The area of the enclosed region is 83.4 square units.
To calculate the integral, first determine the limits, which will be the points where both curves meet.
The area will be integrated with respect to y.
In respect to y:
[tex]2x + y^{2}[/tex] = 24
[tex]2x[/tex] = 24 - [tex]y^{2}[/tex]
[tex]x[/tex] = 12 - [tex]\frac{y^{2} }{2}[/tex]
Finding limits:
y = 12 - [tex]\frac{y^{2} }{2}[/tex]
12 - [tex]\frac{y^{2} }{2}[/tex] - y = 0
Multiply by 2 to facilitate calculations:
24 - [tex]y^{2}[/tex] - 2y = 0
Resolving quadratic equation:
- [tex]y^{2}[/tex] -2y + 24 = 0
- ([tex]y^{2}[/tex] + 2y - 24 ) = 0
Divide both sides the same factor,
[tex]y^{2}[/tex] + 2y - 24 = 0
Use Quadratic formula,
y = (-b ± [tex]\sqrt (b^{2} -4ac)[/tex] ) / 2a
y = (-2 ± [tex]\sqrt{2^{2}-4*1*(-24) }[/tex] ) / 2*1
y = (-2 ± [tex]\sqrt{4+96}[/tex] ) / 2
y = (-2 ± [tex]\sqrt{100}[/tex] ) / 2
y = (-2 ± 10 ) / 2
y = (-2 + 10 ) /2 , y = (-2 - 10 ) /2
y = 8/2 , y = -12/2
y = 4 , y = -6
y = 4 and y = -6
Then, integral to calculate area will be with limits -6<y<4:
A = [tex]\int\limits^[/tex] 12 - [tex]\frac{y^{2} }{2}[/tex] - y dy
A = 12y - [tex]\frac{y^{3} }{6}[/tex] - [tex]\frac{y^{2} }{2}[/tex]
A = 12*4 - [tex]\frac{4^{3} }{6}[/tex] - [tex]\frac{4^{2} }{2}[/tex] - [12(-6) - [tex]\frac{-6^{3} }{6}[/tex] - [tex]\frac{-6^{2} }{2}[/tex] ]
A = 48 - 10.6 - 8 - [ -72 + 36 - 18 ]
A = 48 - 10.6 - 8 + 72 - 36 + 18
A = 83.4
Therefore,
The area of the enclosed region is 83.4 square units.
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What is the perimeter of a rectangle with a length of 8 1/6 feet and a width of 6 2/3 feet
Answer:
29 2/3 ft
Step-by-step explanation:
The perimeter is found using the formula
P = 2 ( l+w)
where l is the length and w is the width
P = 2(8 1/6 + 6 2/3)
Getting a common denominator
P = 2 ( 8 1/6 + 6 4/6)
= 2 ( 14 5/6)
= 28 10/6
Changing the improper fraction to a mixed number
= 28 + 1 4/6
Simplifying
= 29 2/3 ft
car rental agency has two locations in a city. The boxplots below summarize the miles driven for one day of single day car rentals at each location Location A DO Location B 0 100 300 400 200 Miles Driven Based on the boxplota, which statement provides the best comparison of the two locations?A. The number of single day rentals is greater for location A than for location B. The number of single day rentals in less for location A then for location . C Compared with location A, the miles driven for location display more variability and the median is greater D. Compared with location A, the miles driven for location display lese variability, and the median in greater E. Compared with location A, the miles driven for location display less variability, and the median is about the name
Among the given statements, the following statement "Compared with location A, the miles were driven for location B display more variability and the median is greater" provides the best comparison of the two locations.
Hence, option (C) is the correct choice.
For finding the interquartile range for location, first, find the median (middle value) of the bottom half and upper half of the data before calculating the interquartile range (IQR). Quartile 1 (Q1) and Quartile 3 are these values (Q3). The IQR represents the variation between Q3 and Q1.
The interquartile range for location B is Q3 - Q1 = almost 140 - 40 = 100, while it is Q3 - Q1 = nearly 60 - 40 = 20 for location A.
Therefore, the miles travelled for position B are more variable than they are for place A.
Greater than Location A's almost 50 medians is Location B's nearly 80 median.
Therefore, location B's median miles driven is higher than it is for location A.
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HELPPPPPPP im to lazy
Answer: help is on the way
Step-by-step explanation:
hurry please and thank you #2
When the rate of change of AB is -1/5, and line CD is 5 then line AD will be -1
What is linear function ?A linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
The slope is represented as m, The slope by definition is the change of the output values to the input values, otherwise known as the rate of change.
In the figure, the rate of change is given to be -1/5 and by definition rate of change which is the slope has the formula
m = change of the output values / change in the input values
m = AC / CD
-1/5 = AC / 5
hence AC = -1
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wha is the equation of the line that passes through the point (-4,1) and has a slipe of -3/2
The equation that passes through the point (-4,1) y=-3/2x-5
What is the slope-intercept form of a line?The slope-intercept form of a line is represented by y=mx+c where m=slope and c is the y-intercept of the line
Given here, the line that passes through the point (-4,1) and has a slope of -3/2 then let the equation of the line be y=mx+c then we get
⇒1= -3/2×-4+c
⇒c= -5
Hence, The equation that passes through the point (-4,1) y=-3/2x-5
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The plane x + y + z = 1 cuts the cylinder x2 + y2 = 1 in an ellipse. We want to find the points on the ellipse that lie closest to the origin. Using Lagrange Multiplier method, set up a system of equations for such points. Need not solve it. Hint: Let (x, y, z) be the point on the ellipse. Then the goal is to minimize f(x, y, z) = x2 + y2 + z2 (= square of the distance from the origin), under a constraint. Write the constraint function clearly,
The points on the ellipse that lie closest to the origin is (0, 1, 0).
f(x)=x²+y²+z²
h(x)=x²+y²=1
g(x)=x+y+z=1
⟨2x,2y,2z⟩=λ⟨2x,2y,0⟩+μ⟨1,1,1⟩
This results in the equations:
2x = 2xλ +μ
2y = 2yλ + μ
2z = μ
By taking λ = 1
2x = 2x + μ
μ = 0 so z = 0
x + y = 1
y=1 and x=0
The Lagrange multiplier method in mathematics is a technique for locating the local maxima and minima of a function subject to equality restrictions (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables). [1] It bears the name Joseph-Louis Lagrange after the mathematician.
The fundamental concept is to transform a limited problem into a format that still allows the derivative test of an unconstrained problem to be used. The Lagrangian function is a reformulation of the original issue that results from the relationship between the gradient of the function and gradients of the constraints.
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let f(x) = 1 2x . compute lim h→0 f(5 + h) − f(5) h .
The value of f(5 + h) - f(5)h when h =0 is 60.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = 12x
Now,
f(5 + h) = 12 (5 + h) = 60 + 12h
f(5) = 12 x 5 = 60
Now,
f(5 + h) - f(5)h
= 60 + 12h - 60h
h = 0
= 60 + 0 - 0
= 60
Thus,
The value of the limit is 60.
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Describe and correct the error writing 39 over 40 as a percent.
Answer:
Multiply instead of divide
Step-by-step explanation
39/40=0.975 (Correct)
0.975x100=97.5%
If it were me I would just move the decimal point in 0.975 right twice, but since they're asking for a formula you would multiply instead of divide.
Hope this helps :)
Which equation has no solution 4 x 3 2x 6 x 2 5 2 3 2x x 3 x 1?
The equation given in B which is "5 + 2 ( 3 + 2x ) = x + 3 ( x + 1 )" has no solution.
In order to determine which equation has no solution we need to solve the equation to check to see if after solving they give the left-hand side (LHS) and right-hand side (RHS) equal.
If both LHS and RHS are equal, it means the equation has a solution; but if LHS and RHS are not equal, it means that the equation has no solution.
So first solve the equation given in A:
4 ( x + 3 ) + 2x = 6 ( x + 2 )
4 x + 12 + 2 x = 6x + 12
6 x + 12 = 6 x + 12
LHS is equal to RHS so this equation has the solution.
So now solve the equation given in B:
5 + 2 ( 3 + 2x ) = x + 3 ( x + 1 )
5 + 6 + 4 x = x + 3 x + 3
11 + 4 x = 4 x + 3
or
(4 x + 11) = (4 x + 3)
LHS is not 'equal' to RHS so this equation has no solution.
"
Complete question is
Which equation has no solution
A: 4 ( x + 3 ) + 2x = 6 ( x + 2 )
B: 5 + 2 ( 3 + 2x ) = x + 3 ( x + 1 )
"
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If you place a 24-foot ladder against the top of a 22-foot building, how many feet will the bottom of the ladder be from the bottom of the building? Round to the nearest tenth of a foot.
Answer:
9.5ft
Step-by-step explanation:
a²+b²=c²
equation
24²=c²
22²=a²
put in the variables
24²-22²=b²
Rearrange the equation
576-484=92
square
√92
Square root answer
9.5ft
Answer
Click on the graph until the graph that best represents the given statement appears.
Height Above Ground
Time
The graph consists of the relationship between the height of the object and time.
What is the graph?The graph is a demonstration of curves that gives the relationship between the coordinate axes x and y-axis.
here,
In the figure,
The graph shows the relationship between the height of the object dependent on time. Where the vertical axis represents the height of the object, and the horizontal axis represents the time.
Thus, the graph shows the relationship between the height of the object and time.
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what is 860x67 divided by 65
Answer:
886.461538462
Step-by-step explanation:
How much would you need to invest at 8.75% interest rate compounded daily for 50 years to have $1,000,000 at the end of that time period?
Answer:
You would need to invest $12594.78-------------------------
Given:
Interest rate r = 8.75% or 0.0875,Time t = 50 years,Compound number n = 365,Future amount A = $1000000Find the invested amount P using compound interest equation:
[tex]A=P(1+r/n)^{nt}[/tex]Substitute to get:
[tex]1000000=P(1+0.0875/365)^{365*50}[/tex][tex]1000000=P(79.398)[/tex][tex]P=1000000/79.398[/tex][tex]P=12594.78[/tex]How many solutions does the equation y = -2x2 - 7x + 5 have?
The number of solutions which the equation y = -2x² -7x + 5 has as required in the task content is; 2.
What is the number of solutions for the given equation?As evident in the task content; the number of solutions which the given equation has is to be determined.
Since the given equation; y = -2x² -7x + 5 is a quadratic equation.
It follows that the number of solutions which the equation has is two.
PS; Quadratic equations are polynomials with degree 2 and hence, have two solutions.
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a section of lawn that is 25.5 feet by 75.0 feet needs fertilizer. the fertilizer is sold in 5.00 pound boxes and 1.00 pound of fertilizer is needed for 10.0 square yards of lawn. if each box costs $1.65, how much will it cost to fertilize the lawn?
it cost 5 pound then = 1912.5*5= 9562.5 when the fertilizer is sold in 5.00 pound boxes and 1.00 pound of fertilizer is needed for 10.0 square yards of lawn. if each box costs $1.65
a section of lawn that is 25.5 feet by 75.0 feet needs fertilizer.
the fertilizer is sold in 5.00 pound boxes and 1.00 pound of fertilizer is needed for 10.0 square yards of lawn.
if each box costs $1.65, how much will it cost to fertilize the lawn?
We would solve this question by cross multiplication.
If a sound of fertilizer covers 45 square feet of lawn and the lawn is 8666.7 square feet
To get fertilizer quantity we have
1 pound = 45 square
Unknown = 8666.7 square feet
8666.7/45
= 192.59 when approximated we get 193.
Therefore she has to buy 193 pounds of fertilizer
total become 25.5*75=1912.5
it cost 5 pound then = 1912.5*5= 9562.5
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100 PTS HELP
Use the distributive property or simplify to match the equivalent expressions.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
(3 × 4) + (3 × 7)
7(60 + 6)
32 +16 = 48
4(100 − 3)
(5 × 9) − (5 × 6)
(3 × 4) + (3 × 7) = 12 + 21 = 33
7(60 + 6) = 7(66) = 462
4(100 − 3) = 4(97) = 388
(5 × 9) − (5 × 6) = 45 − 30 = 15
So, the correct input-output pairs are:
(3 × 4) + (3 × 7) = 33
7(60 + 6) = 462
4(100 − 3) = 388
(5 × 9) − (5 × 6) = 15
Answer: 33,462,48,388, and 15
Step-by-step explanation:
FOr every 5 coins Carmen gets she gives frankle 2 if Carmen has 9 how many dose frankle have
Answer:2
Step-by-step explanation:
She has 2
9 - 5 = 4
no more to give so only 2
Edward drives his car 12,000 miles per year.how many kilometers does he drive per month
Edward drives 160.9 kilometres per month
How to calculate the distance that Edward travelled per month?Edward drives 12,000 miles per year
There are 12 months in a year, this means that Edward travels 12,000 miles in 12 month
The number of kilometres travelled per month can be calculated as follows
12,000= 12
x= 1
cross multiply both sides
x= 12,000/12
x= 100
The next step is to convert 100 miles to kilometres
100 × 1.609
= 160.9 kilometres
Hence Edward travelled 160.9 kilometres per month
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Jason made a model stop sign for his model train
set. An actual stop sign measures 12 inches on
each side. Jason's model stop sign measures
1 inch on each side.
What is the scale of the model sign to the actual
sign?
On solving the provided proportionality question we got that, U = 7.72, is rounded off nearest to tenth digit.
What is proportionality?When two quantities or variables are linearly related in mathematics, the term "proportional" is used. Both quantities increase by two times when one increases by two. Each variable decreases in proportion to the other when it falls to 1/100th of its previous value.We must determine the ratio of the two quantities for each value supplied in order to determine if two quantities are proportionate. The proportionate link between them is evident if their proportions are equal. Their connection is not proportionate if all the ratios are out of balance.
Here,
U/5 = 17/11
U = 17/11 X 5
U = 7.72
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is the point (2,-1) is true for the system? 3x - y =7 2x+3y=1
Answer:
yes it is true
Step-by-step explanation:
3(2)-(-1)=7 2(2)+3(-1)=1
What is the range of the relation plotted on
the graph?
A. {-1, 0, 1, 3}
B. (-2, 0, 1, 3}
C. {-2, -1, 0, 1, 2, 3}
D. {0, 1, 2, 3}
The range of the relation plotted in the graph is {-2, 0, 1, 3}.
What is the range?Range is a statistical measure of dispersion in mathematics, or how widely spaced a given data collection is from smallest to largest.
Given, A relation plotted on the graph in that there are four points whose coordinates are (0, -2), (3, 0), (-1, 1), and (1, 3)
Since The y-axis on a graph represents the possible output values, or range. Remember that the domain and range of the graph may be larger than the values seen if the graph extends beyond the area that is visible.
Therefore, The graphed relation's range is between -2, 0, 1, and 3.
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You and your friends want to go on a canoe trip. River Run Canoes Charges an initial fee of $10 plus $10 per hour. The cost for Clear Water Canoes is represented by the graph. ( Graph has a y intercept of 16, and goes right 2, so its starting at 16/2 )
The graph of the amount of money that River Run Canoes have a y intercept of 10 and slope of 10.
How to solve an equation?An equation is an expression that shows the relationship between two or more numbers.
The standard form of a linear equation is:
Ax + By = C
Where A, B and C are constants.
The slope intercept form of a linear equation is:
y = mx + b
Where m is the rate of change and b is the initial value (y intercept).
Let y represent the total amount of money that River Run Canoes Charges for a trip lasting x hours.
River Run Canoes Charges an initial fee of $10 plus $10 per hour, hence:
y = 10x + 10
The graph of the amount of money that River Run Canoes have a y intercept of 10 and slope of 10.
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Dishwasher detergent is sold in individual packs. It is sold in 20-, 60-, and 90-pack containers.
a. Which container do you think has the lowest unit rate of dollars per pack? Why?
b. The 20-pack container sells for $5.49. What is the unit rate in dollars per pack? Round your answer to the nearest cent.
c. The 60-pack container sells for $10.97. What is the unit rate in dollars per pack? Round your answer to the nearest cent.
d. The 90-pack container sells for $18.95. What is the unit rate in dollars per pack? Round your answer to the nearest cent.
e. Which container has the lowest unit rate> how does this compare with your answer in part (a)?
Answer:
b) 0.27
c) 0.18
d) 0.21
e) c has the lowest rate per container
Two roses cost $3.50. How many roses can you
buy for $21?
Answer:
6 roses
Step-by-step explanation:
divide 21 and 3.50 hope this helps:)
Answer:6
Step-by-step explanation:
21 Divided by 3.5 = 6
How do you write fractions in Python?
The fraction module in Python can be used to create fractions such as 3/4. This module can be imported and then the Fraction class can be used to create the fraction object. The fraction object can then be printed to display the fraction.
1. Import the fraction module: from fractions import Fraction
2. Create the fraction object: f = Fraction(3, 4)
3. Print the fraction: print(f)
4. The output will be: 3/4
The fraction module in Python is used to create and manipulate fractions. This module can be imported using the following command: from fractions import Fraction. Once imported, the Fraction class can be used to create the fraction object. The Fraction class takes two parameters which represent the numerator and denominator of the fraction. The fraction object can then be printed to display the fraction. For example, to create a fraction of 3/4, the following code can be used: f = Fraction(3, 4). This will create a fraction object which can then be printed with the print() function to display 3/4. The fraction module in Python is a great way to work with fractions in a programmatic way.
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Alexander was offered a job that paid a salary of $34,000 in its first year. The salary was set to increase by 4% per year every year. If Alexander worked at the job for 5 years, what was the total amount of money earned over the 5 years, to the nearest whole number?
The total amount that is earned by Alex in five years is $41528.
What is the total amount that he earns in five years?We have to note that we need to look at the equation that shows the raise in the salary of Alex and we can be able to write from the equation that;
A =Pe^rt
A = amount that is earned after t years
r = rate of the increase of the salary
t = time taken to increase the salary
We now know from the question that
A = ?
P = $34,000
r = 0.04
t = 5
Thus;
A = 34000e^(0.04 * 5)
A = $41528
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What is the y intercept for the 1st graph.
Answer: 2
Step-by-step explanation:
Whatever point the line crosses when crossing the Y axis is the y-intercept.
In this graph it is crossing over 2
The graph shows Michaela’s earnings over time. Marcus’s hourly rate is represented in the table. Who has a greater rate of pay, and how much more than the other will that person earn in 40 hours of work?
A. Complete the table, write an equation, and graph Marcus’s earnings A over time t.
k = 19/2 = ? A = ?
B. Use the graph to determine who is earning a greater rate of pay. Explain how you know.
C. What information do you still need in order to solve the problem? Solve the problem and show your work.
I still need...
Michaela
?/10 = k, or k = ?
A = kt
A = ?t
A = ? (?) = $480
Marcus:
A = kt
A = ?t
A = ? (?) = ?
The completed table is given as follows:
Earnings of $19.00 in 2 hours.Earnings of $38 in 4 hours.Earnings of $47.50 in 5 hours.Earnings of $57 in 6 hours.Earnings of $76 in 8 hours.The greater rate is that of:
Michaela.
The difference for 40 hours of work is given as follows:
$100.
Marcus' graph is given by the image at the end of the answer.
What is a proportional relationship?A proportional relationship is a linear function with an intercept of zero modeled as follows:
y = kx.
In which k is the constant of proportionality.
From the table, Marcus' hourly rate is given as follows:
k = 19/2 = 9.50.
Hence the proportional relationship is:
y = 9.5x.
Which is graphed at the end of the answer.
The table is completed as follows:
When time = 4, y = 9.5(4) = $38.When time = 5, y = 9.5(5) = $47.50.When earnings = 57, time = 57/9.5 = 6.When earnings = 76, time = 57/9.5 = 8.From the graph, Michaela's hourly rate is given as follows:
120/10 = $12.
Which is greater than Marcus'.
The hourly difference is given as follows:
12 - 9.5 = 2.5.
Hence the difference for 40 hours is given as follows:
40 x 2.5 = $100.
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Solve the radical equation.
Check all solutions to eliminate extraneous solutions
and do not include them in your answer.
If your answer is not an integer then type it as a
decimal rounded to the nearest hundredth.
√2x+3-√x+2=0
x=
Check
There doesn't exist any extraneous solution for the given problem.
To assess whether or not your solutions are unnecessary, you must re-enter each one into the original equation.
When you square the two sides of a square root problem, there are two solutions, which leads to the appearance of extraneous solutions (the positive and negative number).
A solution that is added but does not fulfill the starting equation will therefore be represented by one of those figures.
Given, the equation is -
√2x+3-√x+2=0
⇒ √2x+3 = √x+2
Squaring on both sides
⇒ 2x + 3 = x + 2
⇒ 2x - x = 2 - 3
⇒ x = -1
Now, putting x = -1 back in the question,
⇒ √1 = √1
Hence, LHS = RHS, therefore, there doesn't exist any extraneous solution.
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The figures below are similar to each other. Find the scale factor of the smaller figure to the larger figure.
(Given that the triangles are oriented in the same direction)
35
5:2
2:5
20:7
7:20
40
25
14
16
The scale factor of the smaller figure to the larger figure is 5:2
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
Given that two triangles are similar.
The side lengths of the triangle must be proportional.
Let us consider first triangle as ABC, where AB is 35, BC is 40 and AC is 25.
and triangle DEF as DE is 14 and EF is 16.
Now AB/DE=BC/EF
35/14=40/16
5/2=5/2
Hence, the scale factor of the smaller figure to the larger figure is 5:2
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