The volume of the solid obtained by rotating the region bounded by y = x^2, y = 0 and x = 1, about the y-axis is π/2.
We have to determine the volume of the solid obtained by rotating the region bounded by y = x^2, y = 0 and x = 1, about the y-axis.
We will rotate the region near the y-axis using the disc method. Consequently, the curve's equation should be expressed in terms of y.
y = x^2
Taking square root on both side, we get
x = √y
We can write it as
x = y^{1/2}
The volume integral formula is
V = [tex]\pi\int_{a}^{b}R(x)^2dx[/tex]
The values of a and b are taken from the y-axis since the equation for the curve we need is expressed in terms of y.
Using the curve's equation, if x = 0, y = 0, and if x = 1, y = 1, respectively.
Thus, a = 0 and b = 1 are the values.
Now, we may use definite integral to express the volume.
V = [tex]\pi\int_{0}^{1}\left[y^{1/2}\right]^2dx[/tex]
Now simplify
V = [tex]\pi\int_{0}^{1}ydx[/tex]
Now integrating
V = [tex]\pi\left[\frac{y^2}{2}\right]_{0}^{1}[/tex]
V = [tex]\pi\left[\frac{(1)^2}{2}-\frac{(0)^2}{2}\right][/tex]
V = [tex]\pi\left[\frac{1}{2}-0}\right][/tex]
V = π/2
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PLEASE HURRY I HAVE LIMITED TIME!
Question- Find the standard form equation of a circle given a center of (7, 14) and a point on the circle of (4, 15).
Answers-
A.(x-7)^2 + ( y-14)^2 = 10
B.(x-7)^2 + (y-14)^2 = 15
C.(x-7)^2 + (y-14)^2 = 25
D.(x+7)^2 + (y+14)^2 = 2
Answer:
A
Step-by-step explanation:
R = sqrt((7-4)^2+(14-15)^2)=sqrt(10)
The answer is A since that's the only answer with the proper radius, using the formula for a circle.
The supermarket has 20 aisles. 10 of the aisles are empty. What percentage of the aisles are empty?
The percentage of the aisles that are empty, given the number of aisles in total in the supermarket, is 50 %
How to find the percentage of aisles ?To find the percentage of the aisles that are empty, you can use the formula :
= Number of aisles that are empty / Number of total aisles in the supermarket x 100 %
Number of aisles that are empty = 10 aisles
Number of total aisles in the supermarket = 20 aisles
The percentage of aisles empty is:
= 10 / 20 x 100 %
= 0. 5 x 100 %
= 50 %
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Tamisha works as an intern in an architect’s office. A designer drew a scale drawing of a kitchen without using grid paper. In the drawing, 1 inch represents 2 1/2 feet. Tamisha’s supervisor wants her to determine the skill factors for the length and the skill factors for the areas of.
a. Find the scales factor for the lengths
b. Find the scales factors for the areas
Answer:
length: 1:30, area: 1:900
Step-by-step explanation:
1ft = 12 inches, so 2.5' = 30". scale for length is 1:30, for area it's square - 1:900
Find the length of x. Please help I will mark brainlist
Answer:
its 4, but give the other guy brainliest he answered first :D
Step-by-step explanation:
help me out pleaseeeeeeeeeeeeeeeeeee
Answer:
3 and 5
Step-by-step explanation:
Find the mean, median, mode, and range for each data set given.
a. 7, 12, 1, 7, 6, 5, 11
b. 85, 105, 95, 90, 115
c.15, 11, 11, 16, 16, 9
Answer:
Answers are in bold
Data set A:
Mean: 7
Median: 7
Mode: 7
Range: 11
Data set B:
Mean: 78
Median: 95
Mode: No mode or all the numbers (85, 105, 95, 90, 115)
Range: 30
Data set C:
Mean: 13
Median: 13
Mode: 11 and 16
Range: 7
Step-by-step explanation:
You're welcome.
The function f(x) is shown on the graph.
f(x)
O Logarithmic
B 7
O Polynomial
654
-10-9-8-7-6-5-4-3-2-10
3
2
-1
-2
-3
47999
-7
-10
Which type of function describes f(x)?
O Exponential
X
2 3 4 5 6 7 8 9 10
An exponential function is represented by taking into account the fact that the graph has an asymptote and does not cross it.
What is exponential function?A function with the formula f(x)=ax is an exponential function. Here, x is the input and an is a positive, real integer (referred to as the base) (independent variable). The independent variable is always in the exponent for exponential functions, which is important to keep in mind.
It is based on:
where a represents the y-intercept.
The rate of change is b.
The asymptote, which the function does not cross, is y = c.
Consequently, the graph in this issue models an exponential function with an asymptote at y = 0.
An exponential function is represented by taking into account the fact that the graph has an asymptote and does not cross it.
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what is the value of Z?
The square root of 2 or root 2 is represented using the square root symbol √ and written as √2 whose value is 1.414. This value is widely used in mathematics.
What is the value of 2√ 2 ?Well, the basic answer is that the value of root 2 (i.e., 2) is 1.412. We must first understand the concepts of power and roots in order to comprehend what root 2 (2) is and how to calculate its value. √2 = 1.414
You may determine the values of non-perfect square values like root 3, root 5, etc. using the long division method.
The square root or root of a number "n" is a number that, when multiplied by itself, has the value "n". For instance, the square root of 4 is equal to 2. thus 2 + 2 Equals 4. The opposite of squaring a number is finding the square root of that integer.
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The vertices of YEAR are Y(1,-4) E(3,0), A (-1,2) and R( -3,-2) . prove that YEAR is a Square
To prove that YEAR is a square, we need to show that all four sides have the same length and all four angles are right angles (90 degrees).
Side Lengths: To find the lengths of the sides, we can use the distance formula:
d = √((x2 - x1)² + (y2 - y1)²)
For example, to find the length of the side that connects Y and E, we can use the following calculation:
d = √((3 - 1)² + (0 - (-4))²) = √((2)² + (4)²) = √(4 + 16) = √20
We can use the same formula to calculate the lengths of the other sides. By doing so, we will find that the length of all four sides are the same, which is √20. This means that all four sides of YEAR are congruent, and therefore it is a square.
Solve pleaaase i really need help
The equation of the model is (b) 2x = 5
How to determine the equation of the model?From the question, we have the following parameters that can be used in our computation:
Left = x x
Right hand side = 1 1 1 1 1
The above parameters mean that
Left = 2x
Right = 5
When represented as an equation, we have
2x = 5
Hence, the equation is (b)
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Does someone mind helping me with this problem? Thank you!
The total number of $12 tickets are 120 while the $15 tickets are 180.
What is algebraic expression?In addition to using operational signs, algebraic expressions also include numbers and variables. Examples include multiplication, multiplication with the natural exponent, division, and addition, subtraction, and exponentiation. The term "fractional expression" refers to division in an algebraic expression with variables.
The term "rational numbers" refers to numbers that can be expressed as fractions. Integers, repeating decimals, and terminating decimals are a few examples.
Given that x stands for $12 tickets and y stands for $15 given as the equation
12x + 15y = 4140
x + y = 300
y = 300 - x
Substitute the value of y in the first equation
12x + 15(300 - x) = 4140
12 x + 4500 - 15x = 4140
12x - 15x = 4140 - 4500
-3x = −360
x = 360/3
x = 120
y = 300 - (120)
y = 180
Thus, The total number of $12 tickets are 120 while the $15 tickets are 180.
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I NEED HELP ON THIS ASAP!!!!
The volume of an ice cream cone is the measure of how much ice
cream fits inside the cone. An ice cream cone company wants to
make an ice cream cone with a greater height that still holds the
same amount of ice cream.
Write an equation to calculate the volume of a cone.
Then rewrite the equation to solve for the height.
Explain how your equation determines a linear measurement when the original equation determined a cubic measurement
The volume of a cone is V = πr²h/3
The equation rewritten to solve for the height is V = πr²h/3
How to determine the equationIt is important to note that the formula for volume of a cone is expressed as;
V = πr²h/3
The parameters are;
V is the volume of the coneπ takes the constant value, 22/7 or 3. 142h is the height of the coneSince the ice cream fits inside the cone and the height still holds the ice cream, let's make the height subject of formula.
Let's take the following steps;
V = πr²h/3
cross multiply the equation, we get;
V × 3 = πr²h × 1
Multiply the values
3V = πr²h
To make the variable 'h' stand alone, let's divide both sides of the equation by its coefficient
3V/πr² = πr²h/πr²
Divide the values
c
Hence, the equation determines a linear measurement since the value 3 multiply the volume and not divides it.
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The triangle below is equilateral. Find the length of side x to the nearest tenth.
x
12
Answer:
Step-by-step explanation:
Are 3/8 and 3/4 equivalent fractions with a number line
Assume that when adults with smartphones are randomly selected, 37% use them in meetings or classes. If 30 adult smartphone users are randomly selected, find the probability that exactly 19 of them use their smartphones in meeting or classes the probability is (Round to four decimal places as needed.
The probability of adults using smartphones in meetings or classes as per the randomly selected adults is equal to 0.3375.
Percent of randomly selected adults use smartphones in meetings or classes represents the probability of success 'p' = 37%
= 0.37
1 - p = 1 - 0.37
= 0.63
Number of randomly selected adults use smartphone in meetings or classes represents sample size 'n' = 30
Exactly 19 adults use smartphone represented by x
x = 19
Using binomial distribution :
Required probability is :
P(x) = ⁿCₓ× pˣ × ( 1 - p )ⁿ⁻ˣ
⇒P(x) = [ n! / x! (n - x)! ] × pˣ × ( 1 - p )ⁿ⁻ˣ
Substitute the values
⇒P(19) = [ 30! / 19! (30 - 19)! ] × 0.37¹⁹× ( 0.63 )³⁰⁻¹⁹
⇒P(19) = ( 30!/19! ×11! ) × 0.37¹⁹× ( 0.63 )¹¹
⇒P(19 ) = 0.3375
Therefore, the required probability of selecting exactly 19 adults who use their smartphones in meetings or classes is equal to 0.3375.
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What is the solution to StartFraction 5 over 6 EndFraction x minus one-third greater-than 1 and one-third?
x > StartFraction 25 over 18 EndFraction
x < StartFraction 25 over 18 EndFraction
x > 2
x < 2
The value of x is x > 2.
What are Fractions?Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.
Here, a is called the numerator and b is called the denominator.
Any number can be expressed as fractions.
The given expression is [tex]\frac{5}{6}[/tex]x - [tex]\frac{1}{3}[/tex] > 1 [tex]\frac{1}{3}[/tex]
We have to rewrite the expression with x on one side.
[tex]\frac{5}{6}[/tex]x - [tex]\frac{1}{3}[/tex] > 1 [tex]\frac{1}{3}[/tex]
[tex]\frac{5}{6}[/tex]x > 1 [tex]\frac{1}{3}[/tex] + [tex]\frac{1}{3}[/tex]
[tex]\frac{5}{6}[/tex]x > [tex]\frac{4}{3}[/tex] + [tex]\frac{1}{3}[/tex]
[tex]\frac{5}{6}[/tex]x > [tex]\frac{5}{3}[/tex]
x > [tex]\frac{5}{3}[/tex] × [tex]\frac{6}{5}[/tex]
x > 2
So the value of x is greater than 2.
Hence the correct option is x > 2.
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What are the domain and range of f (x) = -5/6 (x + 2)^2 - 8?
Answer:
Option B
Domain: all real numbers
Range [tex]f(x) \le -8[/tex]
Step-by-step explanation:
Given function is:
[tex]f\left(x\right)=-\dfrac{5}{6}\:\left(x\:+\:2\right)^2\:-\:8[/tex]
The domain is the set of all x values that result in a real and defined value for f(x).
The function has no undefined points and x is free to range from -∞ to +∞
So the domain is -∞ < x <∞ which is
All real numbers
The range is the set of all possible values for f(x) given a specific domain. In order to determine the range without too much hard work, let's first examine the function f(x)
The above function is the equation for a parabola.
Some things to note about a parabola equation:
The vertex form equation of a parabola is:Let us compare the general vertex form equation of the parabola with the specific f(x) equation given
General Equation: [tex]a (x - h)^2 + k[/tex]
This example: [tex]-\dfrac{5}{6}\:\left(x\:+\:2\right)^2\:-\:8[/tex]
Comparing the similarity between the two equations we easily see that
[tex]\boxed{a = -\dfrac{5}{6}}[/tex]
This means the parabola opens downward and (h, k) represents a max point in the parabola
[tex]x - h = x + 2\\\\-h = 2\\\\h = -2\\[/tex]
[tex]k = -8[/tex]
So the vertex is at (-2, -8)
Since -8 is the maximum value for f(x), and the parabola extends to infinity on both sides, the range is :
[tex]\boxed{f(x) \le -8}[/tex]
The attached graph may help you understand better
Please help will give brainliest
Write a letter to a student who will be taking this math class next year and give them some advice about this class
A letter to a student who will be taking this math class next year to give them some advice about this class has been written below.
(Sender's address)
20/01/2023
Dearest,
I was happy to see your letter, and I hope this letter finds you in the best of health. I have wanted to go on a trip with you for a long time but I guess that would happen later since you have to start attending classes soon.
I have a list of things to keep in mind when you start your classes. I was always too scared of mathematics, and I know you are too, but I have always wanted to tell you how fruitful it is to learn a subject that will help you in every field you want to go in. Let me know what you think about it after you finish reading this letter. I know it is no secret that maths is a difficult subject but you can master it if you keep what I am going to tell you in mind. Practice your concepts daily. Keep brushing up on whatever your teacher teaches you. Remember the formulas and you will know how to answer any question. I know for sure that it is going to be worth it too.
I will make sure that I meet you next weekend so that we can meet before you begin the classes. If you try hard, you can make this work. See you soon.
Love,
(Sender's name)
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An airplane takes off from the airport. After 2 minutes the plane is at 500 ft. Assume the plane continues at the same rate. The plane’s height and minutes above the ground are related to each other.
A. Write an equation for the situation.
An equation for the situation described above is h = 2m + 500.
How to write an equation to model this situation?In order to write an algebraic equation that model this situation, we would assign a variable to the number of minutes after an airplane takes off from the airport and the plane’s height respectively, and then translate the word problem into algebraic equation as follows:
Let the variable m represent the number of minutes.Let the variable h represent the plane’s height.Next, we would translate the word problem into an algebraic equation based on the fact that after 2 minutes the plane is at 500 feet as follows;
h = 2m + 500.
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A family ha two car. The firt car ha a fuel efficiency of 35 mile per gallon of ga and the econd ha a fuel efficiency of 15 mile per gallon of ga. During one particular week, the two car went a combined total of 1150 mile, for a total ga conumption of 50 gallon. How many gallon were conumed by each of the two car that week?
The first car consumed 35 number of gallons and the second car consumed 15 gallons.
1. Calculate the total efficiency of both cars: 35 mpg + 15 mpg = 50 mpg
2. Calculate total gallons consumed: 1150 miles/50 mpg = 23 gallons
3. Divide total gallons by each car: 23/2 = 11.5 gallons (round down to 11 for the first car and round up to 12 for the second car)
4. The first car consumed 11 gallons and the second car consumed 12 gallons.
The first car consumed 35 gallons and the second car consumed 15 number of gallons.
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PLEASE HELP!! A ladder is leaning against a wall. What is the length of the ladder if it is resting against the wall at a height of 48 feet and it forms an angle of 53 degrees with the ground? Round your answer to the nearest tenths place
The length of the ladder, if it is resting against the wall at the height of 48 feet and it forms an angle of 53 degrees with the ground being 63.7 ft.
First, we need to draw a figure according to the conditions given in the question.
Now, let AC be the length of the ladder, AB is the length of the wall, and BC is the length of the ground, as shown in the figure.
As we know,
tan θ = perpendicular/hypotenuse
tan 53 = AC/AB
AC = tan 53 × AB
AC = 1.327 × 48
AC = 63.7 ft
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. What crimes do these excerpts from the Code of Hammurabi identify?
Which of those are considered crimes today? Which are not?
3) What punishments do these excerpts from the Code of Hammurabi identify?
4) Which of those punishments are used today? Which are not?
5) Based on these short excerpts from the code, how do you think Hammurabi defined justice?
6) In what ways do our codes of law today show similarities to and differences from the concept of justice as shown in these short excerpts from Hammurabi’s Code?
7) In what ways has today's view of justice changed from Hammurabi's? What events and ideas do you think caused these changes?
1. These excerpts from the Code of Hammurabi identify crimes such as theft, assault, and damage to property.
2. Some of these crimes, such as theft and assault, are still considered crimes today. However, some of the punishments specified in the code, such as the punishment for a son striking his father, would not be considered appropriate today.
3. These excerpts from the Code of Hammurabi identify punishments such as fines, imprisonment, and physical punishment such as whipping or amputation.
4. Physical punishments such as whipping or amputation are no longer used in most modern legal systems.
5. Fines and imprisonment are still used as punishments today.
6. Based on these short excerpts from the code, it seems that Hammurabi defined justice as a system of strict punishment for crimes, with different punishments for different classes of people and different severity of crimes.
Our codes of law today show similarities to the Code of Hammurabi in that they both have a system of punishment for crimes. However, there are also many differences, such as the fact that our legal system is considered more fair and equal, and places a greater emphasis on rehabilitation and protecting the rights of the accused.
7. Today's view of justice has changed significantly from Hammurabi's in that it places a greater emphasis on protecting the rights of the accused, rehabilitation, and equality before the law. This change can be attributed to a number of factors, including the development of democratic societies, the influence of human rights movements, and the advancement of legal scholarship and philosophy.
What is Hammurabi code?The 282 rules that make up the Hammurabi code of laws established norms for business dealings and established fines and penalties to satisfy the demands of justice.
A large, finger-shaped black stone stele with Hammurabi's Code carved on it was looted by invaders and only recently found in 1901. One of the most well-known examples of the ancient maxim known as "lex talionis," or the law of retribution, is the Hammurabi Code.
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Drag each tile to the correct box. Consider the given circles. Sector B 9 units 820 Sector c Sector A 6 units 1690 4 units Order the sectors from least to greatest according to their areas, in square units. Sector C Sector B Sector A A
The order from least to greatest is: A, B, C
The order of the sectors from least to greatest according to their areas is:
Sector A, Sector B, Sector C
To find the area of each sector, we need to multiply the central angle measure (in degrees) by the radius squared and divide by 360.
Sector A: 4 units * (1690 / 360) = 46 square units
Sector B: 6 units * (820 / 360) = 69 square units
Sector C: 9 units * (820 / 360) = 103.5 square units
Hence, the order from least to greatest is: A, B, C
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Write and compound inequality-4 is greater than x and less than 2
The compound inequality is x<-4 and x<2.
What is a compound inequality?
A compound inequality in mathematics is a clause that joins two claims with the conjunction "and" or "or." Both of the statements in a compound sentence are true simultaneously if the conjunction "and" is used to connect the statements. If "or" is used to connect the statements, the compound phrase is true if at least one of the statements is true.
We are given that -4 is greater than x
This means that -4>x
Also, it is given that x is less than 2
Therefore, x<2
Hence, the compound inequality is x<-4 and x<2.
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Pls solve 5^2x-1–6(5^x) + 25=0
what is the axis of symmetry of this graph?
Answer:
The axis of symmetry is x = -3.
If you draw a line at x = -3, the graph is reflected over it.
Please answer!!! The inspector at a bottling plant checks 25 bottles. Two bottles do not pass inspection. All the bottles hold the same number of milliliters of sports drink
The equivalent expression for the amount of sports drinks that pass inspection is 23x milliliters.
The inspector at a bottling plant checks 25 bottles, and two bottles do not pass inspection.
To find the amount of sports drinks in milliliters that pass inspection, we can subtract the amount in the two bottles that do not pass inspection from the total amount in all 25 bottles.
Let x be the amount of sports drinks in milliliters in each bottle.
The expression for the milliliters of sports drink that pass inspection is = 25x - 2x
Now, simplifying the expression, we get,
25x - 2x = (25-2)x = 23x
Hence, the equivalent expression for the amount of sports drinks that pass inspection is 23x milliliters.
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The complete question is -
The inspector at a bottling plant checks 25 bottles. Two bottles do not pass inspection. All the bottles hold the same number of milliliters of sports drinks. Write an expression for the milliliters of sports drink that pass inspection. Then simplify it to create an equivalent expression.
One company estimates same-day delivery as more than three less than half the total number of miles which graph represents the overall equation represented by the scenario or points may not apply to the scenario note that the graphs have similar miles for the independent variable on the X axis and the Y axis is a unit of time dependent on the number of miles
A graph that represents the overall equation represented by this scenario is shown in the image attached below.
How to determine the graph?Based on the information provided about this company with respect to its same-day delivery and total number of miles to be covered, we would assign variables to the parameters as follows:
Let the variable x represent be the total number of miles.Let the variable y represent same-day delivery.Next, we would translate the word problem into an algebraic equation by using an inequality:
Half the total number of miles = x/2.
y > x/2 - 3
Furthermore, we would determine the x- and y-intercepts as follows:
When x = 0, we have;
y = 0/2 - 3
y = -3.
Therefore, y-intercept = (0, -3).
For the x-intercept (y = 0), we have:
0 = x/2 - 3
x/2 = 3
x = 6.
Therefore, x-intercept = (6, 0).
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In the first week of July, a record 1,120 people went to the local swimming pool. In the second week, 110 fewer people went to the pool than in the first week. In the third week, 135 more people went to the pool than in the second week. In the fourth week, 137 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
If in the first week of July, a record 1,120 people went to the local swimming pool. the percent decrease in the number of people who went to the pool over these four weeks is 10%.
How to find the percentage decrease?First week:
Number of people went to the local swimming pool =1120
Second week:
Number of people went to the local swimming pool =1120-110
Number of people went to the local swimming pool =1010
Third week:
Number of people went to the local swimming pool =1010+135
Number of people went to the local swimming pool =1145
Fourth week:
Number of people went to the local swimming pool =1145-137
Number of people went to the local swimming pool =1008
Decrease in number of people over four week=1120 -1008
Decrease in number of people over four week = 112
Percentage decrease = 112 /1120 × 100
Percentage decrease = 10%
Therefore the percentage decrease is 10%.
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if 12% of a number is 75, find 4% of that number
Answer:
25.60
Step-by-step explanation:
first divide 12%of a number with 75 Ans will be 6.25 then multiply with 4 Ans will be 25.60
Answer: 25
Step-by-step explanation:
12 divided by 4 = 3
75 divided by 3 = 25
25 = 4%