The derivative of the given expression ln(x)cos(x) can be written as (cos(x))/x - sin(x)ln(x).
What is derivative?
In mathematics, the derivative of a function of a real variable measures how sensitive the function's value (or output value) is to variations in its argument (input value). The derivative is the fundamental tool in calculus. A measure of how quickly an object's position changes over time is its velocity, which is the derivative of that object's position with respect to time.
We can solve this derivation using multiplication property of derivatives:
i.e. [tex]\frac{d}{dx}(uv) = u\frac{dv}{dx} + y \frac{du}{dx}[/tex]
In the given question, lets consider ln(x) as u and cos(x) as v
putting the values from question.
[tex]\frac{d}{dx}(ln(x)cos(x)) = ln(x)\frac{d(cos(x))}{dx} + cos(x) \frac{d(ln(x))}{dx}[/tex]
[tex]= ln(x)(-sin(x)) + cos(x)(\frac{1}{x})[/tex]
= (cos(x))/x - sin(x)ln(x)
To know more about derivative, go to link
https://brainly.com/question/23819325
#SPJ13
hi I'm 9 years old my name is Emma can
Given:
Perimeter = 40 feet,
The measure of the four sides is 11 feet, g, 11 feet, and g.
We know that the perimeter = the sum of the four sides.
[tex]\text{perimeter =11+g+11+g}[/tex]Replace perimeter =40, we get
[tex]\text{40=11+g+11+g}[/tex]Adding 11 and 11, we get
[tex]\text{40=11+11+g+g}[/tex][tex]\text{40=22+g+g}[/tex]Y=-x^2+x+12 write in intercept form and show work
Given that y= x^2+x+12, to write the expression in an intercept form we need to factorize the expression.
[tex]y=-x^2+x+12[/tex]The intercept form is of the format
[tex]y=a(x\pm p)(x\pm q)_{}[/tex]This is obtained by factoring the quadratic equation above
[tex]\begin{gathered} y=-x^2+4x-3x+12 \\ y=-x(x-4)-3(x-4) \\ y=(x-4)(-x-3) \\ y=-1(x+3)(x-4) \end{gathered}[/tex]Hence, the intercept form of the equation is y= -1 (x + 3) ( x - 4 )
An initial amount of $3500 is invested in an account at an interest rate of 6% per year, compounded continuously. Assuming that no withdrawals aremade, find the amount in the account after two years.Do not round any intermediate computations, and round your answer to the nearest cent.
For this problem we use the continuously compounded interest formula:
[tex]M=M_0e^{rt}[/tex]where M_0 is the initial amount, r is the interest rate per year and t is the number of years.
Substituting M_0=$3500, r=0.06, and t=2 we get:
[tex]\begin{gathered} M=3500e^{0.06\cdot2}=3500e^{0.12} \\ M=3946.24 \end{gathered}[/tex]In a group of 80 animals, 32 are dogs. Dogs make upwhat percent of the animals in the group?A. 32.00B. 28.6C. 35.5D. 38.00E 40.00
Let's calculate the percentage of dogs in the animal group
[tex]\begin{gathered} P=\frac{32}{80} \\ P=0.40 \\ P=40\text{ \%} \end{gathered}[/tex]The answer would be 40%.
Suppose you want to have $400,000 for retirement in 25 years. Your account earns 4% interest.
a) How much would you need to deposit in the account each month?
$
b) How much interest will you earn?
$
[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)[/tex]
[tex]\qquad \begin{cases} A=\textit{accumulated amount}\dotfill&\$400000 \\ pmt=\textit{periodic payments}\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &25 \end{cases}[/tex]
[tex]400000=pmt\left[ \cfrac{\left( 1+\frac{0.04}{12} \right)^{12 \cdot 25}-1}{\frac{0.04}{12}} \right]\left(1+\frac{0.04}{12}\right)[/tex]
[tex]\cfrac{400000}{\left[ \frac{\left( 1+\frac{0.04}{12} \right)^{12 \cdot 25}-1}{\frac{0.04}{12}} \right]\left(1+\frac{0.04}{12}\right)}=pmt\implies \cfrac{400000}{\left[ \frac{\left( \frac{301}{300} \right)^{300}-1}{\frac{1}{300}} \right]\left(\frac{301}{300}\right)}=pmt \\\\\\ \cfrac{400000}{515.84}\approx pmt\implies {\Large \begin{array}{llll} 775.43\approx pmt \end{array}}[/tex]
how much will it be in interest alone?
well, for 25 years every month you'd have been putting down that much, so we can just subtract what you put it from the 400,000 and what's left is the interest earned
[tex]400000~~ - ~~(25)(12)(775.43) ~~ \approx ~~ \text{\LARGE 167317}[/tex]
1 4 a) Is the above sequence arithmetic? Justify your answer. b) Write the explicit formula for the above sequence. c) Find the 18th term.
THe length of each cube is inreasing by 1. This means that the increment is in arithmetic sequence.
The formula for determining the nth term of an aritmetic sequence is expressed as
Tn = a + (n - 1)d
Where
a represents the first tem of the sequence
Common difference, d represents the difference between consecutive terms
Given that a = 3, d = 1
Tn = 2 + (n - 1)1
Tn = 2 + n - 1
Tn = 1 + n
For the 18th term, n = 18
T18 = 1 + 18 = 19
The number of boxes in the square for the 19th term is
19 * 19 = 361
the digits 1through 6 are used for a set of locker codes. suppose the digits cannot repeat. find the number of possible two digit codes and three digit codes. describe any pattern and use it to predict the number of possible five digit codes
SOLUTION
This is a permutation problem.
a) To find the number of possible two digits codes
[tex]^6P_2[/tex][tex]^6P_2=\frac{6!}{(6-2)!}[/tex][tex]\begin{gathered} =\frac{6!}{4!} \\ =\frac{720}{24} \\ =30\text{ ways} \end{gathered}[/tex]There are 30 possible two-digit codes pattern.
b) To find the number of three digits codes
[tex]\begin{gathered} ^6P_3=\text{ }\frac{6!}{(6-3)!} \\ \text{ =}\frac{6!}{3!} \\ \text{ =}\frac{720}{6} \\ \text{ = 120 ways} \end{gathered}[/tex]There are 120 possible three-digit codes pattern.
Any other pattern can be calculated using
[tex]\begin{gathered} ^6P_r \\ \text{where r is the number of digits code (1,2,3,4,5,6)} \end{gathered}[/tex]So to predict the number of possible five-digit codes will be:
[tex]^6P_5[/tex][tex]\begin{gathered} =\frac{6!}{(6-5)!} \\ =\frac{6!}{1!} \\ =720\text{ways} \end{gathered}[/tex]There are 720 different possible five-digit codes
the answer of this question is 720 ways
Eddie brought his DVD set to the secondhand store to sell he was paid for all three DVDs in the set before he left Eddie used $15.70 of his earnings to purchase a pair of headphones had $2.30 remaining which equation can you use to find the amount of money Eddie received for each DVD
15.70(d-3)=2.30
3d-15.70=2.30
15.70d-3=2.30
3(d-15.70)=2.30
Eddie brought his DVD set to the secondhand store to sell he was paid for all three DVDs in the set before he left Eddie used $15.70 of his earnings to purchase a pair of headphones had $2.30 remaining which equation can you use to find the amount of money Eddie received for each DVD:
15.70(d-3)=2.30
3d - 15.70 = 2.30
15.70d-3=2.30
3(d-15.70)=2.30
please let me know of question 4 is correct which is not true30 > 1030 < 1010 > 3010 < 30
Number 4
The meaning of the symbols are
> means greater than
< means less than
For the first statement, 30 is greater than 10. It is true
For the second statement, 30 is less than 10. It is not true
For the third statement, 10 is greater than 30. It is not true
For the fourth statement, 10 is less than 30. It is true
A board game that normally costs $30 is on sale for 25 percent off. What is the sale price of the game?
$22.50
$27.50
$32.50
$37.50
Between what two consecutive integers must solution 2^x=7 lie?
Answer:
2 and 3
Explanation:
Given the equation:
[tex]2^x=7[/tex]Now, observe the following:
[tex]\begin{gathered} 2^2=4 \\ 2^3=8 \\ 4<7<8 \\ \implies2^2<2^x<2^3 \end{gathered}[/tex]Taking the indices:
[tex]2Therefore, the solution of 2^x=7 lies between the consecutive integers 2 and 3.Rachel is driving to Denver. Let y represent her distance from Denver (in miles). Let x represent the time she has been driving (in hours). Suppose that x and yare related by the equation y = 475 - 60x.Answer the questions below.Note that a change can be an increase or a decrease.For an increase, use a positive number. For a decrease, use a negative number.-Picture includes the questions-
Given the equation:
[tex]y=475-60x[/tex]Let y = distance
Let x = time
- The distance from Denver when she began is given by x = 0, therefore:
[tex]y=475-60(0)=475-0=475[/tex]Answer 1. 475 miles
- The change for each four hours, this is x = 4, so:
[tex]y=475-60(4)=475-240=235[/tex]Answer 2. 235 miles
Fill in the table using this function rule. y = -10x +3 y X 6 ? 1 0 a 1
the function is
[tex]y=-10x+3[/tex]we must replace the value of x and obtain y
x=-5
[tex]\begin{gathered} y=-10(-5)+3 \\ y=50+3 \\ y=53 \end{gathered}[/tex]x=-1
[tex]\begin{gathered} y=-10(-1)+3 \\ y=13 \end{gathered}[/tex]x=0
[tex]\begin{gathered} y=-10(0)+3 \\ y=3 \end{gathered}[/tex]x=1
[tex]\begin{gathered} y=-10(1)+3 \\ y=-7 \end{gathered}[/tex]a digital music player is marked down from its list price of $249.99 to a sale price of $194.99. What is the discount rate?
The discount rate of the digital player is 22%
How to determine the digital player's discount rate?From the question, we have the given parameters:
List price = $249.99
Sales price = $194.99
Start by calculating the change in the price.
This is calculated as follows
Change = List price - Sales price
So, we have
Change = $249.99 - $194.99
Evaluate the difference
Change = $55
The discount rate of the digital player is then calculated as
Discount = Change/List price x 100%
This gives
Discount = 55/249.99 x 100%
Evaluate
Discount = 22%
Hence, the discount rate is 22%
Read more about discount rate at
https://brainly.com/question/7459025
#SPJ1
How to tell if a sequence is linear, exponential, quadratic or absolute value as simply as possible without graphing (8th grade algebra) examples will be greatly appreciated
We will have the following:
We will be able to tel apart sequences as follows:
Linear sequence: We have that linear sequences follow the form:
[tex]y=mx+b[/tex]Here "x" represents the iteration value for the sequence, "m" the ratio (slope) and "b" a value that modifies the "position" of the sequence. This sequences grows in a linear manner.
Example:
[tex]\begin{cases}y_{}=2x+2 \\ \\ y_1=4 \\ y_2=6 \\ y_3=8 \\ \ldots\end{cases}[/tex]Exponential sequence: We have that exponential sequences follow the form:
[tex]y=a_1(r)^{x-1}[/tex]Here "a1" is the first term of the sequence, "r" is the ratio and "x" the iteration of the sequence.
We obtain the ratio as follows:
[tex]r=\frac{y_n}{y_{n-1}}[/tex]Example:
[tex]\begin{cases}y=1(5)^{x-1}_{} \\ \\ y_1=1 \\ y_2=5 \\ y_3=25 \\ \\ \ldots\end{cases}[/tex]The ratio for this case:
[tex]r=\frac{y_3}{y_2}\Rightarrow r=\frac{25}{5}\Rightarrow r=5[/tex]Quadratic sequence: A quadratic sequence follows the general form
Which formula can be used to find the sum of the mesures of all the interior angles of a regular polygon with n sides?
A. S = (n-2)180 degrees
B. S = (n+2)180 degrees
C. S = (n-2)90 degrees
D. S = (n+2)90 degrees
Answer:180(n – 2),
Step-by-step explanation:
MOSS 79 grom Volume 10 m
Mass=79gram
Volume=10ml
density=Mass/Volume
[tex]\text{Density}=\frac{79\text{gram}}{10ml}=7.9\text{ gram/ml}[/tex]The number of books he collects, n, is defined by n = 140 + 21 where d is the number of days he spends collectingRobert is collecting books to donate to the library.books.What does 14 represent in the context of Robert's book collecting?A represents the number of books per day that are collected,® represents the number of books per week that are collected.represents the number of books per month that are collected.o represents the number of books per year that are collected.
The equation for number of books collected by Robert is given as;
n= 14 d + 21
where d is the number of days he spent collecting .
Answer A. represents the number of books per day that are collected
solve for x. then find the missing piece(s) of the parallelogram for #7
Let us find the angles of the parallelogram below
[tex]\begin{gathered} 2x+30 \\ x=40 \\ 2(40)+30 \\ 80+30 \\ 110^0 \end{gathered}[/tex][tex]\begin{gathered} 2x-10 \\ 2(40)-10 \\ 80-10 \\ 70^0 \end{gathered}[/tex]Theorem+: opposite angles of a parallelogram are the same
Hence the angles of the parallelogram are 110, 70, 110, and 70
Find extreme values of function f(x) = x³ - (3/2)x² on interval [- 1,2]
we have the function
[tex]f(x)=x^3-\frac{3}{2}x^2[/tex]Find out the first derivative of the given function
[tex]f^{\prime}(x)=3x^2-3x[/tex]Equate to zero the first derivative
[tex]\begin{gathered} 3x^2-3x=0 \\ 3x(x-1)=0 \end{gathered}[/tex]The values of x are
x=0 and x=1
we have the intervals
(-infinite,0) (0,1) (1,infinite)
Interval (-infinite,0) -----> f'(x) is positive
interval (0,1) ---------> f'(x) is negative
interval (1,infinite) -----> f'(x) is positive
that means
x=0 is a local maximum
x=1 is a local minimum
Find out the y-coordinates of the extreme values
For x=0 -----> substitute in the function f(x) ---------> f(x)=0
For x=1 ------> substitute in the function f(x) ------> f(x)=-0.5
therefore
The extreme values are
local maximum at (0,0)local minimum at (1,-0.5)-2 decimal 3/% because if you divide the principal in half its 1% of 3
Carolina wants to find out how many different ways can she arrange the apps on her Iphone on the first row. The first row has space for 4 apps, and she has 12 apps to choose from
ANSWER
495 ways
EXPLANATION
Carolina has 12 apps to choose from and she only has space for 4 apps.
To find out how many ways she can do it, we will need to use combination.
That is:
[tex]^{12}C_4[/tex]Note: we use combination because the order of the apps is not a factor
So, we have that:
[tex]\begin{gathered} ^{12}C_4\text{ = }\frac{12!}{(12\text{ - 4)! 4!}}\text{ = }\frac{12!}{8!\text{ 4!}} \\ =\text{ 495 ways} \end{gathered}[/tex]She can arrange them in 495 ways.
The graph models the heights, in feet, of two objectsdropped from different heights after x seconds.Which equation represents g(x) as a transformation off(x)?y45+O g(x) = f(x) -5O g(x) = f(x-5)O g(x) = f(x) + 5O g(x) = f(x + 5)40+35y = f(x)30-25+20-15+10+5+ly = g(x)0.5 1.0 1.5 20
For this problem we know that y=f(x) at x=0 is 5 units above y=g(x). So then the best solution for this case it seems to be:
[tex]f(x)=g(x)+5[/tex]And solving for g(x) we got:
[tex]g(x)=f(x)-5[/tex]2. (5 × 2 + 20/2) + (10 x 2/2 + 5) =
a. 35
b. 42
c. 103
Answer:
a.35
Step-by-step explanation:
10 + 20/2 equals 20
20/2+5 equals 15
20+15 equals 35
What is the solution to the following system of equations. Enter your answer as an ordered pair.3x+2y=17and4x+6y=26As an ordered pairHelp me pls
The system of equation are:
[tex]\begin{gathered} 3x+2y=17 \\ 4x+6y=26 \end{gathered}[/tex]to solve this problem we can solve the second equation for x so:
[tex]\begin{gathered} 4x=26-6y \\ x=6.5-1.5y \end{gathered}[/tex]Now we can replace x in the firt equation so:
[tex]3(6.5-1.5y)+2y=17[/tex]and we can solve for y so:
[tex]\begin{gathered} 19.5-4.5y+2y=17 \\ 19.5-17=2.5y \\ 2.5=2.5y \\ \frac{2.5}{2.5}=1=y \end{gathered}[/tex]Now we replace the value of y in the secon equation so:
[tex]\begin{gathered} x=6.5-1.5(1) \\ x=5 \end{gathered}[/tex]So the solution as a ordered pair is:
[tex](x,y)\to(5,1)[/tex]The Environmental Protection Agency (EPA) fuel economy estimates for automobile models tested recently predicted a mean of 30.8 miles per gallon, with a standard deviation of 4.1 miles per gallon. Assume that a Normal model applies. Find the probability that a randomly selected automobile will average: 1. Less than 28 miles per gallon. Chapter 6 Assignment 2. More than 26 miles per gallon.
I need much help with this normal distribution question.
The normal distribution, often known as the Gaussian distribution, is a symmetric probability distribution about the mean.
What is meant by normal distribution?The probability density function for a continuous random variable in a system defines the Normal Distribution.
A data collection with a normal distribution is put up so that the majority of the values cluster in the middle of the range and the remaining values taper off symmetrically in either direction.
The normal distribution, often known as the Gaussian distribution, is a symmetric probability distribution about the mean. This shows that data close to the mean occur more frequently than data far from the mean. On a graph, the normal distribution is represented by a "bell curve."
To learn more about normal distribution refer to:
https://brainly.com/question/14243195
#SPJ13
2 x— =-------7 x+ 10x = ???
Answer:
x = 4
Explanation:
Given the expression;
2/7 = x/x+10
Cross multiply
2(x+10) = 7x
Expand the bracket
2x + 20 = 7x
Subtract 7x from btoh sides
2x+20-7x = 7x - 7x
2x-7x+20 = 0
-5x + 20 = 0
-5x = -20
Divide both sides by -5;
-5x/-5 = -20/-5
x = 4
hence the value of x is 4
How many different three-digit numbers can be written using digits from the set 5, 6, 7, 8, 9 without any repeating digits?A. 625B. 20C. 120D. 60
Given:
The given numbers are 5,6,7,8,9.
Required:
Find the way so three-digit numbers can be written using digits from the sets 5, 6, 7, 8, 9 without any repeating digits.
Explanation:
Let n is the total number then the way to write m digits number is given by the formula:
[tex]A(n,m)=\frac{n!}{(n-m)!}[/tex]So the way to write 3 digits numbers are:
[tex]\begin{gathered} A(5,3)=\frac{5!}{(5-3)!} \\ =\frac{5!}{2!} \\ =5\times4\times3 \\ =60 \end{gathered}[/tex]Final Answer:
Option D is the correct answer.
Yesterday, Alan had k baseball cards. Today, he gave 19 away. Using k, write an expression for the number of cards Alan has left.
Answer:
k-19
Step-by-step explanation:
If Alan had k baseball card and gave 19 away then he would have 19 less then k
Answer:
K - 19= X
Step-by-step explanation:
I hope this helps!
Alision has an interest in entomology, the study of insects. Her collection of insects from around the world includes the four specimens shown in the table below.
we know that
the mass of Alison's Emperor Scorpio is
[tex]2^{-5}=(\frac{1}{2})^5=\frac{1}{2^5}=\frac{1}{32}\text{ kg}[/tex]The answer is the second optionIf the formula x=1/n, is used to find the mean of the following sample, what is the value of n? 2, 63, 88, 10, 72, 99, 38, 19
Given:
The formula is:
[tex]x=\frac{1}{n}\sum_{i=1}^nx_i[/tex]Series is:
[tex]2,63,88,10,72,99,38,19[/tex]Find-:
The value of "n"
Explanation-:
In the given formula "n" represent the number of member in a series.
Given series is:
[tex]2,63,88,10,72,99,38,19[/tex]The number of members is:
The members are 8.
So the value of "n" is:
[tex]n=8[/tex]The value of "n" is 8.
Answer: The answer to this problem is 6
Step-by-step explanation: i took the quiz, this is the correct answer.
