Answer and Step-by-step explanation: The Trapezoidal and Simpson's Rules are method to approximate a definite integral.
Trapezoidal Rule evaluates the area under the curve (definition of integral) by dividing the total area into trapezoids.
The formula to calculate is given by:
[tex]\int\limits^a_b {f(x)} \, dx = \frac{b-a}{2n}[f(x_{0})+2f(x_{1})+2f(x_{2})+...+2f(x_{n-1})+f(x_{n})][/tex]
The definite integral will be:
[tex]\int\limits^9_4 {\sqrt{x} } \, dx = \frac{9-4}{2.8}[2+2.\sqrt{5} +2.\sqrt{6} +2.\sqrt{7}+2.\sqrt{8}+3][/tex]
[tex]\int\limits^9_4 {\sqrt{x} } \, dx = \frac{5}{16}[25.3193][/tex]
[tex]\int\limits^9_4 {\sqrt{x} } \, dx = 7.9122[/tex]
Simpson's Rule divides the area under the curve into an even interval number of subintervals, each with equal width.
The formula to calculate is:
[tex]\int\limits^a_b {f(x)} \, dx = \frac{b-a}{3n}[f(x_{0})+4f(x_{1})+2f(x_{2})+...+2f(x_{n-2})+4f(x_{n-1})+f(x_{n})][/tex]
The definite integral will be:
[tex]\int\limits^9_4 {\sqrt{x} } \, dx = \frac{9-4}{3.8}[2+4.\sqrt{5} +2.\sqrt{6} +4.\sqrt{7} +4\sqrt{8} +3][/tex]
[tex]\int\limits^9_4 {\sqrt{x} } \, dx = \frac{5}{24}[40.7398][/tex]
[tex]\int\limits^9_4 {\sqrt{x} } \, dx = 8.4875[/tex]
Calculating the definite integral by using the Fundamental Theorem of Calculus:
[tex]\int\limits^9_4 {\sqrt{x} } \, dx = \int\limits^9_4 {x^{\frac{1}{2} }} \, dx[/tex]
[tex]\int\limits^9_4 {\sqrt{x} } \, dx = \frac{2.\sqrt[]{x^{3}} }{3}[/tex]
[tex]\int\limits^9_4 {\sqrt{x} } \, dx = \frac{2.\sqrt[]{9^{3}} }{3}-\frac{2.\sqrt[]{4^{3}} }{3}[/tex]
[tex]\int\limits^9_4 {\sqrt{x} } \, dx = 12.6667[/tex]
Comparing results, note that Simpson's Rule is closer to the exact value, i.e., gives better approximation to the exactly value calculated by the fundamental theorem.
g What is the probability that a randomly selected person with adequate lung capacity is a non-exerciser?
Answer:
Step-by-step explanation:
What is the probability that a randomly selected person with adequate lung capacity is a non-exerciser?
This depends on statistics given in the prior part of the question.
From this question, i can pick that there is an assumption or statement (in the full question) that exercisers have adequate lung capacity, in a population of both exercisers and non-exercisers.
Data that will help solve this include:
- Population Count or Total number of subjects in the population
- Number of exercisers
- Number of non-exercisers
- Number of subjects with adequate lung capacity
- Number of subjects with inadequate lung capacity
The formula to get the desired answer would be:
Number of non-exercisers
Number of persons with adequate lung capacity
The figure you get from this computation is the answer you seek!
Since it is a probability figure, it must lie between the values of 0 and 1.
In which quadrant will each of the following points lie? a. (6, −5) b. (3, 2) c. (−2, −8) d. (6, 4) e. (−1, −12) f. (−3, 4)
Answer:
Quadrant 1:
(6,4) and (3,2)
Quadrant 2:
(-3,4)
Quadrant 3:
(-2,-8) and (-1,-12)
Quadrant 4:
(6,-5)
HOPE THIS HELPS!!!!!! :)
<3333333333
if y varies directly as x, and y is 6 when x is 72, what is the value of y when x is 8
Answer:
Y varies directly as X.
y=kx.
6=K72.
x=6/72.
x=0.08.
Y=0.08x.
when y=?, x=8.
y=0.08×8=0.64.
What is twice a number divided by 5
Answer:
4
just go with it the explaining would take to long
Step-by-step explanation:
y varies directly with x. If x = 16 and y = 2 find y when x = 96
Answer:
y = 12
Step-by-step explanation:
Use the equation y = kx
Plug in x and y to find k:
2 = k(16)
1/8 = k
Then, plug in 1/8 as k and 96 as x to find y:
y = 1/8(96)
y = 12
Find all angles that are coterminal with the given angle. (Let k be an arbitrary integer.) −225°
Answer:
Coterminal angles are angles with the same terminal side.
When we have an angle A, the coterminal angles can be written as:
A + k*(360°)
where k can be any integer number. (Notice that when we have k = 0, means that A is coterminal with itself)
Then the set of all the coterminal angles to -225° is:
{-225° + k*360°I k ∈ Z}
where Z is the set of integer numbers.
Which of the following could be the number shown on the number line
Answer:
i need the number line first lol
Step-by-step explanation:
mark brainliest
Answer: if your on apeand your options were
79,72,63,83 the answer is 72
Which set of data do you believe to be better? Your data or your friend's data?
Answer:
Your friends data
Step-by-step explanation:
The rule of statistics is: the more exact the data, the better.
It looks like you just rounded your data to the nearest tenth. This is good, but not nearly as good as rounding it to the nearest hundredth.
This is because when you have data that is more exact, you get a better estimation for mean, median, etc. This can help make patterns in your data.
This means that your friend had better data than you.
Hope this helped!
Select the correct inequality to make a true statement
Step-by-step explanation:
[tex] \frac{1}{4} \boxed{?} \frac{3}{8} \\ \\ \frac{1}{4} = \frac{2}{8} \\ \\ \because \: 2 < 3 \\ \therefore \: \frac{1}{4} \boxed{ < } \frac{3}{8} [/tex]
la empresa Delta Energy cobra a sus consumidores de energía eléctrica una tarifa de $5 por mes más $0,10 por cada kilowatt-hora. exprese el costo mensual "C" en función de la energía "E" consumida.
Answer:
C=0,10E+5
Step-by-step explanation:
La respuesta es que la expresión que indica el costo mensual "C" en función de la energía "E" consumida es:
C=0,10E+5
Esto teniendo en cuenta que se indica que hay una tarifa fija de $5 por mes y que a esto se debe sumar el resultado de multiplicar la energía consumida por el valor del kilowatt-hora.
POSSIBLE POINTS: 10
The midpoint of QR is M(2, 1.5). One endpoint is R(1, -1). Find the coordinates of endpoint Q. {Write as an ordered pair (X, Y).} Q
Answer:
Q (3.4)
Step-by-step explanation:
Midpoint for point (x1,y1) and (x2,y2) is given by
(x1+x2)/2, (y1+y2)/2.
__________________________________________________________
Given
one endpoint ( R(1, -1)
midpoint is M(2,1.5)
we have to find coordinates of endpoint Q
let Q(x,y)
Thus, for x coordinate of midpoint
2 = (1+x)/2
=> 2*2 = 1+x
=> 4 = 1+x
=> x = 4-1 = 3
x coordinate of midpoint m is 3
________________________
for y coordinate of midpoint
1.5 = (-1+y)/2
=> 2*1.5 = -1+y
=> 3 = -1+ y
=> y = 3 + 1 = 4
y coordinate of midpoint m is 4
Thus, the coordinates of endpoint Q (3.4)
The GCF of 30 and 45 is
3
8
1
2
15
Answer:
The GCF of 30 and 45 is
15.
Hope it helps.
ax + by = c, bx + ay = (1 + c)
Answer:
( x - y ) ( a - b ) = -1
Step-by-step explanation:
ax + by = c and bx + ay = 1 + c
ax + by = c and bx + ay - 1 = c
And now we set c equivalent
ax + by = bx + ay - 1
ax - bx + by - ay = -1
x (a - b) + -y (a - b) = -1
(x - y) ( a - b) = -1
So we can leave it like that, or we can solve for one of the variables.
If we solve for y:
(x - y) ( a - b) = -1
(x - y) = -1 / (a - b)
-y = (-1 / (a - b)) - x
y = (1 / (a-b)) + x
Cheers.
For each of the following questions, solve for the unknown quantity by rearranging the given equation.
For numerical answers, make sure to express all answers in scientific notation with the proper number of
significant figures. Be careful to write out all units and convert if necessary.
3.
F=GMm/r^2
a. M =
b. r =
M=kxa^3/p^2
a. P =
b. a =
Answer:
For F=GMm/r^2
[tex]F = \frac{GMm}{r^{2} }[/tex]
a. [tex]M = \frac{Fr^{2} }{Gm}[/tex]
b. [tex]r = \sqrt{\frac{GMm}{F}}[/tex]
M=kxa^3/p^2
[tex]M = \frac{kxa^{3} }{p^{2} }[/tex]
a. [tex]p = \sqrt{\frac{kxa^{3} }{M}}[/tex]
b. [tex]a = \sqrt[3]{\frac{Mp^{2} }{kx}}[/tex]
Step-by-step explanation:
To solve for the unknown quantity, we will make the unknown quantity the subject of the given equation.
For F=GMm/r^2
a. M =
F=GMm/r^2
[tex]F = \frac{GMm}{r^{2} }[/tex]
The first thing to do is cross multiply, so that the equation gives
[tex]Fr^{2} = GMm[/tex]
Now, divide both sides of the equation by [tex]Gm[/tex], we then get
[tex]\frac{Fr^{2} }{Gm} = \frac{GMm}{Gm}[/tex]
Then, [tex]\frac{Fr^{2} }{Gm} = M[/tex]
Hence,
[tex]M = \frac{Fr^{2} }{Gm}[/tex]
b. r =
F=GMm/r^2
[tex]F = \frac{GMm}{r^{2} }[/tex]
Likewise, we will first cross multiply, we then get
[tex]Fr^{2} = GMm[/tex]
Now, divide both sides by [tex]F[/tex], so that the equation becomes
[tex]\frac{Fr^{2} }{F} = \frac{GMm}{F} \\[/tex]
∴ [tex]r^{2} = \frac{GMm}{F} \\[/tex]
Then,
[tex]r = \sqrt{\frac{GMm}{F}}[/tex]
For M=kxa^3/p^2
a. P =
M=kxa^3/p^2
[tex]M = \frac{kxa^{3} }{p^{2} }[/tex]
The first thing to do is cross multiply, so that the equation becomes
[tex]Mp^{2} = kxa^{3} \\[/tex]
Now, divide both sides by M, we then get
[tex]\frac{Mp^{2} }{M} = \frac{kxa^{3} }{M}[/tex]
∴ [tex]p^{2} = \frac{kxa^{3} }{M}[/tex]
Then,
[tex]p = \sqrt{\frac{kxa^{3} }{M}}[/tex]
b. a =
M=kxa^3/p^2
[tex]M = \frac{kxa^{3} }{p^{2} }[/tex]
Also, we will first cross multiply to get
[tex]Mp^{2} = kxa^{3} \\[/tex]
Then, divide both sides of the equation by [tex]kx[/tex] to get
[tex]\frac{Mp^{2} }{kx}= \frac{kxa^{3} }{kx}\\[/tex]
[tex]\frac{Mp^{2} }{kx}= a^{3}[/tex]
∴ [tex]a^{3} = \frac{Mp^{2} }{kx}[/tex]
Then,
[tex]a = \sqrt[3]{\frac{Mp^{2} }{kx}}[/tex]
Find the area in blue.
Answer: The area is 13[tex]\pi[/tex]ft^2 or 40.84 ft^2
Step-by-step explanation:
First find the area of the square and subtract it from the area of the circle.
The area of a square is one of the side length squared.
A= 6^2
A = 36
Now find the area of the whole circle.As it indicates that the diameter is 14ft and to find the area of a circle,we need square the radius and multiply it by pi.
Since the diameter is 14 divide it by 2 to find the radius. 14/2 = 7
A= 7^2*[tex]\pi[/tex]
A = 49[tex]\pi[/tex] We will leave the area in terms of pi.
49[tex]\pi[/tex] - 36 = 13[tex]\pi[/tex]
ASAP Quadrilateral ABCD is similiar to quadrilateral EFGH. The lengths of the three longest sides in quadrilateral ABCD are 24 feet, 16 feet, and 12 feet long. If the two shortest sides of quadrilateral EFGH are 9 feet long and 18 feet long, how long is the 4th side on quadrilateral ABCD? A. 8 feet B. 12 feet C. 10 feet D. 6 feet
Answer:
D. 6 feet.
Step-by-step explanation:
The third longest side of ABCD is 12 feet long and the third longest side of EFGH is 18 feet long.
As they are similar the corresponding sides are in the same ratio so
12/18 = x/9 where x is the 4th side of ABCD.
2/3 = x/9
3x = 18
x = 6 feet.
what substitution should be used to rewrite 4x^12-5x^6-14=0 as a quadratic equation?
Answer:
Step-by-step explanation:
4x12-5x6-14=0, the highest power of the variable in this equation is 12 so to make it a quadratic equation we should replace x12 by y2. Hence to rewrite the given equation as quadratic just substitute x6=y.
What would be the first step you do to solve the equation below? 2x - 4 = 12 Question 1 options: Add 4 Subtract 4 Divide by 2 Multiply by 2
Answer:
ADD 4
Step-by-step explanation:
you want to get 2x by itself so you want to do opposite of -4 so you would do +4 and they cancel out, and what you do to one side you do to the other so
2x = 12 +4
2x = 16
and then you would divide the 2 on both sides so
x = 8 ... just in case you later need to know what x is :)
Prove that the
ordered pair (3, 4)
is a solution set to
the equation:
2x + 3y = 18
Answer:
Hey there!
2x+3y=18
2(3)+3(4)=18
6+12=18
18=18, so this is a valid ordered pair.
Let me know if this helps :)
A set of three scores consists of the values 3, 7, and 2.
Σ2X – 2 =
Σ(X – 1)² =
Answer:
Step-by-step explanation:
Given the set of datas 3, 7 and 2, we are to evaluate the folowing;
Σ2X – 2 and Σ(X – 1)² =where X are the individual datas.
We will substitute each of the data as value of X and ten take the sum as shown;
For Σ2X – 2
Σ2X – 2 = [2(3)-2]+[2(7)-2]+[2(2)-2]
Σ2X – 2 = (6-2)+(14-2)+(4-2)
Σ2X – 2 = 4+12+2
Σ2X – 2 = 18
For Σ(X – 1)² where x values are also 3, 7 and 2 we will have;
Σ(X – 1)² = (3 – 1)²+(7 – 1)²+(2 – 1)²
Σ(X – 1)² = 2²+6²+1²
Σ(X – 1)² = 4+36+1
Σ(X – 1)² = 41
Which of the following best decribes a function
A line has a slope of 3 and passes through the point (2,31). Write the equation of the line in slope-intercept form
Answer:
y=3x+25
Step-by-step explanation:
So to find the slope-intercept we need to find the slope and the y intercept. we already know the slope so to find the y intercept you subtract 2 from the x coordinate and 6 from the y, because the slope is 3. So the answer is y=3x+23
Answer:
y=3x+25
Step-by-step explanation:
We are given a point and the slope, so let's use the slope-intercept equation.
[tex]y-y_{1}=m(x-x_{1})[/tex]
where m is the slope and (x₁, y₁) is the point given. The slope is 3 and the point is (2,31). Therefore,
[tex]m= 3 \\x_{1}=2\\y_{1}=31[/tex]
Substitute the values into the equation.
[tex]y-31=3(x-2)[/tex]
We want the equation in slope intercept form: y=mx+b. We must isolate y on the left side of the equation.
First, distribute the 3. Multiply each term inside the parentheses by 3.
[tex]y-31= (3*x)+(3*-2)[/tex]
[tex]y-31=(3x)+(-6)[/tex]
[tex]y-31=3x-6[/tex]
Next, add 31 to both sides of the equation.
[tex]y-31+31=3x-6+31[/tex]
[tex]y=3x-6+31[/tex]
[tex]y=3x+25[/tex]
This equation is in slope intercept form, so our final answer is:
y= 3x+25 (slope⇒3 , y-intercept ⇒25)
In a local election, 16,000 people voted. This was an increase of 4% over the last election.
How many people voted in the last election? If necessary, round to the nearest whole
number
Answer:
Hey!
Your answer is 15,360!
Step-by-step explanation:
4% of 16,000 is 640
SO...
To find out the last year's amount of voters we have to minus 640 from 16,000...
16,000 - 640 = 15,360
HOPE THIS HELPED!!
Solve the inequality
The solution is....
Answer:
x ≤ -7
Step-by-step explanation:
Eliminate parentheses using the distributive property.
-8 -2x ≥ 40 +6x +8
-8 ≥ 48 +8x . . . . . . . . . add 2x
-56 ≥ 8x . . . . . . . . . . . subtract 48
-7 ≥ x . . . . . . . . . . . . . . divide by 8
The solution is x ≤ -7.
The quality control manager of a light bulb factory needs to estimate the average life of a large shipment of light bulbs. The process standard deviation is known to be 100 hours. A random sample of 64 light bulbs indicated a sample average life of 350 hours. Given the confidence interval calculated above. do you think the manufacturer has the right to state that the light bulbs last on average 400 hours?
a. No.
b. Yes.
c. Maybe.
d. Do not know
Answer:
b) yes
The manufacturer has the right to state that the light bulbs last on average 400 hours
Step-by-step explanation:
Explanation:-
Given sample size 'n' = 64
Given standard deviation of the Population (σ)=100
Mean of the sample (x⁻) = 350 hours
95% of confidence interval is determined by
[tex](x^{-} -Z_{0.95} \frac{S.D}{\sqrt{n} } , x^{-} +Z_{0.95} \frac{S.D}{\sqrt{n} } )[/tex]
([tex](350 -1.96 \frac{100}{\sqrt{64} } , 350+1.96\frac{100}{\sqrt{64} } )[/tex]
(350-24.5 , 350+24.5)
(325.5 , 374.5)
Conclusion:-
Yes
The manufacturer has the right to state that the light bulbs last on average 400 hours
Round 34,576 to the nearest thousand
Answer:
35000
Step-by-step explanation:
One third of a number Y
Answer:
⅓y
Step-by-step explanation:
[tex] \frac{1}{3} \times y \\ = \frac{1}{3} y[/tex]
Is 1/4 greater than 4/5, 2/4, 1/10, 2/10, 1/5?
Answer:
1/4 is greater than 1/10, 2/10, and 1/5 but not 4/5, and 2/4
Step-by-step explanation:
1/4 = 25%
4/5 = 80%
2/4 = 50%
1/10 = 10%
2/10 = 20%
1/5 = 20%
What is the equation when y=5x+4 is reflected over the x-axis, y-axis & y=x?
Answer:
A) [tex]y=-5x-4[/tex]
B) [tex]y=-5x+4[/tex]
C) [tex]y=\frac{x-4}{5}[/tex]
Step-by-step explanation:
So we have the equation:
[tex]y=5x+4[/tex]
Let's write this in function notation. Thus:
[tex]y=f(x)=5x+4[/tex]
A)
To flip a function over the x-axis, multiply the function by -1. Thus:
[tex]f(x)=5x+4\\-(f(x))=-(5x+4)[/tex]
Simplify:
[tex]-f(x)=-5x-4[/tex]
B) To flip a function over the y-axis, change the variable x to -x. Thus:
[tex]f(x)=5x+4\\f(-x)=5(-x)+4[/tex]
Simplify:
[tex]f(-x)=-5x+4[/tex]
C) A reflection over the line y=x is synonymous with finding the inverse of the function.
To find the inverse, switch x and f(x) and solve for f(x):
[tex]f(x)=5x+4[/tex]
Switch:
[tex]x=5f^{-1}(x)+4[/tex]
Subtract 4 from both sides:
[tex]x-4=5f^{-1}(x)[/tex]
Divide both sides by 5:
[tex]f^{-1}(x)=\frac{x-4}{5}[/tex]
And we're done :)
Simplify: power with a power 5^8*7^8
Answer:
35^8
Step-by-step explanation:
5^8 x 7^8
(5 x 7)^8
=35^8