Answers
Answer:
a) s = 2a sinh(b/a)
b) 18 feet
Step-by-step explanation:
The arc length is:
s = ∫ √(1 + (dy/dx)²) dx
y = a cosh(x/a)
y = ½ a (e^(x/a) + e^(-x/a))
dy/dx = ½ a (1/a e^(x/a) − 1/a e^(-x/a))
dy/dx = ½ (e^(x/a) − e^(-x/a))
(dy/dx)² = ¼ (e^(2x/a) − 2 + e^(-2x/a))
Plugging in:
s = ∫ √(1 + ¼ (e^(2x/a) − 2 + e^(-2x/a))) dx
s = ∫ ½ √(4 + e^(2x/a) − 2 + e^(-2x/a)) dx
s = ∫ ½ √(e^(2x/a) + 2 + e^(-2x/a)) dx
s = ∫ ½ √(e^(x/a) + e^(-x/a))² dx
s = ∫ ½ (e^(x/a) + e^(-x/a)) dx
s = ½ (a e^(x/a) − a e^(-x/a))
s = ½ a (e^(x/a) − e^(-x/a))
Evaluate from x=-b to x=b:
s = ½ a (e^(b/a) − e^(-b/a)) − ½ a (e^(-b/a) − e^(b/a))
s = ½ a e^(b/a) − ½ a e^(-b/a) − ½ a e^(-b/a) + ½ a e^(b/a)
s = a e^(b/a) − a e^(-b/a)
s = a (e^(b/a) − e^(-b/a))
s = 2a sinh(b/a)
We know that s = 48, and b = 20. We also know y = 30 when x = b.
48 = 2a sinh(20/a)
24 = a sinh(20/a)
30 = a cosh(20/a)
Using the given identity:
cosh²(20/a) − sin²(20/a) = 1
a² cosh²(20/a) − a² sin²(20/a) = a²
30² − 24² = a²
a² = 324
a = 18
Therefore, the wire will be 18 feet above the ground at the lowest point.
Related Questions
The vertices of a rectangle are located at the coordinates (2, 2), (2, 6), (5, 6), and (5,2). Find the length of the sides of the rectangle and its perimeter. help meeeee
Answers
Answer:
length of rectangle = 4 units
width of rectangle = 3 units
Perimeter of a rectangle = 14 units
Step-by-step explanation:
Properties of a rectangle:
Opposite sides are parallel and equal in lengthEach interior angle is 90°From inspection, we can see that (2, 2) and (2, 6) have the same x-values. So (2, 6) is above (2, 2) on the same vertical line.
To calculate the distance between them, find the difference between their y-values: 6 - 2 = 4
Therefore, one pair of sides of the rectangle are 4 units in length.
From inspection, we can see that (2, 6) and (5, 6) have the same y-values. So (5, 6) is to the right of (2, 6) on the same horizontal line.
To calculate the distance between them, find the difference between their x-values: 5 - 2 = 3
Therefore, the other pair of sides of the rectangle are 3 units in length.
Therefore:
length of rectangle = 4 unitswidth of rectangle = 3 unitsPerimeter of a rectangle = 2 × length + 2 × width
= 2 × 4 + 2 × 3
= 8 + 6
= 14 units
The length of one leg of a right
triangle is 7 centimeters longer than
the other leg, and the hypotenuse is 13
centimeters find the lengths of the
two legs
Answers
Answer: 5 cm and 12 cm
Step-by-step explanation:
Ms. Russell has 31 students in her class. There are 14 boys and 17 girls. What fraction represents the number of girls in her class.
Answers
14 boys
17 girls
17/31 girls fraction
NEED LINEAR ALGEBRA ANSWER ASAP
B IS INCORRECT
Answers
Answer:
Choice D
Step-by-step explanation:
Multiply the scalar into the matrix
3*2
3*-1
The first matrix becomes
6
-3
6 - 0
-3 =1.5
We are subtracting a negative so it is like adding
6 + 0
-3 + 1.5
6
-1.5
Choice D
Answer:
4th option
Step-by-step explanation:
3 [tex]\left[\begin{array}{ccc}2\\-1\\\end{array}\right][/tex] - [tex]\left[\begin{array}{ccc}0\\-1.5\\\end{array}\right][/tex] ← multiply the components of the first matrix by 3
= [tex]\left[\begin{array}{ccc}6\\-3\\\end{array}\right][/tex] - [tex]\left[\begin{array}{ccc}0\\-1.5\\\end{array}\right][/tex] ← subtract corresponding components
= [tex]\left[\begin{array}{ccc}6-0\\-3-(-1.5)\\\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}6\\-3+1.5\\\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}6\\-1.5\\\end{array}\right][/tex]
HELP ASAP ILL GIVE BRAINLIEST AND EXTRA POINTS
Answers
it going to be number three
10. Read the question carefully and type your answer in the space below. *
3 points
Use each digit shown below to create a 5-digit number with the greatest value and
a 5-digit number with the least value. Each digit can only be used once in each
number. Then write a number sentence using >,<, or = to compare the two
numbers you created.
2, 9, 1, 3, 8
Your answer
This is a required question
Submit
Never submit passwords through Google Forms.
Answers
Answer:
Greatest = 98,321
Least= 12,389
98,321>12,389
Step-by-step explanation:
there are only 5 digits. To get the greatest number, the digits with the most value should be put in front to ensure the great value.
To get the smallest number, the digits with the least value should be put in front.
The greater valued number is greater than the least valued number
Help ASAP!!!!
Use vector operations to draw the resultant vector
Draw 2u – 1/3v.
Answers
Vectors are elements of the vector space, and they can be illustrated by diagrams.
How to draw the vector 2u - 1/3vThe vector expression is given as:
2u - 1/3 v
Split the vector expressions, as follows:
[tex]y_1 = 2u[/tex]
[tex]y_2 = -\frac13v[/tex]
See attachment for the graphs of y1 and y2.
Next, we have:
[tex]y = 2u - \frac13v[/tex]
So, we have:
[tex]y = y_1 + y_2[/tex]
The above expression means that, we add the vectors y1 and y2 to get vector y
See attachment for the graph of 2u - 1/3 v
Read more about vectors at:
brainly.com/question/14480278
Factorise 2x² + 6x + 36
Answers
Answer:
[tex]2 (x^2+3x+18)[/tex]
Step-by-step explanation:
Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions:
y > 3x + 10
y is less than negative 3 over 4 times x minus 1
Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution area. (6 points)
Part B: Is the point (8, 10) included in the solution area for the system? Justify your answer mathematically
Answers
9514 1404 393
Answer:
A) The graph is the quadrant of the coordinate plane that lies between the two lines and to the left of the point (-2 14/15, 1 1/5)
B) no; it does not satisfy either inequality
Step-by-step explanation:
A) The boundary line defined by the first inequality is a dashed line with a slope of 3 and a y-intercept of 10. Shading is above the line (and to its left).
The boundary line defined by the second inequality is a dashed line with a slope of -3/4 and a y-intercept of -1. Shading is below the line (and to its left).
The two lines cross at the 2nd-quadrant point (-2 14/15, 1 1/5). The solution area is the area between the crossing lines and to the left of that point. Neither that point nor any point on either line is part of the solution area.
The solution area is the doubly-shaded area in the attached graph.
__
B) The first-quadrant point (8, 10) is not in the solution area, since the solution area is comprised of parts of quadrants 2 and 3 only.
We can see that (8, 10) will not satisfy either inequality:
10 > 3(8) +10 . . . . not true
10 < -3/4(8) -1 . . . . not true
Find the value of n.
2 + n = 2
Answers
Answer:
n=0
Step-by-step explanation:
Subtract 2 to isolate n.
2+n=2
n=0
8-2(-4-7) not sure how to do this?
Answers
You always have to do what is inside the parenthesis first
-4 - 7 = -11
Next, you have to times that result with 2 (don't mind the negative/minus sign yet)
2 * (-11) = -22
8 - (-22) = 30
Answer = 30
(PLS ANSWER)
Paula made this model to show the sum of two mixed numbers. Write the addition equation shown by the model and solve it.
Answers
Answer:
(3 2/3)+(2 2/3)+ (6 1/3)
so your answer is 12 and 2/3
Step-by-step explanation:
that is the equation I would recommend doing 3+2+6=11 and then 2/3+2/3+1/3= 1 2/3
help 50 poitns Describe the power function f(x)=x^5. What does it look like? Where does it cross the x- and y-axis? How many turns does it make?
What is the end behavior for f(x)=x^5?
Answers
Adding and subtracting fractions with different denominators
Answers
20/6
Simplified = 10/3
18)
29/14
19)
27/28
20)
47/14
Hope that helps :)
anyone PLEASE help me i’ll give brainliest
Answers
Answer:
8
Step-by-step explanation:
sin∅ = opposite over hypotenuse
Since we have a right triangle, we can use trig to help us solve for missing values:
sin30° = 4/x
xsin30° = 4
x = 4/sin30°
x = 8
29 Two expressions are shown. The second expression is not complete.
Expression I: 200r - (-110)
Expression II: + 200r
What number belongs in the box so that Expression I is equivalent to Expression II?
Record your answer and fill in the bubbles on your answer document. Be sure to use the
correct place value.
Please helz?
Answers
The missing number that will make both expressions to be equivalent expressions is: 110.
What are Equivalent Expressions?Two expressions are equivalent if they have the same value.
Given the following expressions:
Expression I: 200r -(-110)Expression II: _ + 200rLet x represent the missing number in the second expression. Thus, equate both expressions and solve for x.
200r -(-110) = x + 200r
200r + 110 = x + 200r
Add like terms
200r - 200r + 110 = x
110 = x
x = 110
Therefore, the missing number that will make both expressions to be equivalent expressions is: 110.
Learn more about equivalent expressions on:
https://brainly.com/question/22365614
make a box-and-whisker plot for the set of data 21,27,27,25,21,13,18,25
Answers
Answer:
See the critical points of the box plot belowStep-by-step explanation:
Find the 5-number summary that indicates the points:
Minimum value, maximum value, median, median of lower half, median of upper halfFirst, put the data in the acsending order:
13, 18, 21, 21, 25, 25, 27, 27Now, find the 5 numbers:
The minimum is 13The median of the lower half is (18 + 21)/2 = 19.5The median is (21 + 25)/2 = 23The median of the upper half is (25 + 27)/2 = 26The maximum is 27Answer:
Step-by-step explanation:
An umbrella is made up of 6 isosceles triangular pieces of cloths. The measurement
of the base of each triangular piece is 28 cm and two equal sides are 50 cm each.
If the rate of cost of the cloth is Rs 0.50 per sq. cm., find the cost of the cloths
required to make the umbrella.
Answers
There you go
PLEASE MARK IT AS A BRILLIANT ANSWER
Pls help me
Question 2 Part B (5 points): Given the area of the square, find the length of each side by factoring completely. Be sure to show all work to receive full credit!
Area: 25y² – 20y + 4 sq units
Answers
formula : area of square = Length²
all the sides in a square is of same measureLength = √area of square
given here the area: 25y² – 20y + 4[tex]\rightarrow \sf Length =\sqrt{ 25y^2 - 20y + 4}[/tex]
[tex]\rightarrow \sf Length =\sqrt{ 25y^2 - 10y -10y+ 4}[/tex]
[tex]\rightarrow \sf Length =\sqrt{ 5y(5y - 2) -2(5y-2)}[/tex]
[tex]\rightarrow \sf Length =\sqrt{ (5y-2)(5y-2)}[/tex]
[tex]\rightarrow \sf Length =\sqrt{ (5y-2)^2}[/tex]
[tex]\rightarrow \sf Length =5y-2[/tex]
subtract 7/10 - 1/5 simplify your answer
Answers
Answer:
1/2
Step-by-step explanation:
7/10 - 1/5
=> 7/10 - 1*2/5*2
=> 7/10 - 2/10
=> (7-2)/10
=> 5/10
=> 1/2
first, you have to make sure they have the same bottom number so you would make 1/5 2/10.
7/10-2/10
which is 5/10
you would simplify it and get 1/2 because 5 is half of 10
Lauren uses a calculator to find 3/4 divided by 3 + 8 And the result of 9/4. .
36
Which statement best describes her work?
A) Lauren determined the correct answer.
B) Lauren determined the result of (3 ÷ 4 ÷ 3) + 9 ÷ 36.
C) Lauren determined the result of 3 ÷ 4 ÷ (3 + 9 ÷ 36).
D) Lauren determined the result of (3 ÷ 4) ÷ 3 + 9 ÷ 36.
Answers
Answer:
b.
Step-by-step explanation:
Answer:
HELP YOUR MOM AND YOURSELF
Step-by-step explanation:
uwu uwu uwu uwu uwu uwu uwu uwu uwu uwu
I need help with a and B on this question
Answers
Answer:
turning point is roughly (-0.3, -2.1)
the roots are: -1.3, 0.8
Step-by-step explanation:
the graph displayed is what is known as a quadratic
the turning point of a quadratic is the bottom of the line (where the line stops going down and starts going up)
the roots of a quadratic graph is where the line crosses the x axis (there are usually two roots but sometimes there are none).
Select the prime number
Answers
But prime numbers are numbers with only 2 factors the number itself and 1
eg {2,5,7,11,13,17,19,23,29,31,37 ...}
Find the percent change. State whether it is an increase or decrease. Round to the nearest tenth of a percent. From 27 to 31
Answers
Given parameters:
Initial value = 27
Final value = 31
Unknown:
Percentage change = ?
Solution:
The percentage change is the difference between the final and initial value divide by the initial value multiplied by 100;
Percentage change = [tex]\frac{Final value - Initial value}{Initial value} x 100[/tex]
Input the parameters and solve;
Percentage change = [tex]\frac{31 - 27}{27} x 100[/tex]
= 14.8%
The percentage change is 14.8%. This is an increase because the value move from 27 to 31.
Can you help me find the surface area of this prism?
Answers
Answer:
To find the surface area of this parallelepiped, we need to know how to find the area of a regular parallelogram.
Formula for area of a parallelogram;
A = BH
Where b represents the base, and h displays as the height.
Once, we know how to find the area of a parallelogram, we find the areas of the three different sides of this figure and multiply it by two since opposite sides have an equal area.
Now we find the area of the front parallelogram:
A = BH
Plug in our values;
A = 4(2)
A = 8, and since opposite sides are equal:-
8(2) = 16, is the area of both the front and back parallelograms.
Now the top and bottom bases of this parallelepiped.
But, to find the height and base of this, we transfer the base of the front parallelogram and the base of the right parallelogram. So our base and height is 4.
A = BH
Plug in our values;
A = 4(4)
A = 16, and since opposite sides are equal:-
16(2) = 256, is the area for both the upper and bottom bases.
Now for the right and left parallelograms;
A = BH
Plug in our values;
A = 4(2.5)
A = 10, since opposite sides are equal:-
10(2) = 20, is the area of both the right and left parallelograms.
Now we add all the areas together:
16 + 256 + 20
= 292 square meters.
6th-grade math help on geometry.
Answers
Answer:
okay , attach a file .
Step-by-step explanation:
Based on the table, what is the number string that corresponds to the text “Hello Raya”?
Answers
The number string is an illustration of the addition operation
The number string that corresponds to the text “Hello Raya” is 97
How to determine the number string?The text is given as:
“Hello Raya”
From the table in the complete question, we have the following representations:
H = 8; E = 5; L = 12; O = 15; R = 18; A = 1; Y = 25; _ or space = 0
The sum of the numerical values of the characters are:
Sum = 8 + 5+ 12 + 12 + 15 +0 + 18 + 1+ 25 + 1
Evaluate the sum
Sum = 97
Hence, the number string that corresponds to the text “Hello Raya” is 97
Read more about addition operation at:
https://brainly.com/question/4344214
find the area pls i need it
Answers
Answer:
521 mm²
Step-by-step explanation:
Hi there !
A = Asemicircle + Atrapeze
Asemicercle formular = d/2 = 20mm/2 = 10mm
Asc = π·r²/2
= 3.14·(10mm)²/2
= 3.14×100mm²/2
= 157 mm²
Atrapeze formulaAt = (b + B)×h/2
= (20mm + 32mm)×14mm/2
= 52mm×7mm
= 364 mm²
A = Asc + At= 157mm² + 364mm²
= 521 mm²
Good luck !
36.012 divided by 3
Answers
i just did it
Choose all of the ordered pairs that are solutions of the equation 2x —3y = 6.
(-3, – 4)
(-1.5, 3)
(0, - 2)
(1.5, -1)
(2 – 3)
(4.5, 1)
Answers
Answer:
Step-by-step explanation:
imagine