Use version 2 of the arc length formula to find the length of the curve defined by 16xy^2 - y^6 = 9 from (9/16,1) to (9/8,2)
The arc length of the curve is 1.3125
What do you understand by length of the curve?The length of an arc is the separation of two locations along a segment of a curve.
A defined integral between the two points is used to calculate the area under a curve between two points. Integrate y = f(x) between a and b's limits to find the area under the curve y = f(x) between x = a & x = b. Integration within the defined bounds can be used to calculate this area.
the arc length formula
[tex]$$L=\int_C d s=\int_a^b \sqrt{1+\left(\frac{d x}{d y}\right)^2} d y$$[/tex]
now
[tex]$$\begin{aligned}16 x y^2-y^6 &=8 \\y^2\left(16 x-y^4\right) &=8 \\16 x-y^4 &=8 y^{-2} \\16 x &=8 y^{-2}+y^4 \\x &=\frac{1}{2} y^{-2}+\frac{1}{16} y^4\end{aligned}$$[/tex]
[tex]\frac{d x}{d y}=-y^{-3}+\frac{1}{4} y^3[/tex]
now differential line element is
[tex]$$\begin{aligned}d s &=\sqrt{1+\left(\frac{d x}{d y}\right)^2} d y \\&=\sqrt{1+\left(-y^{-3}+\frac{1}{4} y^3\right)^2} d y \\&=\sqrt{1+y^{-6}-\frac{1}{2}+\frac{1}{16} y^6} d y \\&=\sqrt{y^{-6}+\frac{1}{2}+\frac{1}{16} y^6} d y \\&=\sqrt{\left(y^{-3}+\frac{1}{4} y^3\right)^2} d y \\&=\left(y^{-3}+\frac{1}{4} y^3\right) d y\end{aligned}$$[/tex]
now arc length of the curve in the given interval
[tex]$$\begin{aligned}L &=\int_C d s \\&=\int_1^2\left(y^{-3}+\frac{1}{4} y^3\right) d y \\&=\left[-\frac{1}{2} y^{-2}+\frac{1}{16} y^4\right]_1^2 \\&=-\frac{1}{2}\left(\frac{1}{2^2}-\frac{1}{1^2}\right)+\frac{1}{16}\left(2^4-1^4\right) \\&=\frac{\mathbf{2 1}}{\mathbf{1 6}} \approx \mathbf{1 . 3 1 2 5}\end{aligned}$$[/tex]
this is the arc length of the curve
to learn more about the length of the curve, Visit: https://brainly.com/question/2879969
#SPJ4
Solve negative four and one third ÷ two and one fifth.
Answer: -2/15 according to the calculator.
Answer:
-1.9681
the 81 is repeating
Step-by-step explanation:
9. What is the slope of the graph of y= 12 x - 19?
12
Explanation:
Slope Intercept form is: y=mx+b
m would be the slope
So in y=12x-19, 12 would be the slope in this case.
Evaluate (f+2)(g+8) , when f=4 and g=2.
Answer:
60
Explanation below
elowHope this helps :)
Step-by-step explanation:
1. Substitute the variables with the given numbers.
(4 + 2) (2 + 8)
2. Add the numbers to get the sum.
(6) (10)
3. Since they are in parenthesis multiply the two numbers.
(6) (10) = 60
What is the standard notation for the following expression?
4.62 × 10⁻³
Answer:
Step-by-step explanation:
Calculate 10 to the power of −3 and get 1 over 1000
4.62(1/1000)
the answer is 231 over 50000 or 0.00462
Simplify the expression
Answer:
A
Step-by-step explanation:
Answer:
your answer will be A the first one
Step-by-step explanation:
A rectangular field is 15m longer than it is wide.
The area of the field is 800m²
Work out the length of the field.
Give your answer to 1 decimal place.
The length of rectangular field is 36.76 m.
What is a length?Distance is quantified by length. A quantity with the dimension of distance is called length in the International System of Quantities. Most measurement systems choose a length base unit from which all other units are derived. The fundamental unit for length in the International System of Units is the metre.
The term "length" refers to the measurement or size of something from end to end. In other terms, it is the greater of the upper two or third dimension of a geometric shape or object.
Area of rectangle is L × W = 800
given L = 15 + W
W × ( 15+ W) = 800
15W + [tex]W^{2}[/tex] = 800
[tex]W^{2}[/tex] + 15W - 800 = 0
by solving the above quadratic equation W= 21.76 m.
L = 15 + W
L = 36.76 m
To learn more about length from the given link:
brainly.com/question/8552546
#SPJ9
are the ratios 1:4 and 3:5 equivalent
Answer:no
Step-by-step explanation:1:4 is not equivalent to 3:5
helpp me teacher said this is a quadratic formula 3x2+x+1
Answer: 0.434
Step-by-step explanation:
Answer:
3 (x + 16) 2 + 11 12
Step-by-step explanation:
brainliest please
Oliver and his friends like to collect and trade cards from a certain combat card game. Oliver used his allowance to purchase 5 booster packs and 4 premade decks, which included a total of 178 cards. For his birthday, he received 4 booster packs and 7 premade decks, which included a total of 264 cards. How many cards come in every booster pack and every premade deck?
Solving system of equations in two variable gives that the number of cards in every booster pack are 10 and number of cards in every premade deck are 32
What is system of equations in two variables and how to find its solution by substitution?
Let x and y be two variables and
a₁x+b₁y =c₁
a₂x+b₂y =c₂
Where a₁, a₂, b₁, b₂, c₁, c₂ are constants then we can solve these simultaneous equations by substitution take value of x from equation (1) and then put it in (2) to get an equation for y only and then solve for y. put value of y in equation (1) to get value of x.
Let the number of cards in every booster pack are x and the number of cards in every premade deck be y
Number of cards in 5 booster packs will be 5x and Number of cards in 4 premade deck will be 4y
As Oliver purchases 5 booster packs and 4 premade decks, which included a total of 178 cards.
Thus we get 5x + 4y = 178 .....(1)
Number of cards in 4 booster packs will be 4x and Number of cards in 7 premade deck will be 7y
As Oliver received 4 booster packs and 7 premade decks, which included a total of 178 cards.
Thus we get 4x +7y = 264 ...(2)
System of equations to be solved is
5x + 4y = 178 .....(1)
4x +7y = 264 ...(2)
From (1) , we get x = [tex]\frac{178-4y}{5}[/tex]
Put this value in (2)
[tex]4(\frac{178-4y}{5}) +7y= 264\\\frac{712}{5} -\frac{16y}{5} +7y = 264\\\frac{712}{5}-264=\frac{16y}{5} -7y\\ y= 32\\x= \frac{178-4(32)}{5 }\\ x=50/5\\x=10[/tex]
Therefore x=10 and y= 32
The number of cards in every booster pack are 10 and number of cards in every premade deck are 32
Learn more about the solution of system of linear equation in two variable at https://brainly.com/question/14495718
#SPJ1
The perimeter of a geometric figure is the distance around the outside of the figure. The perimeter of a rectangle is 44 feet. The length of the rectangle is 6 feet more than the width. What is the measure of the width?
Write the equation for find the perimeter of the rectangle. (Use the variable w)
How fast is the second car traveling>
The width of the rectangle is 8 feet.
What is the Area of Rectangle?
Area of rectangle is the region occupied by a rectangle within its four sides or boundaries. The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides. Hence, we can say, the region enclosed by the perimeter of the rectangle is its area.
Perimeter = 44
Length = width + 6
perimeter formula of rectangle = 2(L +W)
44 = 2(W+6 +W)
22 = 2W +6
11 = W + 3
W = 8
therefore , the width of the rectangle is 8 feet
Read more about Area of Rectangle here:
https://brainly.com/question/20693059
#SPJ1
6. Select all the expressions that result in the same value as
40 + 120.
A. 4 (10
+30)
B. 2 (20 + 120)
C. 40 (1 + 3)
D. 40 (1 +30)
E. 10 (4+12)
Answer:
A, C, E
Step-by-step explanation:
40 + 120 = 160
Remember the correct order of operations, and do the operation inside parentheses first.
A. 4(10 + 30) = 4(40) = 160
B. 2(20 + 120) = 2(140) = 280
C. 40(1 + 3) = 40(4) = 160
D. 40(1 + 30) = 40(31) = 1240
E. 10(4 + 12) = 10(16) = 160
Answer: A, C, E
The sum of all proportions in a frequency distribution should be______.
Convert five hours into minutes
Answer:
300 minutes
Step-by-step explanation:
1 hour = 60 Minutes
60x5=300
Find the quadratic function with vertex (1,-2.9) and no intercepts.
Please help me I really just don't understand how to get the answer y+2.9 = -12(x-1)^2 as I need to mathematically prove this equation works.
Answer:
[tex]y+2.9=-12(x-1)^2[/tex]
Step-by-step explanation:
Vertex form of a quadratic function:
[tex]\boxed{y=a(x-h)^2+k}[/tex]
where:
(h, k) is the vertex.a is some constant.Given vertex: (1, -2.9)
Therefore:
h = 1k = -2.9Substitute the values of h and k into the formula:
[tex]\implies y=a(x-1)^2-2.9[/tex]
As the function has no x-intercepts, and the vertex is in Quadrant IV, the parabola will open downwards. Therefore, "a" will be negative. Without any further information, any number can be substituted for "a". Therefore, according to the given answer, let a = -12:
[tex]\implies y=-12(x-1)^2-2.9[/tex]
Note: If "a" was positive, the parabola would open upwards, which means there would be two x-intercepts (two points at which the curve intercepts the x-axis).
Finally, add 2.9 to both sides of the equation so that the equation is in the format of the given answer:
[tex]\implies y+2.9=-12(x-1)^2-2.9+2.9[/tex]
[tex]\implies y+2.9=-12(x-1)^2[/tex]
the store has a speaker equipment listed for a price of $100 per set of speakers there is a sale, the current selling price is 89.99 how much money does the customer save ?
The amount of money saved by the customer is $10.01
If the selling price is greater than the cost price, then the difference between the selling price and cost price is called profit or the money saved.
If the selling price is less than the cost price, then the difference between the cost price and the selling price is called loss or the money loss.
Profit/ Loss= Cost Price(CP)- Selling Price(SP)
When CP> SP, then we can say there is a profit.
When CP<SP, then we can say there is a loss.
When CP=SP, then we can say neither there is a loss nor profit.
Given data, CP= $100
SP= $89.99
Profit/Loss= CP- SP
= $100- $89.99
= $10.01
As we can see our result is positive, so there is a profit.
Final answer: The amount of money saved by the customer is $10.01
To learn more about profit and loss visit: https://brainly.com/question/21172564
#SPJ9
What can you say about the 3s in 43,862 and 75,398?
Answer:
Step-by-step explanation:
43,862 - place value - 3,000
75,398 - place value - 300
they are also numbers
Hope it helps!!!
:)
Number 8 only is algebra
3
5
Dan reads chapters in
56
hours.
What is the unit rate in chapters per hour?
Write your answer in simplest form.
Answer:
How many chapters does Dan read in 56 hours?
Step-by-step explanation:
Taylor makes $13 per hour at the grocery store. she always works between 10-15 hours per week to leave time for her homework and band practice. her gross wages can be modeled as w(h) = 13h, where h is the number of hours worked per week.
1. how much will her gross wages be if she works 12 hours this week?
2. what is the domain of this function?
3. what is the range of this function?
a) Her gross pay will be $156
b) The domain is D: [10, 15]
c) The range is R: [$130, $195]
What will be her gross wage if she works 12 hours this week?
We know that Taylor earns 13 dollars per hour on her job at the grocery store.
Then, if she works x hours in the week, her gross wage will be given by the linear equation:
g(x) = $13*x
So, if she works 12 hours, her gross pay will be:
g(12) = $13*12 = $156
what is the domain of this function?
we know that she works between 10 and 15 hours peer week, so the domain (set of the possible inputs of the function) is:
10 ≤ x ≤ 15 or [10, 15] in interval notation.
what is the range of this function?The range is the set of the outputs, the minimum of the rane is:
g(10) = $13*10 = $130
The maximum of the range is:
g(15) = $13*15 = $195
The range of the linear function is: [$130, $195]
If you want to learn more about linear functions:
https://brainly.com/question/28560814
#SPJ1
What is the equation of the slant asymptote of the rational function f(x) = 4x^2+6x-1 / x+2?
Answer:
Hello,
y=4x-2
Step-by-step explanation:
1: slope.
[tex]\displaystyle \lim_{n \to \infty} \dfrac{f(x)}{x}\\\\= \lim_{n \to \infty} \dfrac{4x^2+6x-1)}{x(x+2)}\\\\= \lim_{n \to \infty} \dfrac{4x^2}{x^2}\\\\=\boxed{4}\\[/tex]
2:
[tex]\displaystyle \lim_{n \to \infty} (f(x)-4x)\\\\= \lim_{n \to \infty} (\dfrac{4x^2+6x-1}{x+2}-4x)\\\\= \lim_{n \to \infty} (\dfrac{4x^2+6x-1-4x^2-8x}{x+2})\\\\= \lim_{n \to \infty} (\dfrac{-2x-2}{x+2})\\\\= \lim_{n \to \infty} (\dfrac{-2x}{x})\\\\=\boxed{-2}\\[/tex]
Slant asymptote is y=4x-2
q equals 4 l plus 2 k with l on the horizontal axis and k on the vertical axis, draw an isoquant. the slope of this isoquant equals
The slope of this isoquant equals -2.
What is an isoquant?A contour line formed across a set of locations where the same quantity of output is produced while changing the quantities of two or more inputs is called an isoquant (derived from quantity and the Greek word iso, meaning equal). A factor of production, like as labor, money, land, or organization, is typically represented by the x and y axes on an isoquant. Another name for an isoquant is a "Iso-Product Curve" or a "Equal Product Curve."
The isoquant mapping deals with the cost-minimization, profit, and output maximization problems of producers, whereas an indifference curve mapping helps consumers address the utility-maximizing problem. Indifference curves and isoquants diverge much more.
Calculations:
q=4L+2K
So, MPL=dq/dL =4
MPK=dq/dK =2
So,Slope=-MPL/MPK
=-4/2=-2
To learn more about isoquant ,visit:
https://brainly.com/question/19341203
#SPJ4
Charlie drove for 5 hours to get from his house to grandma’s house. He averaged 47 miles per hour on the trip. Write
and solve an expression that represents the approximate distance from Charlie’s house to grandma’s house.
Answer:
Answer:
420 miles
Step-by-step explanation:
Distance traveled per hour = 55 miles
Distance traveled in 6 hours = 55 * 6 = 330 miles
Distance of the trip = 330 + 90 = 420 miles
Step-by-step explanation:
What is 96,902,123 in expanded form
Answer: 90,000,000 + 6,000,000 + 900,000 + 2,000 + 100 + 20 + 3
Step-by-step explanation: you add each one and get 96,902,123
3 is subtracted from three times a number
“a number” is x
Answer:
3x - 3
The answer above matches with the statement:
"Three is subtracted from three times a number."
Hope this helps :)
The coordinates of the endpoints of
DE
are D(–13,–10) and E(3,14). Point F is on
DE
and divides it such that DF:EF is 5:3.
What are the coordinates of F?
Write your answers as integers or decimals.
Using proportions, the coordinates of F are given as follows: F(-3,5).
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
Point F divides the segment such that DF:EF is 5:3, hence the point F is 5/8 of the way, that is:
F - D = 5/8(E - D).
The x-coordinate of F is given by:
x + 13 = 5/8(3 + 13)
x + 13 = 10
x = -3.
The y-coordinate of F is given by:
y + 10 = 5/8(14 + 10)
y + 10 = 15
y = 5.
The coordinates of F are given as follows: F(-3,5).
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Round 45.8 to the nearest whole number
Answer: 46
Step-by-step explanation: 8 is closer to 10, so 45.8 would round to 46
What does the symbol bc represent
Answer:
ray BC
Step-by-step explanation:
A 4-pound box of blackberries costs $16.64. What is the price per ounce?
Cost of 4 pound box of blackberries = $16.64
Cost of 1 pound box of blackberry = [tex]\bf\frac{\cancel{16.64}}{\cancel{4}}4.16[/tex]
Hence, the cost of 1 pound of blackberry is $4.16.
in jeff’s sample, the number of siblings each person has is as follows: one, two, three, four, and ten. what is the median number of siblings in his sample?
If the number of siblings each person has is one, two, three, four and ten, then the median of number of siblings is 3
Given,
The number of siblings each person has = 1,2,3,4 and 10
Arrange them in ascending order =1,2,3,4 and 10
We know the median is the middle term of the ordered pair
The number of terms n= 5
Middle term is = [tex]\frac{n+1}{2}[/tex]
=[tex]\frac{5+1}{2}[/tex]
=3
The 3rd term is 3.
The median = 3
Hence, If the number of siblings each person has is one, two, three, four and ten, then the median of number of siblings is 3
Learn more about Median here
brainly.com/question/28060453
#SPJ4