Please help me with my Calc hw, it is not outside scope of brainly tutor. I am following along diligently, thanks!
Answers
ANSWER
[tex]-2\sqrt[]{1+\cos(x)}+C[/tex]EXPLANATION
To solve this integral we have to use the substitution method. Let u = 1 + cos(x), then du is,
[tex]du=-\sin (x)dx[/tex]Thus, dx is,
[tex]dx=\frac{du}{-\sin (x)}[/tex]Replace the function and the differential in the integral,
[tex]\int \frac{\sin(x)}{\sqrt[]{1+\cos(x)}}dx=\int \frac{\sin(x)}{\sqrt[]{u}}\cdot\frac{du}{-\sin (x)}[/tex]The sin(x) cancels out,
[tex]\int \frac{\sin(x)}{\sqrt[]{u}}\cdot\frac{du}{-\sin(x)}=-\int \frac{1}{\sqrt[]{u}}du[/tex]We have to find a function whose derivative is 1/√u. This function is √u since its derivative is,
[tex]\frac{d}{du}(\sqrt[]{u})=\frac{1}{2\sqrt[]{u}}[/tex]Note that a coefficient 1/2 is missing, so to cancel it out, we have to multiply by 2. Don't forget the constant of integration,
[tex]-\int \frac{1}{\sqrt[]{u}}du=-2\sqrt[]{u}+C[/tex]Finally, we have to replace u with the function we substituted before,
[tex]-2\sqrt[]{u}+C=-2\sqrt[]{1+\cos (x)}+C[/tex]Hence, the result of the integral is,
[tex]-2\sqrt[]{1+\cos(x)}+C[/tex]Related Questions
Where are the minimum and maximum values for f(x)A. min: x =2¹ 2Reset Selectionmax:z = = 0, π, 2πOB. min:z = π max:x = 0, 2OC. min:z = 0, 2π max:x = πOD. min:z = ,,max:x = 0, 3, 4,2=- 3 cos z - 2 on the interval [0, 2π]?2P
Answers
Given:
The function f(x) = 3cos(x) - 2.
Required:
What are the minimum and maximum value of function?
Explanation:
To check maximum and minimum value of function.
First derivate the original function.
After putting first derivative equal to zero, critical points can be found.
Then, do second deritvative to check points of maxima and minima.
The critical points at which second derivative greater than zero. Point will be of minima.
The critical points at which second derivative less than zero. Point will be of maxima.
So,
[tex]\begin{gathered} f(x)=3cos(x)-2 \\ \text{ First derivative} \\ f^{\prime}(x)=-3sinx \\ \text{ Put }f^{\prime}(x)=0 \\ sinx=0 \\ x=0,\pi,2\pi \end{gathered}[/tex]Now, do second derivative test for maximum and minimum points
[tex]\begin{gathered} f^{\prime}^{\prime}(x)=-3cosx \\ \text{ At }x=0 \\ f^{\prime}^{\prime}(0)=-3\times1=-3<0 \\ \text{ At }x=\pi \\ f^{\prime}^{\prime}(\pi)=-3\times cos(\pi)=-3\times-1=3>0 \\ At\text{ }x=2\pi \\ f^{\prime}^{\prime}(2\pi)=-3\times1=-3<0 \\ \end{gathered}[/tex]Answer:
[tex]\text{ The points }0,2\pi\text{ are points of maxima and }\pi\text{ giving minima.}[/tex]
I'm confused about this problem can someone explain?
Answers
Answer:
32.50x + 7.50 < 235
Step-by-step explanation:
All the cost have to be less than 325. x stands for the number of people buying tickets.
What is the slope and y-intercept?
Answers
Answer/Step-by-step explanation:
y = mx + b
Slope = m
y₂ - y₁
---------- = m
x₂ - x₁
----------------------------------------------------------------------------------------------------------
y - intercept = b
y - y₁ = m(x - x₁)
If there's an equation I can solve it, but I hope this helps!
When looking at a graph of a line, there are two things you should look for straight off the bat. First, the y-intercept. And second, the slope.
The equation of a line is y = mx + b, where m is the slope, b is the y-intercept, and x is the input.
What is slope?
Slope is a number that determines how the line changes. It is often referred to as the "rate of change" because it represents how much the y-value of the line changes when the input (x) changes. The formula for slope is:
[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
Breakdown: This formula represents the change in the line, typically left to right. It shows the change in x-value over the change in corresponding y-value. This is also known as "rise over run," because the y-value is how much the line changes vertically, while the x-value is how much it changes horizontally.
Example: Let's say our line has a slope of 4, or m = 4/1. This means the y-value will change 4 units when the x-value changes by 1.
What is y-intercept?
Y-intercept is a value that determines the location of the line. When x = 0, the value of b will be the y-value. Essentially, when the line crosses the y-axis, that will be the y-value of the line.
Given m||n, find the value of x.50°Click heredismiss)
Answers
Let's recall that If a set of 2 parallel lines, line m and line m, are crossed or cut by another line, line T, in our question, we say "a set of parallel lines are cut by a transversal.
Each of the parallel lines cut by the transversal has 4 angles surrounding the intersection.
These are matched in measure and position with a counterpart at the other parallel line.
At each of the parallel lines, there are two pairs of vertical angle. Each angle in the pair is congruent to the other angle in the pair.
In our question, the angle that measures 145 degrees is congruent with the opposites angles of angle x.
Let's recall that x and 145 degrees are adjacent supplementary angles. And these angles add up to 180 degrees. Then, for solve for x, we have:
x = 180 - 145
x = 35 degrees
Find the exact length of the arc intercepted by a central angle on a circle of radius . Then round to the nearest tenth of a unit.
Answers
Given:
Angle subtended at the center = 135 degrees
radius (r) = 4 yd
Solution
The formula for the length (l) of an arc is given as:
[tex]\begin{gathered} l\text{ = }\frac{\phi}{360^0}\text{ }\times\text{ 2}\pi r \\ \text{where }\phi\text{ is the angle subtend}ed\text{ at the center} \end{gathered}[/tex]When we substitute the given parameters, we can find the length (l) of the arc:
[tex]\begin{gathered} l\text{ = }\frac{135}{360}\text{ }\times\text{ 2 }\times\text{ }\pi\text{ }\times\text{ 4} \\ =3\pi \\ \approx\text{ 9.4 yd (nearest tenth)} \end{gathered}[/tex]Answer: 9.4 yd or 3.0 pi
ok so this is multiplying decimals 7.3 x9.6=please show your work and answer thank you
Answers
therefore, the answer is 70.08
Explanation
Step 1
first multiply as if there is no decimal
[tex]\begin{gathered} 7.3\cdot9.6 \\ a)7.3\cdot9.6\Rightarrow73\cdot96 \\ 73\cdot69=7008 \end{gathered}[/tex]Step 2
count the number of digits after the decimal in each factor.
[tex]\begin{gathered} 7.3\Rightarrow1\text{ decimal} \\ 9.6\Rightarrow1\text{ decimal} \\ \text{total }\Rightarrow2\text{ decimals} \end{gathered}[/tex]
Step 3
Put the same number of digits behind the decimal in the product
[tex]7008\Rightarrow put\text{ 2 decimal, }\Rightarrow so\Rightarrow70.08[/tex]therefore, the answer is 70.08
I hope this helps you
· A) A highway noise barrier is 120 m long is constructed in 2pieces. One piece is 45 m longer than the other one. Findthe length of each piece. B) If you are to construct arectangle with each of the sizes of the pieces being thelength and width then what is the perimeter? c) What would bethe area of that rectangle? (Note: Use an Equation to solve)
Answers
A) Let the length of one piece be x. if one piece is 45 m longer than the other one, it means that the length of the other one would be (x + 45) m
Given that the total length of both pieces is 120m, then the equation would be
x + x + 45 = 120
2x + 45 = 120
2x = 120 - 45 = 75
x = 75/2
x = 37.5
Thus, the length of each piece are
37.5 m
37.5 + 45 = 82.5 m
B) The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(length + width)
Given that
length = 82.5
width = 37.5
then
perimeter = 2(82.5 + 37.5) = 2 * 120
perimeter of rectangle= 240 m
C) the formula for determining area of a rectangle is expressed as
Area = length * width
Area of rectangle = 82.5 * 37.5 = 3093.75 cm^2
12x=8x+1 what is the answer
Answers
The answer of the given equation is x = 1/4 or 0.25
We are given the equation:-
12x = 8x + 1
We have to solve the equation to find the value of x.
Rearranging the equation to get the like terms on the same side, we get,
12x - 8x = 1
4x = 1
x = 1/4
Hence, the value of x is 1/4 or 0.25.
Like terms
Like terms can be defined as terms that contain the same variables raised to the same power. Only the numerical coefficients are different. In an expression, only we can combine like terms.
To learn more about Like terms, here:-
https://brainly.com/question/2513478
#SPJ1
Draw the image of the figure under thegiven transformation.8. reflection across the y-axis
Answers
Whne the coordinates are reflected over y -axis, then the coordinates are (x,y) = (-x,y)
.
The coodinates of A(3,0) and after reflection A'(-3,0)
The coordinates B(1,4) and after reflection B'(-1,0)
The coordinates C(5,3) and after reflection C'(-5,3)
Plot the image on the graph
f(x) is concave down on the interval (a, b) if f'(x) is decreasing on (a, b).
O True
O False
Answers
Tell whether the graph would be continuous or discrete2. A pet store is selling puppies for $200 each. It has 8 puppies for sale.AcontinuousB) discrete
Answers
Given:
Cost of each puppy = $200
Number of puppies = 8
Here, the equation for total cost of puppies will be:
C = 200x
Where x represents the number of puppies sold
Cost of 1 puppy = $200
Cost of 2 puppies = $200(2) = $400
Cost of 3 puppies = $200(3) = $600
If you continue with the pattern you'll see the graph has a rate of change of 200
To determine if the graph will be continuous or discrete, we have:
For a graph to be continuous, the points on the graph must be connected with a continuos line, while for a graph to be discrete the points are series of unconnected points just like in a scatter plot.
The graph of this will be a discrete graph. A discrete graph have set of values(points)
ANSWER:
B. discrete
i need the fourth term of one and three all I need is the answers so I can quiz my son.
Answers
The formula for the nth term is expressed as
an = (an - 1)^2 - 3
This is a recursive formula
This means that the second term, a2 is
a2 = (a2 - 1)^2 - 3
a2 = (a1)^2 - 3
a2 = 4^2 - 3 = 16 - 3 = 13
a3 = (a3 - 1)^2 - 3
a3 = (a2)^2 - 3
a3 = 13^2 - 3 = 169 - 3 = 166
a4 = (a4 - 1)^2 - 3
a4 = (a3)^2 - 3
a4 = 166^2 - 3 = 27556 - 3 = 27553
Thus,
a4 = 27553
factor the equationx^2-17x+42
Answers
To factor an expression of the form:
[tex]x^2+Bx+C[/tex]we need to find two integers a and b that fullfil:
[tex]\begin{gathered} a+b=B \\ ab=C \end{gathered}[/tex]then we write the expression as:
[tex]x^2+ax+bx+C[/tex]and factor by agrupation.
Let's do this with the expression:
[tex]x^2-17x+42[/tex]In this case B=-17 and C=42.
If we take a=-14 and b=-3, then:
[tex]\begin{gathered} (-14)(-3)=42 \\ -14-3=-17 \end{gathered}[/tex]then we write the expression as:
[tex]\begin{gathered} x^2-14x-3x+42=x(x-14)-3(x-14) \\ =(x-3)(x-14) \end{gathered}[/tex]Therefore, the factorize expression is:
[tex](x-3)(x-14)[/tex]Quantum Logic recently expanded its operations at a cost of $450,000. Management expects that the value of the investment will grow at a rate of 8% per year compounded quarterly for the next 5 years. Find the future value of the investment
Answers
Given:
Quantum Logic recently expanded its operations at a cost of $450,000.
So, P = 450,000
The rate of growth = r = 8% = 0.08
compounded quarterly, n = 4
We will find the future value of the investment (A) after t = 5 years
We will use the following formula:
[tex]A=P\cdot(1+\frac{r}{n})^{nt}[/tex]Substitute with the given values:
[tex]\begin{gathered} A=450,000\cdot(1+\frac{0.08}{4})^{4\cdot5} \\ \\ A=450,000\cdot1.02^{20}\approx668,676.33 \end{gathered}[/tex]So, the answer will be:
The future investment = $668,676.33
16. Eric is deciding how many trees to plant.
Here are his estimates of the time it will take.
Number of trees
1 tree
2 trees
3 trees
4 trees
5 trees
Time
30 minutes
40 minutes
50 minutes
60 minutes
70 minutes
Answers
With each additional tree , the estimated time increases by 10 minutes .
in the question ,
a table with number of trees and time required to plant them is given .
For planting 1 tree 30 minutes is required to plant them .
for planting 2 trees 40 minutes is required to plant them .
increase in number of tree = 2 tree - 1 tree = 1 tree
change in time required = 40 min - 30 min = 10 min
for planting 3 trees , 50 minutes is required to plant them .
increase in number of tree = 3 trees - 2 trees = 1 tree
change in time required = 50 min - 40 min = 10 min
So, we can see that for every additional tree planted the time increases by 10 minutes .
Therefore , with each additional tree , the estimated time increases by 10 minutes .
Learn more about Subtraction here
https://brainly.com/question/545116
#SPJ1
How many triangles can be formed by joining the vertices of a 10-sided polygon?
Answers
The total number of triangles formed by joining vertices of 10-sided polygon is given by the combination of 10 sides taken at 3, i.e. selection of 3 points from 10 points ( because a triangle has 3 vertices). This gives
[tex]10C3=\frac{10!}{3!(10-3)!}=\frac{10!}{3!\cdot7!}=\frac{10\cdot9\cdot8}{6}=\frac{720}{6}=120[/tex]Then, the answer is the last option: 120
Liz is collecting aluminum cans for a school fundraiser. So far, she has collected 16 cans, which is 20% of her goal. How many cans must she collect to reach her goal?Parts A & B
Answers
Given the word problem, we can deduce the following information:
1. Liz collected 16 cans, which is 20% of her goal.
To determine the number of cans that Liz needs to collect to reach her goal, we use below equation:
[tex]0.20x=16[/tex]where:
x= total number of cans that Liz needs to collect
So,
[tex]\begin{gathered} 0.20x=16 \\ \text{Simplify} \\ x=\frac{16}{0.20} \\ x=80 \end{gathered}[/tex]Hence, the total number of cans is 80.
A.
To complete the double number line, we must determine first the other percent values. It the goal is 100%, we must subtract 20% from 100% and divide it by 4 to get the remaining percent values. So,
[tex]\frac{100-20}{4}=20[/tex]So the other percent values are:
0%
20%
20%+20%=40%
40%+20%=60%
60%+20%=80%
80%+20%=100%
To determine the amount of cans for each percent value,the process is shown below:
[tex]80(\frac{40}{100})=32[/tex][tex]\begin{gathered} 80(.6)=48 \\ \end{gathered}[/tex][tex]80(.8)=64[/tex][tex]80(\frac{100}{100})=80[/tex]Therefore, the answer for double number line is:
Cans : 0 16 32 48 64 80
Percent : 0% 20% 40% 60% 80% 100%
B.
Based on the information gathered from A, for every 16 cans Liz collects, she adds 20% toward her goal. She will have 32 cans if she reaches 40% of her goal. Liz must collect 80 cans to reach her goal.
1. In the figure, angle CAB is 47. What would prove that angle ACD is also 47?
A A reflection of ABC over AC, such that ABC maps to CDA.
B A rotation of ABC 180 clockwise around C, such that ABC maps to ADC.
C A rotation of ABC 180 counterclockwise around A, such that ABC maps to ADC.
D A translation of ABC to the top right, such that ABC maps to ADC.
Answers
The correct option C: A rotation of ABC 180 counterclockwise around A, such that ABC maps to ADC.
What is termed as the rotation?Geometry can be used to determine the meaning of rotation in mathematics. As a result, it is described as the movement of something around a center or an axis. Any rotation is regarded as a specific space motion that freezes at at least one point. In reality, a earth rotates on its axis, which is also an instance of rotation. Because a clockwise rotation has a negative magnitude, a counterclockwise rotation does have a positive magnitude.For the given question;
In triangles ABC angle CAB is 47.
If the triangles ABC and ACD becomes congruent such that angle ACD corresponds to angles ABC.
Then, both angles will be equal.
For, this, a rotation of ABC 180 counterclockwise around A, such that ABC maps to ADC is to be done.
To know more about the rotation, here
https://brainly.com/question/1164739
#SPJ13
Solve this system of linear equations. Separatethe x- and y-values with a comma.7x - by = -414x + 5y = 43
Answers
Answer
x = 2, and y = 3
Explanation:
given the following linear equation
7x - 6y = -4------------- equation 1
14x + 5y = 43 ---------- equation 2
This equation can be solve simultaneously by using elimination method
Step 1 : eliminate x
To eliminate x, multiply equation 1 by 2 qnd equation 2 by 1
7x * 2 - 6y * 2 = -4 * 2
14x * 1 + 5y * 1 = 43 * 1
14x - 12y = -8 ----------------- equation 3
14x + 5y = 43------------------ equation 4
Substract equation 4 from3
(14x - 14x) - 12 - 5y = -8 - 43
0 - 17y = -51
-17y = -51
Divide both sides by -17
-17y/-17 = -51/-17
y = 51/17
y = 3
To find x, put the value of y into equation 1
7x - 6y = -4
7x - 6(3) = -4
7x - 18 = -4
Collect the like terms
7x = -4 + 18
7x = 14
Divide both sides by 7
7x/7 = 14/7
x = 2
Therefore, x = 2 and y = 3
f(x) =-x² + 2x + 6
Find f(-7)
Answers
A data set includes weights of garbage discarded in one week from 62 different households. The paired weights of paper and glass were used to obtain the results shown to the right. Is there sufficient evidence to support the claim that there is a linear correlation between weights of discarded paper and glass? Use a significance level of α=0.05. correlation matrix: Variables Paper Glass Paper 1 0.1983 Glass 0.1983
Answers
There is not enough evidence to support the claim that there is a linear correlation between the weights of discarded paper and glass for a significance level of α = 0.05.
Given,
A data set includes weights of garbage discarded in one week from 62 different households.
significance level of α=0.05.
Now, According to the question:
The correlation matrix provided is:
Variables Paper Glass
Paper 1 0.1853
Glass 0.1853 1
The hypothesis for the test is:
H₀: ρ = 0 vs. H₀: ρ ≠ 0
The test statistic is:
r = 0.1983 ≈ 0.198
As the alternate hypothesis does not specifies the direction of the test, the test is two tailed.
The critical value for the two-tailed test is:
[tex]r_{alpha}/2, (n -2) = r_{0.005}/2 ,(62-2) = 0.250[/tex]
The conclusion is:
Because the absolute value of the test statistic is less than the positive critical value, there is not enough evidence to support the claim that there is a linear correlation between the weights of discarded paper and glass for a significance level of α = 0.05.
Learn more about Statistic at:
https://brainly.com/question/23091366
#SPJ1
Brianna's teacher asks her if these two expressions 3x + 5 and 4x are equivalent.Brianna says the expressions are equivalent because the value of each expression is 20 when x = 5.Is Brianna correct synlainthink ASAP please
Answers
Step 1
Given data
Expression 1 = 3x + 5
Expression 2 =
Twenty students choose a piece of fruit from a list of 4 fruits: apple, banana, grape, and pear. The theoretical probability that a student will choose a banana is .25. Only 1 student chooses a banana. How can the experimental probability get closer to the theoretical probability?A. only give two choices of fruitB. use a smaller sample size of studentsC. use a larger sample size of studentsD. provide more choices of fruit
Answers
Total number of student 20.
Total number of fruits are 4.
The theoretical probability that a student will choose a banana is 0.25
The experimental probability is 1/20=0.05.
Thus there is a huge difference in the theoritical probability and experimental probability.
Thus the experimental probability get closer to the theoretical probability is:
A. only give two choices of fruit.
The best way of getting the experimental probability closer to the theoretical value is by taking a larger sample.
Sadly the fruit selection is not random but based on student preferences.
Because the fruit are unlikely to have equal appeal to students, the theoretical probability is not valid.
Melanie went shopping and spent $18 on scarves. If she spent $77 total, what percentage did she spend on scarves? Round your answer to the nearest percent.
Answers
Answer:
23.4%
Step-by-step explanation:
[tex]\frac{18}{77} =\frac{x}{100}[/tex]
$18 divided by $77 is the equivalent of X(% spent on scarves) divided by 100. To find X you cross multiply and divide. [tex](18*100)/77=23.377...[/tex], rounded, X = 23.4
a bread recipe calls for 3 3/8 cups of white flour and 2 1/2 cups of whole wheat flour. How many cups of flour in all?
Answers
Answer:
5 complete cups and 7/8 of a cup
[tex]5\frac{7}{8}[/tex]Figure 1 and Figure Il are similar figures. Figure I Figure II R S А B F C w T E D V U Which proportion must be true?
Answers
From the diagram,
CD is corresponding to WR
VW is corresponding to BC
RS is corresponding to DE
ST is corresponding to EF
TU is corresponding to FA
Final answer
[tex]\frac{ST}{EF}\text{ = }\frac{WR}{CD}[/tex]The two-way table represents the number of clubs that two hundred high school studentswere involved in.One Club Two clubsBoys 17Girls 28Total 45256893Three or more clubs Total50126292108200What is the probability that a student will be in two clubs only and a girl?
Answers
Given:
The two-way table represents the number of clubs that two hundred high school students
We will find the probability that a student will be in two clubs only and a girl
From the table, we will select the number that represents the number of girls that will be in the two clubs
so, the number = 68
the total number of students = 200
So, the probability will be =
[tex]\frac{68}{200}*100=34\%[/tex]So, the answer will be 34%
Valentina opened a savings account and deposited 1,000.00 as principal the account earns 3%interest compounded monthly what is the balance after 8 years
Answers
According to the problem, the principal is $1,000, the interest is 3% compounded monthly and the time is 8 years.
We have to use the compounded interest formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Replacing the given information, we have
[tex]A=1,000\cdot(1+\frac{0.03}{12})^{12\cdot8}[/tex]Now, we solve for A
[tex]\begin{gathered} A=1,000(1+0.0025)^{96} \\ A=1,000(1.0025)^{96} \\ A\approx1,270.87 \end{gathered}[/tex]Hence, she will have $1,270.87 after 8 years.the company has been
Answers
According to the given diagram, we have 4 shirts in total, where there's only one short-sleeve white shirt, so we just have to divide 1/4
[tex]P=\frac{1}{4}=0.25[/tex]Then, we multiply by 100 to express it in percentage
[tex]P=0.25\cdot100=25[/tex]Hence, the answer is 25%.Wich situation can be represented by 3 + 3s =5s - 7
Answers
3 + 3s = 5s - 7
A. Three times a number increased by 3 ( can be represented by 3s + 3 ) is the same as ( = ) five times a number decreased by 7 ( can be represented by 5s -7 ). 3s + 3 = 5s - 7
Answer: A