The required function of s and decreasing function of s are a) h(s) = V / (s²) b) dh/ds = -2V / (s³).
What is Volume?Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
According to question:(a) We know that the volume of the box, V, is given by the product of its height, h, and its base area, which is s².
we can write the equation:
V = h * s²
Solving for h, we get:
h = V / (s²)
So the height of the box, h, as a function of s can be expressed as
h(s) = V / (s²)
(b) To determine whether h(s) is an increasing or decreasing function of s, we need to look at the sign of its derivative.
The derivative of h(s) with respect to s is given by:
dh/ds = -2V / (s³)
Since the derivative is negative for all positive values of s, h(s) is a decreasing function of s.
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the math club went on a one day field trip. they visited the math museum. the math club members paid 250.00$ for bus transportation plus 12.00$ per ticket. write an expression to represent the total cost for the field trip for the n members of the club.
a.12n+25-
b.12n-250
c.250n+12
d,250n-12
12n+250
because you don't know the amount of tickets
Write the inverse of f(x) = 3x - 1
f -1(x) =
log 3 x + 1
log 3 ( x - 1)
log 3 x - 1
Answer:
see below
Step-by-step explanation:
we need to write the inverse of ,
[tex]\longrightarrow f(x) = 3x -1 \\[/tex]
Substitute [tex] f(x)=y[/tex] ,
[tex]\longrightarrow y = 3x-1 \\[/tex]
Interchange x and y ,
[tex]\longrightarrow x = 3y -1 \\[/tex]
now solve for y ,
[tex]\longrightarrow 3y = x + 1 \\[/tex]
[tex]\longrightarrow y =\dfrac{x+1}{3} \\[/tex]
replace [tex] y[/tex] with [tex] f^{-1}(x)[/tex] as ,
[tex]\longrightarrow \underline{\underline{ f^{-1}(x) =\dfrac{x+1}{3}}}\\[/tex]
And we are done!
Answer:
[tex]f^{-1}(x)=\log_3(x)+1[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=3^{x-1}[/tex]
To find the inverse of the given function, swap y and x:
[tex]\implies x=3^{y-1}[/tex]
Take the log base 3 of each side of the equation:
[tex]\implies \log_3(x)=\log_{3}3^{y-1}[/tex]
[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]
[tex]\implies \log_3(x)=(y-1)\log_{3}3[/tex]
[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]
[tex]\implies \log_3(x)=(y-1)(1)[/tex]
[tex]\implies \log_3(x)=y-1[/tex]
Add 1 to both sides of the equation:
[tex]\implies \log_3(x)+1=y[/tex]
[tex]\implies y=\log_3(x)+1[/tex]
Replace y for f⁻¹(x):
[tex]\implies f^{-1}(x)=\log_3(x)+1[/tex]
Accidental question that had been put out
Answer:
Step-by-step explanation:
ss
Someone please help me
The required solution is given as,
1. 2/5 of the sum of 8 and 4
2. 2/5 [8 + 4]
3. 4 4/5
The expression model is defined as the model of the given situation in the form of an expression using variables and constants.
Here,
From the figure,
It can be concluded that it is 2/5 times the sum of 8 and 4,
Also
= 2/5[8 + 4]
Simplify
= 2/5[12]
= 24/5
= 4 4/5
Thus, the required solution is given as,
1. 2/5 of the sum of 8 and 4
2. 2/5 [8 + 4]
3. 4 4/5
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1. A severe drought affected several western states for 3 years. A Christmas tree farmer is worried about the
drought's effect on the size of his trees. To decide whether the growth of the trees has been re tard ed, the farmer
decides to take a sample of the heights of 25 trees and obtains the following results (recorded in inches).
60 57 62 69 46 54 64 60 59 58 75 51 49
67 65 44 58 55 48 62 63 73 52 55 50
a. Find the average tree height. _______________ Round your answer to one decimal place. You can use
software for this if desired.
b. Find the median tree height. __________________
c. Find the mode tree height. _____________
d. Find the range of this data _____________
e. Find the standard deviation for this sample. ______________ Round your answer to one decimal place.
You can use software for this if desired.
f. The tree farmer feels the normal height of a tree that was unaffected by the drought would be 65 inches.
Using the information you previously found, find the z-score for a tree that is 65 inches tall, rounding to
two decimal places.
The following results are:
a. Average height: 58.84
b. Median height: 58
c. Mode height: 55
d. Range of data: 73 - 44 = 29
e. Standard deviation: 8.23
f. Z-score for 65 inches: (65 - 58.84) / 8.23 = 0.83
What is statistics?Statistics is a process in which we collect, interpret, study and understand the data. We took a small sample from the large quantity and then we did study of the sample then according to results, we did our predictions for events which can happen in future.
Given that,
The height of 25 trees,
following results (recorded in inches).
60 57 62 69 46 54 64 60 59 58 75 51 49
67 65 44 58 55 48 62 63 73 52 55 50
a. Average = Sum of height of all the trees/Total number of trees
= 58.84
b. Median = (N + 1)/2th term after arranging into ascending order
= 58
c. Mode = Highest frequency
= 55
d. range = Highest value - Lowest value
= 73 -44
= 29
e. the standard deviation of the given data, you would need to perform the following steps:
Calculate the mean of the data:
(60 + 57 + 62 + 69 + 46 + 54 + 64 + 60 + 59 + 58 + 75 + 51 + 49 + 67 + 65 + 44 + 58 + 55 + 48 + 62 + 63 + 73 + 52 + 55 + 50) / 25 = 58.84
Find the deviation of each data point from the mean:
60 - 58.84 = 1.16, 57 - 58.84 = -1.84, 62 - 58.84 = 3.16, and so on...
Square each deviation:
1.16^2 = 1.3536, (-1.84)² = 3.3876, 3.16^2 = 9.9876, and so on...
Sum all the squared deviations:
1.3536 + 3.3876 + 9.9876 + ... = 519.24
Divide the sum by the number of data points minus 1 (for a sample) or by the number of data points (for a population):
519.24 / 24 = 21.63
Take the square root of the result:
√21.63 = 4.65
The standard deviation of the given data is 4.65.
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M angle 3 = 48 degrees
M angle 3 = 112 degrees
M angle 3 = 88 degrees
M angle 3 = 68 degrees
The last
M angle 3 = 68 degrees
Step-by-step explanation:
interior angles between parallel lines
sum =180
Dilate H using C as the center and a scale factor of 3. H is 40 mm from C.
Use technology or a z-distribution table to find the indicated area. The weights of grapefruits in a bin are normally distributed with a mean of 261 grams and a stranded deviation of 9.4 grams. Approximately 20% of the grapefruits weigh less than which amount
• 239 g •247 g •253 g •261 g
The amount of grape in bin using probability distribution =253 gm
What is probability?Probability is simply the chance that something will happen.
Whenever the outcome of an event is uncertain, we can talk about the likelihood or likelihood of a particular outcome. Analyzing events according to their probabilities is called statistics.
The best example of understanding probability is coin tossing.
Heads or tails, he has two possible outcomes. Crisps
The probability of an event is between 0 and 1 and can also be expressed as a percentage. event probability
P(A)>P(B)P, left parenthesis, A, right parenthesis, greater than, P, left parenthesis, B, right parenthesis, then event
P(A)=P(B)P, left parenthesis, A, right parenthesis, equal, P, left parenthesis, B, right parenthesis, event AA and BB occurs with equal probability.
Now for the given Question:
You need to find the z-score which is closest to .2000 (20%)
Look at your negative z-score table
Look at z= -.84
So -.84 standard deviations below the mean represents 20%
261 - .84 X (9.4) = 253.1 gm
Hence the amount of grapefruit in bin= 253 gm
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What are the factor's of 54.
Answer:
1, 2, 3, 6, 9, 18, 27 and 54
Step-by-step explanation:
A factor is a number that divides another number without leaving a remainder
Factors of 54:
1 × 54 = 54
2 × 27 = 54
3 × 18 = 54
6 × 9 = 54
9 × 6 = 54
18 × 3 = 54
27 × 2 = 54
54 × 1 = 54
The factors are: 1, 2, 3, 6, 9, 18, 27 and 54
How can you help me with that please also my homework math please
Cooking time 35 minutes to be ready for lunch at 13:00, calculate what time the item should be put in the oven.
Answer:
he item should be put in the oven at 12:25 (in 24-hour format) to be ready for lunch at 13:00.
Step-by-step explanation:
To calculate what time the item should be put in the oven, you need to work backwards from the desired serving time of 13:00 and subtract the cooking time of 35 minutes. Here's how you can do it:
Convert the serving time to 24-hour format: 13:00 is the same as 1:00 PM in 12-hour format. In 24-hour format, it is 13:00.
Subtract the cooking time: Subtract 35 minutes from the serving time of 13:00 to get the time when the item should be put in the oven.
13:00 - 00:35 = 12:25
So, the item should be put in the oven at 12:25 (in 24-hour format) to be ready for lunch at 13:00.
For each equation draw a tape diagram and find unknown value
The solutions are:
a. x = 7
b. x = 7
The tape diagrams are given in the image below.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
Two equations,
a. x + 9 = 16
b. 4x = 28
Solving the first equation,
x + 9 = 16
x = 7
Solving the second equation,
4x = 28
x = 7
The tape diagrams are given in the image below.
Hence, all the unknown values are given above.
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[10 Points] In the standard numbering (shortlex ordering) of strings over the alphabet {a,b,c} what number corresponds to string cbbca cba cbc ?
The number corresponds to the given string is 237880
What is common ratio?
In a geometric sequence, ratio of each term to its immediately preceding term is always constant and is known as common ratio.
The shortlex ordering places the shortest sequences at the front of the list of sequences by cardinality (length), while sequences of the same length are arranged lexicographically.
Given: cbbca cba cbc
length =11
We need to find the number of strings that precede the given string over {a,b,c}
Number of strings of length 0 = 1
Number of strings of length 1 = 3
Number of strings of length 2 = 3²
'
'
'
'
'
Number of strings of length 10 = 3¹⁰
In general, number of strings formed withy length n = 3ⁿ
Add all the strings of length 0 to 10
1+3+3²+......................+3⁻¹⁰
By simple geometric sum formula ,
we have
= (3¹¹⁻¹)/(3-1) = 88573
Number of strings of length 11 starting with either 'a' or 'b' = 2*3¹⁰
Number of strings of length 11 starting with 'ca' = 3⁹
Number of strings of length 11 starting with 'cba' = 3⁸
Number of strings of length 11 starting with 'cbba' or 'cbbb' = 2*3⁷
Number of strings of length 11 starting with 'cbbcaa' or 'cbbcab' = 2*3⁵
Number of strings of length 11 starting with 'cbbcaca' = 3⁴
Number of strings of length 11 starting with 'cbbcacbab' or 'cbbcacbaa' = 2*3²
Number of strings of length 11 starting with 'cbbcacbaca' = 3
Number of strings of length 11 starting with 'cbbcacbacba' or 'cbbcacbacbb' = 2
Total number of strings of length 11 preceding the given string is :
2+3+2*3² +3⁴+ 2*3⁵+ 2*3⁷+3⁸+3⁹ + 2*3¹⁰
= 149306
The number corresponds to the given string
= 88573 + 149306 +1
= 237880
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The circumference of a circular glazed donut with rainbow sprinkles is 9.42 inches. What is the diameter and radius of the circular donut?
The formula for the circumference of a circle is given by 2 * pi * r, where r is the radius. If the circumference is 9.42 inches, then we can write the equation:
9.42 = 2 * pi * r
Solving for r, we get:
r = 9.42 / (2 * pi)
The diameter of the circle is equal to 2 * r, so:
d = 2 * r = 2 * (9.42 / (2 * pi)) = 9.42 / pi
So, the radius of the circular donut is approximately 3 inches, and the diameter is approximately 9.42 inches.
A company makes computer chips from square wafers of silicon. It wants to keep the side length of a wafer very close to 15 mm and it wants to know how the area A(x) of a wafer changes when the side length x changes. Find A` (15) and explain its meaning in this situation.
A'(15) = 2 * 15 = 30.The meaning of A'(15) in this situation is that if the side length of the wafer changes by 1 mm, the area will change by 30 mm^2 when the side length is 15 mm.
The area A(x) of a square wafer is given by A(x) = x², where x is the side length of the wafer. The derivative of A(x) with respect to x, denoted A'(x), represents the rate of change of the area with respect to the side length. To find A'(15), we need to find the derivative of A(x) at x = 15.
A'(x) = 2x
Therefore, A'(15) = 2 * 15 = 30.
The meaning of A'(15) in this situation is that if the side length of the wafer changes by 1 mm, the area will change by 30 mm² when the side length is 15 mm. This means that for every 1 mm increase in the side length, the area of the wafer will increase by 30 mm², and for every 1 mm decrease in the side length, the area of the wafer will decrease by 30 mm².
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Given that 16px + 10q + 10px = 78x + 60. Find the value of P.
Answer:
p = (39x +30 -5q)/13x
Step-by-step explanation:
16px + 10q + 10px = 78x + 60
Solve for p.
Subtract 10 q from each side.
16px + 10q-10q + 10px = 78x + 60 -10q
16px + 10px = 78x + 60-10q
Combine like terms.
26px = 78x + 60-10q
Factor out p.
p(26x) = 78x + 60-10q
Divide each side by 26x.
p = (78x + 60-10q)/(26x)
Simplify.
p = (39x +30 -5q)/13x
Because the mean is very sensitive to extreme values, it is not a resistant measure of center. By deleting some low values and high values, the trimmed mean is more resistant. To find the 10%
trimmed mean for a data set, first arrange the data in order, then delete the bottom 10% of the values and delete the top 10% of the values, then calculate the mean of the remaining values. Use the
axial loads (pounds) of aluminum cans listed below for cans that are 0.0111 in. thick. Identify any outliers, then compare the median, mean, 10% trimmed mean, and 20% trimmed mean.
248 260 267 273 276 278 282 284 284 285
287 287 290 290 293 295 296 299 311 501
Step-by-step explanation:
Outliers: In this data set, the value of 501 is an outlier as it is significantly higher than the other values.
Median: To find the median, we arrange the data in order and find the middle value. In this case, since there are an odd number of values, the median is the middle value: 290.
Mean: To find the mean, we add up all the values and divide by the number of values:
(248 + 260 + 267 + ... + 311 + 501) / 21 = 293.67
10% Trimmed Mean: To find the 10% trimmed mean, we delete the bottom 10% of the values (2 values) and the top 10% of the values (2 values) and then find the mean of the remaining values:
(278 + 282 + 284 + 284 + 285 + 287 + 287 + 290 + 290 + 293 + 295 + 296 + 299 + 311) / 15 = 286.87
20% Trimmed Mean: To find the 20% trimmed mean, we delete the bottom 20% of the values (4 values) and the top 20% of the values (4 values) and then find the mean of the remaining values:
(284 + 284 + 285 + 287 + 287 + 290 + 290 + 293 + 295 + 296 + 299 + 311) / 12 = 288.92
The median, mean, 10% trimmed mean, and 20% trimmed mean can be compared to see how resistant each measure is to outliers. The median is the most resistant measure as it only considers the middle value, whereas the mean is the least resistant measure as it considers all values in the data set. The trimmed means are intermediate measures that are more resistant to outliers than the mean but less resistant than the median. In this case, we can see that the 10% trimmed mean is more resistant to outliers than the mean but less resistant than the 20% trimmed mean.
The perimeter of a rectangle is 108 cm. If the length is 30 cm, how wide is the rectangle?
A) First write an equation you can use to answer this question. Use w as your variable in the equation.
The equation is
B) Solve your equation in part [A] to find the width of the rectangle.
Answer: The rectangle is
cm wide.
Answer:
Step-by-step explanation:
A) The equation for the perimeter of a rectangle is given by 2 * (length + width), so we can write the equation for this rectangle as:
2 * (30 + w) = 108
B) To find the width of the rectangle, we can solve for w:
60 + 2w = 108
2w = 48
w = 24
So, the width of the rectangle is 24 cm.
A baking club wants to form an executive committee. There are 4 people in the baking club, including Mark. In how many ways can the baking club form an executive committee with 2 people?
The number of ways that baking club form an executive committee with 2 people will be 6.
What are permutation and combination?A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.
A baking club wants to form an executive committee. There are 4 people in the baking club, including Mark.
The number of ways that baking club form an executive committee with 2 people will be given as,
⁴C₂ = 4! / [(4 - 2)! x 2!]
⁴C₂ = 4 x 3 x 2! / (2! x 2 x 1)
⁴C₂ = 2 x 3
⁴C₂ = 6
The number of ways that baking club form an executive committee with 2 people will be 6.
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Complete the square in the expression. Then factor the perfect square trinomial.
x2−32x
The perfect square polynomial is x² - 32x + 256 and the factored form is (x - 16)(x - 16)
How to factor perfect square polynomials?A perfect square trinomial is defined as an algebraic expression that is obtained by squaring a binomial expression.
A perfect square polynomial can be represented as follows;
ax² + bx - c = 0
Hence, the perfect square trinomial is x² - 32x + 256.
Now, let's factorise it.
x² - 32x + 256.
x² - 16x - 16x + 256
x(x - 16) -16(x - 16)
Therefore,
(x - 16)(x - 16)
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Answer: x²-32x+16²
Step-by-step explanation:
(x-a)²=x²-32x+a² where .2ax=-32x so, 2a=32 then a=16
then (x-16)²=x²-32x+16²
5. A box containing,74.25 ounces of
pecans was donated to a local store.
The store places the pecans into
8.125-ounce containers and sells each
container for $6.95. Determine which
expression shows how much the store
will earn if they sell all the containers of
pecans. Find the store's earnings.
The earning of the store is $62.55.
What is an equation?
An equation is expression with one or more variables. It can also have more than 1 degree. it is a linear combination of constants and variables.
We are given that a box contains 74.25 ounces of pecans
These pecans are divided in 8.125 ounces of containers
First let us see how many such containers can be made
To find that we divided the two we get
74.25/ 8.125 = 9 such containers can be made
Now Each container is being sold for $6.95
Hence the total earnings are
9 * 6.95 = $62.55
The earning of the store is $62.55
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determine whether each of the following conditional statements is true or false. Be sure to use full sentences, and justify your conclusions. (a) If 10 < 7, then 3 = 4. (b) If 7 < 10, then 3 = 4. (c) If 10 < 7, then 3 + 5 = 8. (d) If 7 < 10, then 3 + 5 = 8.
Previous question
(a) If 10 < 7, then 3 = 4.
This statement is true. Because False ------> False has the truth value T
(b) If 7 < 10, then 3 = 4
This statement is False. Because True ------> False has the truth value F
(c) If 10 < 7, then 3 + 5 = 8.
This statement is true. Because False ------> True has the truth value T
(d) If 7 < 10, then 3 + 5 = 8
This statement is true. Because True ------> True has the truth value T
What is a conditional statement?
A hypothesis and a conclusion are both included in conditional statements. An "If-then" statement is another name for it. The conditional statement is false if the hypothesis is correct but the conclusion is incorrect. The entire sentence is untrue if the hypothesis is incorrect.
(a) If 10 < 7, then 3 = 4.
This statement is true. Because False ------> False has the truth value T
( 10 is not less than 7 and 3 is not equal to 4)
(b) If 7 < 10, then 3 = 4
This statement is False. Because True ------> False has the truth value F
( 7 < 10 and 3 is not equal to 4 )
(c) If 10 < 7, then 3 + 5 = 8.
This statement is true. Because False ------> True has the truth value T
( 10 is not less than 7 , but 3 + 5 = 8 )
(d) If 7 < 10, then 3 + 5 = 8
This statement is true. Because True ------> True has the truth value T
( 7 < 10 and 3 + 5 = 8, both are true )
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(a) If 10 < 7, then 3 = 4.
This statement is true. Because False ------> False has the truth value T
(b) If 7 < 10, then 3 = 4
This statement is False. Because True ------> False has the truth value F
(c) If 10 < 7, then 3 + 5 = 8.
This statement is true. Because False ------> True has the truth value T
(d) If 7 < 10, then 3 + 5 = 8
This statement is true. Because True ------> True has the truth value T
What is a conditional statement?
A hypothesis and a conclusion are both included in conditional statements. An "If-then" statement is another name for it. The conditional statement is false if the hypothesis is correct but the conclusion is incorrect. The entire sentence is untrue if the hypothesis is incorrect.
(a) If 10 < 7, then 3 = 4.
This statement is true. Because False ------> False has the truth value T
( 10 is not less than 7 and 3 is not equal to 4)
(b) If 7 < 10, then 3 = 4
This statement is False. Because True ------> False has the truth value F
( 7 < 10 and 3 is not equal to 4 )
(c) If 10 < 7, then 3 + 5 = 8.
This statement is true. Because False ------> True has the truth value T
( 10 is not less than 7 , but 3 + 5 = 8 )
(d) If 7 < 10, then 3 + 5 = 8
This statement is true. Because True ------> True has the truth value T
( 7 < 10 and 3 + 5 = 8, both are true )
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Please answer the question in the image below, thanks
Based on the volume of the solid, the value of K is 8960.
What is the volume of the solid?The volume of the solid = volume of the cone + volume of the hemisphere
The volume of the cone = ¹/₃hπr²
The volume of the hemisphere = ²/₃πr³
where;
r is radius = 20 cm
h is the height of the cone = ?
The curved surface area of the cone = πrl
The curved surface area of the cone = 580π cm²
πrl = 580π
l = 580/20
l = 29 cm
h = √(29² - 10²)
h = 27.2 cm
The volume of cone = ¹/₃ * 27.2 * 20² * π
The volume of the cone = 3626.7π cm³
The volume of the hemisphere = ²/₃ * π * 20³
The volume of the hemisphere = 5333.3 cm³
The volume of the solid = 5333.3π cm³ + 3626.7π cm³
The volume of the solid = 8960π cm³
The volume of the solid is kπcm³ = 8960π cm³
K = 8960
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which of the following correctly ranks the magnitudes of the electric field at the four labeled points from largest to smallest?
The electric field at points A and C is the same, since they are both the same distance away from the center of the charge. Therefore, the electric field at A and C is the largest, while the electric field at B and D is the smallest. Thus, the correct answer is A. A, C, B, D.
The electric field is determined by the magnitude of the charge, the distance between the charge and the point where the electric field is measured, and the direction of the electric field. In this case, point A and C are the same distance away from the center of the charge, while points B and D are further away. Therefore, the electric field at points A and C is the strongest.
the complete question is :
which of the following correctly ranks the magnitudes of the electric field at the four labeled points from largest to smallest?
Options :
A. a, b, c, d
B. b, c, d, a
C. b, d, c, a
D. d, c, b, a
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Evaluate ∫∫r(x+y)dxdy, where r is the rectangle in the xy plane with vertices (0,1), (1,0), (3,4)and (4,3).
The double integral [tex]\int\limits^a_b {(x+y)} \, dx dy[/tex]over the rectangle r with vertices (0,1), (1,0), (3,4) and (4,3) is equal to 22.
What do you mean by integration?Integration can be thought of as the reverse of differentiation, which is the process of finding the rate of change of a function at a given point.
There are two main types of integration: definite and indefinite integration. The process of integration can be represented symbolically as ∫ (the integral symbol) and the result of an integration is typically represented as an antiderivative. The fundamental theorem of calculus states that differentiation and integration are inverse operations, so the derivative of an antiderivative is the original function.
To evaluate the double integral [tex]\int\limits^a_b {} \, dx dy[/tex]over the rectangle r with vertices (0,1), (1,0), (3,4) and (4,3), we first need to find the limits of integration for x and y.
The x-coordinates of the vertices of the rectangle range from 0 to 4, so the limits of integration for x are 0 to 4. The y-coordinates of the vertices of the rectangle range from 1 to 4, so the limits of integration for y are 1 to 4.
So, the double integral becomes:
[tex]\int\limits^a_b {(x+y)} \, dx dy[/tex] = (2 × 4² + 8 × 4) - (2 × 1² + 8 × 1) = 32 - 10 = 22.
Therefore, the double integral [tex]\int\limits^a_b {(x+y)} \, dx dy[/tex] over the rectangle r with vertices (0,1), (1,0), (3,4) and (4,3) is equal to 22.
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Last night, the Dallas Mavs made 12 free throws. If
their free throw percentage is 75%, how many free
throws were attempted?
Answer: i don't know I just did this so i can get points to ask a question super sorry.
Step-by-step explanation:
Calculate the area of the trapezium 6cm 4cm 5cm 8cm
Answer:
28 cm^2
Step-by-step explanation:
The area will be the height (4) times the average of the bases (8 and 6 , average = 7 )
4 x 7 = 28 cm^2
The interval [0,3] is partitioned into n equal subintervals, and a number xi is arbitrarily chosen in the ith subinterval for each i. Then lim n -> infinity n E i=1 (6xi-3)/n
The limit of the sum (6xi-3)/n as n approaches infinity is 9, which means that as the number of subintervals in the interval [0,3] becomes larger and larger, the sum of the values (6xi-3)/n approaches 9.
The limit is a concept in mathematics that helps us understand what happens as a function or a sequence approaches a certain value.
In this particular problem, we are looking at the limit of a sum of values as the number of subintervals in the interval [0,3] approaches infinity.
The interval [0,3] is divided into n equal subintervals and a number xi is chosen arbitrarily in the ith subinterval. We then look at the sum of the values (6xi-3)/n for all n subintervals.
Mathematically, we can write this sum as:
S = (6xi-3)/n for i = 1, 2, ..., n
And the limit of S as n approaches infinity can be written as:
lim n -> infinity S = lim n -> infinity (6xi-3)/n
Now, we use the concept of a Riemann Sum to evaluate the limit of this sum. A Riemann Sum is a way of approximating the area under a curve by breaking it down into rectangles and summing their areas.
In our case, we can think of the sum S as a Riemann Sum for the function f(x) = 6x-3 over the interval [0,3]. As n approaches infinity, the width of the subintervals approaches 0, and the sum S approaches the definite integral of f(x) over [0,3].
Using the fundamental theorem of calculus, we can find the definite integral of f(x) over [0,3] as:
∫f(x)dx = 6x^2/2 - 3x evaluated from 0 to 3
And this value is 9, so the limit of S as n approaches infinity is 9.
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A tank is full of water. Find the work required to pump the water out of the spout. (Use 9.8 m/s2 for g. Use 1000 kg/m3 as the density of water. Assume r = 6 m and h = 2 m.)
The work required to pump the water out of the spout is 70.9 * 10⁶ joules which is 71 M Joules approx.
Let the spherical tank be divided into a series of horizontal disks.
Let x be the height of each disk, g = gravity and p = density
Volume of each disk = πr2dx
Where r is the radius of each disk and dx is the thickness
By Pythagoras r² = 6² - x²= 36 -x²
Therefore Volume = π*(36-x²)*dx cubic metres
The distance each disk has to be lifted to escape the top of the spout = 2 + 6-x meters = (8-x)
Work needed to lift each disk to outlet = distance * mass where
mass = volume * density * gravity
= pi(36-x²)*p*g = 9800pi(36-x²)dx
dW = (8-x)* 9800pi(36-x²)dx
Since we have already accounted for the height of the spout, the work required is obtained by integrating the above expression from the bottom of the tank to the top. In other words, - 6 to + 6.
W = ⌠(8-x)*9800pi(36-x2)dx = 9800pi⌠[288 - 36x - 8x² +x³]dx
The odd terms evaluate to zero and we can rewrite the above as 2* I from 0 to 6.
W = 9800pi*2 [288x - 8x³/3] at x = 6 = 1152*19600π Joules = 22579200π joules = 70963200j
Total work required = 70.9 * 10⁶ joules
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Which ordered pair is in the solution set of 5x - 2y > 12?
A: (2, -1)
B: (1, 5)
C: (-1, -9)
D: (0.2, 0.5)
The ordered pair that is in the solution set of the given inequality is (-1, -9). The correct answer would be an option (C).
What is an ordered pair?An ordered pair is made up of two components isolated by a comma and put inside parentheses. (x, y) indicates an ordered pair, where 'x' is the first component and 'y' is the second component in the ordered pair.
We can substitute each of the ordered pairs into the inequality to see if it satisfies the inequality:
A: (2, -1)
5x - 2y > 12
5 × 2 - 2 × -1 > 12
10 - 2 > 12
8 > 12 (False)
B: (1, 5)
5x - 2y > 12
5 × 1 - 2 × 5 > 12
5 - 10 > 12 (False)
C: (-1, -9)
5x - 2y > 12
5 × -1 - 2 × -9 > 12
-5 + 18 > 12 (True)
D: (0.2, 0.5)
5x - 2y > 12
5 × 0.2 - 2 × 0.5 > 12
1 - 1 > 12 (False)
So, the only ordered pair that is in the solution set of the inequality is C: (-1, -9).
Hence, the correct answer would be option (C).
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