(q1) Find the area of the region bounded by the graphs of y = x - 2 and y2 = 2x - 4.
Answers
the area of the region bounded by the graphs of y = x - 2 and [tex]y^2 = 2x - 4[/tex], is 0.67. Option D
To find the area of the region bounded by the graphs of y = x - 2 and[tex]y^2 = 2x - 4,[/tex]we need to determine the points of intersection between the two graphs and then integrate the difference between the two functions within the bounds.
Let's begin by finding the points of intersection:
Setting the two equations equal to each other, we have:
x - 2 = 2x - 4
Simplifying the equation, we get:
x = 2
Substituting x = 2 into either equation, we find the corresponding y-value:
y = 2 - 2 = 0
So the points of intersection are (2, 0).
Now, we need to determine the bounds for integration. The graphs intersect at x = 2, so the region of interest lies between x = 0 and x = 2.
To find the area, we integrate the difference between the two functions within these bounds:
A = ∫[0,2] (x - 2 - √(2x - 4)) dx
We can simplify this equation as follows:
A = ∫[0,2] (x - 2 - (2x - 4)^(1/2)) dx
= ∫[0,2] (x - 2 - (2(x - 2))^(1/2)) dx
= ∫[0,2] (x - 2 - 2(x - 2)^(1/2)) dx
To evaluate this integral, we need to use numerical methods or software. Integrating the equation within the bounds gives us an area of approximately 0.67 sq. units.Therefore, the correct answer is Option D
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Related Questions
let X represent the amount of time till the next student will arriv ein the library partking lot at the university. If we know that the dstubtion of arrivlal time can be modeled using an exponential distruibution with a mean of 4 minutes, find the probabiity that it will take between 2 and 132 minutes for the net sutedn to arrive at the library partking lot 0.606531
Answers
Answer:
0.606531 = 60.6531% probability that it will take between 2 and 132 minutes for the student to arrive at the library parking lot.
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
Mean of 4 minutes
This means that [tex]m = 4, \mu = \frac{1}{4} = 0.25[/tex]
Find the probability that it will take between 2 and 132 minutes for the student to arrive at the library parking lot:
This is:
[tex]P(2 \leq X \leq 132) = P(X \leq 132) - P(X \leq 2)[/tex]
In which
[tex]P(X \leq 132) = 1 - e^{-0.25*132} = 1[/tex]
[tex]P(X \leq 2) = 1 - e^{-0.25*2} = 0.393469[/tex]
[tex]P(2 \leq X \leq 132) = P(X \leq 132) - P(X \leq 2) = 1 - 0.393469 = 0.606531[/tex]
0.606531 = 60.6531% probability that it will take between 2 and 132 minutes for the student to arrive at the library parking lot.
A box with a square base and no top is to be built with a volume of 1638416384 in33. Find the dimensions of the box that requires the least amount of material. How much material is required at the minimum
Answers
Answer:
[tex]512\ \text{in}^2[/tex]
Step-by-step explanation:
x = Length and width of base
y = Height of box
Volume of the box is [tex]16384\ \text{in}^3[/tex]
[tex]x^2y=16384\\\Rightarrow y=\dfrac{16384}{x^2}[/tex]
Surface area is given by
[tex]s=x^2+4y\\\Rightarrow s=x^2+4\times \dfrac{16384}{x^2}\\\Rightarrow s=x^2+\dfrac{65536}{x^2}[/tex]
Differentiating with respect to x we get
[tex]s'=2x-\dfrac{131072}{x^3}[/tex]
Equating with 0 we get
[tex]0=2x^4-131072\\\Rightarrow x=(\dfrac{131072}{2})^{\dfrac{1}{4}}\\\Rightarrow x=16[/tex]
[tex]s''=2+\dfrac{393216}{x^4}[/tex]
at [tex]x=16[/tex]
[tex]s''=2+\dfrac{393216}{16^4}=8>0[/tex]
So the function is minimum at x = 16
[tex]y=\dfrac{16384}{x^2}=\dfrac{16384}{16^2}\\\Rightarrow y=64[/tex]
The material required is
[tex]s=x^2+4y=16^2+4\times 64\\\Rightarrow s=512\ \text{in}^2[/tex]
The minimum amount of material required is [tex]512\ \text{in}^2[/tex].
Find the measure of 44.
s
24
158°
ts
64 = [?]
Answers
Answer:
∠4 = 22
Step-by-step explanation:
Hello There!
The angles shown are consecutive interior angles
If you didn't know consecutive interior angles are supplementary angles meaning that the sum of the two angles is 180
So we can find the missing angle by subtracting the given angle (158 in this case) from 180
180 - 158 = 22
so we can conclude that ∠4 = 22
180.timr3fzgncvdfccfxdfdxxfhk
180-158=22
the measure is 44
Which statement is accurate for the right triangle shown below?
Ꮎ
50
1
a
47
Answers
Answer:
The statement that is accurate is csc(θ)=1.06
Step-by-step explanation:
Looking at the reference angle in this triangle, we can see that the side that is 47 units is opposite of it, the side that is 50 units is the hypotenuse, and the side that is 17 units is adjacent to it.
Because we know this, we can plug our sides into the formula for cscθ, secθ, and cotθ.
So:
cotθ=adjacent/opposite = 17/47= 0.36
cscθ=hypotenuse/opposite = 50/47=1.06
Now without even looking at the other statements, we can see that the second one is correct as cscθ=hypotenuse/opposite = 50/47=1.06
Therefore, the statement that is accurate is csc(θ)=1.06.
What Is 20cm rounded to the nearest 10?
Answers
Answer:
20
Step-by-step explanation:
14. Solve 2/3 + 5/6 and put answer in simplest form.
A. 9/6
B.1 1/2
C 2/3
D. 7/6
Answers
Answer:
I believe it is C
Step-by-step explanation:
the answer is supposed to be 3/2 but i dont know
If 141 people attend a concert and tickets for adults cost $3.5 while tickets for children cost $2.5 and total receipts for the concert was $421.5, how many of each went to the concert?
Answers
Answer: There are 69 adults and 72 children went to the concert.
Step-by-step explanation:
Let x be the number of adults, and y be the number of children.
x + y = 141
3.5x + 2.5y = 421.5
x + y =141
x = 141 - y
3.5(141 - y) + 2.5y = 421.5
493.5 - 3.5y + 2.5y = 421.5
493.5 - y = 421.5
-y = -72
y = 72
x + y = 141
x + 72 = 141
x = 69
log²(x + 5) + log²(x - 5) = log²11
Answers
[tex] log_{2}(x + 5) + log_{2}(x - 5) = log_{2}(11) \\ = > log_{2}(x + 5) (x - 5) = log_{2}(11) \\ = > log_{2}( {x}^{2} - 25) = log_{2}(11) \\ cancel \: \: \: out \: \: \: log_{2} \: \: \: from \: \: \: both \: \: \: sides \\ {x}^{2} - 25 = 11 \\ = > {x}^{2} = 11 + 25 \\ = > {x}^{2} = 36 \\ = > x = \sqrt{36} \\ = > x = 6[/tex]
Answer:x = 6
Hope it helps.
Do comment if you have any query.
i need number 22 PLS AND THANK YOU!
Answers
Answer:
For any two given points (x1,y1) and (x2,y2), the slope = (y2-y1)/(x2-x1)
Let's take the points (15,3) and (30, 6):
slope = (y2-y1)/(x2-x1)
= (6-3)/(30-15)
=3/15
=1/5 =0.2
The slope, in general, means the rate of change of y, relative to x. In the context of this question, the slope tells us that the amount of concrete that can be poured (in yards) is a fifth of the time taken (in minutes).
Please help I don’t understand
Answers
Answer:
6:5
Step-by-step explanation:
Step 1: we need to match the b portions of each ration, use a lcm calculator, we see that the least common factor of 1 and 2 is 2
Step 2: For our a:b ratio of 3:1 we need to multiply each portion of the ration by 2 divided by 1 is 2
2 times 3:2 times 1 = 6: 2 our new a b ratio
Step 3: for our bc ratio of 2: 5 we need to multiply each portion of the ratio by 2 divided by 2 equals 1
1 times 2: 1 times 5 = 2:5 our new b:c ratio
since the b portions of each ratio match, we just take a: c = 6:5
GOOD LUCK!
What are the solutions of the quadratic equation 4x2 - 8x – 12 = 0?
Answers
Answer:
see bottom
Step-by-step explanation:
divide through by 4
x2 - 2x - 3 = 0
x2 - 3x + x - 3 = 0
(x2 - 3x) + (x - 3) = 0
x(x - 3) + 1(x - 3) = 0
(x + 1) (x - 3) = 0
x + 1 = 0 and x - 3 = 0
x = -1 and x = 3
This is a picture of a cube and the net for the cube what is the surface area of the cube 196cm 504cm 1176cm 2744cm
Answers
Answer:
The answer is the third one, 1,176
Step-by-step explanation:
A random sample of 80 college students showed that 44 had driven a car during the day before the survey was conducted. Suppose that we are interested in forming a 80 percent confidence interval for the proportion of all college students who drove a car the day before the survey was conducted.
Where appropriate, express your answer as a proportion (not a percentage). Round answers to three decimal places.
Answers
Answer:
The 80% confidence interval for the proportion of all college students who drove a car the day before the survey was conducted is (0.479, 0.621).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
A random sample of 80 college students showed that 44 had driven a car during the day before the survey was conducted.
This means that [tex]n = 80, \pi = \frac{44}{80} = 0.55[/tex]
80% confidence level
So [tex]\alpha = 0.2[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.2}{2} = 0.9[/tex], so [tex]Z = 1.28[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.55 - 1.28\sqrt{\frac{0.55*0.45}{80}} = 0.479[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.55 + 1.28\sqrt{\frac{0.55*0.45}{80}} = 0.621[/tex]
The 80% confidence interval for the proportion of all college students who drove a car the day before the survey was conducted is (0.479, 0.621).
Which story problem COULD not be solved with a expression 3 1/2 x 1/3
Answers
Answer:
C
Step-by-step explanation:
Instead of how much she should've had left it should've asked how much did she use.
1.) Put in order from least to
greatest: 7, -11, 4, -2, -5
Answers
Answer:
least to greatest is how number appear on a number line. numbers less than 0 or indicated with a negative number. if the number is greater than 0 it's indicated without the negative as the plus is implied.
-11, -5, -2 ,4 , 7
find the least common factor of 4,5,6 no links or photo or I will report you
Answers
Answer:
60
Explanation:
The new superset list is
2, 2, 3, 5
Multiply these factors together to find the LCM.
LCM = 2 x 2 x 3 x 5 = 60
In exponential form:
LCM = 22 x 31 x 51 = 60
LCM = 60
Therefore,
LCM(4, 5, 6) = 60
a solid metal ball with a radius of 10 inches is melted and made into smaller spherical metal balls with a radius of 2 inches each. how many smaller spherical balls can be made?
Answers
Answer:
5 i think
Step-by-step explanation:
Huh?! Its me DaBaby less gooo i need your help with this question. Yeah Yeah!
Answers
Answer:
p = 43 :)
Your welcome DaBaby
A coin bank has 17 coins that contains only dimes and quarters. The coins are worth $3.35. How many of each coin are in the bank?
Answers
Answer:7 quarters and 6 dimes
Step-by-step explanation:
What is the shape of the cross section of the figure that is perpendicular to the triangular bases and passes through a
vertex of the triangular bases?
A
a parallelogram that is not a rectangle
O a rectangle
O a triangle that must have the same dimensions as the bases
O a triangle that may not have the same dimensions as the bases
Answers
Answer:
a triangle that may not have the same dimensions as the bases
Step-by-step explanation:
The cross section of the figure that is perpendicular to the triangular bases and passes through a vertex of the triangular bases would be a triangle that may not have the same dimensions as the bases.
A 2-column table with 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries 3, negative 2, negative 3, 0, 7.
What is the rate of change for the interval between 0 and 2 for the quadratic equation as f(x) = 2x2 + x – 3 represented in the table?
one-fifth
4
5
10
Answers
The rate of change for the interval between 0 and 2 for the quadratic equation f(x) = 2x^2 + x - 3, represented in the table, is 6.
To find the rate of change for the interval between 0 and 2 for the quadratic equation f(x) = 2x^2 + x - 3, we can use the values provided in the table.
First, let's calculate the values of f(x) for x = 0 and x = 2:
For x = 0: f(0) = 2(0)^2 + 0 - 3 = -3
For x = 2: f(2) = 2(2)^2 + 2 - 3 = 9
Now, we can find the rate of change by calculating the difference in the values of f(x) divided by the difference in x for the interval [0, 2]:
Rate of change = (f(2) - f(0)) / (2 - 0)
Substituting the values we found:
Rate of change = (9 - (-3)) / (2 - 0)
= (9 + 3) / 2
= 12 / 2
= 6
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Find the mode of the data set. 5, 3, 8, 4, 3, 2, 3, 4, 12, 12, 15, 4, 6, 3, 9
Answers
Answer:
3
Step-by-step explanation:
3 occurs the most in this data set
Answer:
The mode is 3.
Step-by-step explanation:
helppppppppppppppppppppppppppppp
Answers
Answer:
3) Not equivalent
4) Equivalent multiply by 2
5) Equivalent multiply by 2
The heights,in inches,of each of the players on a girls' basketball team are shown. 66,65,66,70,66,68,63,60,66,68,63,65 Which box plot correctly represents the data?
Answers
Given:
Consider the below figure attached with this question.
The given data set is:
66, 65, 66, 70, 66, 68, 63, 60, 66, 68, 63, 65
To find:
The correct box plot for the given data set.
Solution:
We have,
66, 65, 66, 70, 66, 68, 63, 60, 66, 68, 63, 65
Arrange the data set in ascending order.
60, 63, 63, 65, 65, 66, 66, 66, 66, 68, 68, 70
Divide the data set in 4 equal parts by using the parenthesis.
(60, 63, 63), (65, 65, 66), (66, 66, 66), (68, 68, 70)
Minimum value = 60
First quartile: [tex]Q_1=\dfrac{63+65}{2}[/tex]
[tex]Q_1=64[/tex]
Median: [tex]M=\dfrac{66+66}{2}[/tex]
[tex]M=66[/tex]
Third quartile: [tex]Q_3=\dfrac{66+68}{2}[/tex]
[tex]Q_3=67[/tex]
Maximum value = 70
It means the end points of the box plot are 60 and 70. The box lies between 64 and 67. Line inside the box at 66.
The box plot in option A is the only box plot that satisfy the above conditions.
Therefore, the correct option is A.
Find f. f ''(x) = −2 + 36x − 12x2, f(0) = 8, f '(0) = 18 f(x) =
Answers
Answer
its confusing
Step-by-step explanation:
A bird is flying 25 mph. How long will it take to travel
120 miles?
Answers
Answer: 4 hours and 48 minutes
Step-by-step explanation:
120 miles divided by 25 mph
= 4.8
= 4 hours
0.8 x 60
= 48 mins
0 x 60 = 0
quien es el padre de la administración?
Answers
Answer:
Frederick Winslow Taylor
Step-by-step explanation:
The average daily maximum temperature for Shane’s hometown can be modeled by the function f(x)=12.2cos(πx6)+54.9, where f(x) is the temperature in °F and x is the month.
x = 0 corresponds to January.
What is the average daily maximum temperature in March?
Round to the nearest tenth of a degree if needed.
Answers
Answer:
The average daily maximum temperature in March is of 61 degrees.
Step-by-step explanation:
The average daily maximum temperature in his hometown in x months after January is given by:
[tex]f(x) = 12.2\cos{(\frac{\pi x}{6})} + 54.9[/tex]
What is the average daily maximum temperature in March?
March is 3 - 1 = 2 months after January, so this is f(2).
[tex]f(2) = 12.2\cos{(\frac{\pi*2}{6})} + 54.9 = 61[/tex]
The average daily maximum temperature in March is of 61 degrees.
Amanda had five and 6700 pounds of peanuts in her pantry how is this number written in expanded notation
Answers
Answer: 6000+700+00+0
I hope that helps you
O A. negative
O B. parabolic
O C. strong
O D. weak
Which one is it
Answers
Answer:
theres no question to match an answer to, bud..
Step-by-step explanation:
Answer:
plz send full question
Step-by-step explanation:
ok