Where are the minimum and maximum values for f(x) = sin x + 1 on the interval [0, 2π]?A. min:z =OB. min:x=OC. min:z =max:x= = 0, 2πOD. min:z = 0, π, 2π max: z =Reset Selectionmax: 1 =2 2max:z = 0, π, 2π
![Where Are The Minimum And Maximum Values For F(x) = Sin X + 1 On The Interval [0, 2]?A. Min:z =OB. Min:x=OC.](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/8AY2glp1vXAqLpWBiJHh5bKFtTI3QRyi.jpeg)
Answers
Given the function:
[tex]f(x)=sinx+1[/tex]Let's find the minimum and maximum values over the interval [0, 2π].
Let's first find the derivative of the function:
[tex]f^{\prime}(x)=cosx[/tex]Now set the derivative to 0 and solve for x:
[tex]\begin{gathered} cosx=0 \\ \\ \text{ Take the inverse cosine of both sides:} \\ x=cos^{-1}(0) \\ \\ x=\frac{\pi}{2} \end{gathered}[/tex]The cosine function is positive in quadrants I and IV, to find the reference angle(minimum), subtract the first solution from 2π:
[tex]\begin{gathered} x=2\pi-\frac{\pi}{2} \\ \\ x=\frac{2(2\pi)-\pi}{2} \\ \\ x=\frac{4\pi-\pi}{2} \\ \\ x=\frac{3\pi}{2} \end{gathered}[/tex]Plug in the values in the function to determine the minimum and maximum:
[tex]\begin{gathered} f(\frac{\pi}{2})=sin(\frac{\pi}{2})+1=1+1=2 \\ \\ \\ f(\frac{3\pi}{2})=sin(\frac{3\pi}{2})+1=-1+1=0 \end{gathered}[/tex]Therefore, we have the following:
Minimum occurs at: x = 3π/2
Maximum occurs at: x = π/2
ANSWER:
[tex][/tex]Related Questions
Hi - I am trying to get help with a math prob
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1) In this case, let's do it by PEMDAS order of operations.
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
2) So let's begin with the parentheses:
[tex]\begin{gathered} 8\div2(2+2)= \\ 8\div2(4) \\ 4(4) \\ 16 \end{gathered}[/tex]Help!!!A copying service charges a uniform rate for the first one hundred copies or less and a fee for each additional copy. Nancy Taylor paid $7.00 to make 200 copies and Rosie Barbi paid $9.20 to make 310 copies.
What is the cost of the first one hundred copies?
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The answer to both the subparts using equations are:
(A) The initial 100 copies are $5 each.(B) Each extra copy will cost you $0.02.What are equations?A mathematical statement that has two expressions with equal values separated by the symbol "equal to" is called an equation. Consider the formula 3x + 5 = 15. Different types of equations exist, including linear, quadratic, cubic, and others.So, the equations can be formed as:
100a + [(200 - 100)b] = 7 ⇒ 100a + 100b = 7 ..(1)100a + [(310 - 100)b] = 9.20 ⇒ 100a + 210b = 9.2 ..(2)Where a is the price of each of the first 100 copies and b is the price of the extra copies.The elimination method would be used to resolve the two equations that were formed above.
(B) Calculate equation 1 minus equation 2.
110b = 2.2B = 2.2 / 110 is the result of multiplying both sides by 110.
b = 0.02Each extra copy will cost: $0.02
(A) Replace b in equation 1 with:
100a + 100(0.02) = 7100a + 2 = 7Put similar terms together: 100a = 7 - 2
Add comparable terms: 100a = 5
A = 5 / 100, or multiply both sides of the equation by 100.a = 0.05The price for the first 100 copies is $0.05 x 100 = $5.
Therefore, the answer to both the subparts using equations are:
(A) The initial 100 copies are $5 each.(B) Each extra copy will cost you $0.02.Know more about equations here:
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factored from of polynomial need answer fast.(im sorry henry im very confused )
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We have:
[tex]5p^3-10p^2+3p-6[/tex]We factor as follows:
[tex]p(5p^2-10p+3)-6[/tex][tex]\Rightarrow p(-\frac{1}{5}(-5x+\sqrt[]{10}+5)(5x+\sqrt[]{10}-5)-6[/tex]5p + 3 = 15Write a situation that this equation could help you solve and explain how each part of the equation relates to the situation you create.
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Hello! We can see this equation as a function like f(x) = 5x + 3 = 15
Let's think about a problem...
For example, we have a taxi that charges $5 per kilometer + a flat fee of $3.
So, we can write it as a function:
f(x) = 5x + 3
Look that x = kilometers, so this value will grow according to the amount, right?
Knowing that, let's go back to your equation, but thinking in the taxi:
5p + 3 = 15
We can say that the final price of this race was $15, but we don't know how many kilometers were covered. So, we can solve this equation and find the value of p (kilometers). Let's do it?
5p + 3 = 15
5p = 15 - 3
5p = 12
p = 12/5
p = 2.40
Now, we know that the taxi covered 2.4 km charging a fee of r$ 5 per kilometer.
write the slope intercept form:through: (5, 1), perp. to x= -1
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the 7th grade fundraiser gives away a large container of gumballs to the student who is closest to guessing the correct number of gumballs in the container noticing that the container is a cube. Sally decides to count the number of gumballs along the length of one side if Sally get 729 gumballs how many gumballs did she count along one side of the container
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If the container is a cube, every side is a square, so the length and the width are the same.
To get the number of gumballs based on the number of gumballs in one side, we can use the following equation
[tex]TotalGumballs=x^3[/tex]Where x is the number of gumballs along one side. So, replacing the total by 729 and solving for x, we get:
[tex]\begin{gathered} 729=x^3 \\ \sqrt[3]{729}=x \\ 9=x \end{gathered}[/tex]Answer: She counts 9 gumballs along one side of the container
The table shows the results of a survey of students. The survey asked the students whether they have a job and whether they have a car. Job No Job Total Car 38 22 60 No Car 16 18 34 Total 54 40 94 What percentage of the students in the survey have a car?
Answers
Answer:
57.44%
Explanation
Total number of students that has a car = 38 + 16 + 54
Total number of students that has a car = 108
Total number of students = 60 + 34 + 94
Total number of students = 188
Percentage of those that have a car = 108/188 * 100
Percentage of those that have a car = 10800/188
Percentage of those that have a car = 57.44%
Hence the Percentage of those that have a car is 57.44%
A bacteria population is modeling by b(t) = 10e^5t million bacteria after t days. how fast is the population growing after 3 days?
Answers
The population of this bacteria is growing at the rate of 10.897 trillion per day.
What is the growth rate?The growth rate refers to the change from one period to another.
It also refers to the average growth per day, especially in the case of bacteria.
Bacteria population = b(t) = 10e^5t million
The number of days, t = 3
e = 2.71828
10e^5t million = 10 x 2.71828^5x3 million
= 10 x 2.71828^15 million
= 10 x 3268984.38894 million
= 32,689,843,889,400
Growth per day = 10.897 trillion
Thus, we can conclude that the bacteria is increasing at the growth rate of 10.897 trillion per day.
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Divide monomials ( -18p^4 q^7) (-6p^3 q^8) / -36p^12 q^10
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Given:
[tex]\frac{(-18p^4q^7)(-6p^3q^8)}{-36p^{12}q^{10}}[/tex]We will use the following rules of the exponents:
[tex]\begin{gathered} \frac{a^m}{a^n}=a^{m-n} \\ a^m\cdot a^n=a^{m+n} \end{gathered}[/tex]So, the given expression will be as follows:
[tex]\begin{gathered} \frac{(-18p^4q^7)(-6p^3q^8)}{-36p^{12}q^{10}}=(\frac{-18\cdot-6}{-36})\cdot p^{4+3-12}\cdot q^{7+8-10} \\ \\ =(-3)\cdot p^{-5}\cdot q^5 \\ \\ =\frac{-3q^5}{p^5} \end{gathered}[/tex]so, the answer will be:
[tex]\frac{-3q^5}{p^5}[/tex]Solve for x.
-
5(x − 2) = -x + 2
3
x = [?]
I
Enter
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5x-10= -x+2
5x+x = 2+10
6x=12
x=2
Answer: x= -13/4 OR -13=4
Step-by-step explanation: There you go just follow the distribution and then the multi step equations to solve the answer
−5(−2)=−+23
−5+10=−+23
−5=−+13
x = -13/4
Deductive Reasoning / 5913. Copy and complete the proof of Theorem 2-6: If the exterior sides of twoadjacent acute angles are perpendicular, then the angles are complementary.Given: OAI OGProve: Z AOB and 2 BOC are comp. 4.BProof:Statements0Reasons1?1. OA 1 OC2. m ZAOC = 903. m ZAOB + m2 BOC = m 2 AOC4.25. 22. Def. of 1 lines3. 24. Substitution Prop.5. Def. of comp. 4
Answers
Reasons
1. Given
3. Angle addition postulate
Statements
4.
[tex]m\angle\text{AOB}+m\angle\text{BOC}=90º[/tex]5.
[tex]\angle\text{AOB and}\angle\text{BOC are complementary}[/tex]Given the function p(c)=c² +c:
a. Evaluate p(-3).
b. Solve p(c) = 2.
Answers
Answer: a. p(-3) = 6 b. c = -2 , c = 1
Step-by-step explanation:
a. Evaluate p(-3):
Step 1: Plug in -3 into c
p(-3) = (-3)^2-3
Step 2: Use PEMDAS
p(-3) = 9-3
Step 3: Subtract
p(-3) = 6
b. Solve p(c) = 2:
Step 1: Set the equation equal to 2
2 = c^2+c
Step 2: Bring the 2 to the right
c^2+c-2 = 0
Step 3: Factor
(c+2)(c-1) = 0
Step 4: Use the Zero Product Property
c = -2 , c = 1
Step-by-step explanation:
a.
this is totally easy.
we need to put the given value for c (-3) into all the places of c in the functional expression and then calculate.
p(-3) = (-3)² + -3 = 9 - 3 = 6
b.
this is a bit trickier.
p(c) = 2
so,
c² + c = 2
c² + c - 2 = 0
remember, how 2 sums are multiplied with each other :
(a + b)(c + d) = ac + ad + bc + bd
to make it clearer, the functional expression suggests that a = c.
so,
(c + b)(c + d) = c² + cd + bc + bd = c² + c(d + b) + bd
when we compare this to our equation c² + c - 2 = 0, that means
d + b = 1
-2 = bd
when we think about integer numbers, what comes to mind ?
d = 2
b = -1
or vice versa. but the sequence does not matter, because we bring them together in an addition and in a multiplication, where the commutative principle is active (the sequence does not matter).
so,
c² + c - 2 = (c + 2)(c - 1)
and that must be 0.
so,
(c + 2)(c - 1) = 0
when is a product 0 ? when at least one of the factors is 0.
therefore, either
c + 2 = 0
c = -2
or
c - 1 = 0
c = 1
the solution is
c = -2
or
c = 1
i need help with this question it’s for a test. i’m doing summer school to help me prepare for college.
Answers
Ok, so
We got these triangles:
We know that two triangles are similar if there's a ratio between their sides.
So, if we compare,
We got this ratio:
As you can notice, if we relation side by side, the ratio is the same. So, we could say that the bigger triangle is 1.5 times the smaller one. So, they are similar.
pls help a washer and a dryer cost $649 combined.The washer costs $51 less than the dryer.What is the cost of the dryer?
Answers
Given in the question:
a.) A washer and a dryer cost $649 combined.
b.) The washer costs $51 less than the dryer.
From the given description, let's transform them into an equation.
Let,
x = Cost of washer
y = Cost of dryer
a.) A washer and a dryer cost $649 combined.
[tex]\text{ x + y = \$649}[/tex]b.) The washer costs $51 less than the dryer.
[tex]\text{ x = y - \$51}[/tex]From the generated equation, substitute x = y - $51 to x + y = $649.
We get,
[tex]\text{ x + y = \$649}[/tex][tex]\text{ (y - \$51) + y = \$649}[/tex][tex]\text{ y - \$51 + y = \$649}[/tex][tex]\text{ 2y = \$649 + \$51}[/tex][tex]\text{ 2y = \$7}00[/tex][tex]\text{ }\frac{\text{2y}}{2}\text{ = }\frac{\text{\$7}00}{2}[/tex][tex]\text{ y = \$350}[/tex]Therefore, the cost of the dryer is $350.
Let's find the cost of the washer.
[tex]\text{ x = y - \$51}[/tex][tex]\text{ x = \$350 - \$51}[/tex][tex]\text{ x = \$}299[/tex]Therefore, the cost of the washer is $299.
State whether the following statement is true or false.Matrices of different orders can sometimes be multiplied.Choose the correct answer below.FalseTrue
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ANSWER
True
EXPLANATION
We want to verify if matrices of different orders can sometimes be multiplied.
The order of a matrix refers to the configuration of the rows and columns of the matrix.
For matrix multiplication to occur, the dimensions of the matrices must be compatible. In other words, the number of columns inn the first matrix must be the same as the number of rows in the second matrix.
This is not affected by the number of rows in the first matrix or the number of columns in the second matrix.
Hence, under the right condition, matrices of different orders can sometimes be multiplied.
The answer is True.
What step is needed when constructing a circle inscribed in a triangle?
Answers
Given:
Construct a circle inscribed in a triangle.
To find:
The needed step to construct.
Explanation:
The first step should be,
Construct an angle bisector from any two angles of the triangle. Mark the intersecting point as the centre of circle C.
The second step should be,
From point C, construct a perpendicular line to meet at any one side of the triangle and mark it as Y.
The third step should be,
Measure the length of CY. Use a compass to draw a circle in the triangle by using the length of CY.
So, the correct answer is,
Construct the angle bisectors of each angle in the triangle.
Final answer:
Construct the angle bisectors of each angle in the triangle.
given the graph of the function f(x) below what happens to f(x) when x is a very small postitive number
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Hello!
This exercise asks the value of f(x) when x is a very small positive number. To solve it, we can analyze the attached graph below:
So, we are talking about the numbers that are positive and very close to 0 and its corresponding range.
I put a rectangle to show you the range (we have to analyze it).
So, let's look at it:
Each time the value of X gets closer to zero Y (or f(x)) tends to increase.
So, the answer will be the alternative C.
under the pink line is the answer, simply explain the process
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The function is continuous at a = 5
Explanation:Given:
[tex]18)\text{ }f(x)\text{ = }\frac{2x^2+3x+1}{x^2+5x};\text{ a = 5}[/tex]To find:
If the function is continuous at a = 5
For a function to be continuous at a point, the limit exists for the point and the value of the function at that point must be equal to the limit at the point.
when x = 5
[tex]\begin{gathered} f(x)\text{ = }\frac{2(5)^2+3(5)+1}{(5)^2+5(5)} \\ \\ f(x)\text{ = }\frac{50\text{ + 15 + 1}}{25\text{ + 25}} \\ \\ f(x)\text{ = }\frac{66}{50} \\ \\ f(x)\text{ = }\frac{33}{25} \end{gathered}[/tex]Finding the limit at the point:
[tex]\begin{gathered} \lim_{a\to5}\frac{2x^2+3x\text{ + 1}}{x^2+5x} \\ \\ To\text{ get the limit at the point a = 5, we will susbtitute x with 5} \\ =\text{ }\frac{2(5)\placeholder{⬚}^2+3(5)+1}{(5)\placeholder{⬚}^2+5(5)} \\ \\ =\text{ }\frac{50+15+1}{25+25}\text{ = }\frac{66}{50} \\ \\ =\text{ }\frac{33}{25} \end{gathered}[/tex]The value of the function at that point is equal to the limit at the point.
Hence, the function is continuous at a = 5
Select ALL parts of the triangle that are labeled ascongruent.
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Given
Answer
AC congruent to GF
Angle A congurent to Angle G
AB congurent GH
B congurent to H
C congurent to F
BC congurent to FH
Round the following number to 2 decimal places 3.083
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3.083 when rounded up to 2 decimal places is equal to 3.08.
hurry brainiest! if right
Determine which set of side measurements could be used to form a right triangle.
square root of 2, square root of 3, 5
square root of 2, 3, square root of 11
7, 9, 11
5, 10, 14
which set of side measurements could be used to form a right triangle.
square root of 2, square root of 3, 5
square root of 2, 3, square root of 11
7, 9, 11
5, 10, 14
Answers
Answer:
Option 2
Step-by-step explanation:
The side lengths satisfy the Pythagorean theorem.
Answer:
square root of 2, 3, square root of 11
Step-by-step explanation:
ProgScore: 2/101/5 answeredQuestion 2<>A population has parameters u = 245.9 and o= 16.7. You intend to draw a random sample of size n = 83.What is the mean of the distribution of sample means?Hy =What is the standard deviation of the distribution of sample means?(Report answer accurate to 2 decimal places.)=Question Help: D VideoSubmit Question
Answers
For a population with parameters as shown in the image below
(a) Mean of the distribution
[tex]\begin{gathered} \mu_{\bar{x}}\text{ = }\mu\text{ = 245.9} \\ \operatorname{mean}\text{ of the distribution = 245.9} \end{gathered}[/tex](b)Standard deviation of the distribution
[tex]\begin{gathered} \sigma_{\bar{x}\text{ }}\text{ = }\frac{\sigma}{\sqrt[]{n}} \\ \sigma_{\bar{x}\text{ }}\text{ = }\frac{16.7}{\sqrt[]{83}} \\ \sigma_{\bar{x}\text{ }}\text{ = }\frac{16.7}{9.11} \\ \sigma_{\bar{x}\text{ }}\text{ = 1.833} \\ \sigma_{\bar{x}\text{ }}\text{ = 1.83 (2 d.p)} \end{gathered}[/tex]Hence the value of the mean of the distribution = 245.9 and the standard deviation of the distribution = 1.83
which graph represents the equation 2 x + y =2?
Answers
start by writing the equation in the slope-intercept form
[tex]\begin{gathered} 2x+y=2 \\ y=-2x+2 \end{gathered}[/tex]this meand that the line has a slope of -2 and cuts the y-axis over 2.
the graph should look like this
For a standard normal distribution, find:P(Z > c) = 0.7051Find C rounded to four decimal places.
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Answer:
Explanation:
The given expression is
P(Z > c) = 0.7051
P(Z > c) = 1 - P(Z < c)
1 - P(Z < c) = 1 - 0.7051 = 0.2949
From the normal distribution table, the z score for a probability value of
A bacteria population grows by 10% every 2 years. Presently, the population is 80 000 bacteria. Find the population 12 years ago. (Can use log if needed but not “in”)
Answers
In this problem
we have an exponential growth function of the form
[tex]y=a(1+r)^{\frac{t}{2}}[/tex]where
r=10%=0.10
Let
t=0 ---------> 12 years ago
so
Presently -------> t=12 years, y=80,000 bacteria
substitute
[tex]\begin{gathered} 80,000=a(1+0.10)^{\frac{12}{2}} \\ a=\frac{80,000}{1.10^6} \\ \\ a=45,158\text{ bacteria} \end{gathered}[/tex]therefore
The population 12 years ago was 45,158 bacteriaMrs. lin is making several trays of her famous lasagna. She finds the mozzarella cheese on sale for $4.89 per pound at her local grocery store. How much will she pay for four pounds of cheese
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We have the following:
since we have the value of per unit (that is, 1 pound) we only have to multiply by the number of pounds like this:
[tex]4.89\cdot4=19.56[/tex]Therefore, she will pay in total $19.56
The life, in years, of a certain type of electrical switch has an exponential distribution with an average life of β = 5 years. If 200 of these switches are installed in different systems, what is the probability that at most 30 fail during the first year?
Answers
The probability that at most [tex]30[/tex] fail during the first year is 0.14550.
A certain type of electrical switch has an exponential distribution with an average life of [tex]\beta =5[/tex] years.
The installed switches in different systems n = 200.
We have to find the probability that at most 30 fail during the first year.
We can find the probability using,
P [tex]=1-e^{-1/\beta }[/tex]
Putting the value
P [tex]=1-e^{-1/5 }[/tex]
P [tex]=1-e^{-0.2}[/tex]
P [tex]=1-0.8187[/tex]
P = 0.1813
Now we find the mean[tex](\mu)[/tex].
[tex]\mu=n\times[/tex] P
[tex]\mu=200\times 0.1813[/tex]
[tex]\mu=36.26[/tex]
Now finding the standard deviation[tex](\sigma)[/tex].
[tex]\sigma=\sqrt{\mu(1-P)}[/tex]
Now putting the value
[tex]\sigma=\sqrt{36.26(1-0.1813)}[/tex]
[tex]\sigma=\sqrt{36.26\times0.8187}[/tex]
[tex]\sigma=\sqrt{29.686}[/tex]
[tex]\sigma=5.448[/tex]
z score,
[tex]z=\frac{(x-\mu)}{\sigma}[/tex]
Now probability that at most 30 fail during the first year.
From the continuity correction,
P(x ≤ 30) [tex]=P(x < 30.5)[/tex]
P(x ≤ 30) [tex]=P(\frac{x-\mu}{\sigma} < \frac{30.5-36.26}{5.448})[/tex]
P(x ≤ 30) [tex]=P(\frac{x-\mu}{\sigma} < \frac{-5.76}{5.448})[/tex]
P(x ≤ 30) [tex]=P(\frac{x-\mu}{\sigma} < -1.058)[/tex]
From the standard table
P(x ≤ 30) = 0.1455
Hence, the probability that at most [tex]30[/tex] fail during the first year is [tex]0.1455[/tex].
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Find the equation of a line perpendicular to y= 1/2x+1that passes through the point (6,-2).
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the slope must be the opposite reciprocal of 1/2,so it is -2 after you find the slope. use the point slope formula to find the answer
y+2=-2(x-6)
distribute the -2
y+2=-2x+12
subtract 2 to both sides to leave the y by itself
y=-2x+10
In AEFG, the measure of ZG=90°, the measure of ZE=26°, and GE = 4.6 feet. Find the length of FG to the nearest tenth of a foot.
Answers
Using the tangent identity:
[tex]\begin{gathered} \tan (\theta)=\frac{opposite}{adjacent_{}} \\ so\colon \\ \tan (30)=\frac{8.1}{x} \\ x=\frac{8.1}{\tan (30)} \\ x=14.0ft \end{gathered}[/tex]Ben bought a book for $10.75 and a magazine for $3.99. Sales tax was $1.03. He paid with a $20 bill. How much change did he receive?
$4.77
$5.77
$5.23
$4.23
Can someone help I'm way too lazy to do the work rn
Answers
Answer:
4.23
Step-by-step explanation:
10.75+1.03=14.74+1.03=15.77. 20-15.77=4.23
Answer:
$4.23
Step-by-step explanation:
$10.75+3.99=$14.74
$14.74+ $1.03=$15.77
$20.00-$15.77= $4.23
Ben received $4.23 as his change.
