Answer:
a) The function is constantly increasing and is never decreasing
b) There is no local maximum or local minimum.
Step-by-step explanation:
To find the intervals of increasing and decreasing, we can start by finding the answers to part b, which is to find the local maximums and minimums. We do this by taking the derivatives of the equation.
f(x) = ln(x^4 + 27)
f'(x) = 1/(x^2 + 27)
Now we take the derivative and solve for zero to find the local max and mins.
f'(x) = 1/(x^2 + 27)
0 = 1/(x^2 + 27)
Since this function can never be equal to one, we know that there are no local maximums or minimums. This also lets us know that this function will constantly be increasing.
To find the interval of increase and decrease, we need to find where the derivative of the function is positive and negative, respectively. The derivative is positive when x > 0 and negative when x < 0.
Explanation:To find the interval of increase and decrease, we need to find where the derivative of the function is positive and negative, respectively. The derivative of f(x) = ln(x^4 + 27) can be found using the chain rule: f'(x) = (4x^3)/(x^4 + 27).
The derivative is positive when (4x^3)/(x^4 + 27) > 0, which occurs when x > 0.
The derivative is negative when (4x^3)/(x^4 + 27) < 0, which occurs when x < 0.
Therefore, the interval of increase is (0, infinity) and the interval of decrease is (-infinity, 0).
Learn more about Interval of Increase and Decrease here:https://brainly.com/question/11051767
#SPJ3
A community organization surveyed 40 members to determine if they world vote yes or no for the proposition a in the next election
Twelve of the surveyed members said they would vote yes there are a total of 240 members in the community organization how many members are expected to vote yes
Answer:
72 voters
Step-by-step explanation:
Total surveyed members: 40
Total members with a yes vote: 12
Percentage of the voters (voting yes): [tex]\frac{12}{40} * 100 = 30%[/tex]
From analysis, it is observed that 30% of the voters are expected to vote yes in a sample.
Therefore, the number of voters expected to vote yes out of 240 are: 30% of 240
=> [tex]\frac{30}{100} * 240 = 72[/tex]
Answer:
72 voters
Step-by-step explanation:
Two more than a number is the same as 16 decreased by 6 times the number. Find the number .
Baily spends 3 hours each week playing soccer.This is two times the amount of time she spends working out in the weight room.How much time does she spend in the weight room each week?
A. 2w=3
B. 2+w=3
C. w=2.3
D. 3w=2
The correct equation representing the time Bailey spends in the weight room each week is 2w=3. By solving this equation, we find Bailey spends 1.5 hours in the weight room each week.
Explanation:The question tells us that Baily spends 3 hours each week playing soccer and this is two times the amount of time she spends working out in the weight room. We can represent the time she spends in the weight room as w. So, the question gives us the equation 2w=3. Since 2 times what number gives us 3, we can solve for w by dividing both sides of the equation by 2. When we do this, we have w=3/2, which means Baily spends 1.5 hours in the weight room each week.
Learn more about Solving Equations here:https://brainly.com/question/14410653
#SPJ3
Find the limit. use l'hospital's rule where appropriate. if there is a more elementary method, consider using it. lim x → (π/2)+ cos x 1 − sin x
Looks like the limit is
[tex]\displaystyle\lim_{x\to\pi/2^+}\frac{\cos x}{1-\sin x}[/tex]
which yields an indeterminate form [tex]\dfrac00[/tex]. Rewriting as
[tex]\dfrac{\cos x(1+\sinx)}{(1-\sin x)(1+\sin x)}=\dfrac{\cos x(1+\sin x)}{1-\sin^2x}=\dfrac{1+\sin x}{\cos x}[/tex]
we see the numerator approaches 1 + 1 = 2, while the denominator approaches 0. Since [tex]\cos x<0[/tex] for [tex]x[/tex] near [tex]\dfrac\pi2[/tex] with [tex]x>\dfrac\pi2[/tex], the limit is [tex]-\infty[/tex].
Vector u has a magnitude of 5 units, and vector v has a magnitude of 4 units. Which of these values are possible for the magnitude of u + v?
More than one answer is possible
A. 1
B. 9
C. 11
D. 13
Decide if the function is an exponential function. If it is state the initial value and the base y=x^2
Answer:
B
Step-by-step explanation:
The exponential function is the function of the form
[tex]y=a\cdot b^x,[/tex]
where [tex]b[/tex] is the base and [tex]a[/tex] is the initial value.
The function [tex]y=x^2[/tex] is the quadratic function, which cannot be represented as [tex]y=a\cdot b^x.[/tex] Thus, this function is not exponential.
Answer:
The answer is B.
Step-by-step explanation:
10% for infomercials in a 24 got day, how many hours of infomercials are there
Answer:
40 yes it is i got 100 on this
Step-by-step explanation:
There are 2.4 hours of infomercials in a 24-hour day if they account for 10% of the daily broadcast.
Explanation:The question asks us to calculate the amount of time designated for infomercials in a 24-hour day if they make up 10% of the day's broadcast. To find the answer, we can use the basic percentage calculation.
To calculate 10% of a day, we need to know that a day has 24 hours. So 10% of 24 hours is calculated as follows:
(10/100) × 24 = 2.4
Therefore, there are 2.4 hours of infomercials in a 24-hour day.
The senior class of a high school needs to elect a new class president. Ten people want to run for office, but only four are allowed to so the class needs to determine which four people can run.
They randomly select 5 people from each of the ten homerooms and have them select two people out of the ten that they would like to run for office. The table shows the results.
Which four people should be on the ballot to run for office from the results of the survey?
A) George Smith, Jamal Brown, Lucas Hernandez, and Lucy Coen
B) Walter Heyes, Laurie Langston, George Smith, and Jamal Brown
C) Michael Mast, Joel Friedburg, Alice King, and Laurie Langston
D) George Smith, Laurie Langston, Jamal Brown, and Lucas Hernandez
Answer:
A
Step-by-step explanation:
Add up the votes for each person and order them greatest to least and pick the top 4.
The value of [tex]\sqrt[3]{x}[/tex] where x is an integer, is located between 6 and 7 on the number line. What could be the value of x?
[tex]\displaystyle\\6<\sqrt[3]{x}<7~~~\Big|^3\\\\6^3<\Big(\sqrt[3]{x}\Big)^3<7^3\\\\216<x<343\\\\\boxed{x\in\{217,~218,~219,~220,~\cdots~,~340,~341,~342\}}[/tex]
.
Answer:
Step-by-step explanation:
The value would be 6.5
X-treme Sports has skateboards at a 24% discount. Find the sale price of a $384 skateboard using percent paid.
To find the sale price of a $384 skateboard with a 24% discount, convert the paid percentage to a decimal (76% to 0.76) and multiply with the original price, resulting in a sale price of $291.84.
Explanation:To calculate the sale price of a skateboard originally priced at $384 with a 24% discount, we first need to determine what percentage of the original price will actually be paid. Since the discount is 24%, that means 76% of the original price will be paid (100% - 24% = 76%). To convert this percentage to a decimal, we divide by 100, getting 0.76.
Next, we find the sale price by multiplying the original price by the decimal form of the percentage paid:
$384 × 0.76 = $291.84 as the sale price of the skateboard.
For the given line segment, write the equation of the perpendicular bisector.
To find the equation of the perpendicular bisector, find the midpoint of the line segment and determine the slope of the perpendicular line.
Explanation:To find the equation of the perpendicular bisector of a given line segment, we need to find the midpoint of the segment and then determine the slope of the perpendicular line. Let's denote the coordinates of the endpoints of the line segment as (x1, y1) and (x2, y2). The midpoint of the segment can be found using the formula:
M = ((x1 + x2) / 2, (y1 + y2) / 2)
The slope of the perpendicular line can be found using the negative reciprocal of the slope of the given line segment:
Perpendicular slope = -1 / slope of given line segment
Once we have the midpoint and the slope of the perpendicular line, we can use the point-slope form of a linear equation to write the equation of the perpendicular bisector:
y - y1 = perpendicular slope * (x - x1)
Find the area of a circle with a circumference of \blueD{18.84}18.84start color blueD, 18, point, 84, end color blueD units.
Answer:
28.26
Step-by-step explanation:
The circumference of a circle is the distance around the edge of the circle. To find the circumference, we use the formula C = 2πr. The area of the circle is the amount inside the circle and is found using A = πr². Substitute the relevant values in each situation into the formulas to find the circumference and/or area.
Substitute C = 18.84 and solve for r. Then substitute r into the area formula.
C = 2πr
18.84 = 2πr
3 = r
A = πr² = π(3)² = 28.26
Answer:
28.26
Step-by-step explanation:
What is the volume of a sphere with a radius of 4 centimeters? (Use 3.14 for π.)
The volume of a sphere with a radius of 4 centimeters is calculated using the formula V = (4/3)πr³. Substituting 4 cm for the radius and 3.14 for π, the volume is approximately 268 cubic centimeters.
To calculate the volume of a sphere with a given radius, you can use the formula V = (4/3)πr³, where V represents the volume and r is the radius. In our case, the radius is 4 centimeters. Substituting the values into the formula gives us V = (4/3) * 3.14 * (4 cm)³.
Performing the calculation: V = (4/3) * 3.14 * 64 cm³ = 267.94666666666666 cm³. Therefore, the volume of the sphere is approximately 268 cm³ when rounded to a whole number.
Please help me
Find the mode of the following data set
The mode is the number that appears most often.
Looking at the chart, there are two 1's on the right side, so the mode would be 31
2x - y = 5 3x + 2y = 4 Solve the system of equations. A) (3, 1) B) (0, 2) C) (2, -1) D) ( 9 7 , 17 7 )
Solving the system of equation, we get Option (C) (2,-1).
How to solve the given set of equations ?The equations given are 2x - y = 5 and 3x + 2y = 4.
To find the point which solves the two equation, we have to satisfy the given x and y coordinates of the point on the given two equations.
Checking all the other Options, it does not satisfies except Option (C).
Checking the point (2,-1) on the first equation 2x - y = 5 , we get 5 in the left hand side of the equation.
Again checking the point (2,-1) on the second equation 3x + 2y = 4 , we get 4 in the left hand side of the equation.
Therefore the coordinates (2,-1) (Option C) satisfies both the equation which is the required solution.
To learn more about solving system of equation, refer -
https://brainly.com/question/7808225
#SPJ2
There are 70 campers and 6 instructors going to camp loon. If the vans hold 8 people,how many vans do they need?
They need about 9 vans.
Write and equation of the translated or rotated graph in general form (picture below)
Answer:
Option b
Step-by-step explanation:
The equation [tex]4x ^ 2 + 5y ^ 2 = 20[/tex] has center in (0,0).
But the transformation [tex]T(5, -6)[/tex] shifts the center of the equation to the point (5, -6).
Therefore, when applying [tex]T(5, -6)[/tex] we will have the following equation translated.
[tex]4(x-5) ^ 2 + 5(y - (-6)) ^ 2 = 20[/tex].
Simplifying we have:
[tex]4(x-5) ^ 2 + 5(y + 6) ^ 2 = 20[/tex]
Now we expand [tex](x-5) ^ 2[/tex] and [tex](y + 6) ^ 2[/tex]
[tex]4(x ^ 2 -10x +25) + 5(y ^ 2 + 12y +36) = 20\\\\4x ^ 2 -40x + 100 + 5y ^ 2 + 60y + 180 = 20\\\\4x ^ 2 + 5y ^ 2 -40x + 60y +260 = 0[/tex]
The equation of a circle has the form
[tex]h(x-a) ^ 2 + q(y-b) ^ 2 = r[/tex]
For h = 1 and q = 1.
If [tex]h \neq 1[/tex] and [tex]q\neq 1[/tex] then the graph becomes an ellipse.
In this problem h = 4 and q = 5 therefore the figure is an ellipse
Can someone help me please
Answer:
8Step-by-step explanation:
[tex]\text{The quadratic equation:}\ ax^2+bx+c=0.\\\\\text{We have}\ x^2-4x+2=0\\\\a=1,\ b=-4,\ c=2\\\\\text{Substitute to}\ b^2-4ac:\\\\b^2-4ac=(-4)^2-4(1)(2)=16-8=8[/tex]
Ello mates how are yall this fine time of day? what is 2+2?
Answer:
2+2 is 4
Step-by-step explanation:
Answer:
im doing just find what about you mate
Step-by-step explanation:the answer is 4
What are the solution of x^2-2x+17=0
Answer:
x = 1 - 4i or x = 1 + 4iStep-by-step explanation:
[tex]x^2-2x+17=0\qquad\text{subtract 17 from both sides}\\\\x^2-2x=-17\\\\x^2-2(x)(1)=-17\qquad\text{add}\ 1^2\ \text{to both sides}\\\\x^2-2(x)(1)+1^2=-17+1^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(x-1)^2=-17+1\\\\(x-1)^2=-16<0\Rightarrow\boxed{\text{NO REAL SOLUTION}}\ because\ x^2\geq0\\\\\text{In the set of complex numbers}\\\\i=\sqrt{-1}\\\\(x-1)^2=-16\iff x-1=\pm\sqrt{-16}\\\\x-1=-\sqrt{(16)(-1)}\ \vee\ x-1=\sqrt{(16)(-1)}\\\\x-1=-\sqrt{16}\cdot\sqrt{-1}\ \vee\ x-1=\sqrt{16}\cdot\sqrt{-1)[/tex]
[tex]x-1=-4i\ \vee\ x-1=4i\qquad\text{add 1 to both sides}\\\\x=1-4i\ \vee\ x=1+4i[/tex]
A bus travels 36 miles in 45 minutes. How many miles will it travel in 60 minutes at this rate?
Answer:
48 miles
Step-by-step explanation:
At an amusement park, the probability that a child eats popcorn and cotton candy is 0.58. The probability that a child eats popcorn is 0.69 and the probability that a child eats cotton candy is 0.87. What is the probability (rounded to the nearest hundredth) that a child eats popcorn given that the child has already eaten cotton candy?
Hint:
P(A|B)=P(A∩B) / P(B)
0.84
0.67
0.79
0.40
Answer:
The correct answer option is 0.67.
Step-by-step explanation:
We are given that the probability that a child eats popcorn and cotton candy is 0.58, probability that a child eats popcorn is 0.69 and the probability that a child eats cotton candy is 0.87.
We are to find the probability that a child eats popcorn given that the child has already eaten cotton candy.
P (eats popcorn and has already eaten cotton candy) = [tex]\frac{0.58}{0.87}[/tex] = 0.67
Wilson Green sells home security systems. He earns an 11 percent commission on every system he sells. Wilson’s sales for this month totaled $4265.00. What is Wilson’s commission?
Multiply total sales by 11%
4265 x 0.11 = 469.15
His commission was $469.15
Final answer:
Wilson Green's commission is calculated by multiplying his total sales of $4265.00 by his commission rate of 11 percent, which equals $469.15.
Explanation:
Wilson Green earns an 11 percent commission on every home security system he sells. For the month, his total sales amounted to $4265.00. To calculate Wilson's commission, we need to find 11 percent of $4265.00.
The formula for calculating the commission is:
Commission = Total Sales × Commission Rate
By plugging in the numbers:
Commission = $4265.00 × 0.11
Now, let's do the math:
Commission = $469.15
Therefore, Wilson's commission for the month is $469.15
If a flowering tree is cared for properly, the number of blossoms produced on the tree will exponentially increase until the tree reaches maturity. Which graph could show y, the number of blossoms expected on a flowering tree, for each year after the young tree is planted, x?
Answer:
2nd graph
Step-by-step explanation:
Exponential increase will be a graph that increase all throughout and the rate of increase "increases" with age.
We can rule out first graph because if you draw smooth curve along the dots, it shows increase, then decrease.We can rule out third graph because it is increasing BUT not exponentially, rather, at a constant rate.We can rule out fourth graph because it is decreasing (exponentially).The 2nd graph is correct because it shown "increase" as well as "exponential" increase (the rate of increase increases).
Answer: 2nd graph
Your answer is going to be the second graph
An angle represents 1/12 of a circle. Use the numbers to show how to find the measure of the angle in degrees 1/12=1/12x?/?=360
Answer:
The measure of the angle is [tex]30\°[/tex]
Step-by-step explanation:
Let
x-----> the measure of the angle in degrees
we know that
The measure of a complete circle is [tex]360\°[/tex]
so
by proportion
[tex]\frac{360}{1}\frac{degrees}{circle}=\frac{x}{(1/12)}\frac{degrees}{circle}[/tex]
[tex]x=\frac{1}{12}(360\°)[/tex]
[tex]x=\frac{360\°}{12}[/tex]
[tex]x=30\°[/tex]
An angle that represents 1/12 of a circle measures 30 degrees. We found this by understanding that a full circle is 360 degrees and then multiplied 1/12 by 360.
Explanation:The question is asking for the measure in degrees of an angle that represents 1/12 of a circle. As we know, a circle consists of 360 degrees next we measure the angle just like when we are measuring the angle in the sky. To find the angle, we can use a simple proportion. Since the whole circle is 360 degrees, we know that 1/12 of the circle will be equal to 1/12 of 360 degrees.
So, the calculation will be like: 1/12 x 360 = 30 degrees. Therefore, an angle that represents 1/12 of a circle measures 30 degrees.
Learn more about Angles and circles here:https://brainly.com/question/23247585
#SPJ3
Suppose y = 2x + 1 , where x and y are functions of t. (a) if dx/dt = 3, find dy/dt when x = 4. dy dt = (b) if dy/dt = 2, find dx/dt when x = 40. dx dt =
Answer:
Step-by-step explanation:
If y = 2x + 1, then dy/dt = 2(dx/dt).
If y = 2x + 1, then y = 2(40) + 1 when 40 is substituted for x. y = 81.
(a) if dx/dt = 3, find dy/dt when x = 4:
Replacing dx/dt with 3 in dy/dt = 2(dx/dt) yields dy/dt = 2(3) = 6.
(b) if dy/dt = 2, find dx/dt when x = 40:
Replacing dy/dt with 2 in dy/dt = 2(dx/dt) results in 2 = 2(dx/dt), so dx/dt must be 1.
First, you differentiate the given function. Next, apply the chain rule which states dy/dt = dy/dx * dx/dt. Substitute the known values to find dy/dt. For the second part, rearrange the chain rule to find dx/dt = dy/dt / dy/dx and substitute the known values.
Explanation:This question deals with the basic application of the chain rule in differentiation. The given function is y = 2x + 1, where both y and x are functions of t. You are supposed to determine dy/dt and dx/dt.
(a) First, differentiate y = 2x + 1 with respect to x to obtain dy/dx = 2. According to the chain rule in calculus, dy/dt = dy/dx * dx/dt. Substituting the known values from the question, we have dy/dt = 2 * 3 = 6 when x = 4.
(b) For dy/dt = 2, you need to rearrange dy/dt = dy/dx * dx/dt to find dx/dt = dy/dt / dy/dx. As dy/dx = 2, you can evaluate dx/dt = 2 / 2 = 1 when x = 40.
Learn more about Chain Rule of Differentiation here:https://brainly.com/question/27072366
#SPJ3
Solve the equation. Round to the nearest hundredth. Show work.
[tex]2e^{8x} = 1 - e^{4x}[/tex]
Answer:
The value of x = -0.17
Step-by-step explanation:
∵ [tex]2e^{8x}=1-e^{4x}[/tex]
Let [tex]e^{4x}=y[/tex]
∴ [tex]e^{8x}=y^{2}[/tex]
∴ 2y² = 1 - y
∴ 2y² + y - 1 =0 ⇒ factorize
∴ (2y - 1)(y + 1) = 0
∴ 2y - 1 = 0 ⇒ 2y = 1 ⇒ y = 1/2
∴ y + 1 = 0 ⇒ y = -1
∵ [tex]y=e^{4x}[/tex]
Note: [tex]e^{4x}=-1[/tex] ⇒ refused
([tex]e^{ax}[/tex] never gives -ve values)
∴ [tex]e^{4x}= 1/2[/tex] ⇒ insert ln in both sides
∵ [tex]ln(e)^{ax}=axln(e)=ax[/tex] ⇒ ln(e) = 1
∴ 4xln(e) = ln(1/2) ⇒ 4x = ln(1/2)
∴ x = [ln(1/2)]/4 = -0.17
An Olympic floor exercise mat has an area of 144 square meters. It's length is 12 meters.What is the shape of the mat?
Answer:
The shape of the mat is a square
Step-by-step explanation:
we know that
The area of the rectangle (An Olympic floor exercise mat) is equal to
[tex]A=LW[/tex]
we have that
[tex]A=144\ ft^{2}[/tex]
[tex]L=12\ ft[/tex]
substitute the values and solve for W
[tex]144=12W[/tex]
[tex]W=144/12=12\ ft[/tex]
so
The length is equal to the width
therefore
The shape of the mat is a square
Two numbers are between 10 and 20. Their greatest common factor is 3. Which two numbers could they be?
Answer:
12 and 15 or
12 and 18 or
15 or 18
Step-by-step explanation:
The two numbers have to both be divisible by 3, since their greatest common factor is 3. This only leaves..
12, 15, or 18 (no other numbers between 10 and 20 are divisible by 3)
The factors of 12 are: 2, 3, 4, 6, and 12
The factors of 15 are: 3, 5, and 15
The factors of 18 are: 2, 3, 6, 9, and 18
All three numbers have 3 as a greatest common factor, so we have 3 pairs of numbers they could be...
12 and 15 or
12 and 18 or
15 or 18
Answer:
15 and 18
Step-by-step explanation:
Because The number 3 is the greatest common factor of 15 and 18, and both numbers are between 10 and 20.
If 10 boxes of 10 muffins each and each muffin has 10 blueberries use it exponent to write an expression for the total number of blueberries
Answer: [tex]b=10^3[/tex]
Step-by-step explanation:
You know that there are 10 blueberries in each muffin. There are 10 muffins in each box and the total number of boxes is 10.
Then, to calculate the total number of blueberries, you need to multiply the total number of boxes by the number of muffins in each box and multiply this by the number of blueberries in each muffin.
Let be "b" the total number of blueberries. Then:
[tex]b=10*10*10[/tex]
By the Product of powers property:
[tex]a^m*a^n=a^{(m+n)}[/tex]
Then you can write the expression:
[tex]b=10^3[/tex]