In the rectangle, the sides are the same due to congruence theorem.
How to prove the rectangle?Given ABCD is a rectangle.
DAB = ABC
AB Isa common side to both ABC and ABD.
AB is the base of ABC and ABD.
Hence, BA = DC. This is due to the similar side of congruence.
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does anyone know the answer to this?
Answer: x=10
Step-by-step explanation:
x=10 because 10/5=2
Answer:
x = 10
Step-by-step explanation:
please Mark me brainliest
a city is in the shape of a rectangle. in 1995 the width of the city was 3 miles and the length of the city was 8 miles. the width of the city is growing at a rate of 1 mile in 6 years. the length of the city is growing at a rate of 1 mile in 3 years. use the product rule to find how quickly the area of the city is growing in 1995.
The area of the city is growing at a rate of 4/3 square miles per year in 1995.
Let's consider the width of the city w(t) and the length l(t)
where t is the time in years.
In 1995, the width is 3 miles and the length is 8 miles,
w(0) = 3
l(0) = 8
We know that the width is growing at a rate of 1 mile in 6 years
w'(t) = 1/6
Similarly, we know that the length is growing at a rate of 1 mile in 3 years,
l'(t) = 1/3
The area of the city A(t) is given by:
A(t) = w(t) × l(t)
Take the derivative of A with respect to time t:
A'(t) = w'(t) × l(t) + w(t) × l'(t)
Substitute the values
A'(0) = w'(0) × l(0) + w(0) × l'(0)
= (1/6) × 8 + 3 × (1/3)
= 4/3
Therefore, the growth rate is 4/3 square miles per year
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x²=9/25
what is it
need help reply
7 yd.
24 yd.
What is the length of the hypotenuse?
yards
C=
Answer:
25
Step-by-step explanation:
the equation is a^2+b^2=c^2
7^2=49
24^2=576
49+576=625
the square root of 625 is 25
Simplify the expression:
-3(6 - 1.5n)=
Answer:
Step-by-step explanation:
Use distributive property: a*(b +c) =a*b + a*c
-3( 6 - 1.5n) = (-3)*6 - (-3)*1.5n
= -18 + 4.5n
Answer:
-18 + 4.5n
Step-by-step explanation:
-3(6 - 1.5n) = -3(6) -3(-1.5n) Distributive
= -18 + 4.5n Multiplication. Remember (-) (-) = +
The ideal gas law states that the volume V that a gas occupies is directly proportional to the product of the number n of moles of gas and the temperature T (in K) and is inversely proportional to the pressure P (in atmospheres).
(a) Express V in terms of n, T, P, and a constant of proportionality K.
(b) (b What is the effect on the volume if the number of moles is doubled and both the temperature and the pressure are reduced by a factor of one twentieth?
V is multiplied by .....
(a) V = (nRT)/P or V = Knt/T. (b) V is multiplied by 38 if n is doubled, according to ideal gas law, T is reduced by 1/20, and P is reduced by 1/20.
(a) Utilizing the ideal gas regulation, we have PV = nRT, where R is the gas consistent. Reworking the condition, we get V = (nRT)/P. Since V is straightforwardly corresponding to n, T, and K, we can compose V = Knt/T, where K is the steady of proportionality.
(b) Assuming the quantity of moles is multiplied, n becomes 2n. Assuming the temperature and strain are both decreased by a component of 1/20, then, at that point, T becomes 19/20 T and P becomes 1/20 P. Subbing these qualities into the situation V = Knt/T, we get:
V = K(2n)(19/20 T)/(1/20 P)
V = K(38nT/P)
Thus, the volume V is duplicated by a component of 38 when the quantity of moles is multiplied and both the temperature and the strain are diminished by an element of one 20th.
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Will give Brainliest if right
Answer:
11.1
Step-by-step explanation:
Recall the three trig functions remember SOH CAH TOA
Sine = Opposite / Hypotenuse
Cosine = Adjacent / Hypotenuse
Tangent = Opposite / Adjacent
Here we are given an angle as well as the hypotenuse(longest side) and we want to find h which is opposite of the given angle.
When dealing with opposite and hypotenuse we use the trig function sine
Knowing this we create an equation and plug in what we are given
Sin = Opposite / Hypotenuse
Sin(48) = h / 15
==> multiply both sides by 15
15sin(48) = h
==> simplify
11.1 = h
The total cost of renting a movie for different numbers of days is shown in the table.
Which equation was used to create this table?
Movie Rentals
Total Cost,
Number of Days, d
(in dollars)
1
3
2
4
5
7
2
10
12
C = 20
d = 20
C = 2 +
d = 2 +
Answer:C
Step-by-step explanation:
I really need help please
Fill in this outcome (sample space) for this table showing the roll of a 6 sided dice and then the toss of a coin Coin Toss heads Tails Dice Roll What is P(4, T) What is P(odd, H)
Answer:
Benidorm quiz
1. Where is Benidorm holiday resort located?
JORDAN
2. What is the average temperature of Benidorm in summer?
26 C
3. Before 1950s Benidorm was a small ___FISHING______ village.
4. Why did the town council encourage tourism in Benidorm?
TO VISIT BENIDORM
5. How many hotels were found in Benidorm in 1959?
6. Explain package holidays as they were used in Benidorm
7. Give three reasons why Benidorm is an excellent tourist resort
(a)
(b)
©
8. State four tourist attractions at Benidorm
Step-by-step explanation:
Benidorm quiz
1. Where is Benidorm holiday resort located?
JORDAN
2. What is the average temperature of Benidorm in summer?
26 C
3. Before 1950s Benidorm was a small ___FISHING______ village.
4. Why did the town council encourage tourism in Benidorm?
TO VISIT BENIDORM
5. How many hotels were found in Benidorm in 1959?
6. Explain package holidays as they were used in Benidorm
7. Give three reasons why Benidorm is an excellent tourist resort
(a)
(b)
©
8. State four tourist attractions at Benidorm
Couple are marrying later. The median age of men who tied the knot for the firt time in 1970 wa 23. 2. In 1998, the median age wa 26. 7. Write an equation, in lope-intercept form to predict the median age that men marry M for any year t. Ue the equation in #9 to predict the median age of men who marry for the firt time in 2005
The equation in slope intercept form is : \(y = \frac{1}{8} x - 223.05\)
The slope intercept form is a process used to determine the equation of a straight line in the coordinate plane. It can be used to determine the equation of a line when given the slope of the straight line and the y-intercept
The slope-intercept form of a line is:
y = mx+b
where m is the slope of the line and b is an intercept of the y-axis.
\(m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }\)
\(m = \frac{26.7 - 23.2 }{1998- 1970}\)
\(m = \frac{1}{8}\)
So,
\(y = \frac{1}{8} x + b\)
To find b we get the point (1970, 23.2) and introduce it in the previous equation.
\(23.2= \frac{1}{8} (1970)+ b\)
⇒ 23.2 - 246.25 = b
⇒ b = - 223.05
Then, the equation is : \(y = \frac{1}{8} x - 223.05\)
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Find the area.I will mark the BRAINIEST
Answer: C. 64 ft
Step-by-step explanation:
a six-sided dice is rolled twice. find the probability that the larger of the two rolls was equal to 3.
A six-sided dice is rolled twice then the probability that the larger of the two rolls was equal to 3, is 0.1389.
A six-sided dice is rolled twice.
Then the possibility of getting numbers in one rolled = 6
The possibility of getting numbers in second rolled = 6
So the possibility of getting numbers in both rolled = 6 × 6
The possibility of getting numbers in both rolled = 36
Let A be the event that have the larger of the two rolls was equal to 3.
So the possible outcomes;
A = {(1,3), (2,3), (3,3), (3,2), (3,1)}
So total number of possible outcomes to getting larger of the two rolls was equal to 3 = 5
Then the probability that the larger of the two rolls was equal to 3 = Number of possible outcome/Total of possible outcome
The probability that the larger of the two rolls was equal to 3 = 5/36
The probability that the larger of the two rolls was equal to 3 = 0.1389
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The histogram gives information about the ages of the 115 members of a social club. 80% of the members who are over 50 years old are female. Work out an estimate for the number of female members who are over 50 years of age.
Answer:
An estimate of the number of female members who are over 50 years of age is 28 members
Step-by-step explanation:
The covered area art
0 - 20 = 1.6 * 20 = 32
20 - 30 = 1.9 * 10 = 19
30 - 40 = 1.8*10 = 18
40 - 60 = 1.1 * 20 = 22
> 60 = 0.8*30 = 24
Adding together gives;
32 + 19 + 18 + 22 + 24 = 115
The number of members that are 50 years and over is given as follows;
Half of the members in the 40 to 60 range plus all members that are over 60
Which give;
1/2*22 + 24 = 35
Given that 80% of the members over 50 are female, we have that the number of members that are female and over 50 = 0.8*35 = 28 members.
Answer:
Estimated Value = 28
Step-by-step explanation:
0 - 20 = 1.6 x 20 = 32
20 - 30 = 1.9 x 10 = 19
30 - 40 = 1.8 x 10 = 18
40 - 60 = 1.1 x 20 = 22
60 = 0.8 x 30 = 24
32 + 19 + 18 + 22 + 24 = 115
1/2 x 22 + 24 = 35
50 = 0.8 x 35 = 28
An advertisement firm reports that the proportion of consumers who respond favorably to a certain advertisement is 0.70. Three simulations, A, B, and C, were designed to create a sampling distribution of a sample proportion from a population with proportion 0.70. Each simulation consisted of 2,500 trials. For each trial of a simulation, a sample of size n was selected at random, and the sample proportion was recorded. The value of n varied among the simulations. The following histograms summarize the results of the simulations. Simulation A Relative Frequency 0.50 0.60 0.70 0.80 0.90 Relative Frequency 0.68 0.72 0.69 0.70 0.71 Simulation C Relative Frequency 0.60 0.65 0.70 0.75 0.80 .Which of the following lists the simulations in order from the least sample size n to the greatest sample size n ? A) Simulation A, simulation B, simulation C B) Simulation A, simulation C, simulation B C) Simulation B, simulation A, simulation C Simulation B, simulation C, simulation A D) Simulation C, simulation A, simulation B
Based on this information, we can conclude that the order of simulations from the least sample size (n) to the greatest sample size (n) is:
C) Simulation B, simulation A, simulation C
Based on the given information, we can determine the order of simulations from the least sample size (n) to the greatest sample size (n) by examining the histograms.
Looking at the histograms, we can see that the relative frequencies for each simulation are centered around the population proportion of 0.70.
However, we need to consider the relative frequencies that are closest to 0.70, as they indicate the simulations with sample sizes closest to the population size.
Comparing the histograms, we can see that the relative frequency closest to 0.70 in Simulation A is 0.69. In Simulation C, the relative frequency closest to 0.70 is also 0.70.
However, in Simulation B, the relative frequency closest to 0.70 is 0.80.
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What is the radius of a cylinder with a volume of 1650
cubic feet and a height of 10 feet?
Answer:
The radius of cylinder = 7.428 feet
Step-by-step explanation:
Volume of cylinder = 1650 cubic feet
Height = 10 feet
We need to find radius of cylinder
The formula used is: \(Volume=\pi r^2h\)
Putting values and finding radius
\(Volume=\pi r^2h\\1650=3.14\times r^2 \times 10\\1650=31.4\times r^2\\r^2=\frac{1650}{31.4}\\r^2=52.547\\Now,\:taking\:square\:root\:on\:both\:sides\\\sqrt{r^2}=\sqrt{52.547}\\r= 7.248\:feet\)
So, the radius of cylinder = 7.428 feet
Boubacar has a loyalty card good for a 11% discount at his local grocery store. If the total cost, before tax and discount, of all the items he wants to buy is c, which expression represents the cost after the discount?
The expression that represents the cost after the 11% discount is 0.89c. This means that Boubacar will pay 89% of the original cost after the discount has been applied.
How to calculate discount?To calculate the discount, you need to determine the discount rate, which is usually a percentage of the original price. Multiply the discount rate by the original price to find the amount of the discount.
Finally, subtract the discount amount from the original price to get the discounted price.
The discount that Boubacar gets on his purchase is 11% of the total cost before tax and discount. To calculate the discount, we multiply the total cost (c) by 11% or 0.11, which gives us:
Discount = 0.11c
To find the cost after the discount, we subtract the discount from the total cost. This gives us:
Cost after discount = c - Discount
Cost after discount = c - 0.11c
Cost after discount = 0.89c
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Those are the right answer
Answer:
100 yes there are trust me
Find the value
25 points in it for you, a thanks, 5 star rating and brainliest ON THE CORRECT ANSWER
Answer:
tan z =2.4
Step-by-step explanation:
1.)label the sides
opposite=24
adjacent=10
hypotenuse=26
2.)use the formula
tan [°]=opp/adj
tan z =24/10
tan z = 2.4
*if you want to find z,take the inverse of the answer
\(z = { \tan}^{ - 1} (2.4)\)
\(z = 67.38\)
help me please need answers now
Answer: 14
Step-by-step explanation:
What is the slope of the line x=3
Answer: The slope is infinite
Step-by-step explanation:
An infinite slope is simply a vertical line. When you plot it on a line graph, an infinite slope is any line which runs parallel to the y-axis. You can also describe this as any line that doesn't move along the x-axis but stays fixed at one constant x-axis coordinate, making the change along the x-axis.
Find the volume of the solid whose base is the semicircle \( y=\sqrt{16-x^{2}} \) where \( -4 \leq x \leq 4 \), and whose cross sections perpendicular to the \( x \)-axis are squares. Volume \( = \)
To find the volume of the solid, we need to integrate the area of each cross-section with respect to the \(\( x \)-axis.\) So, evaluating the integral , we get:
\(\( \text{Volume} = \frac{128}{3} \)\) cubic units.
To find the volume of the solid, we need to integrate the area of each cross-section with respect to the \(\( x \)-axis.\)
The base of the solid is a semicircle given by the equation \(\( y = \sqrt{16 - x^2} \), where \( -4 \leq x \leq 4 \).\)
The cross sections perpendicular to the \(\( x \)\)-axis are squares.
Since squares have equal side lengths, we can find the side length of each square by doubling the value of \( y \).
So, the side length of each square is \(\( 2y = 2\sqrt{16 - x^2} \).\)
To find the area of each cross-section, we square the side length:
\(\( (\text{Area}) = (2\sqrt{16 - x^2})^2 = 4(16 - x^2) \).\)
Now, we integrate this area from \(\( x = -4 \) to \( x = 4 \)\) to find the volume:
\(\( \text{Volume} = \int_{-4}^{4} 4(16 - x^2) \, dx \).\)
Evaluating this integral, we get:
\(\( \text{Volume} = \frac{128}{3} \)\) cubic units.
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4√2 + √2 with work
8√3 - 4√3 with work
2√3 x √32 with work
Step-by-step explanation:
4√2 + √2 = 5√2 we add 4 and the invisible 1 in front of √2, the common root stays same
8√3 - 4√3 = 4√3 subtract 4 from 8 the common root stays same
2√3 x √32 ➡ 2√3 x 4√3 too add the expressions we first need to make the roots common then add 4 and 2
Answer:
1. \(5\sqrt{2}\)
2. \(4\sqrt{3}\)
3. \(8\sqrt{6}\)
Step-by-step explanation:
Number 1:
We can treat \(\sqrt{2}\) as a variable in which we are multiplying 4 by. Let's call \(\sqrt{2}\) x.
This makes our expression \(4x + x\). Combining like terms, we get \(5x\). This means that \(4\sqrt{2} + \sqrt{2} = 5\sqrt{2}\).
Number 2:
Again, we can use the same logic as we did in number 1. Let's treat \(\sqrt{3}\) as a variable y.
\(8y-4y\)
Subtracting a y term from a y term will equal the difference between the coefficients times y. So it's \(4y\). This means that \(8\sqrt{3}-4\sqrt{3}=4\sqrt{3}\)
Number 3:
When we multiply radicals, we want to put the radicals in \(\sqrt{x}\) form.
\(\sqrt{32}\) is already in this form.
However \(2\sqrt{3}\) is not.
\(2\sqrt{3}\) is the same thing as \(\sqrt{3\cdot2^2} = \sqrt{3\cdot4} = \sqrt{12}\).
Now we multiply these radicals by multiply the term inside the square root sign
\(\sqrt{32}\cdot\sqrt{12}=\sqrt{32\cdot12} =\sqrt{384}\)
384 is divisible by 64, so:
\(\sqrt{384} = \sqrt{64\cdot6} = 8\sqrt{6}\)
Hope this helped!
А.
En un café Internet está publicado el siguiente cartel.
SERVICIO DE INTERNET
$2. 000 la primera hora
$1. 000 cada hora adicional
después de la primera hora
SI P es el valor total por pagar por el servicio de Internet yn es el número de horas
adicionales después de la primera hora que un cliente usa
sa el servicio, ¿cuál de las
siguientes expresiones muestra correctamente el valor total por pagar, suponiendo que el
cliente consume al menos una hora?
A. P= 2. 000n + 1. 000
C. P = n(2. 000 + 1. 000)
B. P= 2. 000 + 1. 000n
D. P = 2. 000 + 1. 000(n+1)
MATEMATICAS-TECNOLOGÍA GUÍA 1 PAG: 7
Step 1: Calculate the total cost for the first hour. The total cost for the first hour is $2,000.
Step 2: Calculate the cost for each additional hour. The cost for each additional hour is $1,000.
Step 3: Calculate the total cost. To calculate the total cost, add the cost for the first hour ($2,000) to the cost for each additional hour ($1,000) multiplied by the number of additional hours (n). This gives us a total of P = 2,000 + 1,000(n + 1).
Therefore, the correct expression for the total cost is P = 2,000 + 1,000(n + 1).
C(x)=F+V is the generic form of the cost function formula (x) C(x) = F + V(x), where x is the number of units, V(x) is the total variable cost, and C(x) is the overall cost of production.
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at the local college, a study found that students earned an average of 13.2 credit hours per semester. a sample of 80 students was taken. what is the best point estimate for the average number of credit hours per semester for all students at the local college?
13.2 credits are earned per semester.
The outcome you receive when you add together two or more numbers and divide the sum by the variety of amounts: Since the sum of the three numbers is 39 and 39 divided by three is 13, the average of the three numbers 7, 12, and 20 is 13.
The sample size \((x bar)\) provides the most accurate point estimate of the genuine population mean (μ) ( if the true population mean is unknown).
Given: A study at the nearby institution using a sample of 80 students discovered that each student obtained 13.2 credit hours on average per semester.
\(x bar\) = 13.2 credits per semester, for example.
The sample mean, or μ = \(x bar\)= 13.2 credit hours per semester, should thus be considered the best point estimate for the average number of credit hours per semester for all students at the local college.
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What is the probability of landing on a number greater then 5 and then landing on a number greater then 4
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the formula for calculating probability
\(Probability=\frac{number\text{ of required outcomes}}{number\text{ of total possible outcomes}}\)STEP 2: Find the probability of landing on a number greater than 5
\(\begin{gathered} Pr(greater\text{ than 5\rparen}=Pr(6\text{ and above\rparen} \\ Pr(greater\text{ than 5\rparen}=Pr(6)=\frac{1}{4} \end{gathered}\)STEP 3: Find the probability of landing on a number
Need help asap!!!!
Here's a screenshot:
Answer:
C
Step-by-step explanation:
a) Arrange the following numbers so that the sum of any two neighbouring numbers is a perfect square.
7 , 11 , 9 , 14 , 16 , 2 , 25
Ex. 3+6 = 3^2 and 6+10 = 4^2
b) Find a way to arrange all of the intervenes from 1 to 17 to a list with the property from part a)
I'll do part (a) to get you started.
One possible answer to part (a) is 25,11,14,2,7,9,16
There are likely other possible answers.
The explanation is below.
==============================================================
Let's say 7 is the anchor value and we want to see which values could be its next door neighbor.
It can't be 11 since 7+11 = 18 isn't a perfect square.But 9 works because 7+9 = 16 is a perfect square (4^2 = 16)14 doesn't work because 7+14 = 21 isn't a perfect square16 doesn't work either since 7+16 = 23 isn't a perfect square2 however does work since 7+2 = 9 is a perfect squareLastly, 25 won't work because 7+25 = 32 isn't a perfect squareTo summarize this subsection, the anchor value 7 could have the neighbors 9 and 2.
So we could have 2,7,9 or 9,7,2 as a subsequence. We'll keep this in mind for later.
------------------------------------------------
Now we'll make 11 the anchor. We already checked 7 and it doesn't work.
9 doesn't work either because 11+9 = 20 isn't a perfect square
11+14 = 25 does work11+16 = 27 doesn't work11+2 = 13 doesn't work11+25 = 36 does workOf that list, only 14 and 25 are possible neighbors of the anchor value 11.
So we could have the subsequence 14,11,25 or 25,11,14.
------------------------------------------------
If 9 is the anchor, then,
9+7 = 16 works like we found earlier (section 1)9+11 = 20 doesn't work9+14 = 23 doesn't work9+16 = 25 does work9+2 = 11 doesn't work9+25 = 34 doesn't workThe values 7 and 16 are possible neighbors of 9. We could have the subsequence 7,9,16 or 16,9,7
Let's go back to the subsequence 2,7,9 and tack 16 at the end to get 2,7,9,16
------------------------------------------------
If 14 is the anchor, then,
7 doesn't work because 14+7 = 2111 does work either because 14+11 = 259 doesn't work because 14+9 = 2316 doesn't work because 14+16 = 302 does work because 14+2 = 1625 doesn't work since 14+25 = 39We could have the subsequence 11,14,2 or 2,14,11
Let's go with the first option and stick "11,14,2" in front of "2,7,9,16" to end up with the larger subsequence 11,14,2,7,9,16
We can then stick 25 at the front because 25+11 = 36 is a perfect square.
------------------------------------------------
So one possible sequence of values is 25,11,14,2,7,9,16
Here's the verification
25+11 = 36 is a perfect square (6^2 = 36)11+14 = 25 is a perfect square (5^2 = 25)14+2 = 16 is a perfect square (4^2 = 16)2+7 = 9 is a perfect square (3^2 = 9)7+9 = 16 is a perfect square (4^2 = 16)9+16 = 25 is a perfect square (5^2 = 25)Each pair of adjacent terms add up to a perfect square, so the answer is confirmed.
There are probably other solutions as well.
Side note: The video math channel "Numberphile" has a video discussing this topic in which you might be interested in. Search out "The square sum problem" with quotes (the presenter/teacher in the video is Matt Parker).
Answer:
25, 11, 14, 2, 7, 9, 16.
Step-by-step explanation:
25 + 11 = 6^2
11 + 14 = 5^2
14 + 2 = 4^2
2 + 7 = 3^2
7 + 9 = 4^2
9 + 16 = 5^2
Can anyone help me on this , please don’t send the link things .
Answer:
D
Step-by-step explanation:
1/2 is the same as square root
the square of 8 is 2 root 2
then x squared is 2
and y is 2
16 is to the power of 1/4 is 2
Consider the function f defined by f(x)=(e^X)cosx with domain[0,2pie] .a. Find the absolute maximum and minimum values of f(x)b. Find the intervals on which f is increasing.c. Find the x-coordinate of each point of inflection of the graph of f.
The absolute maximum of f(x) is e^(2pi), which occurs at x = 2pi, and the absolute minimum of f(x) is approximately -1.30, which occurs at x = 5*pi/4
a. To find the absolute maximum and minimum values of f(x), we can use the first derivative test and the endpoints of the given interval.
First, we find the first derivative of f(x):
f'(x) = e^xcos(x) - e^xsin(x)
Then, we find the critical points of f(x) by setting f'(x) = 0:
e^xcos(x) - e^xsin(x) = 0
e^x(cos(x) - sin(x)) = 0
cos(x) = sin(x)
x = pi/4 or x = 5*pi/4
Note that these critical points are in the domain [0, 2*pi].
Next, we find the second derivative of f(x):
f''(x) = -2e^xsin(x)
We can see that f''(x) is negative for x in [0, pi/2) and (3pi/2, 2pi], and f''(x) is positive for x in (pi/2, 3*pi/2).
Therefore, x = pi/4 is a relative maximum of f(x), and x = 5*pi/4 is a relative minimum of f(x). To find the absolute maximum and minimum of f(x), we compare the values of f(x) at the critical points and the endpoints of the domain:
f(0) = e^0cos(0) = 1
f(2pi) = e^(2pi)cos(2pi) = e^(2pi)
f(pi/4) = e^(pi/4)cos(pi/4) ≈ 1.30
f(5pi/4) = e^(5*pi/4)cos(5pi/4) ≈ -1.30
Therefore, the absolute maximum of f(x) is e^(2pi), which occurs at x = 2pi, and the absolute minimum of f(x) is approximately -1.30, which occurs at x = 5*pi/4.
b. To find the intervals on which f(x) is increasing, we look at the sign of f'(x) on the domain [0, 2pi]. We know that f'(x) = 0 at x = pi/4 and x = 5pi/4, so we can use a sign chart for f'(x) to determine the intervals of increase:
x 0 pi/4 5*pi/4 2*pi
f'(x) -e^0 0 0 e^(2*pi)
f(x) increasing relative max relative min decreasing
Therefore, f(x) is increasing on the interval [0, pi/4) and decreasing on the interval (pi/4, 2*pi].
c. To find the x-coordinate of each point of inflection of the graph of f, we need to find where the concavity of f changes. We know that the second derivative of f(x) is f''(x) = -2e^xsin(x), which changes sign at x = pi/2 and x = 3*pi/2.
Therefore, the point (pi/2, f(pi/2)) and the point (3pi/2, f(3pi/2)) are the points of inflection of the graph of f.
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What are the 4 levels of measurement statistics?
The four levels of measurement in statistics are nominal, ordinal, interval, and ratio. They differ in terms of the properties of the data and the types of statistical analyses that can be performed on the data.
Nominal level involves data that can be placed into categories or groups with no inherent order or ranking. Examples of nominal data include gender, race, and occupation.
Ordinal level involves data that can be ranked or ordered, but the differences between the data points are not necessarily equal. Examples of ordinal data include educational levels (e.g., high school, college, graduate), or rankings of movies on a scale of 1-5.
Interval level involves data where the differences between the data points are equal, but there is no true zero point. Examples of interval data include temperature (measured in Celsius or Fahrenheit) and calendar years.
Ratio level involves data that has a true zero point and the differences between data points are equal. Examples of ratio data include height, weight, and time.
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