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
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Find v.
Answer in simplest radical form.
Answer:
2.8mm
Step-by-step explanation:
using the sine rule.
Nolan has a lot of tennis balls in his garage he has 4 green tennis balls only 5 percent of his tennis ball are green how many does does he have altogether
Answer:
2
Step-by-step explanation:
4 green balls
5%
would equal 2
Which statement about geometric figures is true?
O A ray has exactly two endpoints.
O On a coordinate plane, parallel lines have the same slope.
O Two lines on a coordinate plane that do not intersect are perpendicular.
O An angle is formed by a set of points that are all equidistant from a common point.
Answer:
B
Step-by-step explanation:
On a coordinate plane, parallel lines have the same slope as geometric figures are true. Thus option B is correct.
What are geometric figures?Marks, splines, spheres, and curved are used to build enclosed geometric shapes. We can see these shapes all around us. Illustrations of geometric shapes include circles, rectangles, triangles, and others. Any configuration of points, columns, or angles is a geometry figure.
A point is the most fundamental algebraic concept because it has no boundaries. Simply put, a point upon that plane is a location. A dot is used to symbolize it. A plane can be identified by three non-straight-line points.
As two or much more vectors seldom cross each other and are located on the same dimension, these are said to be parallel. The slope of these lines is constant. Coplanar lines that seem to be parallel are the ones that don't cross. Therefore, option B is the correct option.
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Find the Rate of Change between each pair of points
Answer:
-3
Step-by-step explanation:
The formula for the rate of change (slope) between two points is:
[tex]\frac{y_2 - y_1}{x_2-x_1}[/tex]
So, we plug in the two points:
[tex]\frac{-20-(-5)}{6-1} =\frac{-15}{5} =-3[/tex]
The rate of change is -3
Pls help simplify fast
Need help with this question
The series of transformations that map figure T onto figure U will be first rotated and then translate.
What is a transformation of a shape?A point, line, or numerical figure can be changed over in one of four ways, and each meaningfully affects the item's construction or potential position. Picture, after interpretation, alludes to the article's definitive association and arrangement. Not long before the alludes to the material's underlying condition.
Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.
The translation does not change the shape and size of the geometry. But changes the location.
The series of transformations that map figure T onto figure U will be first rotated and then translate.
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HELP PLEASE!! PLS EXPLAIN ON HOW U GOT THE ANSWER!!
Mia is building a three-sided shelter for her action figures. The shelter will resemble a rectangle with one of the long sides removed. She has boards that measure 36 inches, 39 inches, and 42 inches in length; all the boards are the same width. Mia will need to convert some of these measurements into other imperial units to build the shelter the way she wants.
Mia will use one of these boards for the length of the shelter. She knows she wants the length of the shelter to measure 3.25 feet. She will use a different board for the width of the shelter. The width of the shelter will be shorter than the length.
Which board will Mia use for the length of the shelter, given that 1 foot = 12 inches?
What is the width of the shelter, measured in feet?
Mia needs to cut the third board to match the width of the shelter. How many feet of board will she need to cut off the existing board to reach this goal?
so, she has three boards, 36, 39 and 42 inches, hmmm but she wants the length or longer side to be 3.25 ft, hmmm 36 ÷ 12 is just 3, so that won't do, 42 ÷ 12 is 3.5 ft, nope not that one, 39 ÷ 12 is 3.25, well, that's our board.
so the width has to be smaller than the length, and it has to be a full board, so since we used the 39 incher already, smaller than 39 is 36, so we'll use the 36 incher for the width, that is, the 3 feet one.
From the 3rd board, Mia is going to have to make it match with the 36 incher, that means she needs to saw it off by 6 inches, 42 - 6 = 36, and 6 inches is just 6 ÷ 12 = 0.5 feet.
Check the picture below.
You tie a spherical balloon that is 2 feet in diameter to a stake in the ground.The string is 15 feet long.The wind blows and you observe that the top of the balloon is 8 feet over from the stake,as shown in the diagram.what is the height,b,of the balloon?
To solve this problem, we can use the Pythagorean theorem to find the height of the balloon. In particular, we can consider the right triangle formed by the stake, the top of the balloon, and the part of the string that is attached to the stake.
[asy]
unitsize(2 cm);
pair A, B, C, D, E;
A = (0,0);
B = (0,8);
C = extension(A,B,A+(1,0),B+(1,0));
D = extension(A,C,A+(0,1),C+(0,1));
E = extension(B,D,B+(0,-1),D+(0,-1));
draw(A--B--C--cycle);
draw(A--D--E--cycle);
draw(rightanglemark(A,D,C,2));
label("$A$", A, S);
label("$B$", B, N);
label("$C$", C, E);
label("$D$", D, E);
label("$E$", E, W);
[/asy]
Let $a$ be the distance from the stake to the top of the balloon, $b$ be the height of the balloon, and $c$ be the length of the string. We know that $a = 8$ feet and $c = 15$ feet, so we can use the Pythagorean theorem to find $b$:
$a^2 + b^2 = c^2$
$8^2 + b^2 = 15^2$
$64 + b^2 = 225$
$b^2 = 161$
$b = \sqrt{161} = \boxed{12.8}$ feet
Therefore, the height of the balloon is approximately 12.8 feet.
A 2-kilogram bag of sand costs $2.66. What is the unit price?
Submit
per kilogram
Answer:
2662
Step-by-step explanation:
it is really good to this 2.66÷2 X 100
what is a type ii error? multiple choice failing to reject a false null hypothesis accepting a false alternate hypothesis rejecting a false null hypothesis rejecting a false alternate hypothesis
A type II error is when you fail to reject a false null hypothesis. This means that you conclude that the null hypothesis is true, even though it is actually false. This error occurs when you do not have sufficient evidence to reject the null hypothesis, and you end up accepting it as true.
Here are the possible options for type II errors:
1.Failing to reject a false null hypothesis (correct answer).
2.Accepting a false alternate hypothesis.
3.Rejecting a false null hypothesis.
4.Rejecting a false alternate hypothesis.
What does "hypothesis" actually mean?A hypothesis is a tested assertion about the relationship between two or more variables or a theory put up to explain an observed occurrence in a scientific environment.
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The diagonal of a polygon is directly proportional to its
perimeter. The perimeter of the polygon having a diagonal
of 8 units, is equal to 36 units. What is the perimeter of a
polygon having a diagonal of 10 units
Answer:
45 units
Step-by-step explanation:
Given that the perimeter and diagonal length of a polygon are proportional and that a polygon with a diagonal of 8 units has a perimeter of 36 units, you want the perimeter for a diagonal of 10 units.
ProportionThe proportion of interest is ...
P/d = p/10 = 36/8
Multiplying by 10 gives ...
p = 10(36/8) = 45
The perimeter of the larger polygon is 45 units.
which of these two expressions are equivalent to 5^-3
Answer:
1/125
Step-by-step explanation:
Answer:
1\/125 and 1/5^3
Step-by-step explanation:
based on the design of the study, would a statistically significant result allow the researchers to conclude that receiving treatments at the clinic you selected in part (a-ii) causes a higher percentage of successful treatments than at the other clinic? explain your answer.
No, a statistically significant result would not allow the researchers to conclude that receiving treatments at the clinic selected in part (a-ii) causes a higher percentage of successful treatments than at the other clinic.
The study design is a comparison of the success rates of the two clinics without controlling for any other variables that may influence the results. In order to conclude that the clinic you selected causes higher success rates, the researchers would need to control for other variables, such as the types of treatments, the types of patients, the experience of the clinicians, etc.
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4
1 point
Solve for x. Round to the nearest tenth.
24
X
14
--DO
We need to use the concept of Pythagorean theorem. The value of x in the given triangle is 16.
What is Pythagorean theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this rule, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse, or the side across from the right angle. This theorem can be expressed as the Pythagorean equation, which is an equation connecting the lengths of the sides a, b, and the hypotenuse c: [1]
a^{2}+b^{2}=c^{2},
CalculationSo mark the given triangle as ABC in which B is right angled.
AC=24+x
Mark the height of the given triangle as BD and BD=14.
Now using pythagoras theorem,
(BC)2=(CD)2 + (BD)2
⇒(BC)2=(24)2 + (14)2
∴(BC)2=772
Now after finding BC we need to find AB using pythagoras theorem.
(AD)2 +(BD)2 =(AB)2
⇒(x)2 + (14)2 =(AB)2 - eq1
⇒ (AB)2 + (BC)2 = (24+x)2 - eq2
Substitute eq1 in eq2
⇒(x)2 + (14)2 + (BC)2 =(24+x)2
⇒(x)2 + 576 +772 = 576 + (x)2 + 48x
⇒772=48x
∴x=16.0833
x≈16.
We need to use the concept of Pythagorean theorem. The value of x in the given triangle is 16.
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Is my answer correct?
what is answer of this question?
The accuracy of the given test for meningitis is; 95%
How to find the accuracy of the test?The accuracy of a test is gotten by dividing the number of correct results by the number of tests.
In this problem, there were 80 volunteers who took the tests, of which the number that had correct results is;
80 - 2 - 2 = 76
Thus, the accuracy is given by:
A = 76/80 = 0.95 = 95%.
That gives us the accuracy of the meningitis test.
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the total surface area of a cube is 294cm(2). work out the volume of the cube
Step-by-step explanation:
S=6a^2
294=6a^2
294/6=a^2
a^2=49
a=
[tex] \sqrt{49} [/tex]
a=7
V=a^3
V=7^3
V=343cm3
NEED THIS ASAP!!!! it for math
Answer:
Step-by-step explanation:
red
Remainder Theorem, (refer to attached image) please help
The statement about the polynomial is an example of deductive reasoning. This is shown by the Option labelled A
What is deductive reasoning?We know that the term deductive reasoning has to do with the kind of knowledge that we arrive at by the consideration of the facts of the problem that has been set before us.
In effect, we can be able to define deductive reasoning as a kind of reasoning that moves from the general to the particular. We are looking at the fact that the result that we have in the given instant is obtained after the consideration of a more general proposition.
In this case, we have been told that the remainder would be zero based on the kind of polynomial that we have and this has been induced by looking at the polynomial.
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Please help me respond this question!
The percentile rank of a core of 71 in the given test is 26.67% and the score of Viktor for the 60th percentile is 85.
How to calculate the percentile rank and the percentile?The formula for calculating the percentile rank of a set of data is
percentile rank for 'x' = (number of data values below 'x')/total number of data values × 100 i.e., Percentile rank = n/N × 100.
The formula for calculating the percentile is
percentile = rank × total number of data values
Where rank = percentile ÷ 100
Calculation:A teacher recorded unit 4 test scores from her class.
The scores data is as follows:
58, 64, 68, 70, 71, 75, 77, 80, 84, 85, 87, 90, 93, 95, 96
So, the total number of data values N = 15
The percentile rank for a score of 71 on this test is
The number of data values below score 71 is n = 4
Then,
Percentile Rank = n/N × 100 = 4/15 × 100 = 26.67%
Viktor's score, when he is in the 60th percentile is
percentile = rank × 15
Rank = 60 ÷ 100 = 0.6
⇒ percentile = 0.6 × 15 = 9
The data value after 9 positions from the left to right in the data set is 85. So, the score in the 60th percentile is below 85.
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pls help
its for tmmr please
Answer:
1) a) 0,1
b) 1,2
c) -2,1
d) -3,-2
Step-by-step explanation:
what is the unit of measure for roll batt insulation? what is type of information should be noted on the estimate?
The unit of measure for roll batt insulation is usually in square feet. On the estimate, you should note the type of insulation being used, the type of coverage being provided, the cost of the insulation, and any installation fees.
Roll batt insulation is a type of insulation that is often used to insulate walls, attics, and other areas of the home. The unit of measure for roll batt insulation is usually in square feet. When getting an estimate for the cost of the insulation, it is important to note the type of insulation being used, the type of coverage being provided, the cost of the insulation, and any installation fees that may be involved. This type of information should be noted on the estimate in order to ensure that you are getting the most accurate estimate for the insulation that you need.
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Which of the following best describes the quadrilaterals shown below?
A.
Quadrilateral 1 and quadrilateral 2 are similar because quadrilateral 2 can be created by rotating, reflecting, and/or translating and dilating quadrilateral 1.
B.
Quadrilateral 1 and quadrilateral 2 are congruent because quadrilateral 2 can be created by rotating, reflecting, and/or translating quadrilateral 1.
C.
Quadrilateral 1 and quadrilateral 2 are similar because quadrilateral 2 can be created by rotating, reflecting, and/or translating quadrilateral 1.
D.
Quadrilateral 1 and quadrilateral 2 are congruent because quadrilateral 2 can be created by rotating, reflecting, and/or translating and dilating quadrilateral 1.
Answer:
The answer is quad 1 and quad 2 are congruent because quad 2 can be created rotating and then translating quad 1
Step-by-step explanation:
Write the equation of the line described below in slope-intercept
form.
Find the equation of the line that is
perpendicular to the line y = 3x - 5 and
passes through the point (8, -7).
The slope intercept form of the equation is y = -1/3 x - 13/3
What is an equation of a line?
The set of points that make up a line in a coordinate system are represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y.
Given equation of the line is y = 3x - 5 .
Compare the equation with y = mx + c
m = 3 and c = -5
The slope of the line that perpendicular to the given line is - 1/m = - 1/3
The equation of line that passes through the point (x₁, y₁) with slope m is y - y₁ = m (x - x₁).
Given point is (8,-7).
Putting m = - 1/3, x₁ = 8, y₁ = -7 in y - y₁ = m (x - x₁):
y - (-7) = - 1/3 (x - 8)
Rewrite the above equation in the form y = mx + c:
y + 7 = -1/3 m + 8/3
Subtract 7 from both sides:
y = -1/3 m + 8/3 - 7
y = -1/3 m - 13/3
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researchers estimated that 0.07%, by mass, of a 12- gram sample of an orchid plant consists of the fatty acid eicosadienoic acid. based on this estimate, what is the mass of eicosadienoic acid, in grams, in this orchid sample?
We are aware that the researchers estimated that the fatty acid eicosadienoic acid made up 0.07 percent by mass of a 12-gram sample of an orchid plant.
Therefore, the mass of the acid in this sample is 0.0084 grams, or 0.07% of 12 grams.
Therefore, this orchid sample's mass of eicosadienoic acid is 0.0084 grams.
Using the formula 0.07% of 12 grams, we can determine the mass of acid in this orchid sample.
In this orchid sample, eicosadienoic acid has a mass of 0.0084 grams.
What, in layman's terms, is mass?It is the most fundamental property of matter and one of the fundamental quantities in physics. Mass can be defined as the amount of material in a body. The kilogram (kg) is the SI unit of mass. Note: A body's mass remains constant over time.
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Enter the value of x below.
x+5=10
Answer:
x = 5
Step-by-step explanation:
x + 5 = 10 Subtract 5 from both sides
x + 5 - 5 = 10 - 5
x = 5
check:
x+ 5 = 10
5 + 5 = 10
10 = 10
Value of x is 5. It is a linear equation.
An equation is said to be linear if the greatest power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the standard form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the standard form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.
Given equation is
x+5=10
therefore, by shifting the given values
x+5=10
x=10-5
x=5
Therefore, the answer of the given equation is x=5.
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what is the value of x.
The value of x in the triangle is 140 degrees.
How to find the angle in a triangle?The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Applying the exterior angle theorem,
40 + 100 = x
140 = x
x = 140 degrees.
Therefore, x is 140 degrees.
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a medical institution requests 1 g of bismuth 214 which has a half life of 20 minutes how many grams of bismuth 214 must be prepared if the shipping time is 2 hours
64grams of bismuth-214 must be prepared if the shipping time is 120minutes.
What is half cycle?
Time required for a quantity to reduce to half of its initial value is termed as half life. It can help us to know how quickly unstable atoms undergo radioactive decay. This is used generally to characterize any type of exponential decay. It occurs when unstable atomic particles lose energy. Twenty-nine elements are capable of this process.
Rutherford applied the principle of a radioactive element's half-life in the age determination of rocks by calculating the decay period of radium to lead-206.
Given half life of 20min of 1g of Bismuth-214
If the shipping time is 120minutes, then
10min/20min/half life
=6 half life
=1/2^6=1/64
Grams of bismuth-214 that can be prepared in 120 min,
=1gm*64
=64grams.
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Sebastian has xx nickels and yy pennies. He has at least 20 coins worth at most $0.65 combined. Solve this system of inequalities graphically and determine one possible solution.
The system of equation to show Sebastian's coin is
xx + yy ≥ 15
0.1xx + 0.05yy ≤ $0.65
From the graph, the solution of the system of equation is (-2, 7)
How to find the equation as requiredThe equation to represent the information is written bearing in mind that
10 dimes = 1 dollar = 20 nickels
1/10 = 0.1
1/20 = 0.05
let the dimes be xx and the nickels be yy
Sebastian has at least 20 coins worth at most $0.65 combined, is represented as
xx + yy ≥ 15
0.1xx + 0.05yy ≤ $0.65
the graph shows the solution to be the solution is (-2, 7)
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What 's two ways to find the answer to this ? ( Show your work)
Ahmed needs 8 cups of yogurt and 4 cups of milk corresponding to the 12 cups of mango,
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Ingredient of mango lassi,
3 cups of mango,
2 cups of yogurt,
1 cup of milk,
So,
3 cups of mango = 2 cups of yogurt
1 cup of mango = 2 / 3 cups of yogurt,
12 cups of mango = 12 (2/3) yogurt
= 8 cups of yogurt
Now,
3 cups of mango = 1 cup of milk
1 cup of mango = 1/3 cup of milk
12 cup of mango = 12 / 3 cup of milk
12 cup of mango = 4 cups of milk
Thus, Ahmed needs 8 cups of yogurt and 4 cups of milk corresponding to the 12 cups of mango.
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