To manufacture a panels that are u = 48 in. wide and 2 in. thick with the profile of the roofing takes the shape of a sine wave with equation y = sin(pi x/12) from flat sheet, the width of the flat sheet would be 49.59in.
Therefore the answer is 49.59
To find the arc length of a continuous function, you need to first define the function and the interval over which you want to find the arc length. Then you can use the following formula:
Arc Length = ∫√(1+(f'(x))^2) dx
Here, f(x) is the function and the interval is [a, b].
The width, w of the flat metal sheet needed to make the panel is the arc length of the sine curve from x = 0 to x = 48in
In this case, f(x) = sin(pi x/12), so the derivative of f(x) is
f'(x) = (pi/12)cos(pi x/12)
Arc Length = ∫√(1+((pi/12)cos(pi x/12))^2) dx from x=0 to x=48
Arc Length ≈ 49.59 in
To know more on arc length
https://brainly.com/question/2005381
#SPJ4
3) n+ 5(n-1) = 7
4) 15=-2(2t - 1)
Answer:
3. n = 2
4. t = -13/4
Step-by-step explanation:
3)
. . . . (3a) Distribute (multiply) +5 into the expression (n-1)
. . . . . . . . [tex]n + 5n - 5 = 7[/tex]
. . . . (3b) Add like terms (terms with the same variable)
. . . . . . . . [tex]6n - 5 = 7[/tex]
. . . . (3c) Add 5 on both sides of the equation to "get rid" of the -5
. . . . . . . . [tex]6n -5 +5 = 7 +5[/tex]
. . . . . . . . [tex]6n = 12[/tex]
. . . . (3d) Divide both sides by 6 to isolate the variable
. . . . . . . . [tex]6n/6 = 12/6[/tex]
. . . . . . . . [tex]n = 2[/tex]
4)
. . . . (4a) Distribute (multiply) -2 into the expression (2t-1)
. . . . . . . . [tex]15 = -4t + 2[/tex]
. . . . (4b) Subtract 2 on both sides of the equation to "get rid" of the +2
. . . . . . . . [tex]15 -2 = -4t +2 -2[/tex]
. . . . . . . . [tex]13 = -4t[/tex]
. . . . (4c) Divide both sides by -4 to isolate the variable
. . . . . . . . [tex]13/-4 = -4t/-4[/tex]
. . . . . . . . [tex]-13/4 = t[/tex]
What mixed number is equal to 11/6?
Answer:
1 5/6
Step-by-step explanation:
Take 11 divided by 6; we can have 1 number 6 and 5/6 left. So, the answer is 1 5/6
Let's test:
1 5/6 = 11/6
So, my answer is correct!
if f(x)=(2x)^2, find f(-4)
Answer:
y=32
Step-by-step explanation:
substitute x for (-4)
(2 x -4)^2= 32
Lamonte earned $269.10 at his job when he worked for 13 hours. How much money did he earn each hour?
Answer:
Step-by-step explanation:
To solve this problem, we need to divide the total amount of money Lamonte earned ($269.10) by the number of hours he worked (13 hours).
We can write this as an equation as follows:
earnings per hour = $269.10 / 13 hours
To solve for earnings per hour, we can divide both sides of the equation by 13:
earnings per hour = $269.10 / 13 hours / 13 = $269.10 / 13^2 = $269.10 / 169 = $1.60
Therefore, Lamonte earned $1.60 per hour.
How many terms are there in 4xy 5?
The number of terms that the expression 4xy +5 has is 2 terms.
What is an algebraic expression?
An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
How to determine terms?
To determine the number of terms in an algebraic expression, we only have to count the spaces (addition and/or subtraction symbols) and add the unit, in this way we will have the number of terms.
4xy +5 has 2 spaces
1 + 1 = 2 terms.
Learn more about expression in:
brainly.com/question/27578903
#SPJ4
Which financial tool is most important?
The financial tool that is most important is creating a budget.
What is the financial toll about?The ideal financial instrument for long-term planning objectives is You'll be able to set away money each week or month with the use of a budget.
You may track where your money is going and determine how much you have to spend on items besides expenses by utilizing a budget.
A budget can help you prioritize your spending and saving, and ensure that you have enough money set aside to reach your goals. Here is a step-by-step explanation of how to create a budget:
Learn more about financial tool from
https://brainly.com/question/14234253
#SPJ1
Convert 400 liters per day to gallons per week show work
Answer:
400 liters per day is equivalent to 105.66 gallons per week.Step-by-step explanation:
To convert from liters per day to gallons per week, we need to use the conversion factors for these units. One gallon is equivalent to 3.785 liters, and one week is equivalent to 7 days.
We can use these conversion factors to write the following conversion equation:
1 gallon/week = (3.785 liters/gallon) / (7 days/week)
We can then use this equation to convert 400 liters per day to gallons per week by multiplying the number of liters per day by the conversion factor. This gives us:
400 liters/day * (1 gallon/week) / (3.785 liters/gallon) / (7 days/week)
We can simplify this expression by canceling out the units that appear on both the numerator and denominator. This gives us:
400 / 3.785 / 7 = 105.66
Therefore, 400 liters per day is equivalent to 105.66 gallons per week
Is physics 100 hard?
Yes, it is hard but with a lot of practice and putting effort one cam also find it easy.
Why physics is hard?Physics requires the ability to solve problems, which can only be acquired via practice. In addition to these difficult ideas, there are theoretical concepts, mathematical calculations, and laboratory experiments.
How to deal with physics?It is better to comprehend the derivations than to memorize the formulas. Making a mess of several formulas will just increase your anxiety over the topic. Instead, if you strive to comprehend where they originate, you will begin to appreciate physics and its applications.
Physics is a difficult topic since it combines science and arithmetic, which may be challenging for the best of us. Nevertheless, despite how difficult it is, you can achieve if you follow a few simple guidelines and put yourself through some practice.
To learn more about physics visit the link:
https://brainly.com/question/28021242
#SPJ4
The sum of present age of father and son is 50years.After 5years the age of father is thrice the age of son .Find their present age
Answer:
age of father is 40 and son is 10
Step-by-step explanation:
let age of father be x
and age of son is y
At present,
x+y=50 eq 1
After 5 years,
Ages are,
Father = x+5
Son = y+5
As age of father is thrice so,
x+5 = 3(y+5)
x+5 = 3y+15
x-3y= 10 eq 2
Multiply eq 1 by 3
3x + 3y = 150 eq 3
Now, Add eq 2 and 3
4x = 160
x = 40 .................... ....... Age of father
Put x in eq 1
40 + y = 50
y = 10 ......................... Age of Son
How do you tell if a system has no solution or infinitely many?
The system of linear equations are said to have no solution if they are parallel to each other or have infinitely many solutions if they are coincident.
Considering two system of equations:
y1 = mx +c and y2 = px+ q.
The lines are said to be parallel if their slopes m and p are equal but the y intercepts c and q are not equal. Which further concludes that the system of equations has no solution.
The lines are said to be coincident if their slopes m and p are equal along with the y intercepts c and q being equal. And hence we conclude that the system of equations have infinitely many solutions.
To know more about system of equations:
https://brainly.com/question/29775312
#SPJ4
What is the variance if the standard deviation is 4?
the primary function of jails is to: group of answer choices a. hold persons for less than 1 year. b. hold persons for more than 1 year. c. hold persons for more than 5 years. d. hold persons for more than 10 years.
The jail's function is to hold inmates (A) for terms that are shorter than a year.
What do we mean by jails?A prison sometimes referred to as a jail, jail, penitentiary, detention center, correction center, correctional institution, lock-up, hoosegow, or remand center, is a place where people are imprisoned against their choice and typically denied a range of freedoms as retribution for various offenses.
The only purpose of a jail is to house inmates for a period of time shorter than a year.
With very few exceptions, modern jails are municipal or county-level detention centers run by local police departments or correctional facilities.
Like their historical forebears, they are employed to hold those who pose a flight risk or a threat to public safety while they await trial.
Therefore, the jail's function is to hold inmates (A) for terms that are shorter than a year.
Know more about jails here:
https://brainly.com/question/10190308
#SPJ4
What are special segments of a triangle?
There are Four special line segments of a triangle.
SPECIAL LINE SEGMENTS OF TRIANGLES
The four special line segment of a triangle are ,
Angle bisectorPerpendicular bisectorMedianAltitudeLet's see about mentioned segment in detail,
1.) Angle Bisector :
The angle bisector divides an angle into two equal parts.
2.) Perpendicular bisector :
A line that cuts through the middle of a side and is also perpendicular to that side is known as a triangle's perpendicular bisector.
3.) Median :
A line segment connecting a vertex to the middle of the other side is the median of a triangle.
4.) Altitude :
A triangle's altitude is defined as a line segment passing through its apex and parallel to (or at a right angle to) the side that is deemed to be its base.
For more clarity see the image given below.
To read more about Special segments of a triangle.
https://brainly.com/question/2437195
#SPJ1
In the figure, j∥k and m∠2 = 117°.
What is the m∠3?
Enter your answer in the box. |__|
Step-by-step explanation:
angle3 is the supplementary angle to angle2.
that means together they are 180°.
180 = 117 + angle3
angle3 = 180 - 117 = 63°
HELP
Michelle jogs 3 miles in 36 minutes. At the same rate, how many miles would she jog in 60 minutes?
A. 6.5
B. 6
C. 4.5
D. 5
Explain you work pls
Answer:
d) 5 miles
Step-by-step explanation:
Minutes for jogging 1 mile is,
→ 36/3
→ 12 minutes
Formula we use,
→ Total time ÷ Time needed for 1 mile
Then the distance she cross in 60 min,
→ 60 ÷ 12
→ 5 miles
Hence, she will cross 5 miles.
Population density is the number of people per unit of area. The population density of a certain region is 50 people per square kilometer. If the region covers 26 square kilometers, what is the population of the region?
The population of the region is 1300 people.
How to calculate the population?It should be noted that population simply means the number of people on a particular region or area. Population density is the number of people per unit of area.
Since the population density of a certain region is 50 people per square kilometer and the region covers 26 square kilometer, the population will be:
= Number of square kilometers × Number of region
= 50 × 26
= 1300
The population is 1300 people.
Learn more about population on:
brainly.com/question/25630111
#SPJ1
a restaurant offers the following limited lunch menu. main courses: turkey, spaghetti, meatloaf, shrimp, hamburger vegetables: peas, squash, cauliflower, eggplant beverages: coffee, tea, milk, soda, shakes desserts: sundaes, mousse, pie, brownies if one item is selected from each of the four groups, in how many ways can a meal be ordered? there are ways a meal can be ordered
800 ways meal be ordered.
There are 5 main courses to choose from, so there are 5 ways to choose a main course. There are 4 vegetables to choose from, so there are 4 ways to choose a vegetable. There are 5 beverages to choose from, so there are 5 ways to choose a beverage. And there are 4 desserts to choose from, so there are 4 ways to choose a dessert.
The total number of ways to order a meal is the product of the number of choices for each category.
So there are 5 * 4 * 5 * 4 = 800 ways to order a meal.
Hence, 800 ways meal be ordered.
To know more about Arrangement visit,
https://brainly.com/question/26719078
#SPJ4
Abag contains n beads. 6 of the beads are red and the rest are blue. Ravi is going to take at random 2 bead
The number of beads if A bag contains n beads. 6 of the beads are red, and the rest are blue. Ravi is going to take random 2 beads, is 18.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a value between 0 and 1.
Given:
A bag contains n beads. 6 of the beads are red, and the rest are blue. Ravi is going to take random 2 beads,
The probability of same color beads = 9 / 17
Calculate the probability as shown below,
ⁿ⁻⁶C₂ / ⁿC₂ + ⁶C² / ⁿC₂ = 9 / 17
(n - 6) (n - 7) / 2 / n(n - 1) / 2 + 15 / n(n - 1) / 2 = 9 / 17
8n² - 212n + 1224 = 0
Solve for the value of x as shown below,
x = 18
Thus, the number of beads is 18.
To know more about Probability:
https://brainly.com/question/743546
#SPJ1
What is the value of 994 1/3 According binomial theorem?
The value of 994 to the power 1/3 is 9.97.
The binomial theorem involves the method of expanding an expression which is raised to a finite power. A binomial theorem has its application in probability, algebra, etc.
A binomial expression is said to have two dissimilar terms.
The total number of terms in (x + y)ⁿ are n+1.
The expansion of (1 + x)ⁿ can be written as,
(1 + x)ⁿ = 1 + nx + [n*(n-1)]/2! x² + [n*(n-1)*(n-2)]/3! x³ + ....
Let us find the value of 994 to the power 1/3,
⇒ (993 + 1)¹/³
⇒ 1 + 993/3 + 993* 993* [1/3* (-2/3)]/2! + 993* 993* 993* [1/3* (-2/3)* (-5/3)]/3! + ...
⇒ 1 + 331 - 54780.5 + 60441151.67 - ...
⇒ 9.97
Thus, the required value is 9.97.
To know more about binomial theorem:
https://brainly.com/question/20411764
#SPJ4
Is it possible to make an equation from these two equations? If so, do they have infinite solutions, no solutions, or one solution?
Consider the mathematical sentence 2 = 2.
Is there any variable or constant that you could add to or subtract from both sides, or multiply or divide both sides by using the Properties of Equality to make this true sentence false? Choose variables and constants to create new mathematical sentences to justify your conclusion
Consider the mathematical sentence 2 ≠ 3.
Is there any variable or constant that you could add to or subtract from both sides, or
multiply or divide both sides by using the Properties of Equality to make both sides equal? Choose variables and constants to create new mathematical sentences to justify your conclusion.
Answer:
For the equation 2 = 2, it is not possible to make this equation false by using the Properties of Equality. This is because the equation is already true, and any manipulation of the equation using the Properties of Equality would not change this fact. Therefore, this equation has one solution.
For the equation 2 ≠ 3, it is not possible to make both sides equal by using the Properties of Equality. This is because the equation is stating that the two sides are not equal, and any manipulation of the equation using the Properties of Equality would not change this fact. Therefore, this equation has no solutions.
What two arguments did Mary Wollstonecraft?
Both men and women have duties to their families and duties to the state.
According to Wollstonecraft, women are important to the country because they educate their children and because they have the potential to be "companions" to their husbands rather than merely spouses. She also contends that women should have an education appropriate to their status in society.
She asserts that in God's view, men and women are on an equal footing. But these affirmations of equality conflict with her assertions that the strength and bravery of males are superior. It is now challenging to label Wollstonecraft as a modern feminist due to her equivocal views on gender equality.
Wollstonecraft differs from the majority of her male Enlightenment contemporaries because of her emphasis on the rights of women.
To learn more about Wollstonecraft's arguments refer to:
brainly.com/question/28006055
#SPJ4
According to her, men and women are treated equally in God's eyes. However, these claims of equality run counter to her claims that men are stronger and bolder than women. Due to Wollstonecraft's conflicted opinions on gender equality, it is currently difficult to categorize her as a modern feminist.
Wollstonecraft's emphasis on women's rights sets her apart from the rest of her male Enlightenment peers.
please help it’s due today by 10pm
The size of the angle C is θ = 56°, given that BC and DE are tangents to the circle.
Tangent to a circle theoremThe tangent to a circle theorem states that a line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency
Considering the Isosceles triangle ∆AOB and its exterior angle ∠BOD;
∠BOD = 180° - 2(48) {exterior angle of a triangle equals 2 opposite interior angles}
∠BOD = 96°
If the line DE is extended to line BC at E' we will have a quadrilateral BODE' and a triangle ∆CE'D, hence;
∠B = ∠D = 90° (angles between radius and lines tangent to the circle)
so;
∠BOD + ∠OBD + ∠ODE' + ∠BE'D = 360° {sum of interior angles of a quadrilateral}
96° + 90° + 90° + ∠BE'D = 360°
276° + ∠BE'D = 360°
∠BE'D = 360° - 276° {subtract 276° from both sides}
∠BE'D = 84°
Considering triangle ∆CE'D;
∠DE'C = 180° - 84° {sum of angles on a straight line}
∠DE'C = 96°
We thus derive θ using the triangle ∆CE'D;
θ = 180° - (28 + 96)° {sum of interior angles of a triangle}
θ = 180° - 124°
θ = 56°
In conclusion, we have derived the size of the angel θ as 56° by proper application of the tangent to a circle theorem.
Learn more about tangent to a circle here:https://brainly.com/question/11067500
#SPJ1
which expressions are equivalent to -6+3(2+(-4t) choose all that apply A)-12t , B) 12t-12, C) none of the above
The correct answer is A) -12t.
To evaluate this expression, we need to use the order of operations. The order of operations is a set of rules that specifies the sequence in which operations should be performed in a math expression to get the correct result. The order of operations is typically abbreviated as PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Following the order of operations, we first need to evaluate the expression inside the parentheses, which is 2+(-4t). This gives us 2-4t. Next, we need to perform the multiplication, which gives us 3(2-4t) = 6-12t. Finally, we need to perform the addition, which gives us -6+6-12t = -12t. Therefore, the expression -6+3(2+(-4t)) is equivalent to -12t.
Option B) 12t-12 is incorrect because the multiplication and addition operations are not performed in the correct order.
Option C) none of the above is incorrect because the correct answer is A) -12t.
To learn more about Expression Equivalence follow link : https://brainly.com/question/9657981
#SPJ1
A recipe calls for 112 1 1 2 teaspoons of cinnamon to make 2 dozen oatmeal cookies. How many teaspoons of cinnamon are needed to make 60 oatmeal cookies?.
Fraction [tex]3 \frac{3}{4}[/tex] teaspoons of cinnamon are needed to make 60 oatmeal cookies.
Given that,
A recipe calls for [tex]1\frac{1}{2}[/tex] teaspoons of cinnamon to make 2 dozen oatmeal cookies.
A fraction is numerical value that is a part of a whole. It is evaluated by dividing a whole into number of parts. For example, ½ represents half of a whole number or a thing.
Then,
We will find number of teaspoons needed to make one oatmeal cookies.
1 dozen = 12
2 dozens = 24
So,
We can write,
[tex]1\frac{1}{2}[/tex] divide by 24,
Convert mixed fraction into improper fraction:
[tex]\frac{3}{2}[/tex] divide by 24
Convert to division problem by flipping the second fraction as:
= [tex]\frac{3}{2}[/tex] * [tex]\frac{24}{1}[/tex]
= [tex]\frac{3}{48}[/tex]
= [tex]\frac{1}{16}[/tex]
Now, we will multiply amount needed for one cookie by 60 to find amount needed to make 60 cookies as:
= [tex]\frac{1}{16}[/tex] * 60
= [tex]\frac{15*4}{4*4}[/tex]
= [tex]\frac{15}{4}[/tex]
= [tex]3 \frac{3}{4}[/tex]
Therefore,
Fraction [tex]3 \frac{3}{4}[/tex] teaspoons of cinnamon are needed to make 60 oatmeal cookies.
To learn more about Fraction problems visit :
brainly.com/question/10708469
#SPJ4
What is the solution of y 3x 5?
The linear equation y = 3x + 5 has an infinitely many solutions.
Define the term solution of linear equation?We looked for as many solutions as possible to the given equation.
y = 3x + 5 is a linear equation with two variables as of ax + by + c = 0.
Thus,
Put x = 0, y = 0 + 5 = 5. Thus, (0, 5) is one solution.Put x = 1, y = 3 × 1 + 5 = 8. Thus, (1, 8) is another solution.Put y = 0, 3x + 5 = 0, x = -5/3. Thus, (-5/3, 0) is another solution.We are aware that for various values of x, we obtain varied values for y. As a result, any value that may be used to replace x with in given equation will result in another answer. As a result, there are an infinite number of unique solutions that can be derived by replacing x in the above linear equation with real numbers.A linear equation with two variables hence has an endless number of solutions.
y = 3x + 5 thus has an endless number of solutions.
To know more about the Linear equation, here
https://brainly.com/question/2030026
#SPJ4
The correct question is-
What is the solution of y = 3x + 5?
A jazz band wants to sell $2,800 worth of tickets. If each ticket costs $70, how many tickets will the band have to sell to meet its goal?
Answer:
40 tickets
Step-by-step explanation:
2800 = 70x
x is the number of tickets. You have to solve for x
Divide each side by 70
2800/70 = 70x/70
40 = x
given a coordinate of (2, -12) and a slope of -19, what is the second coordinate?
ANWSER NEEDED ASAP
The second coordinate are ( 7 , 2 )
What is the formula for finding a slope?To determine a line's inclination or steepness, use the slope formula. By calculating the ratio of the change in the y-axis to the change in the x-axis, it may be used to calculate the slope of any line. A line's slope is determined by how its "y" coordinate changes in relation to how its "x" coordinate changes.m = (y2 - y1)/ is the slope formula (x2 - x1)Write the equation of the line in slope-intercept form to determine the slope from the equation. Utilize inverse procedures to find y, then write it as y=mx+b. Since the slope is the x variable's coefficient, or the number before x, you can thus readily observe the slope.Given data :
Formula of slope, m = (y2 - y1)/(x2 - x1)
y2 - ( -12 ) / x2 - 2 = -19 / 1
To get -19 / 1
we have to apply suitable no to y2 & x2
7 - (-12) / 3 - 2 = -19 / 1
so, the second coordinate are ( 7 , 2 )
Learn more about slope-intercept form refer to :
https://brainly.com/question/25722412
#SPJ1
4(2x + 5) = [ ]x + [ ]
rewrite using the distributive property
Answer:
Step-by-step explanation:
first you do 4 x 2x=8x
next you do 4 x 5=20
then you get 8x + 20 :)
How much paint do I need for 2200 square feet?
6 cans are needed to paint an area of 2200 units square.
The cans of paints and areas are illustrations of equivalent ratios.
The quantity of paint required for a certain area of house can be found out using the area of the house.
As the area is given in this problem, it is easier to calculate the amount of paint.
The given parameter is,
Cans: area = 1: 400
Putting it in the form of fraction,
Cans/area = 1/400
Cross multiplying, we have,
Cans = 1/400 × 2200 = 5.5 ≈ 6
Thus, 6 cans are needed to paint a 2200 square feet.
The question is incomplete. The complete question is 'How many cans of paint are needed to cover an area of 2200 square units if one can of paint covers in area 400 square units.'
To know more about paint:
https://brainly.com/question/12799603
#SPJ4
Who has invented India?
Vasco da Gama has invented India
An invention is a brand-new or original product, process, composition, idea, or tool. A device, item, or method can be improved using an invention to boost functionality or cut costs. It could also be a brand-new idea. An concept can be patented if it is distinctive enough, either as a stand-alone innovation or as a major improvement over the work of others.
Portuguese explorer Vasco de Gama becomes the first European to reach India via the Atlantic Ocean when he arrives at Calicut on the Malabar Coast.
Da Gama sailed from Lisbon, Portugal, in July 1497, rounded the Cape of Good Hope, and anchored at Malindi on the east coast of Africa. With the aid of an Indian merchant he met there, he then set off across the Indian Ocean. The Portuguese explorer was not greeted warmly by the Muslim merchants of Calicut, and in 1499 he had to fight his way out of the harbor on his return trip home. In 1502, he led a squadron of ships to Calicut to avenge the massacre of Portuguese explorers there and succeeded in subduing the inhabitants. In 1524, he was sent as viceroy to India, but he fell ill and died in Cochin.
hence Vasco da Gama has invented India
To know more about invention visit : brainly.com/question/23538626
#SPJ4
Vasco da Gama has invented India
In July 1497, Vasco da Gama set sail from Lisbon, Portugal, crossed the Cape of Good Hope, and stopped at Malindi on the continent's east coast. He then embarked on a journey across the Indian Ocean with the help of an Indian merchant he met there. The Muslim traders of Calicut did not welcome the Portuguese explorer with open arms, and on his way back to Portugal in 1499, he had to fight his way out of the harbor. He successfully subdued the locals in 1502 after leading a fleet of ships to Calicut to revenge the massacre of Portuguese explorers there. He was appointed viceroy of India in 1524 but passed away in Cochin after becoming unwell.