4%/100 = 0.04 per year,
then, solving our equation
t = 1200 / ( 6000 × 0.04 ) = 5
t = 5 years
The time required to
accumulate simple interest of $ 1,200.00
from a principal of $ 6,000.00
at an interest rate of 4% per year
is 5 years.
An isosceles triangle includes two 72°
angles. Which equation could be used to
find the measure of the third angle?
A X + 72 = 180
B X = 180 - 72
C 72-X= 180
D 180 - 2(72) = X
I don't understand the options but I will explain it to u!
Step-by-step explanation:
An Isosceles triangle has two equal sides that means , In this question it is given that there are two 72°angles so,
72+72+x =180
(Transpose)
x = 180-(72+72)
x = 180-(144)
Therefore, x= 36
In an isosceles triangle, two sides are equal and their opposite angles are also equal. Then the correct option is D.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
An isosceles triangle includes two 72° angles.
In an isosceles triangle, two sides are equal and their opposite angles are also equal.
And the sum of the angles of the triangle is 180°.
Let the third angle be x. Then we have
72° + 72° + x = 180°
180° - 2(72°) = x
Thus, the correct option is D.
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