Use the method of disk or washer to set up, but do not evaluate, an integral for a volume of the solid obtained by rotating the region bounded by the given curves about the given line.
y=√x and y=x and y=1
Answers
Answer:
V = π /2 volume units
Step-by-step explanation:
Volume of y = √x bounded by y = x and y = 1
y = √x
limits of integration ( see Annex )
By simple inspection limits of integration are x = 0 to x = 1
or y = √x and y = x
solving these two equations
x = 0 y = 0 x = 1 y = ± 1
V = ∫ π*f(x)²*dx
V = π * ∫₀¹ x*dx = π * x²/2 |₀¹
V = π * (1/2) - 0
V = π /2 volume units
Related Questions
Robert planted 12 daffodil bulbs and 18 tulip bulbs in his garden last winter. If all the bulbs sprout and
bloom this spring, what will be the ratio of tulips to daffodils in Robert's garden? Express as a simplified
ratio.
Answers
Answer:
Ratio 2:3 I think :)
Step-by-step explanation:
A house is infested with mice and to combat this the householder acquired four cats cyd, Greg, Ken, and Rom, The householder observes that only half of the creatures caught are mice. A fifth are voles and the rest are birds. 20% of the catches are made by Cyd, 45% by Greg, 10% by Ken and 25% by rom. a) What is the probability of a randomly selected catch being a mouse caught by Cyd? b) Bird not caught by Cyd? c) Greg's catches are equally likely to be a mouse, a bird or a vole. What is the probability of a randomly selected d) The probability of a randomly selected catch being a mouse caught by Ken is 0.05 . What is the probablity that a catch being a mouse caught by Greg? e) Given that the probability of a randomly selected catch is a mouse caught by Rom is 0.2 verify that the catch made by Ken is a mouse? probability of a randomly selected catch being a mouse is 0.5 . f) What is the probability that a catch which is a mouse was made by Cyd?
Answers
Note that the probabilities are given below.
What are the probabilities?
a) the probability of a randomly selected catch being a mouse caught by Cyd
p(Catching a mount) x p(Cyd made the catch)
= 0.5x .2
= 0.1
b) the probability of a bird not caught by Cyd is 0.5 x 0.8 = 0.4.
Thus
P(that a catch is a bird) x p(the Cyd didn't make the catch)
= 0.3 x 0.8
=0.24
c) The probability of a randomly selected catch being caught by Greg is 0.45
To calculate, we say
(0.5 x0.45) + (0.3 x 0.45) + (0.2 x .45)
= 0.45.
d)
P (mouse caught by Greg) = (0.45 x 0.5) / 1
= 0.225.
e) P(catch is a mouse caught by Ken and catch is a mouse)
= P(catch is a mouse | catch is made by Ken) x P(catch is made by Ken)
= 0.05 x 0.1
= 0.005
f)
P (catch made by Cyd | catch is a mouse)
= 0.1 x 0.2 / 0.5
= 0.04
Learn more about probabilities at:
https://brainly.com/question/3003478
#SPJ1
The two data sets below show the approximate number of gallons of gasoline Josie and Olivia put into their cars the last 10 times they filled their gas tanks. A dot plot titled josie's Gasoline (gallons). The number line goes from 8 to 12. There are 2 dots above 8, 2 above 9, 6 above 10, and 0 above 11 and 12. A dot plot titled Olivia's Gasoline (gallons). The number line goes from 8 to 12. There are 0 dots above 8 and 9, 6 above 10, 3 above 11, and 1 above 12. Which measure of variability would most accurately compare the two data sets and why?
Answers
Answer:
c
Step-by-step explanation:
i got it right on edg 2020
Answer:
c
Step-by-step explanation:
What is 265,738rounded to nearest hundred thousands
Answers
Answer:
The answer is 270000....
The hockey team won 60 out of the 80 games it played this year. What percent of the games did the team win?
Answers
Find the value of 36.8 divided by 2.3 show your reasoning
Answers
Answer:
the answer is 16
Step-by-step explanation:
because if you do long divison
Simplify
8!/(8-2)
A. 720
b. 0.018
C. 8
d. 56
e. 40320
f. 1.333
Answers
Answer:
D) 56
Step-by-step explanation:
\(\displaystyle \frac{8!}{(8-2)!}=\frac{8!}{6!}=\frac{8*7*6*5*4*3*2*1}{6*5*4*3*2*1}=8*7=56\)
Triangle ABC with vertices at A(4, 3), B(3, −2), C(−3, 1) is dilated using a scale factor of 1.5 to create triangle A′B′C′. Determine the vertex of point A′.
Answers
The vertex of point A' in the dilated triangle A'B'C' is (6, 4.5).
1. Start by calculating the distance between the vertices of the original triangle ABC:
- Distance between A(4, 3) and B(3, -2):
Δx = 3 - 4 = -1
Δy = -2 - 3 = -5
Distance = √((-\(1)^2\) + (-\(5)^2\)) = √26
- Distance between B(3, -2) and C(-3, 1):
Δx = -3 - 3 = -6
Δy = 1 - (-2) = 3
Distance = √((-6)² + 3²) = √45 = 3√5
- Distance between C(-3, 1) and A(4, 3):
Δx = 4 - (-3) = 7
Δy = 3 - 1 = 2
Distance = √(7² + 2²) = √53
2. Apply the scale factor of 1.5 to the distances calculated above:
- Distance between A' and B' = 1.5 * √26
- Distance between B' and C' = 1.5 * 3√5
- Distance between C' and A' = 1.5 * √53
3. Determine the coordinates of A' by using the distance formula and the given coordinates of A(4, 3):
- A' is located Δx units horizontally and Δy units vertically from A.
- Δx = 1.5 * (-1) = -1.5
- Δy = 1.5 * (-5) = -7.5
- Coordinates of A':
x-coordinate: 4 + (-1.5) = 2.5
y-coordinate: 3 + (-7.5) = -4.5
4. Thus, the vertex of point A' in the dilated triangle A'B'C' is (2.5, -4.5).
For more such questions on triangle, click on:
https://brainly.com/question/1058720
#SPJ8
The population of a city has increased by 15% since it was last measured if the current population is 43700 what was the previous population?
Answers
Answer:
37,145
Step-by-step explanation:
43,700×15%= 6,555
43,700-6,555= 37,145
the previous population was 37,145
may i have the different proofs for this thank you
Answers
The proof for AB ≅ CD is:
Step Statement Reason
1 ∠B ≅ ∠D, BC || AD Given
2 ∠BCA ≅ ∠CAD Alternate Interior angles
3 AC ≅ AC common side
4 ΔABC ≅ ΔADC Angle-Angle-Side rule of congruency
5 AB ≅ CD Corresponding sides of congruent triangle
Consider triangle ABC and triangle ADC.
Here, side BC is parallel to side AD.
From the attached figure we can observe that AC is a transversal.
so, ∠BCA and ∠CAD would be alternate angles formed by two parallel lines and transversal.
By property of Alternate Interior angles,
∠BCA ≅ ∠CAD
Also, we can observe that side AC is common side to ΔABC and ΔADC.
We rewrite this proof as,
Step Statement Reason
1 ∠B ≅ ∠D, BC || AD Given
2 ∠BCA ≅ ∠CAD Alternate Interior angles
3 AC ≅ AC common side
4 ΔABC ≅ ΔADC Angle-Angle-Side rule of congruency
5 AB ≅ CD Corresponding sides of congruent triangle
This is the required proof.
Learn more about congruent triangles here:
https://brainly.com/question/29789245
#SPJ1
Ciana earns an hourly wage of $30 at her job. In order to purchase her sneakers she will have to take time off work, so each hour away from her job
costs her $30 in lost Income. Assume that ciana travel time is the same each way (to and from the store) and that it will take her 30 minutes once
she reaches a store to complete her shopping. Assume throughout the question that ciara incurs no additional costs other than the sneakers, such as
gas.
complete the following table by computing the opportunity cost of ciana’s time and the total cost of shopping at each location
Answers
Ciana should purchase the skirt at the store across town because the total economic cost will be lowest.
How to determine the opportunity cost?Ciana makes $30 per hour at her work, and her purchase decision includes the opportunity cost of lost wages:
Total economic cost:
Local store = $114 + [1/4 hours x 2 (round trip) x $30] + (1/2 hours x $30 spent shopping) = $144
Across town = $86 + [1/2 hours x 2 (round trip) x $30] + (1/2 hours x $30 spent shopping) = $131
Neighboring city = $60 + [1 hour x 2 (round trip) x $30] + (1/2 hours x $30 spent shopping) = $135
Ciana should buy a skirt at the store across town. Because it has the lowest total economic cost ($131).
Opportunity cost is the lost benefit or additional cost of choosing one activity or investment over another. Economic costs include both accounting costs and opportunity costs.
Read more about Opportunity Cost at: https://brainly.com/question/1549591
#SPJ1
For the following exercises, use this scenario: The population of a city has risen and fallen over a 20-year interval. Its population may be modeled by the following function: y=12,000+8,000sin(0.628x), where the domain is the years since 1980 and the range is the population of the city.. Over this domain, when does the population reach 18,000? 13,000?
Answers
Solve the equation:
10x^2 + x - 21 = 0
Answers
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 10, b = 1, and c = -21. Substituting these values into the formula, we get:
x = (-1 ± sqrt(1^2 - 4(10)(-21))) / 2(10)
x = (-1 ± sqrt(841)) / 20
Simplifying the square root, we get:
x = (-1 ± 29) / 20
This gives us two solutions:
x = -3/2 or x = 7/5
Therefore, the solutions to the equation 10x^2 + x - 21 = 0 are x = -3/2 and x = 7/5.
choose the two numerical expressions that correctly represent this phrase: twice the sum of nine and four.
Answers
Answer: The two numerical expressions that correctly represent the phrase "twice the sum of nine and four" are:
2 * (9 + 4) = 2 * 13 = 26
2(9 + 4) = 2(13) = 26
Both expressions use the correct mathematical operations to represent the phrase "twice the sum of nine and four" and both will yield the same result of 26.
Step-by-step explanation:
Decrease $260 in the ratio 3:5
Answers
32.5 x 3= $97.50
32.5 x 5 = $162.50
$97.50:$162.50
f a vector coincides with its orthogonal projection onto a subspace, then the vector must be in the subspace.
Answers
The Orthogonal projection of A on Z i.e subspace formed by X and Y is A cos (90- θ) = A sin (θ).
A figure projected in parallel rays. In this projection, tangencies are preserved. On parallel lines, parallel lines converge. Both the length-to-area ratio and the length-to-area ratio of parallel segments are maintained. Any triangle can be positioned so that an orthogonal projection results in an equilateral shadow.
Let's say we have a vector. A and vector X and Y
Consider the subspace that is vector-formed. X and Y are perpendicular to the subspace vector Z, where Z = X + Y.
Cos = (X * Y) can be used to calculate the angle between X * Y and A.
A/|(X * Y)| * |A|
Now, Z and A are at a 90° angle.
As a result, A's projection onto Z, or the subspace created by X and Y, is given by A cos (90 - ) = A sin ().
The angle between the subspace and the vector whose projection we are trying to find must be determined in order to find the projection.
Use MATLAB Code for locating a projection on vector a on the subspace defined by vectors x and y. so that it will be more easy to understand
% cross product of x and y vector
xCrossY = cross(x, y);
% angle between xCrossY and vector 'a'
angle_radian = dot(xCrossY,a)/(norm(xCrossY)*norm(a));
% angle in degrees
angle_deg = rad2deg(angle_radian);
% projection of a on subspace made by x and y is asin(angle_deg)
projection = norm(a)*sin(angle_deg);
A cos (90- ) = A sin () is the orthogonal projection of A on Z, i.e. the subspace created by X and Y.
To learn more about Orthogonal projection visit:
brainly.com/question/2292926
#SPJ4
Is each statement true for parallelogram DEFG? Drag each statement into the correct box.
DF=EG
EF=DG
∠DEG ≅ ∠FGE
Answers
The statements DF=EG, EF=DG and ∠DEG ≅ ∠FGE are true for parallelogram DEFG.
What is Quadrilateral?a quadrilateral is a four-sided polygon, having four edges and four corners.
DEFG is a parallelogram.
A parallelogram is a simple quadrilateral with two pairs of parallel sides.
The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
DF=FG is a true statement.
The diagonal passing through a parallelogram are equal in length.
EF=DG is a true statement
The opposite sides of a parallelogram are equal.
∠DEG ≅ ∠FGE are congruent angles.
Because the opposite angles of a triangle are equal in meausure.
Hence, the statements DF=EG, EF=DG and ∠DEG ≅ ∠FGE are true for parallelogram DEFG.
To learn more on Quadrilateral click:
https://brainly.com/question/29934440
#SPJ2
1. DRAGONS The Luck Dragons that live
in the Enchanted Forest weigh 4x
pounds when they are x years old.
Write a function table that can be used
to find the weights of 6-year old, 8-year
old, and 10-year old Luck Dragons.
Answers
8yr=32pounds
10yr=40pounds
|2x| if x<0
Help please
Answers
The expression simplifies to |2x| = -2x, when x<0 by definition of absolute value
If x<0, then the expression |2x| simplifies to -2x.
The absolute value of a number is the distance of the number from zero on the number line.
Since x is negative in this case, 2x will be negative as well.
Taking the absolute value of -2x will give us the opposite of -2x, which is 2x.
However, since we know that x<0, this means that -2x will always be a positive number.
Hence, the expression simplifies to |2x| = -2x, when x<0.
To learn more on Expressions click:
https://brainly.com/question/14083225
#SPJ1
Complete question
Simplify the expression |2x| when x is less than 0, x<0
Question 2 of 33 -Triangle Test 2020Two sides of a triangle measure 14 inches and 8 inches. Which cannot be the length of the remaining side?06 in8 in.14 in0 21 in
Answers
We would apply the triangle inequality theorem which states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side. Looking at the given triangle, the length of the two given sides are 14 inches and 8 inches. The sum of the length of the two sides is
14 + 8 = 22
looking at the given options, they are lesser than 22. Thus, they can all form the remaining sde of the triangle.
How does the jet stream affect weather around the world?for 60 points!,
Answers
Answer:
jet streams can drive and direct storms, creating devastating droughts and floods.
Step-by-step explanation:
give me brainliest.In which of these numbers does the digit 4 represent 4/100
A: 34.99
B: 106.314
C: 15.4
D:9.94
Answers
The first place after the decimal represents the tenths place, the second place represents the 100ths place and so on.
Suppose that a committee is studying whether there is waste of time in our judicial system. It is interested in the mean amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomly surveyed 81 people who recently served as jurors. The sample mean wait time was eight hours with a sample standard deviation of four hours. Construct a 95% confidence interval for the population mean time wasted. Which distribution should you use for this problem
Answers
Answer:
The t-distribution is used, as we have the standard deviation of the sample.
The 95% confidence interval for the population mean time wasted is between 7.12 hours and 8.88 hours.
Step-by-step explanation:
We have the standard deviation for the sample, which meas that the t-distribution should be used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 81 - 1 = 80
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 80 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.95}{2} = 0.975\). So we have T = 1.99
The margin of error is:
\(M = T\frac{s}{\sqrt{n}} = 1.99\frac{4}{\sqrt{81}} = 0.88\)
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 8 - 0.88 = 7.12 hours.
The upper end of the interval is the sample mean added to M. So it is 8 + 0.88 = 8.88 hours.
The 95% confidence interval for the population mean time wasted is between 7.12 hours and 8.88 hours.
Soo-Jung used the subtraction property of equality to solve an equation for y. Which equation could be the one that Soo-Jung solved? 4 y = 12 StartFraction y Over 4 EndFraction = 12 2 (4 y) = 12 y + 4 = 12
Answers
Answer:
D= y + 4 = 12
Step-by-step explanation:
Bc Im smart
two angles of a triangle measure 55° and 20°
Answers
Answer: All triangles have a 180 degree to them so 55+20 is 75 AND 180 degrees - 75 gives us 105 degrees. Although I know my math is correct a picture of this triangle would be helpful
Step-by-step explanation:
A fish tank is being drained at a constant rate. The graph shows the linear relationship between the volume of water in the fish tank in liters and the time in minutes the tank has been draining.
Answers
The rate of change in the volume of water will be -6 L/min in the fish tank. which is the correct answer would be an option (A).
The given graph shows the linear relationship between the volume of water in the fish tank in liters and the time in minutes the tank has been draining.
To determine the rate of change in the volume of water in the fish tank
The rate of change in the volume of water is equal to the slope of the given linear function.
As per the given graph, we take two points (0, 60) and (10,0)
The slope of the linear function = (0 - 60) / (10 - 0)
The slope of the linear function = -60/10
The slope of the linear function = -6
Therefore, the rate of change in the volume of water will be -6 L/min in the fish tank.
Learn more about the graphs here:
brainly.com/question/16608196
#SPJ1
The question seems to be incomplete the correct question has been attached below.
Can someone please help me and explain I’ll mark brainliest
Answers
Part (a)
Answer: x = -8------------------
Work Shown:
2(x-1) = 3(x+2)
2x-2 = 3x+6 .... distribute
2x = 3x+6+2 .... adding 2 to both sides
2x = 3x+8
2x-3x = 8 .... subtracting 3x from both sides
-x = 8
x = -8 ..... multiply both sides by -1
===========================================================
Part (b)
Answer: x = 5/11------------------
Work Shown:
-4(2x-2) = 3(x+1)
-8x+8 = 3x+3 ..... distribute
-8x = 3x+3-8 .... subtract 8 from both sides
-8x = 3x-5
-8x-3x = -5 ... subtract 3x from both sides
-11x = -5
x = -5/(-11) .... divide both sides by -11
x = 5/11
In decimal form, this is approximately equal to 5/11 = 0.4545
HELP ME PLZZZ ASAP!!!!
Answers
Answer:
544
Step-by-step explanation:
10×14 =140 × 2 surfaces = 280
12 x 14 =168
1/2 b × h
6x8 = 48 x 2 surfaces areas = 96
Combine
Yesterday, drove 44 and 1 half
miles. used 1 and 1 fourths
gallons of gasoline. What is the unit rate for miles per gallon?
Answers
Answer:
The unit rate for miles per gallons is 35.6 miles per gallon used by him.
Step-by-step explanation:
In the given condition he drove 44 and 1/2 miles and used a total of 1 and 1/4 gallons of gasoline.
Now, we have to calculate the number of miles he travelled in each gallon.
So, 44 and 1/2 miles can be written as 44.5 miles.
And 1-1/4 gallons can be written as 1.25 gallons.
Now, we need to form an equation from the above condition;
=> 44.5 = 1.25
=> x = 1 (here, x is the number of miles per gallon)
Now, after cross multiplying the equation;
=> 44.5 × 1 = 1.25 × x
=> 44.5 = 1.25 x
=> 44.5 / 1.25 = x
=> x = 35.6 miles per gallon
Therefore, the unit rate for miles per gallons is 35.6 miles per gallon used by him.
To know more about this topic, click here:
https://brainly.com/question/791578
#SPJ9
What is the slope of the line that passes through the points (2, -3)and (2,13)?
Write your answer in simplest form.
Answers
Slope = change in y / change in x
Both x values are the same, they are both 2’s. 2-2 = 0
Because the change in x is 0 the slope is undefined.
An undefined slope means the line is a vertical line ( straight up and down with no angle)
Answer:
Slope = change in y / change in x
Both x values are the same, they are both 2’s. 2-2 = 0
Because the change in x is 0 the slope is undefined.
An undefined slope means the line is a vertical line straight up and down with no angle
Step-by-step explanation:
hope this helps =)