Answers
Answer:
(-1,5), (0,4), and (-6,7)
Step-by-step explanation:
One may enter each point in both equations and solve matematically to find which points satisfy both equations. But with access to a free, and easy, online graphing utility, it is more illuminating to plot both inequalites to identify the region containing mutual points (faster, also). The attached plot illustrates the result. Each inequality adds a shaded area showing the points satisfying the equation. The color is darkest where the solution areas overlap, as seen in the upper left of the graph. All points in this area satify both inequalities. They are:
(-1,5)
(0,4), and
(-6,7)
Of the remaining three, only (2,-3) satifies neither equation.
Answer:
(-1,5), (0,4), and (-6,7)
Step-by-step explanation:
Related Questions
the beam is constructed from two boards fastened together at the top and bottom with three rows of nails spaced every 4 in.
Answers
the beam is constructed from two boards fastened together at the top and bottom with three rows of nails spaced every 4 in is[tex]487.5lb .[/tex]
Calculate the moment of inertia by using following expression,
\begin{aligned}
[tex]I & =\frac{1}{12} b d^3 \\& =\frac{1}{12} \times 6 \times(4)^3 \\& =32 \mathrm{in}^4\end{aligned}\\[/tex]
The centroid at center is,
[tex]\begin{aligned}Q & =\bar{y}_1 A \\& =1 \times 6 \times 2 \\& =12 \mathrm{in}^3\end{aligned}$$[/tex][tex]\begin{aligned}q & =\frac{V Q}{I} \\& =\frac{650 \times 12}{32} \\& =243.75 \mathrm{lb} / \mathrm{in}\end{aligned}$$[/tex]
The shear flow is,
[tex]\begin{aligned}q & =\frac{V Q}{I} \\& =\frac{650 \times 12}{32} \\& =243.75 \mathrm{lb} / \mathrm{in}\end{aligned}[/tex]
Since, there is 3 rows of nails so the shear force resisted by each nail is,
[tex]\begin{aligned}\tau & =\frac{1}{3} q s \\& =\frac{1}{3} \times 243.75 \times 6 \\& =487.5 \mathrm{lb}\end{aligned}$$[/tex]
Therefore, the shear force resisted by each nail is 487.5
[tex]487.5lb .[/tex]
To learn more about beam visit:
https://brainly.com/question/14228527
#SPJ4
Find the measure of each angle indicated.
A. 100 degree
B. 80 degree
Help!!!
Answers
Answer:
B. 80 degree
Step-by-step explanation:
These angles are same-side interior angles. Which means both angles have to add up to 180 degrees. One angle is 100 degrees; the other must be 80 degrees!
Answer: 80 degree
(100 + 80 = 180)
sketch the region enclosed by the given curves. y = 4/x, y = 16x, y = 1 4 x, x > 0
Answers
In order to plot the region enclosed by the given graphs we have to find the intersection points of all the 3 graphs taking 2 at a time
so finding intersection point of the y=4/x and y=16x
4/x=16x
=> = 1/4
=> x = 1/2 as x>0
and y=16x
=> y =8
now finding intersection point of y=4/x and y=1/16x
=> 4/x =x/16
=> = 64
=> x = 8 as x>0
and y= 4/x
=> y=1/2
now finding intersection point of y=16x and y=1/16x
the intersection point of both line is x=0
so y=16x
=> y=0
so we will get the intersection point of all the lines now after plotting all the points below we will get the graph as attached below.
To know more about intersection point click on below link:
brainly.com/question/14217061#
#SPJ4
how i can do this? (7-i)(7+i)
Answers
You can do the box method A or foil method B. Both will give you the same answer. Remember thst -i^2 is always 1 that’s how we got 50. By combining like terms, 7i & -7i will get canceled out.
How much work is done on a car if you push with 100 Newtons of force but it does not move?
Answers
Answer:
0 Joules (No work)
Step-by-step explanation:
The amount of work done on an object is equal to the force applied to the object times the distance over which the force is applied. In this case, the force applied to the car is 100 newtons, but the car does not move, so the distance over which the force is applied is 0 meters.
Therefore, the amount of work done on the car is 100 newtons * 0 meters = 0 joules. This means that no energy has been transferred to or from the car as a result of the force applied to it.
I do everything correctly, and it still says that it's wrong! I do it the exact way my teacher taught me!
Answers
[tex]-\cfrac{5}{7}(-42k-56)\implies -\cfrac{5}{7}(-42k)\left[ -\cfrac{5}{7}(-56) \right]\implies +\cfrac{5}{7}(42k)+\left[ \cfrac{5}{7}(56) \right] \\\\\\ \cfrac{5(42k)}{7}+ \cfrac{5(56)}{7}\implies 5\cdot \cfrac{42}{7}k + 5\cdot\cfrac{56}{7}\implies 5\cdot 6k+5\cdot 8\implies {\Large \begin{array}{llll} 30k+40 \end{array}}[/tex]
a study found an association between preferred warm beverage and stress level. it showed tea drinkers have lower stress levels than coffee drinkers. tea drinkers are known to have a higher proportion of yoga practitioners than coffee drinkers, and they exercise on average two hours per week more than their coffee-drinking counterparts. what is the term used to describe these additional factors that might have an effect on the stress levels of tea drinkers? responses categorical variables categorical variables cause-and-effect variables cause-and-effect variables confounding variables confounding variables quantitative variables quantitative variables response variables
Answers
Confounding variables is the term used to describe these additional factors that might have an effect on the stress levels of tea drinkers.
What is confounding variables?Confounding variables are those that have an effect on other factors in such a way that misleading or distorted relationships between two variables result. They misinterpret the "real" relationship between two variables. Confounding variable illustration You track sunburns and ice cream consumption. You discover that eating more ice cream increases your chances of becoming sunburned. To establish if a particular risk factor produced confounding, compare the estimated measure of association before and after controlling for confounding. To put it another way, compute the measure of association before and after correcting for a potential confounding factor.
Here,
Confounding variables are the terms used to explain these other elements that may have an influence on tea users' stress levels.
To know more about confounding variables,
https://brainly.com/question/29419015
#SPJ4
What is the slope of the line through (-9, 6) and (3,-9)?l
Answers
Answer:
-5/4
Step-by-step explanation:
the main answer is -5/4
A teacher makes an annual salary of $65,800.
If the income tax withholding is 14%, how
much income tax is paid?
Answers
The income tax can be paid by the teacher =$ 9212.
What is income tax:An income tax is a sort of tax that is levied on the earned and unearned income of an individual or corporation.
For instance, the United States levies a federal income tax on its residents, regardless of where they reside—in the country or overseas. The majority of the money the US government receives comes from this income tax.
Here we have
The annual salary of a teacher is $ 65,800
The rate of income tax = 14%
The income tax can be paid = 14% of 65800
=> [tex]\frac{14}{100} \times 65800[/tex]
= [tex]14 \times 658[/tex]
= 9212
Therefore,
The income tax can be paid by the teacher =$ 9212
Learn more about Income tax problems at
https://brainly.com/question/20085616
#SPJ1
Find the volume of the given prism.
Answers & photo below
↓
a. 64,288 ft3
b. 1,312 ft3
c. 2,009 ft3
d. 23,208 ft3
Answers
The volume of the cuboid is 64288 ft³
Volume of CuboidVolume of cuboid is the total space occupied by the cuboid in a three-dimensional space. A cuboid is a three-dimensional structure having six rectangular faces. These six faces of the cuboid exist as a pair of three parallel faces. Therefore, the volume is a measure based on the dimensions of these faces, i.e. length, width and height.
The formula of volume of a cuboid is given by
V = L * W * H
v = volume of cuboidl = length of cuboidw = width of cuboidh = height of cuboidSubstituting the values into the formula;
v = 41 * 32 * 49
v = 64288 ft³
The volume is 64288 ft³
Learn more on volume of a cuboid here;
https://brainly.com/question/22694657
#SPJ1
The option that indicates the correct volume of the rectangular prism in the photo that has the dimensions of length, 41 feet, width, 32 feet, and height, 49 feet is option a.
a. 64,288 ft³
What is a rectangular prism?A rectangular prism is a solid that has six rectangular faces, and twelve edges, in which each face has a parallel and congruent face on the opposite side of the prism, that has eight corners.
The dimensions of the rectangular prism in the question are;
Length of the rectangular prism = 41 feet
Width of the rectangular prism box = 32 feet
Height of the prism = 49 feet
The volume, V, of the rectangular prism is the product of the width, the length and the height as follows;
Volume of a rectangular prism, V = Width × Length × Height
The volume of the rectangular prism in the question is therefore;
V = 32 feet × 41 feet × 49 feet = 64,288 feet³
The volume of the rectangular prism in the question is; 64,288 ft³Learn more about rectangular prisms here:
https://brainly.com/question/3789826
#SPJ1
Can you please help me?
Answers
Answer:
The smallest angle is CODStep-by-step explanation:
Angle AB = 180°
so
180 = 2a + 62 + 54 - a + 5a - 20
180 = 6a + 96
180 - 96 = 6a
84 = 6a
a = 14
find angle AOC2a + 62 =
2 * 14 + 62 =
28 + 62 =
90°
find angle COD54 - a =
54 - 14 =
40°find angle DOB5a - 20 =
5 * 14 - 20 =
70 - 20 =
60°
Brianne's annual contribution to her union dues is $200. If her salary is $38,500, approximately what is her percentage
rate contribution?
0.05%
0.5%
O 1%
5%
NEXT QUESTION
:
ASK FOR HELP
TURN IT IN
Answers
Approximately, Brianne percentage rate of contribution is 0.5%.
How to find the percentage rate contribution?Brianne's annual contribution to her union dues is $200. Her salary is $38,500.
Approximately, her percentage rate of contribution can be calculated as follows:
percentage rate of contribution = union dues / salary × 100
union dues = 200 dollars
salary = 38500
percentage rate of contribution = 200 / 38500 × 100
percentage rate of contribution = 20000 / 38500
percentage rate of contribution = 0.51948051948
Therefore,
percentage rate of contribution ≈ 0.5%
learn more on percentage here: https://brainly.com/question/21896610
#SPJ1
three hearts are dissected from individuals with unknown histories. two of the three hearts are enlarged. what is a possible reason why the two hearts may be enlarged
Answers
they belong to high-performance athletes
It may be a sign of a family history of early heart disease. If one of your close relatives, such as a parent or sibling, has experienced a heart attack, a stroke, or was previously diagnosed with heart disease before the age of 60. Thus, option B, C is correct.
What individuals with a history of heart disease?The CDC's Response to the Risk Factors in the Country. Leading causes of heart disease and stroke risk factors include high blood pressure, high levels of low-density lipoprotein (LDL) cholesterol, diabetes, smoking, exposure to second-hand smoke, obesity, a poor diet, and inactivity.
People who are aware of their situation make wiser decisions, live longer, and experience greater well-being. Even if you have heart failure, it is still possible to lead a regular life. The secret to success is realizing heart failure and taking charge of it.
Therefore, They are from well-trained professional athletes, and They are from individuals with a history of heart disease.
Learn more about hearts here:
https://brainly.com/question/16566688
#SPJ2
The question is incomplete, complete question with option given below:
Three hearts are dissected from individuals with unknown histories. Two of the three hearts are enlarged. Select all of the possible reasons the two hearts may be enlarged.
A. They are from individuals who had low blood pressure histories.
B. They are from well-trained professional athletes.
C. They are from individuals with a history of heart disease.
D. They are from individuals who had arthritis issues.
a 10-ft vertical post casts a 20-in shadow at the same time a nearby cell phone tower casts a 125-ft shadow. how tall is the cell phone tower?
Answers
Answer:
750 ft
Step-by-step explanation:
the 2 situations are similar ( both right triangles ) with corresponding sides being in proportion.
let h be the height of the cell phone tower
We require the dimensions to be the same, using the conversion
1 foot = 12 inches , then
10 ft = 10 × 12 = 120 in
125 ft = 125 × 12 = 1500 in
then we obtain
[tex]\frac{h}{1500}[/tex] = [tex]\frac{120}{20}[/tex] = 6 ( multiply both sides by 1500 to clear the fraction )
h = 1500 × 6 = 9000 in ( divide by 12 to convert to ft )
h = 9000 in ÷ 12 = 750 ft
that is the cell phone tower is 750 ft tall.
Which systems have infinite solutions? check all that apply. y = 0.5x 2.75 and 2y = x 2.75 y = 0.5x 2.75 and y – 0.5x = 2.75 y = 0.5x 2.75 and 0.5x y = 2.75 y = 0.5x 2.75 and y = 0.5(x 5.5) y = 0.5x 2.75 and y = –2(–0.25x ) 2.75
Answers
Both equations y = 0.5x + 2.75 and y – 0.5x = 2.75 are equal. Hence, these systems will have infinite solutions. Hence, Option a is the most suitable answer to this question.
The system of equations having an infinite number of solutions must be the same.
In option a -
we have, y = 0.5x + 2.75 and 2y = x + 2.75
Rewriting the second equation 2y = x + 2.75 in slope-intercept form, we get,
2y = x + 2.75
y = x/2 + 2.75/2
y = 0.5x + 1.375
Both equations are not similar.
Hence this option is not the right choice.
Similarly, we will check for option b -
we have, y = 0.5x + 2.75 and y – 0.5x = 2.75
From the second equation y - 0.5x = 2.75, this can be expressed as y = 0.5x + 2.75 in the slope-intercept form.
Here, we get both equations equal.
Thus, y = 0.5x + 2.75 and y – 0.5x = 2.75 will have infinite solutions.
Similarly, checking for other options, we do not get any similar equations.
Hence, option b is the correct answer to this question.
Read more about equations:
brainly.com/question/11966980
#SPJ4
The complete question is -
Which systems have infinite solutions? Check all that apply.
a) y = 0.5x + 2.75 and 2y = x + 2.75
b) y = 0.5x + 2.75 and y – 0.5x = 2.75
c) y = 0.5x + 2.75 and 0.5x + y = 2.75
d) y = 0.5x + 2.75 and y = 0.5(x + 5.5)
e) y = 0.5x + 2.75 and y = –2(–0.25x )+ 2.75
Answer: look at the screenshot below I hope it helps you, my friend
have a lovely day :3 :) :D
UWU
Step-by-step explanation:
A beverage distributor conducts regular surveys of consumer spending on its products. The average weekly household spending (in dollars) on cow milk and almond milk for each of 12 states was recorded. A scatterplot of spending on cow milk versus almond milk is shown. Which of the following statements is true?
Select one:
a. Point (1, 12) is an outlier.
b. There is clear evidence of a positive association between spending on cow milk and almond milk.
c. The equation of the least-squares regression line for this plot is approximately ŷ = x + 12.
d. The correlation for these data is r = −1.
e. The observation in the upper right corner of the plot is influential for the least-squares regression line.
Answers
Answer:
The observation in the upper right corner of the plot is influential for the least-squares regression line.
Step-by-step explanation:
9. Triangles CDE and NOP are similar. The lengths of CD and NO are 53 in and 212in, respectively. DE
is 106 inches long and NP is 318 inches (draw a diagram and then answer the questions below)
a) Find OP and CE.
b) What is the perimeter of NOP?
c) What is the perimeter of CDE?
d) What is the ratio between the two perimeters?
Answers
Answer:
op
Step-by-step explanation:
Find the slope of the line:
Answers
please help it’s for tomorrow..
one segment measures 161 cm. Calculate its multiple according to the number 3 and its submultiple according to the number 7
Answers
Answer:
78
Step-by-step explanation:
The answer is 78 or 87 dear friend its a mystery
Multiple = (Given Number) x (Smallest Integer that is greater than or equal to the Given Number)
For example, to find the multiple of 161 according to 3, you can use the following steps:
Divide 161 by 3 to get 53.66666666666667.
Round up the result to the nearest integer to get 54.
Multiply 3 by 54 to get 162, which is the multiple of 161 according to 3.
To find the submultiple of a number according to a given number, you can use the following formula:
Submultiple = (Given Number) / (Greatest Integer that is less than or equal to the Given Number)
For example, to find the submultiple of 161 according to 7, you can use the following steps:
Divide 161 by 7 to get 23.0.
Round down the result to the nearest integer to get 23.
Divide 161 by 23 to get 7, which is the submultiple of 161 according to 7.
Therefore, the multiple of 161 according to 3 is 162, and the submultiple of 161 according to 7 is 7.
Which of the following expressions will have a product greater than 4? four times ninety-nine hundredths four times eight-eighths three-fourths times four one hundred and one-one hundredths times four
Answers
The correct expression that has a product greater than 4 is one hundred and one hundredths times four.
What is an expression?A mathematical expression is a sentence with at least two numbers or variables and at least one mathematical operation. Math operations include addition, subtraction, multiplication, and division.The most common type of algebraic expression is a monomial expression. A binomial expression. A polynomial expression.There are four expressions given as
(a) four hundredths of a percent
= 4 × 99/100
= 4 × 0.99
= 3.96
(b) four times the eighth
= 4 × 8/8
= 4 × 1
= 4
(c) four times three-fourths
= 3/4 × 4
= 3
(d) one hundred and one hundredths multiplied by four
= 1.01 × 4
= 4.04
As a result, the expression with a product greater than four is one hundred and one hundredths times four.
To learn more about expressions refer to :
brainly.com/question/1859113
#SPJ1
Which statements are true about the linear inequality y > 3/4x-2? Select three options.
Answers
The linear inequality y > 3/4x - 2 is true about the graph passes through the x - axis at 2.67, the graph passes through the y - axis at -2 and the graph has a straight broken line to denote the ">" inequality sign.
What is Linear Inequality?Linear inequalities are inequalities that involve at least one linear algebraic expression, that is, a polynomial of degree 1 is compared with another algebraic expression of degree less than or equal to 1. To represent various kinds of linear inequalities.
In the given, we can represent this on a graph.
The graph of y > 3/4x - 2 shows these properties
The graph passes through the x - axis at 2.67 and the y - axis at -2
The graph has a straight broken line shows the ">" inequality sign.
The correct option is A.
Learn more on linear inequality here;
brainly.com/question/25839052
#SPJ1
Complete Question:
Which of the statement are true about the linear inequality y > 3/4x - 2
I. The graph has a broken line
II. The graph has an unbroken line
III. The graph passes through y - axis at -2
IV. The graph passes through the x - axis at 2.67
gerardo is 9 feet away from his car when he begins walking directly away from his car at a constant speed of 3 feet per second. if gerardo is 24 feet from his car, how many seconds have elapsed since he started walking away from his car?
Answers
The time that has elapsed since Gerardo started walking away from car will be equal to 5 seconds.
We solve this problem by converting it into a linear equation that has three variables in it. Since we have distance, time and speed the three variables will be d, t and s respectively. The expression which shows the distance of Gerardo will be expressed as
d = (s×t) + 9; we have the constant as 9 because Gerardo was 9 feet away from his car.
Now, we have the distance as d = 24 feet and the speed is constant that is equal to 3 feet per second and we need time which will be
24 = (3×t) + 9
15 = 3×t
=> t = 15/3
=> t = 5 seconds
Learn more about Linear equation at:
brainly.com/question/2030026
#SPJ4
There are 8 grams of sugar in 1 portion of a certain cereal. How is the amount of sugar
related to the number of portions of cereal?
Answers
Answer:
y = 8x
Step-by-step explanation:
The amount of sugar in grams is 8 times the number of portions.
For example, 1 portion has 8 grams of sugar.
Two portions have 16 grams of sugar.
If you let y = number of grams of sugar and x = number of portions, then
y = 8x
In which of the following cases is the construction of a triangle ABC possible?
(a) AB = 4cm, CA= 3cm, BC=1cm
(b) AB= 8cm, CA= 10cm, BC=8 cm
(c) AB= 7cm, BC= 10cm, CA=8 cm
Answers
By using the property of triangle, it can be calculated that-
A triangle is possible for case b) and c)
What is a triangle?
A triangle is a three sided two dimensional figure. A triangle has three sides and three interior angles.
We know that sum of two sides of a triangle is always greater than the third side
For a)
CA + BC = 3 + 1 = 4 which is not greater than AB = 4
A triangle is not possible in this case
For b)
CA + BC = 10 + 8 = 18 > AB = 8 cm
AB + AC = 8 + 10 = 18 > BC = 8cm
AB + BC = 8 + 8 = 16 > AC = 10 cm
A triangle is possible in this case
For b)
CA + BC = 8 + 10 = 18 > AB = 7 cm
AB + AC = 7 + 8 = 15 > BC = 10cm
AB + BC = 7 + 10 = 17 > AC = 8 cm
A triangle is possible in this case
So a triangle is possible for case b) and c)
To learn more about triangle, refer to the link-
https://brainly.com/question/1058720
#SPJ1
Trapezoid PQRS is shown on the coordinate plane.
-10
40
s
e
O m/M>m/P
O m/M> m/Q
m/M = m/R
O m/M = m/S
R
10
If trapezoid PQRS is reflected across the y-axis and rotated 90° clockwise about the origin to form trapezoid KLMN, which must
be true?
H
Search
J
Answers
The true statement is (d) the angle measures of trapezoid PQRS are equal to the corresponding angle measures of trapezoid KLMN
How to determine the true statement?From the question, we have the following parameters that can be used in our computation:
Trapezoid PQRS
The transformation is given as
Reflection across the y-axisRotation 90 degrees clockwiseAs a general rule of transformation, reflection and rotation are rigid transformations and they do not change the size and angles in a shape
This means that we get a congruent figure to that figure after the transformations
Thus, when PQRS is reflected and rotated 90° about the origin to form trapezoid KLMN, the trapezoid KLMN is congruent to trapezoid PQRS.
⇒ By the definition of congruence,
The corresponding sides and angle of trapezoid KLMN are congruent to that of trapezoid PQRS.
⇒ ∠P ≅ ∠K, ∠Q ≅ ∠L, ∠R ≅ ∠M and ∠S ≅ ∠N
⇒ Option D) is correct.
Note: KMLN is a trapezoid ⇒ Sum of the angle measures of trapezoid P'Q'R'S' is also 180°
Option A) is incorrect.
Since, trapezoid KMLN is congruent to trapezoid PQRS.
⇒ Option B) is incorrect.
We know that if two shapes are congruent then their area must be equal.
⇒ Area of trapezoid KMLN = Area of trapezoid PQRS
Thus, Option C) is incorrect.
Read more about transformation at
https://brainly.com/question/29744094
#SPJ1
Complete question
Trapezoid PQRS is shown on the coordinate plane. If trapezoid PQRS is reflected across the y-axis and rotated 90° clockwise about the origin to form trapezoid KLMN, which must
A) The sum of the angle measures of trapezoid PQRS is 180° less than the sum of the angle measures of trapezoid KLMN.
B) Trapezoid PQRS is not congruent to trapezoid KLMN
C) The area of trapezoid PQRS is less than the area of trapezoid KLMN
D) The angle measures of trapezoid PQRS are equal to the corresponding angle measures of trapezoid KLMN
Select all the correct answers.
Michael is graphing the parabola represented by this equation.
y = -(x - 3)² - 1
Which features should he include in his graph?
Answers
The features that Michael should include on the graph of the parabola are given as follows:
Focus at (3, -3/2).Vertex at (3,-1).How to graph the parabola?The parabola for this problem is defined as follows:
y = -0.5(x - 3)² - 1.
Comparing to the vertex form definition, the coordinates of the vertex are given as follows:
(3, -1).
The equation can also be written as follows:
-0.5(x - 3)² = y + 1
(x - 3)² = -2(y + 1).
Then the coefficient p is obtained as follows:
4p = -2
p = -0.5
Then the coordinates of the focus are given as follows:
(3, -1 - 0.5) = (3, -3/2),
The equation of the directrix is then given as follows:
y = 1 - 0.5
y = 1/2.
More can be learned about the equation of a parabola at https://brainly.com/question/4061870
#SPJ1
1.) Graph the system of equations on the grid below.
4x +2y=-12
3x-5y = -35
Answers
Answer:
first equation = red line
second equation = blue line
Step-by-step explanation:
First, we solve for y for both equations
4x + 2y = -12
2y = -12 - 4x
2y = -4x -12
y = -2x - 6
3x - 5y = -35
-5y = -35 - 3x
-5y = -3x - 35
y = (-3/5)x + 7
to divide data with a high value of h and a low value of l into k classes, the class interval must be:
Answers
The number of classes should be an integer and this value will typically be a fraction. The limit needs to be raised in order to take into account all observations when this calculation yields an integer.
The fixed and variable costs can be determined by solving the system of equations if the variable cost is a fixed charge per unit and the fixed costs stay the same. The high-low method can, however, produce more or less accurate findings based on the distribution of values between the highest and lowest monetary values or quantities, therefore it is important to use caution when applying it.
Learn more about integers at
https://brainly.com/question/26009132
#SPJ4
find the exact length of the curve.x = 1/3 √y (y - 3), 16 ≤ y ≤ 25
Answers
The length of the curve x = 1/3 √y (y − 3) is 64/3.
What is arc length?The distance between two point along a segment of a curve is known as the arc length.
The equation of the curve is given by:
x = 1/3 √y (y − 3), 16 ≤ y ≤ 25
Length of the curve y = f(x) between point x =a to x = b is given by:
[tex]\int\limits^b_a {\sqrt{1+[f'(x)]^2} } \, dx[/tex]
√1 + [f′(x)]2 dx.
x = 1/3 √y (y − 3)
x = 1/3 * [tex]y^\frac{3}{2}[/tex] - [tex]y^\frac{1}{2}[/tex]
Let's find the first derivative of x.
dx/dy = 1/3. 3/2. [tex]y^\frac{1}{2}[/tex]- 1/2 . [tex]y^\frac{1}{2}[/tex]
dx/ dy = 1/2 ( [tex]y^\frac{1}{2}[/tex] - [tex]y^\frac{-1}{2}[/tex])
(dx/dy)^2= 1/4 ( [tex]y^\frac{1}{2}[/tex] - [tex]y^\frac{-1}{2}[/tex])^2
= 1/4(y + [tex]y^-^1[/tex]-2)
1 + {f′(x)}2 = 1 + 1/4(y +[tex]y^-^1[/tex]-2)
= 1/4 y + 1/4[tex]y^-^1[/tex]+ 1/2
1 + {f′(x)}2= 1/4 (y + [tex]y^-^1[/tex] + 2)
√[1 + {f′(x)}2] = 1/2 ( [tex]y^\frac{1}{2}[/tex] + [tex]y^\frac{-1}{2}[/tex])
Length of curve is given by:
25
∫ [tex]\frac{\sqrt{y} }{2} +\frac{1}{2\sqrt{y} }[/tex] dy
16
= [tex]\left \{ {{y=25} \atop {x=16}} \right.[/tex] [[tex]y^\frac{3}{2}[/tex]/3 + √y]
= [(25)3/2 /3 + √25] - [(16)3/2 /3 + √16]
= [125/3 + 5] - [64/3 + 4]
= 140/3 - 76/3
= (140 - 76)/3
= 64/3
So the length of the curve is 64/3
To know more about arc length click on below link:
https://brainly.com/question/14319881#
#SPJ4
Yeterday,255 guet at a hotel went kiing, and 170 guet did not go kiing, What percentage of guet at thi hotel went kiing yeterday?
Answers
The percentage of the guests at this hotel who called for room service yesterday is 40%
When provided,
170 visitors in total requested room service.
The total number of visitors who did not request room service was 255.
We can now determine the overall number of guests.
Total guests equal (total guests who requested room services) plus (total number of guests who did not call for room services)
so,
there are overall guests of
=170+255
=425
We can now find the percentage
the proportion of visitors to this hotel who requested room service yesterday is
170/425 *100%
=40
The percentage of the customers at this hotel who called for room service yesterday is 40%.
Find out more on Percentage at:
https://brainly.com/question/24877689
#SPJ4