Answer:
[tex]\displaystyle \displaystyle \int {sin(3x)} \, dx = \frac{-cos(3x)}{3} + C[/tex]
General Formulas and Concepts:
Calculus
Antiderivatives - Integrals
Integration Constant C
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Trig Integration: [tex]\displaystyle \int{sin(x)} \, dx = -cos(x) + C[/tex]
U-Substitution
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \int {sin(3x)} \, dx[/tex]
Step 2: Identify Substitution Variables
u = 3x
du = 3dx
Step 3: Integrate
[Integral] Rewrite: [tex]\displaystyle \frac{1}{3}\int {3sin(3x)} \, dx[/tex][Integral] U-Substitution: [tex]\displaystyle \frac{1}{3}\int {sin(u)} \, du[/tex][Integral] Trig Integration: [tex]\displaystyle \frac{1}{3}[-cos(u)] + C[/tex][Expression] Multiply: [tex]\displaystyle \frac{-cos(u)}{3} + C[/tex][Expression] Back-Substitute: [tex]\displaystyle \frac{-cos(3x)}{3} + C[/tex]Paula lives 1 9/10miles from school. Nate lives 1 3/4 miles from school. Cristian lives 11/8 miles from school. Who lives closest to school?
Cristian lives closest to school in linear equation.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Paula = 1 9/10miles
Nate = 1 3/4 miles
Cristian = 11/8 miles
Paula = 19/10
Nate = 7/4
Cristian = 11/8
now take LCM
Total distance from school is 40 miles
Paula = 19/10 * 40 = 76
Nate = 7/4 * 40 = 70
Cristian = 11/8 * 40 = 55
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K-12. Grade 7th.
Multiply.
(−1217)⋅(−16)
What is the product?
Enter your answer as a simplified fraction in the box.
what does GCF stand for?
Answer:
Greatest Common Factor
Step-by-step explanation:
Answer:
greatest common factor
Step-by-step explanation:
Pam has 125 gummy bears. Bob has 87 more than Pam. How many gummy bears does Bob Have?
Answer:
212 gummy bears
Step-by-step explanation:
Just add 125 and 87 together
Answer: 212
Step-by-step explanation:
Its simple addition.
for the following function: g=2x-10 find g(20)
Answer:
-20 beacause - x + = - and you do 2x10
Two machines just completed projects at the same time. Machine A completes a project every 5.5 minutes. Machine B completes a project every 5.25 minutes. How long will it be until both machines complete a project at the same time?
It would take 2.69 minutes for both machines to complete the project at the same time
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
Machine A completes a project every 5.5 minutes. Machine B completes a project every 5.25 minutes.
Let t represent time it would take both machines to complete the project, hence:
(1/5.5 + 1/5.25)t = 1
86t/231 = 1
t = 2.69 minutes
It would take 2.69 minutes to complete
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a queuing model that follows the m/m/1 assumptions. a customer can be served every 4 minutes. customers arrive independently at the rate of one customer every 5 minutes according to a poisson distribution. the average number in the system is
For the m/m/1 queuing model, the average number in the system is equals to the four. So, the correct answer is option (c).
This is the most widely used queuing system in analytics. M/M/1 is a good approximation for a large number of
mass service systems. The M/M/1 quening system assumes a Poisson arrival process. This assumption is a very good approximation for the process of arriving at real systems that satisfy the following rules,
The number of customers in the system is very large.The influence of one customer on system performance is very small, i.e. one customer consumes a very small percentage of system resources.All customers are independent, i.e. their decision to use the system is independent of other users.We have, customer service is every 4 minutes. So, the Service rate μ = 1 customer/4 minutes = 0.25 customer/minute or 15 per hour.
Customers arrive individually at a rate of one customer every 5 minutes according to the distribution of poisons.
Number of customer service= 1
The arrival rate is 1/ (mean time between arrivals) . Here, the rate of arrival of customers/5 minutes is λ = 0.2 customers/min or 12 per hour. Therefore,
Utilization factor = (arival rate /service rate)100 = λ/μs
Utilization factor = (12/15) 100%
= (4/5)100 = 80%
Utilization factor = 80%
Average number in the system = λ/( μ - λ)
= (60/5)/[ (60/4)-(60/5)]
= 12/3 = 4
So, the average number in the system is 4.
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Complete question:
A queuing model that follows the m/m/1 assumptions. a customer can be served every 4 minutes. customers arrive independently at the rate of one customer every 5 minutes according to a poisson distribution. the average number in the system is
a) 7
b) 5
c) 4
d) 6
todd noticed that both porportional and linear relationships form a straight line when graphed , and he concludes that all linear relationships must be porportional . Do you agree? why or why not
Todd's conclusion is therefore incorrect, not all linear relationships are proportional, they can be represented by a linear equation but they don't need to have a constant ratio between the two variables.
What is a linear relationship?
A linear relationship is a relationship between two variables in which the change in one variable is directly proportional to the change in the other variable. Linear relationships can be represented by a linear equation, which is an equation that can be written in the form of y = mx + b, where m and b are constants.
Proportional relationships also have a constant ratio between the two variables, but the relationship between the variables is not always linear. Proportionality can be represented by the equation y = kx, where k is a constant.
In general, it is not true that all linear relationships must be proportional. While it is true that a proportional relationship will always result in a linear graph, there are also many other types of linear relationships that do not fit this definition. For example, the equation y = 2x + 3 describes a linear relationship, but it is not proportional because the ratio between y and x is not constant.
Hence, Todd's conclusion is therefore incorrect, not all linear relationships are proportional, they can be represented by a linear equation but they don't need to have a constant ratio between the two variables.
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Help please
Select the values that make the inequality -3q ≤ 51 true. Then write an equivalent
inequality, in terms of q.
(Numbers written in order from least to greatest going across.)
Therefore , the solution of the given problem of inequality comes out to be -17 is the figure that meets the inequality .
Define inequality.When both sides of a mathematical expression are not equal, an inequality exists. In inequality, we compare values in contrast to equations. The equal sign is substituted by the signs smaller than (or lower than or identical to), wider than (or greater or comparable to), or even not equal to. Olivia, for instance, is selected for the 12U Softball level. How old is Olivia? You don't know Olivia's age because "equals" is missing from the sentence. But since you know she needs to be less than or similar to 12, so can enter Olivia's Age 12.
Given:
-3q ≤ 51
Currently, -17 is the figure that meets the inequality out of all the numbers that have been provided.
Due to the fact that a negative integer has a higher value the smaller it is, -3 5 1.
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Classify AABC by its sides. Then determine whether it is a right triangle,
A(6, 6), B(9, 3), C(2, 2)
The triangle ABC seems to be an scalene triangle since all of the sides AB, BC and CA have different lengths, and also the triangle is not a right angled triangle.
What is a scalene Triangle?A scalene triangle is a type of triangle in which all three sides have different lengths. In other words, none of its sides are of equal length. As a result, all three angles in a scalene triangle are also different. It is different from an Isosceles triangle, where at least two sides are of equal length and an equilateral triangle where all sides are of equal length.
What is a right angled triangle?A right triangle is a type of triangle in which one angle is a right angle (90 degrees). This makes it different from other types of triangles such as acute triangle and obtuse triangle. The side opposite to the right angle is called the hypotenuse, and the other two sides are called legs. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. This theorem is used to determine if a triangle is a right triangle or not.
The triangle ABC is a scalene triangle, as its sides have different lengths.
To determine whether it is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (legs) is equal to the square of the length of the longest side (hypotenuse).
To find the side lengths, we can use the distance formula, which is
d = √((x2 - x1)² + (y2 - y1)²)
AB = √((9 - 6)² + (3 - 6)²) = √(3² + (-3)²) = √18 = 3√2
BC = √((9 - 2)² + (3 - 2)²) = √(7² + 1²) = √50 = 5√2
AC = √((2 - 6)² + (2 - 6)²) = √(4² + 4²) = √32 = 4√2
We know that in a right triangle, one of the side should be the hypotenuse and the other two should be the legs. We can check if any one of the side is satisfying that. But in this case, we can see that none of the sides are satisfying that condition, therefore the triangle ABC is not a right triangle.
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consider the polynomial function.
f(x)=-2(x-5)(x+6)(x+7)
which zeros can be used to graph the polynomial function?
a.) x=-7, -6, and 5
b.) x=-7, -6, -2, and 5
c.) x=-5, 6, and 7
d.) x=-5, -2, 6, and 7
Answer:
a
Step-by-step explanation:
to find the zeroes let f(x) = 0 , that is
- 2(x - 5)(x + 6)(x + 7) = 0
equate each factor to zero and solve for x
obviously multiplying any value by - 2 will not give zero
so only consider the binomial factors
x + 7 = 0 ⇒ x = - 7
x + 6 = 0 ⇒ x = - 6
x - 5 = 0 ⇒ x = 5
Phil and Meredith work for a book publisher editing mathematics textbooks. Phil has less experience and takes four times as long as Meredith to edit a textbook. Together, it takes them 16 hours to edit a textbook.
How long does it take Phil to edit a textbook if he works alone?
How long does it ake Meredith to edit a textbook if she works alone?
Let x be the time (in hours) it takes Meredith to edit a textbook alone. We know that Phil takes 4x hours to edit a textbook alone, since he takes four times as long as Meredith.
We also know that it takes them 16 hours to edit a textbook together. We can use this information to set up the equation:
x + 4x = 16
5x = 16
x = 16/5
So it takes Meredith 16/5 hours to edit a textbook alone.
We know that Phil takes 4x to edit a textbook alone, so we can substitute in the value we found for x to find his time:
4x = 4(16/5) = 16/5 * 4 = 64/5
So it takes Phil 64/5 hours to edit a textbook alone.
Evaluate x/y for X=2/3 and Y= 6/7
Answer:
7/9
Step-by-step explanation:
Simplify the following:
(2/3)/(6/7)
Multiply the numerator by the reciprocal of the denominator, (2/3)/(6/7) = 2/3×7/6:
(2×7)/(3×6)
2/6 = 2/(2×3) = 1/3:
7/(3×3)
3×3 = 9:
Answer:7/9
To evaluate x/y for x = 2/3 and y = 6/7, you need to substitute these values into the expression x/y and simplify the result.
x/y = (2/3) / (6/7)
To simplify the fraction, you can cross multiply the numerator and denominator by 7, which is the denominator of the second fraction:
(2/3) / (6/7) = (2/3) * (7/6) = (27) / (36) = 14/18
The fraction can be simplified further by dividing both the numerator and denominator by their greatest common divisor (GCD) which is 2:
14/18 = (14/2) / (18/2) = 7/9
So x/y = 7/9 when x = 2/3 and y = 6/7
It's important to note that the result is a fraction, if you want to express it as decimal you can divide 7 by 9 or use a calculator to get 0.7777 repeating.
2 1/4 * 1 1/2 Area and Mixed Numbers.
Answer:
21/4 * 11/2=5.25*5.5
Step-by-step explanation:
21/4 * 11/2=5.25*5.5
= 28.875
Algebra 2 big ideas math please help me
Answer:
Step-by-step explanation:
9
Determine if the equations are parallel, perpendicular, or neither. 2y=-3x = 6 and y = -3/2x + 5
You can use the formula y=mx+b, where m is the slope.
Your gradient is -3/2.
What are Equations?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.
A statement is not an equation if it has no "equal to" sign.
According to our question-
y=-3/2x+1
Your slope in the second equation is -3/2 since y=-3/2x+5 is already in the form y=mx+b and m is the slope.
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for what values of k will the line be tangent to the circle ?x^2 + y^2 = 25 where y = x+k.please help I have an exam tomorrow
Answer: To find the values of k for which the line y = x + k is tangent to the circle x^2 + y^2 = 25, we need to substitute y = x + k into the equation of the circle and solve for x.
x^2 + (x + k)^2 = 25
Expanding the square, we get:
x^2 + x^2 + 2xk + k^2 = 25
2x^2 + 2xk + k^2 = 0
Now we can solve for x by using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Where a = 2, b = 2k and c = k^2
x = (-2k ± √(4k^2 - 42k^2)) / 2*2
x = (-k ± √(-3k^2)) / 4
Since the square root of a negative number is not a real number, we can see that there is no real value of x that will make the equation true. Therefore, the line y = x + k is never tangent to the circle x^2 + y^2 = 25
Answer:
Step-by-step explanation:
To find the values of k that will make the line y = x + k tangent to the circle x^2 + y^2 = 25, we need to set the equation of the line equal to the equation of the circle and solve for k.
First, we'll substitute y = x + k into the equation of the circle:
x^2 + (x + k)^2 = 25
Next, we'll expand the square on x + k:
x^2 + x^2 + 2xk + k^2 = 25
Now we'll combine like terms:
2x^2 + 2xk + k^2 = 25
We'll rearrange the equation so that x^2 is on one side
2x^2 + 2xk + k^2 - 25 = 0
Now we'll divide by 2
x^2 + xk + k^2/2 - 25/2 = 0
Now we'll complete the square
x^2 + xk + (k^2/2 - 25/2) = 0
x^2 + xk + (k^2/2 - 25/2) + (25/2) = (25/2)
(x + k/2)^2 = 25/2
Now we'll take the square root of both sides
x + k/2 = +-sqrt(25/2)
Now we'll solve for x
x = sqrt(25/2) - k/2 or x = -sqrt(25/2) - k/2
Now we'll substitute these values of x into the equation y = x + k and find the value of k.
x = sqrt(25/2) - k/2
y = x + k
y = sqrt(25/2) - k/2 + k
y = sqrt(25/2)
x = -sqrt(25/2) - k/2
y = x + k
y = -sqrt(25/2) - k/2 + k
y = -sqrt(25/2)
So the line y = x + k is tangent to the circle x^2 + y^2 = 25 when k = sqrt(25/2) or k = -sqrt(25/2)
A music streaming service charges $7 per month for the first user, and $4 more per month for each additional user. Which function represents the monthly bill y in terms of the number of additional users x ?
The function for the monthly bill can be written as y = 7 + 4x.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a music streaming service charges $7 per month for the first user and $4 more per month for each additional user.
The equation can be written as,
y = 4x + 7
Here, y is the monthly charge and x is the number of months.
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elise is a project manager
Elise average pay per hour in 2017 is 13.73 pounds
How to calculate the average pay?Elise earned 2100 as a monthly salary in 2016.In 2017, she got a 3% pay increase on her monthly salary.
So, in 2017 she got a monthly salary of (1+3/100)*2100= 2163
Then her yearly salary in the year 2017 became (2163 × 12) =25956
In 2017, Elise worked for 1890hours.
Therefore, her average pay per hour for the year 2017 will be:
= 25956 / 1890
= 13.73
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Complete question
in 2016, she earned a monthly salary of £2100
In 2017, she earned a 3% pay increase on her monthly salary.
Given that in 2017 Elise worked 42 hours per week for 45 weeks work out her average pay per hour for the year.
This recipe makes 5 portions of porridge. Complete the amount of each ingredient that is needed to make just 2 portions. Recipe: Serves 5 250 g oats 1.4 litres milk 90 g sugar
DO THIS NOW URGENTLY
The amount of ingredient that is needed to make just 2 portions are:
100 grams of oats0.48 liters of milk36 grams of sugar.What does a Portion mean?Generally, the term "portion" refers to how much food is served to you or how much you eat. Portion sizes can differ from meal to meal. For example, you might serve yourself two small pancakes in one portion at home, but at a restaurant, you might get a stack of four pancakes as one portion.
Data
Needed 2 portions
Recipe: 250 g oats, 1.4 litres milk, 90 g suga
Portion of Oat:
250/5 * 4 = 50 *2 = 100g oats
Portion of milk:
1.2/5 * 2 = 0.48l milk
Portion of sugar:
90/5 * 2 = 18*2 = 36g sugar
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solve the file please
Answer:
z + 4 × 9
Sorry if this is wrong.
Simple Interest Example I Calculate the new value of the Sum of N1,500 Investment is alero micro finance bank at a simple rate of 15% per annum for 2 years.
Answer: The new value of the sum of N1,500 investment at a simple rate of 15% per annum for 2 years is N1950
Step-by-step explanation:
Simple interest is calculated by multiplying the principal amount, interest rate, and time.
The formula for simple interest is:
Simple Interest = (principal x rate x time) / 100
In this case, the principal amount is N1,500, the interest rate is 15% per annum and the time is 2 years.
So the simple interest earned on the investment is:
Simple Interest = (1500 x 15 x 2) / 100
Simple Interest = N450
To find the new value of the investment, we add the simple interest earned to the principal amount.
New value = Principal + Simple Interest
New Value = 1500 + 450
New Value = N1950
Explanation: Simple interest is calculated by multiplying the principal amount, interest rate, and time. By using this formula, the interest earned on the investment was N450. And by adding the interest to the principal amount, we can find the new value of the investment which is N1950.
The table below shows Addison's novel collection on her bookshelf.
Type of Novel Number of Books
Nonfiction 2
Mystery 4
Fiction 5
What is the ratio of mystery novels to all novels?
4 to 5
2:4
5 over 11
4 to 11
The ratio of the mystery novel to all novels from Addison's novel collection, is D. 4 to 11.
How to find the ratio ?Mathematicians use the term "ratio" to compare two or more numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another. Two quantities are compared using division in a ratio. In this case, the dividend is referred to as the "antecedent" and the divisor as the "consequent."
The ratio of the mystery novels to all novels can therefore be found by first finding the total number of novels :
= 2 + 4 + 5
= 11 novels
The ratio would then be:
Number of mystery novels : Number of all novels
4 : 11
Which is 4 to 11.
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Which of the following functions is graphed below?
Answer: it's a function
Step-by-step explanation:
A neurosurgeon is saving for retirement and invests $25,000 at a rate of 5.63% per year compounded continuously. If the neurosurgeon plans to retire in 28 years, what is the final value of the investment? Round the answer to the nearest penny. $64,410.00 $95,937.73 $119,658.03 $120,937.73
At the end of 28years the neurosurgeon will have an amount of $115875.00
What is compound interest?Compound interest is when you earn interest on both the money you've saved and the interest you earn.
The amount earned or paid after compounded interest is given as A = P(1+r/100)^t
Where P is the principal saved
t is the time for saving
and r is the rate of interest
Here t = 28 years
P = 25,000
and r = 5.63% per annum
therefore A = P(1+r/100)^t
A = 25000(1+5.63/100)^28
A = 25000(1+0.0563)^28
A = 25000(1.0563)^28
A = 25000× 4.635
A= $115875.00
This means at the end of 28 years, the neurosurgeon will have a amount of $115875.00
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Use the quadratic formula to find the complex roots
X^2+6x+14
The required distinct roots of the following equation using the quadratic formula is x = -3±√5i.
What is the quadratic formula?Any quadratic problem can be solved using the quadratic formula.
The equation is first changed to have the form ax2+bx+c=0, where a, b, and c are coefficients.
After that, we enter these coefficients into the following formula: (-b(b2-4ac))/(2a).
So, the quadratic formula:
x = -b±√b²-4ac/2a
Now, insert values and calculate for roots as follows:
x = -b±√b²-4ac/2a
x = -b±√b²-4*4(1)*14/2(1)
x = -b±√36/56/2
x = -b±√-20/2
Discriminant: b² - 4ac < 0
Now,
x = -6± 2√5i/2
x = -6/2 ± 2√5i/2
x = -3±√5i
Therefore, the required distinct roots of the following equation using the quadratic formula is x = -3±√5i.
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4 more than the difference of 30 and a number r
Christine got a prepaid debit card with $2s on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 14 cents per yard. If after that purchase there was $18.42 left on the card, how many yards of ribbon did Christine buy?
Answer:
To calculate the number of yards of ribbon Christine bought, we need to determine how much money she spent on the ribbon. We know that the card had $20 on it initially and that $18.42 was left on the card after her purchase, so we can subtract the remaining balance from the original balance to find out how much she spent:
$20 - $18.42 = $1.58
We also know that the ribbon was 14 cents per yard, so we can divide the amount spent on the ribbon by the price per yard to find out how many yards Christine bought:
$1.58 / $0.14 = 11.285714285714286
So, Christine bought 11.285714285714286 yards of ribbon.
Sam has 26 seashells.
He collects 31 more seashells.
• Then he gives 14 seashells away.
Which equation shows the number of seashells, s, Sam has now?
Answer:
hshs7hhs7bs7bs8be8
Step-by-step explanation:
26+31= 57-14=43
Answer:
26+31-14
Step-by-step explanation:
using pendant you should answer that correctly so...
26+31=57-14 and you should get 43
in written form...
Sam has 31 seashells to his 26 seashells giving him the total of 57. Sam then gave away 14 of the 57 seashells away leaving him with 43 seashells.
hope this helps
Compare 3/5 and - 8/5
The correct statement is,
⇒ - 8/5 < 3/5
What is mean by Fraction?A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
Given that;
The numbers are,
⇒ 3/5 and - 8/5
Now, By comparing, we get;
⇒ 3/5 and - 8/5
⇒ 3/5 > - 8/5
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