Answer:
logₐ(420)
Step-by-step explanation:
Answer:
The answer is
[tex] log_{a}(420) [/tex]
Step-by-step explanation:
You have to use Logarithm Law,
[tex] log_{a}(b) + log_{a}(c) ⇒ log_{a}(b \times c) [/tex]
* Take note, number b and c can only be multiplied when they have the same base, a
So for this question :
[tex] log_{a}(6) + log_{a}(70) [/tex]
[tex] = log_{a}(6 \times 70) [/tex]
[tex] = log_{a}(420) [/tex]
What is the value of m squared minus 2 m n + n squared for m = negative 2 and n = 4?
-4-2×-2×64
-4+4×64
-4+256
=252
Answer: (36)
hope this helps you have a wonderful day
Step-by-step explanation:
Fraction - Multiplication : 3/4 x 1/7
Answer:
given
3/4×1/7
=3×1/4×7
=3/28
thus the answer is 3/28
[tex]answer = \frac{3}{28} \\ solution \\ \frac{3}{4} \times \frac{1}{7} \\ = \frac{3 \times 1}{4 \times 7} \\ = \frac{3}{28} \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
1.
On hand: Magnesium sulfate 30 grams is mixed in 500 ml Lactated Ringers. Order: infuse a
maintenance dose of magnesium sulfate at 4 grams/hour. At what rate should the nurse set the
pump:
Answer:
The IV will run [tex]66.67 \ ml /hr[/tex]
Step-by-step explanation:
From the question we are told that
The mass of Magnesium sulfate is [tex]m_g = 30 \ g[/tex]
The volume of the Magnesium sulfate [tex]V_R = 500ml[/tex]
The rate at which the dose of the solution (Magnesium sulfate + Lactated Ringers. ) is infused is [tex]R = 4g/hr[/tex]
The concentration of Magnesium sulfate in Lactated Ringers is mathematically evaluated as
[tex]C_m = \frac{m_g}{V_R}[/tex]
substituting values
[tex]C_m = \frac{30}{500}[/tex]
[tex]C_m = 0.06\ g/ ml[/tex]
This implies that
0.06 g of Magnesium sulfate is in every 1 ml of Lactated Ringers
So 4 g of Magnesium sulfate is in x ml of Lactated Ringers
So
[tex]x = \frac{4}{0.06}[/tex]
[tex]x = 66.67 \ ml[/tex]
So the amount of the solution in ml that is been infused in 1 hour is
[tex]66.67 \ ml /hr[/tex]
If a sequence c1,c2,c3,...has limit K then the sequence ec1,ec2,ec3,...has limit e^K. Use this fact together with l'Hopital's rule to compute the limit of the sequence given by
bn=(n)^(5.6/n).
Answer:
Step-by-step explanation:
If a sequence c1,c2,c3,...has limit K then the sequence ec1,ec2,ec3,...has limit e^K. Use this fact together with l'Hopital's rule to compute the limit of the sequence given by
bn=(n)^(5.6/n).
a)
[tex]L = \lim_{n \to \infty} b_n \\\\\\L= \lim_{n \to \infty} n^{\frac{5.6}{n} }[/tex]
Log on both sides
[tex]In (L) = \lim_{n \to \infty} In (n)^{\frac{5.6}{n} }\\\\= \lim_{n \to \infty} \frac{5.6}{n} In(n)[/tex]
[tex]=5.6 \lim_{n \to \infty} \frac{d}{dn} In(n)/\frac{d}{dn} (n)\\\\=5.6 \lim_{n \to \infty} \frac{1}{n} /1 \\\\=5.6 \lim_{n \to \infty} \frac{1}{n} \\\\=5.6 \times 0\\\\In(L) =0\\\\L=e^0\\\\L=1[/tex]
[tex]\therefore \lim_{n \to \infty} (n)^{\frac{5.6}{n} =1[/tex]
The limit value of given sequece is 1.
To understand more, check below explanation.
Limit of function:The given sequence is,
[tex]b_{n}=n^{5.6/n}[/tex]
We have to find limit of above sequence.
[tex]L=\lim_{n \to \infty} b_n \\\\L=\lim_{n \to \infty}n^{5.6/n} \\\\ln(L)=\lim_{n \to \infty}\frac{5.6}{n}ln(n) \\\\ln(L)=5.6\lim_{n \to \infty}\frac{ln(n)}{n} \\\\ln(L)=5.6\lim_{n \to \infty}\frac{1/n}{1} \\\\ln(L)=5.6*0=0\\\\L=e^{0}=1[/tex]
Therefore, the limit value of given sequece is 1.
Learn more about the limit of function here:
https://brainly.com/question/2166212
Identify the level of measurement of the data, and explain what is wrong with the given calculation. In a survey, the favorite sports of respondents are identified as 100 for basketball comma 200 for baseball comma 300 for football comma and 400 for anything else. The average (mean) is calculated for 597 respondents and the result is 256.1 .The data are at the _________________
level of measurement.
Answer:
The data are at the Nominal level of measurement.
The given calculation is wrong because average (mean) cannot be calculated for nominal level of measurement.
Step-by-step explanation:
The objective here is to Identify the level of measurement of the data, and explain what is wrong with the given calculation.
a)
The data are at the Nominal level of measurement due to the fact that it portrays the qualitative levels of naming and representing different hierarchies from 100 basketball, 200 basketball, 300 football, 400 anything else
b) We are being informed that, the average (mean) is calculated for 597 respondents and the result is 256.1.
The given calculation is wrong because average (mean) cannot be calculated for nominal level of measurement. At nominal level this type of data set do not measure at all , it is not significant to compute their average (mean).
graph the equation in a coordinate plane, x+2y=4
Hope this helps!
Stay safe, have a good day :D
Find the value of a. a) 15 b) 10 c) 25 d) 20
Answer:
answer d) 20
Step-by-step explanation:
Because the two lines are parallel two by two, the figure is a parallelogram.
In a parallelogram the opposite corners are identical.
Given:
opposite corner1 = 130°
opposite corner2= (6a + 10)°
Because corner1 = corner2 we now have:
(6a + 10) = 130
6a + 0 = 130 -10
6a = 120
a = 20
Which is answer d).
What’s the correct answer for this question?
Answer:
D.
Step-by-step explanation:
In the attached file
outline the procedure for finding the probabilities of any given compound event
Explanation:
We will discuss the probability of any given Compound event under two broad heading. Exclusivity and Dependence.
Two or more events are mutually exclusive if they cannot occur at the same time.
In mutually excusive events,
[tex]P(A \cap B)=0[/tex]
The probability of two mutually exclusive events is given as:
P(A or B)=P(A)+P(B)
If however the two events can occur at the same time, they are mutually inclusive and: [tex]P(A \cap B)\neq 0[/tex].
For mutually inclusive events A and B,
[tex]P(A or B)=P(A)+P(B)-P(A \cap B [/tex].
Two events are independent if the outcome of one does not affect the outcome of the other.
For two independent events, the probability of A and B,
[tex]P(A \cap B)=P(A) \times P(B)[/tex].
Two events are not independent if the outcome of one affect the outcome of the other.
For two dependent events, if A is dependent of B, we say that the probability of A given B,
[tex]P(A|B)=\dfrac{P(A) \cap P(B)}{P(B)}[/tex].
Express 1.8meter in seconds given answer in scientific notation
Answer:
Dear user,
Answer to your query is provided below
Scientific notation = 1.8x10^0
Step-by-step explanation:
This is usually expressed simply as 1.8 (Recall that 10^0 = 1.)
1.8×10^0
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
D. Time ( length)
Step-by-step explanation:
The function is measuring the length of the race, and the time it took to complete. So, it would be D.
// have a great day //
Answer:
D. Time(length)
Step-by-step explanation:
→The time is on the outside because, according to the information that has been given/provided, the length of the race depends on the time taken to complete the race.
This means the correct answer is "D. Time(length)."
please very soon I offer the crown !!! + 10 points urgently !!!
Answer:
a. 3
b. 5
c. 4
d. 4
e. 10
Step-by-step explanation:
Answer:
read below
Step-by-step explanation:
a.3
b.5
c.2
d.2
6. 8p
you need 418 yards of blue silk to make one bridesmaid’s dress and 358 yards of the same fabric to make another. How many yards of blue silk do you need to make both dresses?
Answer: you would need 776 yards to make both dresses
Step-by-step explanation:
You would need to find the sum of the amount if yards needed for both dresses.
The first dress needs 418 yards
The seconds dress needs 358 yards
418 + 358 = 776
Therefore you would need 776 yards to be able to make both of the dresses
Harasti was inspired to build his hotels after he saw seahorses living in old fishing traps. What is the volume of a fishing trap that is 2 feet wide, 5 feet long, and 3 feet tall?
HELP ME DO THIS !!!!
Answer:
volume of rectangular prism = 30 ft³
Step-by-step explanation:
The fishing trap he wants to build to house sea houses are mostly rectangular prism. The traps are mostly glass like. The volume of the fishing trap will be the volume of the rectangular prism.
volume of rectangular prism = LWH
where
L = length
W = width
H = height
volume of rectangular prism = LWH
Length = 5 ft
width = 2 ft
Height = 3 ft
volume of rectangular prism = 5 × 2 × 3
volume of rectangular prism = 10 × 3
volume of rectangular prism = 30 ft³
If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (9-1(3)?
Answer:
( g − f ) ( 3 ) = 23
Step-by-step explanation:
(g-f)(x)=g(x)-f(x)
=6x-(4-X(2))
=x(2)+6x-4
to evaluate (g-f) (#) substitute x=3 into (g-f)(x)
(g-f)=(9)+(6 x 3) -4=23
Suppose f '' is continuous on (−[infinity], [infinity]). (a) If f '(−5) = 0 and f ''(−5) = −1, what can you say about f ? At x = −5, f has a local maximum. At x = −5, f has a local minimum. At x = −5, f has neither a maximum nor a minimum. More information is needed to determine if f has a maximum or minimum at x = −5. (b) If f '(1) = 0 and f ''(1) = 0, what can you say about f ? At x = 1, f has a local maximum. At x = 1, f has a local minimum. At x = 1, f has neither a maximum nor a minimum. More information is needed to determine if f has a maximum or minimum at x = 1.
Answer:
Step-by-step explanation:
a) The first derivative helps considering f decreases or increases. Also, when f'(x) = 0, the function gets local max/min depends on how it acts.
The second derivative helps determining the concave up/down.
At x = -5, f"(-5) = -1 <0 That means the function f have concave down. Also, it shows f increases before -5 and decreases after -5.
Hence f'(-5) = 0 shows f gets maximum at -5.
b) At the point where f" =0, the function has a reflecting point and we need more information to determine if f has a local max/min there.
Using concepts of critical points, it is found that:
a) At x = −5, f has a local maximum.
b) At x = 1, f has neither a maximum nor a minimum.
-----------------------
A critical value of a function f(x) is a value of [tex]x^{\ast}[/tex] for which: [tex]f^{\prime}(x^{\ast}) = 0[/tex].
The second derivative test is also applied:
If [tex]f^{\prime\prime}(x^{\ast}) > 0[/tex], [tex]x^{\ast}[/tex] is a minimum point.If [tex]f^{\prime\prime}(x^{\ast}) < 0[/tex], [tex]x^{\ast}[/tex] is a maximum point.If [tex]f^{\prime\prime}(x^{\ast}) = 0[/tex], [tex]x^{\ast}[/tex] is neither a maximum nor a minimum point.Item a:
[tex]f^{\prime}(-5) = 0, f^{\prime\prime}(-5) = -1[/tex], thus, a maximum point, and the correct option is:At x = −5, f has a local maximum.
Item b:
[tex]f^{\prime}(1) = 0, f^{\prime\prime}(1) = 0[/tex], thus, neither a maximum nor a minimum point, and the correct option is:At x = 1, f has neither a maximum nor a minimum.
A similar problem is given at https://brainly.com/question/16944025
You are conducting a study to see if the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.3. A random sample of 735 men over the age of 50 found that 203 have their prostate regularly examined. Do the sample data provide convincing evidence to support the claim
Answer:
[tex]z=\frac{0.276 -0.3}{\sqrt{\frac{0.3(1-0.3)}{735}}}=-1.42[/tex]
Now we can claculate the p value with this formula:
[tex]p_v =P(z<-1.42)=0.0778[/tex]
If we use a signifiacn level of 5% we see that the p value is higher than 0.05 so then we have enough evidence to fail to reject the null hypothesis and we can't conclude that the true proportion is significantly higher than 0.3 at 5% of significance.
Step-by-step explanation:
Information to given
n=735 represent the random sample taken
X=203 represent the number of people who have their prostate regularly examined
[tex]\hat p=\frac{203}{735}=0.276[/tex] estimated proportion of people who have their prostate regularly examined
[tex]p_o=0.3[/tex] is the value to verify
z would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to test if the true proportion is less than 0.3, the ystem of hypothesis are.:
Null hypothesis:[tex]p \geq 0.3[/tex]
Alternative hypothesis:[tex]p < 0.3[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info we got:
[tex]z=\frac{0.276 -0.3}{\sqrt{\frac{0.3(1-0.3)}{735}}}=-1.42[/tex]
Now we can claculate the p value with this formula:
[tex]p_v =P(z<-1.42)=0.0778[/tex]
If we use a signifiacn level of 5% we see that the p value is higher than 0.05 so then we have enough evidence to fail to reject the null hypothesis and we can't conclude that the true proportion is significantly higher than 0.3 at 5% of significance.
A population has the following characteristics.(a) A total of 25% of the population survives the first year. Of that 25%, 75% survives the second year. The maximum life span is 3 years.(b) The average number of offspring for each member of the population is 3 the first year, 5 the second year, and 3 the third year.The population now consists of 144 members in each of the three age classes. How many members will there be in each age class in 1 year?0 ≤ age ≤ 1 = 1 ≤ age ≤ 2 = 2 ≤ age ≤ 3 = In 2 years?0 ≤ age ≤ 1 = 1 ≤ age ≤ 2 = 2 ≤ age ≤ 3 =
Answer:
After 1st year, the age distribution will be
[tex]x_1 = \left[\begin{array}{ccc}1584\\36\\108\end{array}\right][/tex]
After 2nd year, the age distribution will be
[tex]x_2 = \left[\begin{array}{ccc}5256\\396\\27\end{array}\right][/tex]
Step-by-step explanation:
A population has the following characteristics.
A total of 25% of the population survives the first year. Of that 25%, 75% survives the second year.
The average number of offspring for each member of the population is 3 the first year, 5 the second year, and 3 the third year.
From the above information, we can construct a transition age matrix.
[tex]A = \left[\begin{array}{ccc}3&5&3\\0.25&0&0\\0&0.75&0\end{array}\right][/tex]
The population now consists of 144 members in each of the three age classes.
From the above information, we can construct the current age matrix.
[tex]x = \left[\begin{array}{ccc}144\\144\\144\end{array}\right][/tex]
How many members will there be in each age class in 1 year?
After 1st year, the age distribution will be
[tex]x_1 = A \cdot x[/tex]
[tex]x_1 = \left[\begin{array}{ccc}3&5&3\\0.25&0&0\\0&0.75&0\end{array}\right] \times \left[\begin{array}{ccc}144\\144\\144\end{array}\right][/tex]
The matrix multiplication is possible since the number of columns of first matrix is equal to the number of rows of second matrix.
[tex]x_1 = \left[\begin{array}{ccc}1584\\36\\108\end{array}\right][/tex]
After 2nd year, the age distribution will be
[tex]x_2 = A \cdot x_1[/tex]
[tex]x_2 = \left[\begin{array}{ccc}3&5&3\\0.25&0&0\\0&0.75&0\end{array}\right] \times \left[\begin{array}{ccc}1584\\36\\108\end{array}\right][/tex]
[tex]x_2 = \left[\begin{array}{ccc}5256\\396\\27\end{array}\right][/tex]
What is 27 ÷ 4 rounded to the nearest tenth?
Answer:
6.8
Step-by-step explanation:
27 / 4 = 6.75, which rounded to the nearest tenth, is 6.8.
The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the number of bids an item will receive based on the list price. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.Price in Dollars 23 34 40 46 47Number of Bids 1 3 4 5 7Step 1 of 6:Find the estimated slope. Round your answer to three decimal places.Step 2 of 6:Find the estimated y-intercept. Round your answer to three decimal places.Step 3 of 6:Determine if the statement "All points predicted by the linear model fall on the same line" is true or false.Step 4 of 6:Find the estimated value of y when x=46. Round your answer to three decimal places.Step 5 of 6:Determine the value of the dependent variable y^ at x=0.Step 6 of 6:Find the value of the coefficient of determination. Round your answer to three decimal places.
Answer:
1) Estimated slope = b₁ = 0.215
2) Estimated y-intercept = b₀ = -4.185
3) Not all the points predicted fall on the same straight line, but the model gives a close to ideal estimate of the line of best fit.
4) The estimated value of y when x=46 is 5.705
5) The value of the dependent variable y^ at x=0 is -4.185
6) The coefficient of determination = 0.951
Step-by-step explanation:
To solve this, we apply regression analysis
y = b₀ + b₁x
Price in Dollars | 23 | 34 | 40 | 46 | 47
Number of Bids | 1 | 3 | 4 | 5 | 7
For this question, we want to predict the number of bids (dependent variable, y), given the list price of the item (independent variable, x)
So, running the analysis on a spreadsheet application, like excel, the table of parameters is obtained and presented in the first attached image to this solution.
Σxᵢ = sum of all the independent variables (sum of all the list prices)
Σyᵢ = sum of all the dependent variables (sum of all the number of bids in the table)
Σxᵢyᵢ = sum of the product of each dependent variable and its corresponding independent variable
Σxᵢ² = sum of the square of each independent variable (list prices)
Σyᵢ² = sum of the square of each dependent variable (number of bids)
n = number of variables = 5
The scatter plot and the line of best fit is presented in the second attached image to this solution
Then the regression analysis is then done
Slope; m = b₁ = [n×Σxᵢyᵢ - (Σxᵢ)×(Σyᵢ)] / [nΣxᵢ² - (∑xi)²]
Intercept b: b₀ = [Σyᵢ - m×(Σxᵢ)] / n
Mean of x = (Σxᵢ)/n
Mean of y = (Σyᵢ) / n
Sample correlation coefficient r: r =
[n*Σxᵢyᵢ - (Σxᵢ)(Σyᵢ)] ÷ {√([n*Σxᵢ² - (Σxᵢ)²][n*Σyᵢ² - (Σyᵢ)²])}
And -1 ≤ r ≤ +1
All of these formulas are properly presented in the third attached image to this answer
The table of results; mean of x, mean of y, intercept, slope, regression equation and sample coefficient is presented in the fourth attached image to this answer.
Hence, the regression equation is
y = -4.185 + 0.215x
y = b₀ + b₁x
Intercept = b₀ = -4.185
Slope = b₁ = 0.215
And the regression coefficient = 0.951 (Which is very close to 1 and indicates statistic significance)
Hence, we can use this answer obtained to answer the questions attached
1) Find the estimated slope.
Estimated slope = b₁ = 0.215
2) Find the estimated y-intercept.
Estimated y-intercept = b₀ = -4.185
3) Determine if the statement "All points predicted by the linear model fall on the same line" is true or false.
Taking a few of sample data
x = 23 when y = 1
y = -4.185 + 0.215x
y = -4.185 + 0.215 (23) = 0.76 ≈ 1
x = 34, y = 3
y = -4.185 + 0.215 (34) = 3.125 ≈ 3
Hence, it is evident that not all the points predicted fall on the same straight line, but the model gives a close to ideal estimate of the line of best fit.
4) Find the estimated value of y when x=46.
The linear model is
y = -4.185 + 0.215x
when x = 46
y = -4.185 + 0.215(46) = 5.705
5) Determine the value of the dependent variable y^ at x=0.
y = -4.185 + 0.215x
when x = 0
y = -4.185 + 0.215(0) = -4.185
6) Find the value of the coefficient of determination.
The coefficient of determination = regression coefficient = 0.951 (as calculated above)
Hope this Helps!!!
not sure help please
Answer:
The area of a trapezoid is 1/2 (b₁ + b₂) * h where b₁ and b₂ are the bases and h is the height. The answer is 1/2 * (3 + 4) * 1 = 3.5.
Please answer this correctly
Answer:
5
Step-by-step explanation:
There are two ways you can solve this. First is to just count all the numbers in the list given that are within the range 15-19. This is an inclusive range meaning the numbers 15 and 19 are a part of it. The second method is to count how many numbers are in the list given and count all the numbers that have already been put on the table. There are 19 total numbers, and 14 have already been counted. If you subtract you are left with 5 numbers that are within the range. So the answer is 5.
Explanation:
One method is to count all of the values that are between 15 and 19. Those values are highlighted in the diagram below. There are 5 values marked.
An alternative method is to note there are 19 values total. The items in the given table add to 5+2+1+2+4 = 14, so there must be 19-14 = 5 items missing to completely fill out the table.
What Ln(z) is answer????!!
Write z in exponential form:
[tex]z=1-i=\sqrt2 e^{-i\frac\pi4}[/tex]
Then taking the logarithm, we get
[tex]\mathrm{Ln}(z)=\ln(\sqrt2) + \ln e^{-i\frac\pi4} = \boxed{\ln(\sqrt2)-\dfrac\pi4i}[/tex]
so a is the correct answer.
HURRY! WILL GIVE BRAINLIEST! HURRY
[tex]answer \\ = - 0.5 \\ please \: see \: the \: attached \: picture \: for \: \\ full \: solution \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
Answer:
Step-by-step explanation:
Marcus is trying to find 4 5/6-1 3/6. His work shown. What is Marcus's mistake?
Step 1: Subtract the wholes. 4-1=3
Step 2: Subtract the fractions. 5/6-3/6=2/6
Step 3: Subtract the differences. 3-2/6=2 4/6
Answer:
Step 3
Step-by-step explanation:
The mistake was made in Step 3.
Step 1: Subtract the wholes. 4 - 1 = 3
Step 2: Subtract the fractions. 5/6 - 3/6 = 2/6
After Step 2, He should have added them instead of subtracting them:
3 + 2/6 = 3 2/6
So, step 3 was his mistake.
Answer:step 3
Step-by-step explanation: he should have added
After the accounts have been adjusted at December 31, the end of the fiscal year, the following balances were taken from the ledger of Pioneer Delivery Services Co.:
Kerry Buckner, Capital. $9,556,300
Kerry Buckner, Drawing 80,000
Wages Expense 1,878,400
Rent Expense 1,415,500
Supplies Expense 125,000
Fees Earned 30,600
Miscellaneous Expense 22,100
Journalize the two entries required to close the accounts.
Debby is working on her typing.
• At first, Debby typed at a rate of 80 words per minute
After she took a typing class, she could type 300 more words per hour than she could before the typing class.
How many words per minute could Debby type after taking the typing class?
85
130
220
e
300
Answer:
300/60=5 more words per minute
80+5 = 85 words per minute
or
80 x 60 = 4800 + 300 = 5100
5100 / 60 = 85 words per minute
Hope this helps
Step-by-step explanation:
Can anyone help me with my homework ?
2x+3y=20
7x+2y=53
Answer:
x=7, y=2
Step-by-step explanation:
Solve2x+3y=20for x:
2x+3y=20
2x+3y+−3y=20+−3y
2x=−3y+20
2x/2=-3y+20/2
x= -3/2 y
if f(x)=ln(sin(2x)), f''(π/4) is equal to
Use the chain rule to compute the second derivative:
[tex]f(x)=\ln(\sin(2x))[/tex]
The first derivative is
[tex]f'(x)=(\ln(\sin(2x)))'=\dfrac{(\sin(2x))'}{\sin(2x)}=\dfrac{\cos(2x)(2x)'}{\sin(2x)}=\dfrac{2\cos(2x)}{\sin(2x)}[/tex]
[tex]f'(x)=2\cot(2x)[/tex]
Then the second derivative is
[tex]f''(x)=(2\cot(2x))'=-2\csc^2(2x)(2x)'[/tex]
[tex]f''(x)=-4\csc^2(2x)[/tex]
Then plug in π/4 for x :
[tex]f''\left(\dfrac\pi4\right)=-4\csc^2\left(\dfrac{2\pi}4\right)=-4[/tex]
Does anyone know this?
