The derivatives for this problem are given as follows:
a) [tex]f^{\prime}(x) = -4\sin{x} + \frac{1}{x + 1}[/tex]
b) [tex]f^{\prime}(x) = \sec{x}\tan^{2}{x} + \sec^3{x}[/tex].
What is the derivative of the sum?The derivative of the sum is the sum of the derivatives.
In this problem, the function is:
[tex]f(x) = 4\cos{x} + \ln{(x + 1)}[/tex]
Using a derivative table for the derivatives of the cosine and the ln, the derivative of the function is:
[tex]f^{\prime}(x) = (4\cos{x})^{\prime} + (\ln{(x + 1)})^{\prime}[/tex]
[tex]f^{\prime}(x) = -4\sin{x} + \frac{1}{x + 1}[/tex]
What is the product rule?
The derivative of the product is given as follows:
[tex](f(x) \times g(x))^{\prime} = f^{\prime}(x)g(x) + g^{\prime}(x)f(x)[/tex]
In this problem, we have that:
[tex]f(x) = \sec{x}, f^{\prime}(x) = \sec{x}\tan{x}[/tex].[tex]g(x) = \tan{x}, f^{\prime}(x) = \sec^2{x}[/tex].Hence the derivative is:
[tex]f^{\prime}(x) = \sec{x}\tan^{2}{x} + \sec^3{x}[/tex].
More can be learned about derivatives at https://brainly.com/question/2256078
#SPJ1
A man walks to a coffee shop which is 4 km from his house in 20 minutes. Again, he walks to another shop at the same rate, and the total distance covered by him is 10 km in 50 minutes. What is his speed between the coffee shop and the other shop?
a. 10 km/hr
b. 8 km/hr
c. 12 km/hr
d. 6 km/hr
Answer:
c. 12km/hr
Step-by-step explanation:
Speed = distance/time
Coffee shop: Divide distance traveled by time taken to get the speed in km/min, then convert minutes to hours, and finally simplify to calculate the speed in km/hr
4km/20min * 60min/1hr = 240km/20hr = 12km/1hr = 12km/hr
Other shop: Same task, in the question it already says he is traveling at the same rate so this is only useful to check your answer
10km/50min * 60min/1hr = 600km/50min = 12km/1hr = 12km/hr
Does anyone know how to do this please help
18 + 5 + 23=46
Step-by-step explanation:
Answer:
1238
Step-by-step explanation:
solve for x
A:10 B:14.5 C:20 D:6÷3
By applying Cathetus theorem, the value of x is equal to 10 units.
How to determine the value of x?In order to determine the value of x, we would apply Cathetus theorem (leg rule), which states that each leg of a right-angled triangle is the geometric mean that's directly proportional between the hypotenuse and the part of the hypotenuse that's directly below the leg.
In this context, we have:
x² = m × a
x² = (21 + 4) × 4
x² = 25 × 4
x² = 100
x = √100
x = 10 units.
Read more on Cathetus theorem here: https://brainly.com/question/11357448
#SPJ1
The student council members are selling tickets to a school performance. Tickets are $10 for adults, a, and $5 for students, s, and they expect that twice as many students as adults will attend. Their goal is to earn $1500 from ticket sales.
Answer:
How about 100 adults and 100 students?
Step-by-step explanation:
Could you respond?
help me solve this need help asap
Answer:
(-5-5x)/(4x+3
Step-by-step explanation:
Replace x with y to get (-3y-5)/(4y+5). Solve for y to get (-5-5x)/(4x+3).
I need help with this please
There are 36 possible combinations that can occur when 2 dice are rolled. For the sake of this question, we'll count instances where dice 1 = 3/dice 2 = 2 and dice 1 = 2/dice 2 = 3.
Now, let's think about all of the possible ways a total of 5 could be rolled.
1 + 4
2 + 3
3 + 2
4 + 1
That's 4 possibilities to roll a total of 5 out of 36 possible outcomes.
4 / 36 = ? / 180
---Now, we need to use a proportion in order to figure out the possibilities out of 180.
36x = 720
x = 20
If you rolled a pair of fair dice 180 times, you would expect to roll a total of 5, 20 times.
Hope this helps!
Find the surface of the rectangular solid
Answer: 80.28 square feet
Step-by-step explanation:
[tex]2(6.1\cdot 3+3\cdot 2.4+2.4 \cdot 6.1)=80.28[/tex]
find the midpoint of the segment with endpoints at (-2,1) and (0,9) using (x1+x2,y1+y2)
Answer:
(-1, 5)
Step-by-step explanation:
Midpoint between two points
[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]
Define the endpoints:
[tex]\textsf{let}\:(x_1,y_1)=(-2,1)[/tex][tex]\textsf{let}\:(x_2,y_2)=(0,9)[/tex]Substitute the defined points into the formula:
[tex]\begin{aligned}\implies \textsf{Midpoint} & =\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\\\\ & =\left(\dfrac{0+(-2)}{2},\dfrac{9+1}{2}\right)\\\\& =\left(\dfrac{-2}{2},\dfrac{10}{2}\right)\\\\& =\left(-1,5\right)\end{aligned}[/tex]
Therefore, the midpoint of the segment with endpoints (-2, 1) and (0, 9) is (-1, 5).
Find the value of y.
A. 4
B. 6
C. 10
D. 12
Answer:
y=12
Step-by-step explanation:
30,60,90 triangle
8*rad3=8rad3
8rad3/2=4rad3
4rad3*rad3=12
HELP PLSSS WILL GIVE BRAINLIEST PLSSSS
Houa works at an electronics store as a salesperson. Houa earns a 4% commission on the total dollar amount of all phone sales she makes, and earns a 5% commission on all computer sales. Houa had $600 more in computer sales than in phone sales and earned a total of $129 in commission. Write a system of equations that could be used to determine the dollar amount of phone sales Houa made and the dollar amount of computer sales she made. Define the variables that you use to write the system.
One of the two equations required in the system of equations needed to determine the dollar amount of phone and computer sales Houa made is y = x + 600.
How do we write the system of equations?Let x represents the dollar amount of phone sales Houa made, and y represents the dollar amount of computer sales she made.
Therefore, a system of equations that could be used to determine x and y can be written as follows:
y = x + 600 ........................................................... (1)
0.04x + 0.05y = 129 ......................................... (2)
Learn more about the system of equations here: https://brainly.com/question/21620502.
#SPJ1
You are flying a kite and have let out 30 feet of string but it got caught in an 8ft tree. What is the angle of elevation to the location of the kite? Show your work finding the angle of elevation and state the measure of the angle. You are flying a kite and have let out 30 feet of string but it got caught in an 8ft tree . What is the angle of elevation to the location of the kite ? Show your work finding the angle of elevation and state the measure of the angle . PLEASE SHOW ALL WORK !!!
Answer:
use a sin cos tan calculator.
Step-by-step explanation
on calculator
2nd tan
tan x = 30/8
there's ur answer
What is the quadratic regression equation that fits these data?
X
-4
-3
-2
-1
0
1
2
3
4
O A. ý = 0.82x2 + 0.78x+7.23
OB. 9=1642 +1.24x+8.08
O c. y = 2.13x² +0.13x+ 6.39
O D. = 16.76 1.02*
40
28
10
8
7
10
16
26
40
Using a calculator, the quadratic regression equation that fits the data is:
C. y = 2.13x² + 0.13x + 6.39
How to find the equation of regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
In this problem, the points are:
(-4,40), (-3,28), (-2, 10), (-1, 8), (0,7), (1,10), (2,16), (3,26), (4,40).
Hence the equation is:
C. y = 2.13x² + 0.13x + 6.39
More can be learned about quadratic regression at https://brainly.com/question/24028025
#SPJ1
Whats the correct answer answer asap
The environmental threat in Japan and Korea that threatens food security is: B. soil erosion.
What is Soil Erosion?Soil erosion can be defined as the washing away of the top soil that supports plants growth and also contains vital nutrients for plants growth.
Crops are grown majorly on land. The disruption of soil nutrients by soil erosion poses a serious environmental threat to food security in both Japan and Korea. Therefore, the answer is: B. soil erosion.
Learn more about soil erosion on:
https://brainly.com/question/17905503
#SPJ1
Points out
1.00
P Flag
question.
Instructions: Given the preimage and image, find the dilation scale factor. Use the forward slash (i.e.
"/") for all fractions (e.g. -1/2 is the same as
-6 -5
Scale Factor:
5
J'
-3 -2 -1
P
KT
3
T
4
5 6
The dilation scale factor used to form polygon K'T'P'J' from polygon KTPJ is 1/2
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Dilation is the increase or decrease in size of a figure by a scale factor.
The scale factor of the image = K'T'/KT = 1/2 ÷ 1 = 1/2
The dilation scale factor used to form polygon K'T'P'J' from polygon KTPJ is 1/2
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
If p = the price of a pair of basketball shoes, which algebraic expression
represents the phrase below?
4
the difference of the price of the shoes and 5 dollars
A. 5p
B. p+5
c. ff
D. p-5
Hello :
The difference of the price of the shoes and 5 dollars is p - 5.
Consider the equation y = 12 – 3x.
Which of the following is a graph of this equation?
Answer:
second graph
Step-by-step explanation:
looking at the y intercept. 12 is y int
Answer:
Second line
Step-by-step explanation:
our equation rearranged is y=-3x+12
meaning that y-intercept is 12, that is where the line cuts the y axis
we find that the second line cuts the y axis around that 12 therefore it is the most relevant line here
Given the functions f and g below, find f(g(0)).
After calculation, the composite function f(g(0)) returns the value 2 as the response.
Given, the values of the functions are:
f(x) = √₋x₊1 and g(x) = ₋x₋3
we need to find f(g(0)) = ?
F of g of x is another name for a composite function. Normal representations include f(g(x)) or (f g)(x), which denote that x = g(x) should be used in place of f(x). While the function g (x) is referred to as an inner function, the function f (x) is referred to as an outer function.
It means that every instance of an x in the function f is replaced with the function g(x).
∵ g(x) = ₋x₋3 so we can substitute this in the following expression:
g(0) = -(0) ₋ 3
g(0) = ₋3
Now in place of g(0) we can write ₋3, hence the changed expression becomes:
f(g(0)) = f(₋3)
= √₋(₋3)₊1
= √4
∴ f(g(0)) = 2
Hence we get the calculated function value as 2.
Learn more about "Functions" here-
brainly.com/question/6561461
#SPJ10
The amount of syrup that people put on their pancakes is normally distributed with mean 60 mL and standard deviation 11 mL. Suppose that 12 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible.
What is the distribution of
X
?
X
~ N(
,
)
What is the distribution of
¯
x
?
¯
x
~ N(
,
)
If a single randomly selected individual is observed, find the probability that this person consumes is between 59.3 mL and 61.2 mL.
For the group of 12 pancake eaters, find the probability that the average amount of syrup is between 59.3 mL and 61.2 mL.
For part d), is the assumption that the distribution is normal necessary? YesNo
Using the normal distribution and the central limit theorem, we have that:
The distribution of X is [tex]X \approx N(60,11)[/tex].The distribution of [tex]\bar{X}[/tex] is [tex]\bar{X} \approx (60,3.1754)[/tex].0.0637 = 6.37% probability that a single person consumes between 59.3 mL and 61.2 mL.0.2351 = 23.51% probability that the sample mean of the consumption of 12 people is between 59.3 mL and 61.2 mL. Since the sample size is less than 30, a normal distribution has to be assumed.Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem, the parameters are given as follows:
[tex]\mu = 60, \sigma = 11, n = 12, s = \frac{11}{\sqrt{12}} = 3.1754[/tex].
Hence:
The distribution of X is [tex]X \approx N(60,11)[/tex].The distribution of [tex]\bar{X}[/tex] is [tex]\bar{X} \approx (60,3.1754)[/tex].The probabilities are given by the p-value of Z when X = 61.2 subtracted by the p-value of Z when X = 59.3, hence, for a single individual:
X = 61.2:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{61.2 - 60}{11}[/tex]
Z = 0.11
Z = 0.11 has a p-value of 0.5398.
X = 59.3:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{59.3 - 60}{11}[/tex]
Z = -0.06
Z = -0.06 has a p-value of 0.4761.
0.5398 - 0.4761 = 0.0637.
0.0637 = 6.37% probability that a single person consumes between 59.3 mL and 61.2 mL.
For the sample of 12, we have that:
X = 61.2:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{61.2 - 60}{3.1754}[/tex]
Z = 0.38
Z = 0.38 has a p-value of 0.6480.
X = 59.3:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{59.3 - 60}{3.1754}[/tex]
Z = -0.22
Z = -0.22 has a p-value of 0.4129.
0.6480 - 0.4129 = 0.2351 = 23.51% probability that the sample mean of the consumption of 12 people is between 59.3 mL and 61.2 mL. Since the sample size is less than 30, a normal distribution has to be assumed.
More can be learned about the normal distribution and the central limit theorem at https://brainly.com/question/24188986
#SPJ1
Need help with number 9 and number 10
Answer:
9. 3 acute angles
10: a) Acute Isosceles
b) Acute Scalene
Step-by-step explanation:
9: Sum of Interior angle theorem: Sum of the interior angles of a Triangle = 180°
An Acute angle is a angle that is less than 90°
the sum of the two acute angles must be less than 180°
The base angles of an isosceles triangle are congruent.
So For example,
the base angles of the isosceles are ∠1 and ∠2
Lets make the three angle measure closer:
if ∠1 = 46° then ∠2 also have to be 46° and ∠3 = 88°
all three angle are less than 90° and two angles are congruent.
Which expression is equivalent to (43) (
what is the following product?
(2√7 + 3√6) (5√5 +4√3)?
Select the correct answer. Suppose that 3 boys and 2 girls go to the theatre and occupy 5 seats in a row. In how many ways can they be seated if all 3 boys sit together?
Answer:
Possibly 3
Step-by-step explanation:
Lets say
g=girls
b=boys
1st option: gbbbg
2nd option: bbbgg
3rd option: ggbbb
let A and B sets. when do we say set A is equal to set B
Answer:
We say sets A and B are equal, and write A = B if they have exactly the same elements.
Step-by-step explanation:
Answer:
When set A is equal to set B. It is denoted as A = B.
Have a nice day!
Complete the table of inputs and outputs for the given function. F(x)= -5(x+7)
The table of inputs that satisfy the given function is (-2, 25), (-1, -30), (0, 35), (1, -40) and (2, -45).
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Given the function f(x) = -5(x + 7)
When x = -2; f(-2) = -5(-2 + 7) = -25
When x = -1; f(-1) = -5(-1 + 7) = -30
When x = 0; f(0) = -5(0 + 7) = -35
When x = 1; f(1) = -5(1 + 7) = -40
When x = 2; f(2) = -5(2 + 7) = -45
The table of inputs that satisfy the given function is (-2, 25), (-1, -30), (0, 35), (1, -40) and (2, -45).
Find out more on equation at: https://brainly.com/question/13763238
#SPJ1
What is the approximate area of a circle with a radius of 10 in?
[tex]\huge\boxed{\textsf{A.}\ 78.5\ \text{in}^2}[/tex]
Correction to your question text: diameter, not radius.
The area of a circle is given by:
[tex]A=\pi r^2[/tex]
The radius is half of the diameter.
[tex]A=\pi\cdot\left(\dfrac{10}{2}\right)^2[/tex]
Substitute and solve.
[tex]\begin{aligned}A&=\pi\cdot\left(\frac{10}{2}\right)^2\\&=\pi\cdot5^2\\&=\pi\cdot25\\&\approx\boxed{78.5}\end{aligned}[/tex]
What set of transformations could be applied to rectangle ABCD to create A″B″C″D″? 'Rectangle formed by ordered pairs A at negative 4, 2, B at negative 4, 1, C at negative 1, 1, D at negative 1, 2. Second rectangle formed by ordered pairs A double prime at 2, negative 4, B double prime 1, negative 4, C double prime at 1, negative 1, D double prime at 2, negative 1. Reflected over the x‒axis and rotated 180° Reflected over the y-axis and rotated 180° Reflected over the x‒axis and rotated 90° counterclockwise Reflected over the y-axis and rotated 90° counterclockwise
The set of transformations that could be applied to ABCD, to create A″B″C″D″ is a reflection over the y-axis, followed by a rotation of 180°
What is reflection?"It is a geometric transformation where all the points of an object are reflected on the line of reflection."
For the given question,
The Rectangle ABCD is formed by ordered pairs A at (-4, 2), B at (-4, 1), C at (-1, 1), D at (-1, 2)
The Rectangle A″B″C″D″ is formed by ordered pairs A" at (-4, -2), B" at (-4, -1), C" at (-1, -1) and D" at (-1, -2)
We can observe that the coordinates of ABCD are of the form (-x, y) where x, and y, are positive numbers
The form of the ordered pair of the vertices of the A″B″C″D″ will be (-x, -y)
The coordinates of the point (-x, y) after a reflection over the y-axis would be of the form (x, y)
And after rotation of 180°, the coordinates would be (-x -y).
Hence, the set of transformations that could be applied to ABCD, to create A″B″C″D″ is a reflection over the y-axis, followed by a rotation of 180°.
Learn more about geometric transformations here:
brainly.com/question/15577335
#SPJ1
Firm X is a monopolist with marginal cost of $37/unit. If elasticity of demand is -9, use the markup formula to determine the price Firm X should charge to maximize profit.
Step-by-step explanation:
hggggggggggggggggggggg
Solve the system of equations. Type in all points of intersection for the two functions and round to the nearest tenth if necessary f(x)=sr5x+25-1 g(x)=x^2-2x-3
The solution to the system of equations are (-1.7, 3.1) and (4.1, 5.8)
How to solve the system of equation?The equations are given as:
[tex]f(x)=\sqrt{5x+25}-1[/tex]
[tex]g(x)=x^2-2x-3[/tex]
Next, we plot the graph of the equations (see attachment)
From the attached graph, we can see that both equations intersect at (-1.7, 3.1) and (4.1, 5.8)
Hence, the solution to the system of equations are (-1.7, 3.1) and (4.1, 5.8)
Read more about system of equations at:
https://brainly.com/question/12895249
#SPJ1
Need help please with number 2!!!
Answer:
Step-by-step explanation:
The length of a rectangle is four times its width. The perimeter is 100 cm. What is the number of square centimeters in the area of the rectangle?
let width be 'x'
according to the question,
length = 4x
perimeter = 100 cm
we know ,
perimeter of rectangle = 2(l+b)
100= 2(4x+x)
100= 10x
x= 10
then length = 4x = 4×10= 40
and , area of rectangle = l×b
= 40 × 10 = 400
area of rectangle is 400cm
Answer:
Step-by-step explanation:
let width=x
length=4x
2(x+4x)=100
2×5x=100
x=100/10=10
width=10 cm
length=4×10=40 cm
area=l×b=40×10=400 cm²
The table shows the size of outdoor decks (x) in square feet, and the estimated dollar cost to construct them (y).
y
xy
100
600
10,000
60,000
144
850
20,736
122,400
225
1,300
50,625
292,500
324
1,900
104,976
615,600
400
2,300
160,000
920,000
Σχ=1,193 | Σy=6,950 | Ex?=346,337 | Σxy=2,010,500
Which regression equation correctly models the data?
X
xy=5.83x-1.04
y = 5.83x + 17
y = 5.71x + 29
y
= 5.71x + 27.6
Submitted
The regression equation of the table is y = 5.71x + 27.6
How to estimate the regression equation?From the table of values, we have the following parameters:
[tex]\sum x = 1193[/tex]
[tex]\sum y = 6950[/tex]
[tex]\sum x^2 = 346337[/tex]
[tex]\sum xy = 2010500[/tex]
Calculate A using
[tex]A = \frac{\sum y * \sum x^2 - \sum x * \sum xy}{n\sum x^2 - (\sum x)^2}[/tex]
This gives
[tex]A = \frac{6950 * 346337 - 1193 * 2010500}{5 * 346337 - (1193)^2}[/tex]
Evaluate
[tex]A = \frac{8515650}{308436}[/tex]
Divide
A = 27.6
Calculate B using
[tex]B = \frac{n\sum xy - \sum x * \sum y}{n\sum x^2 - (\sum x)^2}[/tex]
This gives
[tex]B = \frac{5 * 2010500 - 1193 * 6950}{5 * 346337 - (1193)^2}[/tex]
Evaluate
[tex]B = \frac{1761150}{308436}[/tex]
Divide
B = 5.71
The regression equation is represented as:
y = Bx + A
So, we have
y = 5.71x + 27.6
Hence, the regression equation of the table is y = 5.71x + 27.6
Read more about regression equation at:
https://brainly.com/question/14184702
#SPJ1