Answers
The indefinite integral, given the integral can be found to be √14x + C.
How to find the indefinite integral ?An indefinite integral is an antiderivative of a function. More specifically, if f(x) is a function, then an antiderivative of f(x) is a function F(x) such that F'(x) = f(x), where F'(x) represents the derivative of F(x) with respect to x.
To find the indefinite integral of a constant (in this case, √14) with respect to x, simply multiply the constant by x and add a constant of integration (C):
∫√14 dx = √14 × ∫dx = √14 × x + C
So, the indefinite integral of √14 with respect to x is:
√14x + C
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Related Questions
Creating an object model
Think back to the Sales Bonus Problem you created in a prior lesson.
A more elegant solution to that problem would incorporate objects. This week you are going to revise it to an object oriented program. To do that you need to identify the objects that you need to create to support the program.
Create UML diagrams for each of the object(s) you need and using the concept of design by contract, identify the responsibilities.
For this part of the assignment I only want the UML design document and the contract responsibilities. You will use these design documents to create the program in the next assignment.
Answers
Here is an example of how to create an object model, UML diagrams, and contract obligations in general.
What justifies the response given above?Let's have a look at a basic "Bank Account" system, where a customer may deposit money, withdraw it, and see the amount of their account. The following classes would be represented in the UML class diagram for this system:
Bank Account Client
The following characteristics would be included in the Bank Account class:
string Account Number
stability: float
and the subsequent techniques:
deposit(float amount) = None
withdrawal(float :amount) = None
float: check Balance()
The following characteristics would apply to the Customer class:
string name
list of accounts[Bank Account]
and the subsequent techniques:
account: Bank Account; add account(account) -> None
account: Bank Account; remove Account(account: None)
Bank Account: get Account(Account number: string)
For the Bank Account class, the design by contract obligations would be:
Pre-conditions:
amount > 0
withdraw(amount): amount > 0 and balance >= amount
Check Balance(): None
Post-conditions:
deposit(amount): balance += amount
withdraw(amount): balance -= amount
Check Balance(): return balance
The design by contract responsibilities for the Customer class would be:
Pre-conditions:
Add account(account): account not in accounts
Post-conditions:
Add account(account): accounts. append(account)
remove (account): accounts.
get account (account number): return the Bank Account object with the given account Number.
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The length of one side of a golden rectangle is 4.9 metersFind the length of the other side that the other side could be other longer or shorter than the given side
Answers
The length of the other side will be 3.
How to obtain the lengthTo obtain the length of the other side of the rectangle, given the approximation of 1.62, we will first divide 4.9, the known side by x, the unknown side, and equate this to 1.62.
If we are using the approximation of 1.62, then the length of the other side of the rectangle will be 4.9/x = 1.62
1.62x = 4.9
x = 3
So, the length of the other side, which in this case is shorter is 3.
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a swim team consists of 7 boys and 7 girls. a relay team of 4 swimmers is chosen at random from the team members. what is the probability that 3 boys are selected for the relay team given that the first election was a girl?
Answers
The probability that 3 boys are selected for the relay team given that the first election was a girl is approximately 0.122, or 12.2%.
The Bayes theorem can be used,Let B represent the decision to select three boys for the relay team whereas A represents the scenario when a girl was chosen first.
P(B|A) is the conditional probability of B given A.
The Bayes theorem gives us:
P(B|A) is equal to P(A|B)*P(B)/P(A).
Given that the relay team consists of 3 boys, the probability that a girl would be chosen as the first team member is P(A|B). Therefore:
P(A|B) = 7/13 * 6/12 * 5/11 * 7/10 = 0.0871
P(B) represents the likelihood of choosing three males for the relay team in an arbitrary manner.
P(B) = (7C3 * 7C1) / (14C4) = 35/143
P(A) represents the likelihood that a girl will be chosen as the first team member without any restrictions.
P(A) = 7/14 = 1/2
Combining everything, we get the following: P(B|A) = P(A|B) * P(B) / P(A) = 0.0871 * 35/143 / (1/2) = 0.1220.122, or 12.2%.
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Please help with this question A circle is separated into eight sectors of equal area. These eight sectors are arranged to form a shape similar to a parallelogram.
The area of the circle (πr2
) is equal to the area of the parallelogram (bh
).
Select from the drop-down lists to correctly complete each sentence.
The height of the parallelogram is equal to the
of the circle. The base of the parallelogram is equal to
of the circle. Therefore, the area of the circle (πr2
) is equal to the
, and the circumference of the circle is equal to
.
Answers
The height of the parallelogram is equal to the diameter of the circle. The base of the parallelogram is equal to half of the circumference of the circle. Therefore, the area of the circle (πr2) is equal to bh and the circumference of the circle is equal to 2b.
The height of the parallelogram is equal to the diameter of the circle. This can be seen because each of the eight sectors has the same area, so they are all the same size. If we place them next to each other in the shape of a parallelogram, we can see that the height of the parallelogram is equal to the diameter of the circle.
The base of the parallelogram is equal to half of the circumference of the circle. This is because the circumference of the circle is divided equally into eight sectors, and the base of the parallelogram is formed by placing two adjacent sectors together. Therefore, the base of the parallelogram is equal to the arc length of one sector plus the arc length of its adjacent sector. Each sector is 1/8th of the circle, so the arc length of one sector is 1/8th of the circumference. Adding the arc lengths of two adjacent sectors gives 1/4th of the circumference, which is half of the base of the parallelogram.
Therefore, the area of the circle (πr2) is equal to the area of the parallelogram (bh), where h is the diameter of the circle and b is half of the circumference of the circle. Additionally, the circumference of the circle is equal to the base of the parallelogram multiplied by 2.
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V(d)V, left parenthesis, d, right parenthesis models Erica's vertical distance from the top of the valley (in kilometers) after walking
d
dd kilometers along the trail.
What does the statement
V
(
2
)
=
T
V(2)=TV, left parenthesis, 2, right parenthesis, equals, T mean?
Answers
The meaning of V(2) is the Erica's vertical distance after walking 2 kilometers along the trail.
How to calculate the numeric value of a function or of an expression?To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The input and output variables for this problem are given as follows:
Input: number of kilometers walked along the trail.Output: vertical distance.V(2) means that the number of km is of 2, hence the meaning of V(2) is the Erica's vertical distance after walking 2 kilometers along the trail.
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Carly ordered shoes online from her favorite store. The shipping costs for her
purchase is $5.50. Her total cost for the entire purchase is $60.75. Which
equation below could be used to calculate s, the cost of her shoes without
shipping included?
Answers
The equation to calculate the cost of her shoes without shipping included is: x = 55.25
The equation to calculate s, the cost of her shoesLet x be the cost of Carly's shoes.
The problem states that the total cost of her purchase (including shoes and shipping) is $60.75, so we can set up the equation:
x + 5.50 = 60.75
To find the cost of her shoes without shipping, we need to isolate x. We can do this by subtracting 5.50 from both sides:
x + 5.50 - 5.50 = 60.75 - 5.50
Simplifying:
x = 55.25
Therefore, the equation to calculate the cost of her shoes without shipping included is: x = 55.25
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1 and 1/4 times 1 and 1/3 equals
Answers
Please help if you can calculate it!
A survey was conducted one month ago to review the calories of lunch boxes provided by the supplier "Better
Lunch". In a sample with 300 lunch boxes, there were 273 lunch boxes with calories below 650 and the other
27 lunch boxes with calories above 650. Besides, the mean calories was 550 and standard deviation was 40.
(a) Find the point estimate of the population proportion of lunch boxes provided by "Better Lunch" had
calories above 650.
(b) Calculate the sampling error at 98% confidence level for the estimate of the population proportion of
lunch boxes provided by "Better Lunch" had calories above 650.
(c) Construct a 98% confidence interval estimate of the population proportion of lunch boxes provided by
"Better Lunch" had calories above 650.
(d) "Better Lunch" follows government's suggestions to change the menu in order to reduce the lunch boxes'
calories. Suppose after the menu update, each lunch box's calories can be reduced by 4%. Find the
sample mean and sample standard deviation of calories of the above sample after the change. Hence,
construct a 90% confidence interval estimate of the population mean calories in a lunch box after the
change.
Answers
The 90% confidence interval estimate of the population mean calories in a lunch box after the change is between 524.2 and 531.8.
How to construct a 90% confidence interval estimate of the population mean calories in a lunch box after the change.(a) The point estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 is 0.09, which is equal to 27/300.
(b) The sampling error at 98% confidence level for the estimate of the population proportion can be calculated using the following formula:
Sampling error = z*(standard deviation/square root of sample size)
Where z is the critical value at 98% confidence level, which can be found using a standard normal distribution table or calculator. For a 98% confidence level, the z value is 2.33.
Substituting the values, we get:
Sampling error = 2.33*(sqrt(0.09*0.91/300)) = 0.049 or 4.9%
Therefore, the sampling error at 98% confidence level for the estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 is 4.9%.
(c) The 98% confidence interval estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 can be calculated using the following formula:
Confidence interval = point estimate ± (z*standard error)
Where point estimate is 0.09, z is the critical value at 98% confidence level which is 2.33, and standard error is the standard deviation divided by the square root of sample size.
Substituting the values, we get:
Confidence interval = 0.09 ± (2.33*sqrt(0.09*0.91/300)) = 0.09 ± 0.114 or (0.026, 0.154)
Therefore, the 98% confidence interval estimate of the population proportion of lunch boxes provided by "Better Lunch" had calories above 650 is between 0.026 and 0.154.
(d) After the menu update, the sample mean of the calories of the above sample can be calculated as follows:
New sample mean = 0.96 * 550 = 528
The sample standard deviation after the change is still 40, assuming the variability of calories is not affected by the menu update.
To construct a 90% confidence interval estimate of the population mean calories in a lunch box after the change, we can use the following formula:
Confidence interval = sample mean ± (t*standard error)
Where t is the critical value at 90% confidence level with degrees of freedom (df) = sample size - 1. Using a t-distribution table or calculator with df = 299, we find that t = 1.645.
The standard error can be calculated as follows:
Standard error = standard deviation/sqrt(sample size) = 40/sqrt(300) = 2.31
Substituting the values, we get:
Confidence interval = 528 ± (1.645*2.31) = 528 ± 3.8 or (524.2, 531.8)
Therefore, the 90% confidence interval estimate of the population mean calories in a lunch box after the change is between 524.2 and 531.8.
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if tan68° = 1/m, express the following in terms of m:
1. tan22°
Answers
tan(3 * 22°) = (3tan22° - tan^3(22°)) / (1 - 3tan^2(22°))
Solving for tan(22°), we get:
tan(22°) = (3tan(3 * 22°) - tan^3(3 * 22°)) / (3tan^2(3 * 22°) - 1)
Now, using the identity tan(3θ) = (3tanθ - tan^3θ) / (1 - 3tan^2θ), we can also say that:
tan(3 * 68°) = (3tan68° - tan^3(68°)) / (1 - 3tan^2(68°))
Given that tan68° = 1/m, we can substitute this value into the equation above to get:
tan(3 * 68°) = (3/m - 1/m^3) / (1 - 3/m^2)
Simplifying this expression, we get:
tan(3 * 68°) = (3 - m^2) / (m^3 - 3m)
Now, substituting the value of tan(3 * 22°) = (3 - √3) / (3√3 - 1) into the equation for tan(22°), we get:
tan(22°) = (3(3 - √3)/(3√3 - 1) - (3 - √3)^3/(3√3 - 1)^3) / (3(3 - √3)/(3√3 - 1)^2 - 1)
Simplifying this expression, we get:
tan(22°) = (27 - 9√3 - 27√3 + 9√3) / (27√3 - 9 - 3√3 + 1)
tan(22°) = (18 - 18√3) / (26√3 - 8)
Therefore, we can express tan(22°) in terms of m as:
tan(22°) = (18 - 18√3) / (26√3
tan(68° - 46°) = (tan 68° - tan 46°)/(1 + tan 68° * tan 46°)
tan 22° = (tan 68° - tan 46°)/(1 + tan 68° * tan 46°)
We know that tan 68° = 1/m, so we can substitute:
tan 22° = (1/m - tan 46°)/(1 + (1/m) * tan 46°)
Therefore, tan 22° can be expressed in terms of m as:
tan 22° = (1/m - tan 46°)/(1 + tan 46°/m)
1. Danny has $500. He wants to buy 4 identical tires for his truck. He needs to save at least $25 for a car wash.
Which inequality could Danny use to find x, the amount he can spend on each tire?
A 4x + 500 ≥ 25
B 500 - 4x ≤ 25
C 4x + 500 ≤ 25
D 500 - 4x ≥ 25
Answers
Is (9,8) a solution to this system of equations?
6x - 5y = 16
X = 9
yes
no
Answers
6x-5y=16
(6x9)-5y=16
54-5y=16
-5y=16-54
-5y=-38
y=38/5
What fraction is equivalent to 1/4
The numbers are: 2,4,6,8,10,12
Answers
What is the volume and surface area of a rectangular prism that is 11 ft long, 8 ft wide, and 4 ft tall?
Answers
Answer:
Here
Step-by-step explanation:
The volume of a rectangular prism is found by multiplying the length, width, and height.
Volume = Length x Width x Height
Volume = 11 ft x 8 ft x 4 ft
Volume = 352 cubic feet
The surface area of a rectangular prism is found by adding up the areas of all six faces.
Surface area = 2lw + 2lh + 2wh
Surface area = (2 x 11 ft x 8 ft) + (2 x 11 ft x 4 ft) + (2 x 8 ft x 4 ft)
Surface area = 176 + 88 + 64
Surface area = 328 square feet
Therefore, the volume of the rectangular prism is 352 cubic feet and the surface area is 328 square feet.
for justin beibers part only pls help
Answers
On day zero, the number of students who know the rumor are 2 people who are Susanna and Liz.
On day 2, the number of students would be 12 students.
The number of days till 32 students know the rumor is 6 days.
2 students (Susanna and Liz) know the rumor on day 0.
On day 2, the number of students who know the rumor will be the initial number of students (2) plus 5 students for each day that has passed (5 * 2 = 10). So, on day 2, 2 + 10 = 12 students know the rumor.
To find the number of days it will take for 32 students to know the rumor, we can set up an equation using the given information:
2 (Susanna and Liz) + 5 x number of days = 32
Now, we can solve for the number of days:
5 x number of days = 32 - 2
5 x number of days = 30
number of days = 30 / 5
number of days = 6
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Write a quadratic function with zeroes – 1 and 6. Write your answer using the variable x and in standard form with a leading coefficient of 1.
Answers
Answer:
If the zeroes of a quadratic function are -1 and 6, then its factored form is:
(x + 1)(x - 6) = 0
Expanding the left side:
x^2 - 5x - 6 = 0
So the quadratic function in standard form is:
f(x) = x^2 - 5x - 6
Answer:
f(x) = x^2 - 5x - 6
Step-by-step explanation:
To create a quadratic function with zeroes -1 and 6, we can start by using the zero product property to write out the factors of the equation:
(x + 1)(x - 6) = 0
Expanding the factors, we get:
x^2 - 5x - 6 = 0
This quadratic equation is in standard form with a leading coefficient of 1. Therefore, the quadratic function with zeroes -1 and 6 is:
f(x) = x^2 - 5x - 6
This function can also be graphed on the coordinate plane as a parabola with a vertex at (2.5, -10.25) and its axis of symmetry at x = 2.5. The graph would intersect the x-axis at -1 and 6, confirming that these are the zeroes of the function.
Jason is planning to surprise his wife with a trip to Turkey this summer. He had difficulty making hotel reservations during
tourist season, but managed to reserve a room for two weeks in a nice hotel in Cappadocia in central Turkey. From there, he
plans to rent a car to take him and his wife to see the sights. After making all of his hotel and rental car reservations, Jason
is surprised to see that the trip will cost much more than he anticipated. What change(s) should Jason make to his vacation
to lower the overall cost?
Answers
The changes that Jason should make are:
1. Plan a trip not during the tourist season.
2. In place of renting car, use transportation services of the country.
3. He should go to other places to find a nice hotel.
The solution has been obtained by using cost planning.
What is cost planning?
Estimating expenses, establishing an agreed-upon budget, and managing actual and projected expenditures in relation to that budget are all parts of cost planning and control.
The changes that Jason should make are:
1. Plan a trip not during the tourist season. This is because during the tourist season prices are high.
2. In place of renting car, use transportation services of the country. This is because the local transport will cost him less that the rental.
3. He should go to other places to find a nice hotel. This is because central Turkey is costly and he might find a nice hotel in other areas in less price.
Hence, the required solution has been obtained.
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Solve for AB using the given info.
#11
Answers
The length of AB of the parallelogram is determined as 14.36 inches.
What is the length AB?The length of AB of the parallelogram can be determined by applying cosine rule as shown below:
The cosine rule, also known as the law of cosines, is a mathematical formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is commonly used to find the length of an unknown side or the measure of an unknown angle in a triangle when the lengths of two sides and the measure of the included angle are known.
Length AB = Length AD = x
DB² = AB² + AD² - 2(AB x AD) cos (A)
22² = x² + x² - 2x²(cos 100)
484 = 2x² + 0.347x²
484 = 2.347x²
x² = 484/2.347
x² = 206.2
x = √206.2
x = 14.36 inches
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Determine the equation of the circle graphed below.
Answers
The equation for the circle graphed in the coordinate axis is:
(x - 5)^2 + (y - 6)^2 = 16
How to determine the equation for the circle?Remember that the equation for a circle whose center is at (a, b) and has a radius R is.
(x - a)^2 + (y - b)^2 = R^2
On the graph, we can see that the center of the circle is at (5, 6), and the radius of the circle is R = 4 units. Then the equation for the circle in the graph is:
(x - 5)^2 + (y - 6)^2 = 4^2
(x - 5)^2 + (y - 6)^2 = 16
That is the equation we wanted to find.
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Calculate the length of IG. *
3
square root 20
square root 50
square root 10
square root 25
Answers
The length of LG in the plane is
square root 50How to find the length of LGTo find the distance between two points in a 2D plane, we can use the distance formula:
distance = √((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can find the distance between L(4,4) and G(9,9):
distance = √((9 - 4)^2 + (9 - 4)^2)
= √(5^2 + 5^2)
= √50
= 5√2
Therefore, the distance between L(4,4) and G(9,9) is 5√2, which is approximately 7.07 units.
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Help pls
Stuck on this question
Answers
Answer:
x = 35
Step-by-step explanation:
since the figures are similar then the ratios of corresponding parts are in proportion, that is
[tex]\frac{x}{10}[/tex] = [tex]\frac{14}{4}[/tex] = [tex]\frac{7}{2}[/tex] ( cross- multiply )
2x = 7 × 10 = 70 ( divide both sides by 2 )
x = 35
El m.c.m y m.c.d de 15 21 y 63
Answers
El M.C.M es 315.
Y el M.C.D es 3
Find the equation of a line that passes through the points (4, 1) and (12, -3).
Answers
The equation of the line that passes through the points (4, 1) and (12, -3) is y = (-1/2)x + 3.
Explain the term equation
An equation is a mathematical statement that expresses the equality of two expressions or values. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to represent relationships between quantities and to solve problems in various fields, including mathematics, physics, and engineering.
According to the given information
We can use the point-slope form of the equation of a line to find the equation of the line that passes through the two given points.
The point-slope form of the equation of a line is:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is a point on the line.
To find the slope of the line that passes through (4, 1) and (12, -3), we can use the slope formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (4, 1) and (x2, y2) = (12, -3)
m = (-3 - 1) / (12 - 4) = -4 / 8 = -1/2
Now that we have the slope of the line, we can use one of the two given points and the slope to find the equation of the line. Let's use the point (4, 1):
y - y1 = m(x - x1)
y - 1 = (-1/2)(x - 4)
Distributing the -1/2, we get:
y - 1 = (-1/2)x + 2
Adding 1 to both sides, we get:
y = (-1/2)x + 3
Therefore, the equation of the line that passes through the points (4, 1) and (12, -3) is y = (-1/2)x + 3.
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What is 7x7 using an exponent
Answers
Answer:
7²
Step-by-step explanation:
You want to know what 7×7 is when it is written using an exponent.
ExponentAt its most basic, an exponent signifies repeated multiplication. It represents the number of times a value appears as a factor in the product.
The expression 7×7 has 7 as a factor 2 times. It can be written as 7 with an exponent of 2.
7×7 = 7²
<95141404393>
Need the answer quickly!!!
Answers
Matching each function with the transformation that took place gives:
g(x) = -(x - h)ⁿ: Reflection across the x-axis
j(x) = axⁿ + k: Translation of k units up
m(x) = (x + h)ⁿ - k: Translation of h units to the left
Vertical dilation: Functions of form f(x) = 2ⁿ are vertically dilated.
What is transformation?In mathematics, a transformation refers to a process of changing the size, position, or orientation of a geometric object or a function.
Transformations are usually expressed as a set of rules or equations that determine how each point or element in the original object or function maps to a corresponding point or element in the transformed object or function. Common types of transformations include translations, rotations, reflections, dilations, and combinations of these operations.
Transformations are widely used in many areas of mathematics, physics, engineering, and computer science to study and model complex systems and phenomena.
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College Level Trigonometry question any help will do
Answers
Answer:
16.58. my answer needs to be more than 20 characters, soooo... how is your day going?
PLEASE Help me answer these 2 math questions!!!
Answers
1. The equation for the function is defined as follows: g(x) = (1/3)^x - 2.
2. The range of the function is given as follows: The set of real numbers less than -5.
How to define an exponential function?An exponential function has the definition presented as follows:
y = ab^x.
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.For item 1, the function has an horizontal asymptote at y = -2, hence it is defined as follows:
y = a(1/3)^x - 2.
When x = 0, y = -1, hence the parameter a is obtained as follows:
-1 = a - 2
a = 1.
Thus the function is:
g(x) = (1/3)^x - 2.
For item 2, we have that the function is:
Reflected over the y-axis, due to the negative sign of a.Has an horizontal asymptote at y = -5.Hence the range of the function is given as follows:
The set of real numbers less than -5.
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Mrs. Evans wants to buy enough dog food to feed her dog for 90 days. Her dog eats 4 ounces of dog food twice a day. How many pounds of dog food should she buy?
Answers
The quantity of pounds of dog food that Mrs. Evans should buy that would be enough for her dog = 720 ounces.
How to calculate the quantity of pounds of dog food needed?The total number of days the food is required to last = 90 days.
The quantity of dog food in ounce the dog eat per day = 4 × 2 = 8 ounces.
Therefore the quantity of pounds that will be enough for the dog for the whole 90 days would be = ?
That is;
1 day = 8 ounces
90 days = X
Make X the subject of formula;
X = 90× 8
= 720 ounces
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You are given that cos(A)=−5/13, with A in Quadrant II, and sin(B)=24/25, with B in Quadrant II. Find cos(A+B). Give your answer as a fraction.
Answers
The value for the trigonometric expression cos(A+B) is (5√7 - 288)/325
Explain trigonometry.
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It includes the study of trigonometric functions such as sine, cosine, and tangent, which are used to calculate unknown angles or sides of a triangle. Trigonometry has many practical applications in fields such as engineering, physics, and navigation.
According to the given information
We can use the trigonometric identity cos(A + B) = cos(A)cos(B) - sin(A)sin(B) to find cos(A + B).
Since cos(A) = -5/13 and A is in Quadrant II, we can use the Pythagorean identity sin²A + cos²A = 1 to find sin(A). Solving for sin(A), we get sin²A = 1 - cos²A = 1 - (-5/13)² = 144/169. Since A is in Quadrant II, sin(A) is positive, so sin(A) = √(144/169) = 12/13.
Similarly, since sin(B) = 24/25 and B is in Quadrant II, we can use the Pythagorean identity to find cos(B). Solving for cos(B), we get cos²B = 1 - sin²B = 1 - (24/25)² = 7/625. Since B is in Quadrant II, cos(B) is negative, so cos(B) = -√(7/625) = -√7/25.
Substituting these values into the identity for cos(A + B), we get:
cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
= (-5/13)(-√7/25) - (12/13)(24/25)
= (5√7)/(13*25) - (12*24)/(13*25)
= (5√7 - 288)/(13*25)
= (5√7 - 288)/325
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35 Points! Multiple choice. State the domain and range of the function graphed. Photo attached. Thank you!
Answers
Domain and range of function is (D)=D={x|x≥2}, R={y|y≥0}.
Define domain and range of functionIn mathematics, the domain of a function is the set of all possible input values for which the function is defined. The range of a function is the set of all possible output values that the function can produce, based on its input values. In other words, the domain is the set of all x-values that the function can take, while the range is the set of all corresponding y-values that the function can take.
The given graph is oriented toward x direction
Domain of function =x≥2
For every value of x the y is always positive
So, range =y≥0
Hence, domain and range of function is (D)=D={x|x≥2}, R={y|y≥0}
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The vectors v and w lie in the coordinate plane such that their initial points are at the origin. Vector v has a magnitude of 2 and direction of 45° North of East. Vector w has a magnitude of 2 and a direction of 45° South of East. What is the magnitude of the vector v+w?
Answers
The vector v+w has a magnitude of 2√2 and its direction is along the positive x-axis.
What is meant by vector?
A vector is a quantity that has both magnitude and direction. It is represented as an arrow with its length representing the magnitude and its direction representing the direction of the quantity.
What is meant by the x-axis?
The x-axis is the horizontal line on a coordinate plane that is used as a reference for plotting and describing the positions of points in two-dimensional space. It is often referred to as the "horizontal axis" or the "abscissa".
According to the given information
Here the vector v has a magnitude of 2 and a direction of 45° so the components of vector v are:
v_x = 2 cos 45° = √2
v_y = 2 sin 45° = √2
Vector w has a magnitude of 2 and a direction of 45° South of East. This means that the angle between vector w and the positive x-axis is 45°, and the angle between vector w and the negative y-axis is 45°. Therefore, the components of vector w are:
w_x = 2 cos 45° = √2
w_y = -2 sin 45° = -√2
Now we can add the components of vectors v and w to find the components of the vector v+w:
(v+w)_x = v_x + w_x = √2 + √2 = 2√2
(v+w)_y = v_y + w_y = √2 - √2 = 0
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