Find the area enclosed by x2=2y and y2=16x
Answers
Answer: [tex]\dfrac{32}{3}[/tex]
Step-by-step explanation:
Given
The parabolas are [tex]x^2=2y[/tex] and [tex]y^2=16x[/tex]
Find the point of intersection of two parabolas
[tex]\Rightarrow \left(\dfrac{x^2}{2}\right)^2=16x\\\\\Rightarrow x^4=64x\\\Rightarrow x(x^3-64)=0\\\Rightarrow x=0,4[/tex]
Obtain y using x
[tex](x,y)\rightarrow (0,0)\ \text{and }(4,8)[/tex]
Area enclosed between the two is
[tex]\Rightarrow I=\int\limits^4_0 ({4\sqrt{x}-\dfrac{x^2}{2}}) \, dx\\\\\Rightarrow I=\left ( 4\times \dfrac{2}{3}x^{\frac{3}{2}}-\dfrac{x^3}{2\times 3} \right) _0^4\\\\\Rightarrow I=\left ( \dfrac{8}{3}\times 8-\dfrac{4^3}{6} \right )-0\\\\\Rightarrow I=\dfrac{128-64}{6}\\\\\Rightarrow I=\dfrac{64}{6}\\\\\Rightarrow I=\dfrac{32}{3}[/tex]
Thus, the area bounded by the two parabolas is [tex]\dfrac{32}{3}[/tex] sq. units.
Related Questions
What is the radius of C?
Answers
Which graph represents an exponential function?i
Answers
Which statement best describes the function below?
f(x) = 2x3 + 212
1
A. It is not a function,
B. It is a many-to-one function,
0 OOO
C. It fails the vertical line test.
D. It is a one-to-one function!
Answers
Answer:
B
Step-by-step explanation:
Letters a, b, c, and d are angle measures. Which should equal 105° to prove that f is parallel to g? a
b
c
d
Answers
Answer:
D
Step-by-step explanation:
Answer:
Choice is D) D
Step-by-step explanation:
Got it right on Edge
Calculate the surface area of the figure.
Answers
Answer:
2800 yd^2
Step-by-step explanation:
Faces = (1/2 (28*36)) 4 = 2016
Base = 28*28 = 784
2016 + 784 = 2800
4. What is the conditional relative frequency that a customer prefers pepperoni given that the customer is female? 14 perfer pepperoni
Answers
Answer:
5123
Step-by-step explanation:
1425
how many times bigger is the interior angle of a nonogon than a exterior angle
Answers
A nonagon consists of 9 angles. The sum of angles of a nonagon is 1260°.
A nonagon has 9 exterior angles. The sum of angles of the exterior angles of a nonagon is 360°.
Alexander is building a rectangular pen in his backyard for his dog. The pen will have a length of 13 feet and a width of 2x feet.
Answers
4x+26
Step-by-step explanation:
to buy fencing, you need to find the perimeter of the pen. The perimeter is found by adding all sides together.
So, 13+13+2x+2x=4x+26
The choices are agree or disagree
Answers
Answer:
agree
Step-by-step explanation:
Answer:
Agree
Step-by-step explanation:
If you multiply 0.2 by 3, you get 0.6
If you multiply 0.6 by 3, you get 1.8
If you multiply 1.8 by 3, you get 5.4
If you multiply 5.4 by 3, you get 16.2
If you multiply 16.2 by 3, you get 48.6
48.6 is close to being half of the island.
A line passes through (3, -2) and (6, 2).
a. Write an equation for the line in point-slope form.
b. Rewrite the equation in standard form using integers.
Answers
Answer:
Step-by-step explanation:
Point-slope form implies that we need the slope. Let's find that first. Point-slope form, btw, is [tex]y-y_1=m(x-x_1)[/tex], and the formula to find slope is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] so filling in:
[tex]m=\frac{2-(-2)}{6-3}=\frac{4}{3}[/tex] so the slope is a fraction. No problem. It looks the point (3, -2) was used to write the line, so the line in point-slope form using that point is
[tex]y-(-2)=\frac{4}{3}(x-3)[/tex] which simplifies a bit to
[tex]y+2=\frac{4}{3}(x-3)[/tex]. Rewriting in standard form using integers means that we get x and y on the same side of the equals sign, and no fractions allowed. Begin by distributing through the parenthesis to get
[tex]y+2=\frac{4}{3}x-4[/tex] and get rid of the 3 in the denominator by multiplying everything by 3:
3y + 6 = 4x - 12. Now get the x and y on the same side and the constants on the other side.
-4x + 3y = -18. The choice you want is the first one.
Suppose that you collect a random sample of 250 salaries for the salespersons employed by a large PC manufacturer. Furthermore, assume that you find that two of these salaries are considerably higher than the others in the sample. Before analyzing this data set, should you delete the unusual observations
Answers
Answer:
It depends and analysis maybe with the values kept and with the values deleted depending on what we intend to find with the data.
Step-by-step explanation:
When conducting data analysis, a large chunk of time is usually spent trying to ensure that the data is prepared to be used for the require analysis. To ensure this, we tidy up the data by doing the following :
Changing the data format for variables whose units do not conform and so on.
The method of dealing with missing data is essential during data analysis. Missing data may be replaced with the mean value of the observation or completely removed. Based on the scenario, the sample size is 250 ; number of values with unusually high salary values are just 2, hence, removing this values shouldn't pose much of a threat to our data and shouldn't have much effect on the outcome. Hence, removing the Outliers.
Similarly, this unusually high values may signify certain purpose or give certain critical information about the salary and hence may not be deleted
Depending on what we hope to discover from the data, an analysis may be performed
What is a random sample?A simple random sample is a subset of persons picked at random, all with the same probability, from a larger set of individuals. It is a method of choosing a sample at random.
When performing data analysis, a significant amount of work is typically dedicated to making sure the data is ready to be used for the required analysis. We clean up the data in the following ways to make sure of this
changing the data format for variables with non-conforming unit measurements.
During data analysis, the way missing data are handled is crucial. Missing data can either be fully eliminated or replaced with the observation's mean value. According to the scenario, the sample size is 250 there are only 2 values with abnormally high salary values, therefore deleting these values shouldn't constitute significant harm to our data or have a significant impact on the results. thus eliminating the Outliers
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Question
I have a large pot containing 6 liters of soup broth. If I divide the soup broth into 33/3 liters for
vegetable soup and 15/8 liters for beef soup, find the leftover liters of soup broth.
Answers
Answer:
3 / 8 litres
Step-by-step explanation:
Total soup broth = 6 liters
Vegetable soup = 3 3/3 litres = 3 + 1 = 4 litres
Beef soup = 1 5/8 litres
Fraction of soup left :
Total - (vegetable + beef)
6 - (4 + 1 5/8)
6 - 5 5/8
6 - 5 - 5 /8
1 - 5/8
(8 - 5) / 8
= 3 / 8 litres
Which of the following are remote interior angles of Z1? Check all that apply.
1
5
6
3
2.
A. 24
B. 23
C. 22
D. 26
E. 21
F. 25
Answers
Find all angles, 0°
sin a= 0
Answers
Answer:
theta = 0 theta = 180
Step-by-step explanation:
sin theta = 0
sin ^-1 (sin theta) =sin^-1( 0)
theta = 0 theta = 180 for the limits of theta between 0 and 360
Use y = mx + b to determine the equation of a line with a slope -5, passing through the point (-2,4).
Answers
Answer:
[tex]y=-5x-6[/tex]
Step-by-step explanation:
Hi there!
In [tex]y=mx+b[/tex], m is the slope of the line and b is the y-intercept (the value of y when x is 0). y and x remain the same but m and b are replaced with numbers.
Given that the slope is -5, plug it into [tex]y=mx+b[/tex]:
[tex]y=-5x+b[/tex]
Now, to solve for b, plug in the given point (-2,4):
[tex]4=-5(-2)+b\\4=10+b[/tex]
Subtract 10 from both sides to isolate b:
[tex]4-10=10+b-10\\-6=b[/tex]
Therefore, the y-intercept of this line is -6. Plug this back into [tex]y=-5x+b[/tex] as b:
[tex]y=-5x-6[/tex]
I hope this helps!
differentiate 7x²
differentiate 7 x square
Answers
Answer:
y' = 14x
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightCalculus
Derivatives
Derivative Notation
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify
y = 7x²
Step 2: Differentiate
Basic Power Rule: y' = 2 · 7x²⁻¹Simplify: y' = 14xTopic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
What is the length of side x? If necessary, round your answer to two decimal places. 19 12
Answers
Answer:
D. 14.73
Step-by-step explanation:
According to Pythagoras,
19^2 = 12^2 + x^2
x^2 = 19^2 - 12^2
x^2 = 361 - 144
x^2 = 217
x = [tex]\sqrt{217}[/tex]
x = 14.73
Leena consumes 400 calories at breakfast and 350 calories at lunch. She consumes StartFraction 2 Over 3 EndFraction. of her daily calories at dinner. If x represents the calories consumed at dinner, which statements describe the situation? Check all that apply.
Leena consumed 1,500 calories at dinner.
The equation StartFraction 2 Over 3 EndFraction left-parenthesis x plus 400 plus 350 right-parenthesis equals x.(x + 400 + 350) = x can be used to model the situation.
Leena consumed 500 calories at dinner.
The equation StartFraction 2 Over 3 EndFraction left-parenthesis x right-parenthesis equals x left-parenthesis 400 plus 300 right-parenthesis.(x) = x(400 + 300) can be used to model the situation.
Leena consumed 1,000 calories at dinner.
The equation StartFraction 2 Over 3 EndFraction x left-parenthesis x plus 400 plus 350 right-parenthesis equals x.x(400 + 300) = x can be used to model the situation.
Answers
Answer:
A and B
Step-by-step explanation:
Answer:
A & B
Step-by-step explanation:
PLEASE HELP!! ITS A TEST!!
DB is a diagonal of
А
105
parallelogram ABCD.
What is the measure of ZADB;
35°
D
Enter your answer in the box.
Answers
Answer:
40°
Step-by-step explanation:
A parallelogram is a quadrilateral (a four-sided object) with parallel sides
Some of the characteristics of a parallelogram includes:
1. Opposite sides and angles are congruent.
2. Opposite angels are congruent
3. Consecutive angles are supplementary
4. The diagonals bisect each other
Angle DBC = ABD = 35 (alternate angles are equal)
Angle ADB = 180 - 35 - 105 = 40
I subtracted from 180 because sum of angles in a triangle is equal to 180
Find the length of the arc of a circle of diameter 6 meters subtended by a central angle of 2π/3 radians.
Answers
Answer:
Step-by-step explanation:
[tex]arc->s\\s=r\theta={0.5diameter\theta}=0.5*6m*{2\pi\over{3}}=2\pi[/tex]
The length of the arc of a circle of diameter 6 meters subtended by a central angle of 2π/3 radians is; 8.8 meters.
What is the arc of the circle?The arc period of a circle can be calculated with the radius and relevant perspective using the arc period method.
angle= arc/radius
= 2π/3 radians
The diameter = 6 m
Then radius = 3 m
Length of arc = radius x central angle in radians
⇒3 x 2/3
= 2 m
= 44 / 5
= 8.8
Hence the arc of a circle is 8.8 m.
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Use the drawing tools to form the correct answer on the graph.
Graph the line that represents this equation:
3x-4y=8
Answers
Answer:
See attachment for graph
Step-by-step explanation:
Given
[tex]3x - 4y = 8[/tex]
Required
Graph the line
First, we calculate the intercepts
Set x = 0
So:
[tex]3x - 4y = 8[/tex]
[tex]3*0 - 4y = 8[/tex]
[tex]- 4y = 8[/tex]
Divide by -4
[tex]y = -2[/tex]
So, we have:
[tex](x,y) = (0,-2)[/tex]
Next, set y = 0
So:
[tex]3x - 4y = 8[/tex]
[tex]3x - 4 * 0 = 8[/tex]
[tex]3x = 8[/tex]
Divide by 3
[tex]x = 8/3[/tex]
So, we have:
[tex](x,y) = (8/3,0)[/tex]
The graph to be plotted must pass through [tex](x,y) = (0,-2)[/tex] and [tex](x,y) = (8/3,0)[/tex]
Here's my answer
hope it helps
I need to turn this in by 10:00 plz help thank you :)
Answers
Answer:
11 is one 0f them
Step-by-step explanation:
11x11
Which equation best represents the relationship between x and y in the graph?
I’ll give brainliest
Answers
The box plot shows the total amount of time, in minutes, the students of a class spend studying each day:
A box plot is titled Daily Study Time and labeled Time (min). The left most point on the number line is 40 and the right most point is 120. The box is labeled 57 on the left edge and 112 on the right edge. A vertical line is drawn inside the rectangle at the point 88. The whiskers are labeled as 43 and 116.
What information is provided by the box plot?
A. The lower quartile for the data
B. The number of students who provided information
C. The mean for the data
D. The number of students who studied for more than 112.5 minutes
Answers
Not B or D because we don’t know the total, just where the data falls. Since we don’t know the total number of data points, we also can’t find the mean from C
Work out the following calculations and give your answers to the nearest 1000
a) 251 x 638
Answers
Answer:
160,000
Step-by-step explanation:
251
× 638
_______________
2008
753
+ 1506
__________________
160138
Product to the nearest thousand = 160,000
Pleaseee help me answer this question
Answers
Put the following equation of a line into slope-intercept
form, simplifying all fractions.
x + 4y = 24
ASAP!!!!
Answers
Answer:
y = -1/4x + 6
Step-by-step explanation:
Answer:
y = -1/4x + 6
Step-by-step explanation:
Get y alone:
x + 4y = 24
-x = -x
4y = -x + 24
Divide:
4y = -x + 24
4 = 4
Distribute division:
y = -1/4x + 24/4
Reduce fractions:
y = -1/4x + 6
#1 Which rectangular prism will have more volume (left or right) or will they be the same?
#2 What are their volumes?
Answers
Answer:
They will have the same volume
Step-by-step explanation:
Given the rectangular prisms above :
Prism 1 dimension = (3 * 1 1/2 * 2 1/2) inches
Prism 2 dimension = (2 1/2 * 3 * 1 1/2) inches
Recall; Volume of a rectangular prism is :
V = length * width * height
Prism 1 :
V = (3 * 1 1/2 * 2 1/2) = 11.25 in³
Prism 2 :
V = (2 1/2 * 3 * 1 1/2) = 11.25 in³
Hence, Volume of prism will be the same
SOMEONE SMART PLEASE HELP!! if ax^2+bx+c=0, and a≠0, then x=
Answers
Step-by-step explanation:
Hey there!
Simply, ax²+bx+c = 0 is a standard quadratic equation form.
When any equation is in this form where a ≠ 0;
[tex]x = \frac{ - b \: \: \: + - \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
Hope it helps!
Find the zeros of the quadratic function: y= 6(7x + 9)(8x - 3).
A) (-9/7,0), (3/8,0)
B)(-7/9,0), (8/3,0)
C) (-3/8,0), (°/7,0)
D) (-8/3,0), (7/9,0)
Answers
Answer:
A) (-9/7,0), (3/8,0)
Step-by-step explanation:
Zeros of a quadratic function:
x for which y = 0.
In this question:
[tex]y = 6(7x + 9)(8x - 3)[/tex]
It's 0 if one of the factors is 0. 6 is never 0, now about the other to:
[tex]7x + 9 = 0[/tex]
[tex]7x = -9[/tex]
[tex]x = -\frac{9}{7}[/tex]
So (-9/7, 0) is a zero of the quadratic function.
The other is:
[tex]8x - 3 = 0[/tex]
[tex]8x = 3[/tex]
[tex]x = \frac{3}{8}[/tex]
(3/8,0) is the other zero.
Thus, the correct answer is given by option A.