Answers
Answer:[tex](1,1),\ \dfrac{1}{3}[/tex]
Step-by-step explanation:
Given
Equation of the curves are [tex]y=x^2,\ y^2=x[/tex]
The intersection of the curve is
[tex]\Rightarrow y^4-y=1\\\\\Rightarrow y(y^3-1)=0\\\\\Rightarrow y=0,1\\[/tex]
So, x coordinates are [tex]x=0,1[/tex]
points of intersection are[tex](0,0),(1,1)[/tex]
So, the area bounded between the curves
[tex]\Rightarrow I=\int_{0}^{1}\left ( \sqrt{x}-x^2\right )dx\\\\\Rightarrow I=\int_{0}^{1}\sqrt{x}dx-\int_{0}^{1}x^2dx\\\\\Rightarrow I=\left ( \frac{2}{3}x^{\frac{3}{2}} \right )_0^1-\left ( \frac{1}{3}x^3 \right )_0^1\\\\\Rightarrow I=\frac{2}{3}\left ( 1-0 \right )-\frac{1}{3}\left ( 1^3-0 \right )\\\\\Rightarrow I=\frac{2}{3}-\frac{1}{3}\\\\\Rightarrow I=\frac{1}{3}[/tex]
The area bounded by them is [tex]\frac{1}{3}[/tex]
Related Questions
PLEASE HELP Water flowed out of a tank at a steady rate. A total of 18 and one-half gallons flowed out of the tank in 4 and one-fourth hours. Which expression determines the quantity of water leaving the tank per hour?
Answers
The expression determines the quantity of water leaving the tank per hour is (18 1/2 gallons)/(4 1/4 hours)
How to find which expression determines the quantity of water leaving the tank per hour?
Rate is the ratio of a certain number of units of one quantity to units of another quantity. Mathematically, rate is one quantity divided by the other quantity.
If a total of 18 and one-half gallons flowed out of the tank in 4 and one-fourth hours. We can write that the rate as follows:
rate = (18 1/2 gallons)/(4 1/4 hours)
rate = 4 6/17 gallons per hour
Thus, the expression determines the quantity of water leaving the tank is (18 1/2 gallons)/(4 1/4 hours)
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Justin invested $7,300 in an account paying an interest rate of 1.5% compounded
quarterly. Assuming no deposits or withdrawals are made, how long would it take, to
the nearest tenth of a year, for the value of the account to reach $8,560?
Answers
Answer: 10.7 years.
Step-by-step explanation:
7,300 * (1 + 0.015)^x = 8,560 <=>
7,300 * 1.015^x = 8,560 <=>
1.015^x = 8,560 / 7,300 <=>
1.015^x = 1.1726 <=>
x = 10.694
To the nearest tenth:
x = 10.7 years
HELP ILL GIVE BRAINLIEST!!!
dividing mixed numbers^^
Answers
Answer:
1) 1[tex]\frac{59}{70}[/tex]
2)[tex]1\frac{7}{44}[/tex]
3)[tex]\frac{22}{25}[/tex]
4)[tex]2\frac{4}{33}[/tex]
5)[tex]\frac{38}{45}[/tex]
6) [tex]\frac{80}{141}[/tex]
What is the median of the following data set? {3, 4, 2, 8, 5}
a 2 b 3 c 4 d 6
Answers
Answer:
C. 4
Please mark as brainliest if answer is right
Have a great day, be safe and healthy
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Answer:
c. 4
Step-by-step explanation:
first arrange the data in order.(you can use both ascending and descending order).
2,3,4,5,8
there are 5 numbers and 5 is odd so simply the middle value is the median.
but if it is even the average of the middle values is the median
PLEASE HELP ME I WILL GIVE BRAINIEST IM STUDYING HELP A PERSON OUT NO SCAMMSSS>S>>S
Answers
Answer:
White
Step-by-step explanation:
20 divided by 4 = 5
White was spun 5 times.
Good morning, is there any guinea pig expert or anybody with a small creature know what's going on cause inside my guinea pig eye (not outer) have this white spot in the pupil, it expands and shrinks.. please help
Answers
I would like to ask you to go to the vet, or attempt to, as this might be a worm in the eye. The same thing happened to my dog.
I want to know how to get the GCF and LCM of 8,24,48
Answers
Answer:
GCF = 8
LCM = 48
Step-by-step explanation:
Jess and Brian are playing the following game: Jess thinks of a fraction, and Brian flips a coin. If the coin turns up heads, Jess multiplies the number she's thinking of by $\frac{5}{6}$. If the coin turns up tails, she multiplies the number she's thinking of by $\frac{6}{5}$. Brian flips the coin ten times, and after each flip Jess multiplies the number in her head by either $\frac{5}{6}$ or $\frac{6}{5}$, depending on the coin flip. The ten coin flips turn out to be:\[ \text{THTTHTHTTT}, \]where H means 'heads' and T means 'tails.' What number is Jess thinking of at the end of the game if she starts out with the fraction $\frac{5}{9}$
Answers
Starting out with the fraction of 5/9, Jess would be thinking of the fraction 144/125 at the end of the game if the ten coin flips turn out to be {THTTHTHTTT}.
What is the probability of getting H or T in a coin flip?Since both outcomes are equally likely, the probability of getting heads is 0.5 and the probability of getting tails is also 0.5. Alternatively, the probability of getting H or T in a coin flip is 1.
What is the significance of probability?Probability is an important method for comprehending and making judgments regarding uncertain occurrences in many disciplines, including statistics, finance, and science. It aids in quantifying and forecasting the probability of specific events, enabling us to make better educated choices and comprehend the degree of risk involved with various activities. In summary, probability is a key idea in decision-making and risk management because it is a potent instrument for comprehending and managing uncertainty.
Taking the sequence of coin flips in ten tires, i.e THTTHTHTTT , and starting from the fraction 5/9, the fraction that jess would be thinking at the end of the game can be calculated as,
5/9 * (6/5)^7 *(5/6)^3 , since there are 7 Tails and 3 Heads during the whole game. Which is equal to the fraction 144/125.
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Marcelle and Megan realized that they could express their ages more specifically if they used fractions. Doing this will allow them to calculate their difference in their ages. Marcelle is $15\frac{1}{2}$ years old, and Megan is $7\frac{7}{12}$. What is the difference in their ages? Express your answer as a simplified mixed number.
Answers
The difference between their ages is obtained as 35/12.
What is the difference?Let us recall that the term fraction has to do with a part of a whole. In this case, we have been told that Marcelle and Megan realized that they could express their ages more specifically if they used fractions.
Age of Marcelle = 15 1/2 or 31/2 years
Age of Megan = 12 7/12 or 151/12 years
The difference between their ages is;
31/2 - 151/12
=186 - 151/12
=35/12
There ages would have a difference of 35/12.
In the computation that has gone on above, we can clearly see that the difference in the ages is 35/12.
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Missing parts;
Marcelle and Megan realized that they could express their ages more specifically if they used fractions. Doing this will allow them to calculate their difference in their ages. Marcelle is 15 1/2 years old, and Megan is 7 7/12. What is the difference in their ages? Express your answer as a simplified mixed number.
9) Which point is a solution to the equation 3x + 2y = 9?
A. (0,4) B. (4,0) C. (1,3) D. (3, 1)
Answers
Answer:
c. (1, 3)
Step-by-step explanation:
The coordinates that best suite the equation, given it the answer.
A woman has 23 coins in her pocket, all of which are dimes and quarters. If the total value of the coins is $ 4.10, how many
dimes and how many quarters does she have?
Answers
Answer:
Step-by-step explanation:
there is 1 dime and 12 quarters
Find the circumstances
Answers
Answer:
15π = 47.12
Step-by-step explanation:
C = pi(diameter)
C= 15π
Answer:
Solution given:
diameter [d]=15m
circumference =?
we have
circumference of circle =πd=π×15=15π or 47.12m
Select the correct answer. How can you write the expression 7(b – 2) in words? A. Two subtracted from the quotient of seven divided by b B. Seven added to difference of b minus two C. The quotient of seven divided by b minus two D. Two subtracted from seven times b E. The product of seven and the difference of b minus two
Answers
Answer:
its e
Step-by-step explanation:
help pls...
Three side lengths of a right triangle are given. Use the drop-down menus to explain why matters where you substitute the lengths in the Pythagorean Theorem.
In the Pythagorean Theorem, the (two ahortest sides) / (one short side and the hypotenuse) must always be substituted for the side lenghts, not (a short side) / (the hypotenuse).
Answers
Answer:
?
Step-by-step explanation:
18+x=27
please answer soon:)
Answers
Answer:
x = 9
Step-by-step explanation:
18 + x = 27
x = 27 - 18
x = 9
Please give a real answer. What is the surface area of this composite figure?
Answers
Answer:
[tex]\huge \boxed{SA=294cm^2}[/tex]
Step-by-step explanation:
[tex]SA=(6*7)+(6*7)+2[6*4/2]+4(6)+(6*6)[/tex][tex]168+42+24+24+36[/tex][tex]SA=294 cm^2[/tex][tex]-------------[/tex]
hope it helps..
have a great day!!
Benji's flight from Chicago to San Jose took 0.5 hour longer than his return flight from San Jose
to Chicago. If Benji's flight from Chicago to San Jose was 4.5 hours long, how long was his return
flight, in hours?
Choose 1 answer:
A
3.5
B 4
C 4.5
D
assroom
5
Answers
The time taken for his return flight, in hours could be 4 hours.
What is time ?
Time is defined as the sequence of events that occurs which can be from past through present or to future.
Given,
Benji's flight from Chicago to San Jose took 0.5 hour longer than his return flight from San Jose to Chicago.
If Benji's flight from Chicago to San Jose was 4.5 hours long
let,
chicago to san jose = san jose to chicago+0.5
4.5 - 0.5 = san jose to chicago
san jose to chicago = 4 hours
Hence, How long was his return flight, in hours is 4 hours.
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Find the derivative.
y = x tanh^-1(x) + ln (√( 1 −x2))
Answers
The answer is:
- 1 < x < 1
I hope this is correct
Mhanifa please help this is due soon
Answers
Answer:
Step-by-step explanation:
Geometric mean = 7.3
Answer:
#1This is the isosceles right triangle as one of the angles is 45°.
The second leg is same as the first and the hypotenuse is √2 times the leg.
x = 5√2y = 5#2This is the 30°x60°x90° triangle and the ratio of sides is:
1 : √3 : 2Since the hypotenuse is 16, the other sides are:
y = 16/2 = 8x = 8√3#3Geometric mean of two numbers is the square root of their product.
√9*6 = √54 = 7.3 (rounded)Correct choice is C
How many solutions does the equation 6a - 3a - 6 = 2 + 3 have?
Answers
Answer:
One, a=11/3.
Step-by-step explanation:
6a-3a-6=2+3
3a-6=5
3a=5+6
3a=11
a=11/3
What is the volume of a cylinder with a radius of 30 cm and a height of 15 cm PLEASE IM BEGGING PLEASE HELP
Answers
Answer:
We need to find the area of the base/circle then multiply it by the height so if you know the formula area of a circle your good to go.
30^2 = 900
900 x 3.14 =2,826
Now lets multiply the base's area/circle by the height!
2,826 x 15 = 42,390 cm^3(cm cubed) is your answer.
A rectangular prism is 12 feet by 10 ft by 3 ft. What is the volume of the prism?
A 186 ft
B 360 ft
C 372 ft2
D 720 ft
HELP PLS
Answers
PLEASE HELP!! WILL GIVE BRAINLIEST IF RIGHT
what is the value of x + y for the system of equations?
y = 2/3x - 9
y= 8 - 2x
Answers
Answer:
I got decimals when I graphed but I got (6.25,-4.75)
Step-by-step explanation:
I made a graph and placed the 2 equations in and marked where they intercepted which is (6.25,-4.75)
What is the common difference for this arithmetic sequence? 45, 40,35, 30.25,...
Answers
Answer:
It decreases by 5 each time. -5 would be another way to state it
Step-by-step explanation:
Answer:
d = - 5
Step-by-step explanation:
The common difference d is the difference between consecutive terms, so
d = a₂ - a₁ = 40 - 45 = = 5
please help it's due today, And please if you don't know the answers don't put any links or apps. And if you do know the answer plz help me.I'll mark as brainliest
Answers
the first one is 3. and the second is 1.
Answer:
B (1): iii
B(2): ii
Step-by-step explanation:
B(1): answer choice 3 is the only answer increasing at a constant rate.
B(2): answer choice two is the only answer not increasing at a constant rate
How do you find the inverse of a 4x4?
Answers
By adding a duplicate of the identity matrix to the augmented matrix, which was formed, it is possible to find the inverse of a square matrix using row reduction.
If the matrix is capable of being reduced to the identity, the identity matrix will simultaneously change into the inverse matrix. A rectangular array of numbers, arranged in rows and columns, is referred to as a matrix. The dimension, or order, of a matrix, indicates how many rows and columns there are in the array. For example, if a matrix has m rows and n columns, its order is expressed as mxn.
Correct Question :
How do you find the inverse of a 4x4 matrix?
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Use algebra tiles to solve 2x + 1 = 9 on IXL
Answers
Answer: 4
Step-by-step explanation:
1. Question: 2x+1=9
2. Subtract 1 from the 9
Answer to step 2: 2x=8
3. Divide 8/2 (4x2)
4. Answer: x=4
Answer: X= 4; look below for the explanation of algebra tiles
Step-by-step explanation: First, we need to determine the value of x. We can use the rule of inverse operations. So, the opposite of addition is subtraction, and the opposite of multiplication is division. Now, using that, we start with the inverse operations of 1 + 9. That'd be 9 - 1. So, that's 8. Now, according to the order of inverse operations, we divide the 2 by 8. So, 8 divided by 2 is 4. Therefore x = 4.
Now, using the tiles, we need to get 8 tiles, + 1 tile, which should get you your answer. I hope this helped!
why is the product of the circumradius and the area of the triangle equal to the product of the sides of the triangle
Answers
Answer:
It isn't.
The correct relation is 4r·Area = abc.
Step-by-step explanation:
You want to show the relation between the product of triangle side lengths and the product of the triangle area and the radius of the circumcircle.
Triangle areaThe area of the triangle in the attached diagram can be found by ...
Area = 1/2(bc)sin(α)
Side lengthThe inscribed angle theorem tells you the measure of the arc subtended by an inscribed angle is twice the measure of the inscribed angle. That means the opposite chord will be twice the length of the product of the radius and the inscribed angle value:
a = 2r·sin(α)
Circumradius productThe product of the circumradius and the area of the triangle is ...
r·Area = r·(1/2)(bc)sin(α) = 1/4(bc)(2r·sin(α)) = 1/4abc
Without the fractions, the relation is ...
4r·Area = abc
__
Additional comment
As a simple example, consider a 3-4-5 right triangle. The area of the triangle is ...
A = 1/2(3)(4) = 6
The circumradius is half the length of the hypotenuse, r = 5/2.
The relation of interest is ...
4r·Area = abc
4(5/2)(6) = 3·4·5
60 = 60 . . . . . . . . . . as expected
This could be a very simple way to find the circumradius of a triangle.
Don’t know need help
Answers
I think that the answer would be 14
Ross had 85 papers to grade from his students. He has graded 60 of them. Approximately what percentage of papers does he have left to grade?
Answers
well, our origin amount will be 80, so 80 is the 100% or all papers, now, she has graded 60, so what's leftover is 20, what's 20 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 80 & 100\\ 20& x \end{array} \implies \cfrac{80}{20}~~=~~\cfrac{100}{x} \\\\\\ 4 ~~=~~ \cfrac{ 100 }{ x }\implies x=\cfrac{100}{4}\implies x=25[/tex]