The solution to the initial value problem is:
[tex]y = -(x^2-5)ln|x^2-5| + (7+3ln3)/9[/tex]
To solve this initial value problem, we can use the method of integrating factors.
First, we identify the coefficients of the equation:
[tex](x^2 - 5) y' - 2xy = -2x(x^2 - 5)[/tex]
Next, we multiply both sides of the equation by the integrating factor, which is given by:
[tex]IF = e^{-∫(2x/(x^2-5)dx)} = e^{-2 ln|x^2-5|} = e^{ln(x^2-5)}^{(-2)} = (x^2-5)^{(-2)}[/tex]
Multiplying both sides of the equation by the integrating factor, we get:
[tex](x^2-5)^{-2} (x^2 - 5) y' - 2x(x^2-5)^{-2} y = -2x(x^2-5)^{-1}[/tex]
Simplifying the left-hand side using the product rule, we get:
[tex]d/dx [(x^2-5)^(-1)] y = -2x(x^2-5)^{-1}[/tex]
Integrating both sides with respect to x, we get:
[tex](x^2-5)^(-1) y = -ln|x^2-5| + C[/tex]
where C is an arbitrary constant of integration.
Multiplying both sides by [tex](x^2-5)[/tex], we get:
[tex]y = -(x^2-5)ln|x^2-5| + C(x^2-5)[/tex]
To find the value of C, we use the initial condition y(2) = 7:
[tex]7 = -(2^2-5)ln|2^2-5| + C(2^2-5)[/tex]
7 = -3ln3 + 9C
C = (7+3ln3)/9.
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Becca's car engine has a capacity of 3.6 quarts and
contains 1.2 quarts of engine oil. One bottle of engine oil is
0.5 quart. Approximately how many bottles of engine oil
does Becca need to completely fill her car engine?
Becca needs approximately 5 bottles of engine oil to completely fill her car engine.
How to determine the number of bottles of engine oil?Since Becca's car engine has a capacity of 3.6 quarts and contains 1.2 quarts of engine oil, the remaining space left in her car engine is given by:
Space = 3.6 - 1.2
Space = 2.4 quarts.
By applying direct proportion, we have:
1 bottle = 0.5 quart.
x bottles = 2.4 quarts.
Cross-multiplying, we have:
0.5x = 2.4
x = 2.4/0.5
x = 4.8 ≈ 5 bottles.
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Last-Minute Shopper #1 paid $102 for 3 gizmos and
6 thingamajigs. Last-Minute Shopper #2 paid $179
for 5 gizmos and 11 thingamajigs. Assume they both
shopped at the same store and bought the same
brands and model numbers, and then answer the
questions below.
a) How much did each gizmo cost?
b) How much did each thingamajig cost?
The cost of one gizmo is $18.
The cost of one thingamajigs is $9
What are the linear equations that represent the question?3g + 6t = 102 equation 1
5g + 11t = 179 equation 2
Where:
g = cost of one gizmo t = cost of one thingamajigs.What is the cost of one gizmo and thingamajigs?Multiply equation 1 by 5 and equation 2 by 3
15g + 30t = 510 equation 3
15g + 33t = 537 equation 4
Subtract equation 3 from equation 4
3t = 27
t = 27 / 3
t = $9
Substitute for t in equation 1
3g + 6(9) = 102
3g + 54 = 102
3g = 102 - 54
3g = 48
g = 48 / 3
g = $18
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In algebra, we transfer these same skills to expressions involving variables. what elementary skills have you used so far in this course, and how have you extended them?
( 1 ) 0.006 m (cm) =
( 2 ) 17, 605 mm (km) =
( 3 ) 1,001,00 dm (km) =
the value of the given figures in the other units can be found to be:
0.006 m = 0.6 cm17,605 mm (km) = 0.017605 km1,001,000 dm = 10.01 kmwhat are the converted values of the figures?A meter is 100 cm so:
= 0.006 x 100
= 0.6 cm
A kilometer is 1,000,000 mm so:
= 17,605 / 1,000,000
= 0.017605 km
A kilometer is 10,000 dm:
= 1,001,00 dm / 10,000
= 10.01 km
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In the figure, is the perpendicular bisector of .
Prove:
A line CD is a perpendicular bisector of another line AB. A triangle is drawn by the points of A, B, and C.
Complete the proof.
CD is the perpendicular bisector of another line AB which can be proven below.
What is perpendicular bisector?Perpendicular bisector is a line that divides another line into two equal halves in such a way that it creates an angel of 90°.
To proof that CD is the perpendicular bisector of another line AB the following is carried out;
Draw a line segment AB with length of about 5 cm.With any radius greater than 2.5 cm, and compass fixed at A, draw 2 arcs, one above and one below AB.With the same radius, compass at B, cut the 2 arcs drawn in step 2.The line joining these two arcs is the perpendicular bisector of AB.Learn more about perpendicular lines here:
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Answer:
heres what i got
Step-by-step explanation:
2. definition of a perpendicular bisector
5. reflexive property of congruence
11. definition of square root
A teacher is experimenting with computer-based instruction. In which situation could the teacher use a hypothesis test for a population mean?.
the correct option is : (i)
She gives each student a pretest. Then she teaches a lesson using a computer program
What is Hypothesis testing?
Hypothesis testing is the process of evaluating two frequently contradictory claims based on population data and test data.
The appropriate response is provided by choice (i).
Simply said, a hypothesis is a supposition that we form based on our perceptions.
Therefore, statistics is all about information, a vast amount of information that is as valuable to us as information if we can analyze it and eventually come to some conclusions about it. To find out interpretation and conclusions about the information we mostly use.
Therefore,
the correct option is (i)
She gives each student a pretest. Then she teaches a lesson using a computer program. Afterward, she gives each student a pretest. The teacher is interested in seeing if the disparity in results indicates an improvement.
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I understand that the question you are looking for is:
"A teacher is experimenting with computer-based instruction. In which situation could the teacher use a hypothesis test for a difference in two population means?
(i) She gives each student a pretest. Then she teaches a lesson using a computer program. Afterwards, she gives each student a posttest. The teacher wants to see if the difference in scores will show an improvement.
(ii) She randomly divides the class into two groups. One group receives computer-based instruction. The other group receives traditional instruction without computers. After instruction, each student has to solve a single problem. The teachers wants to compare the proportion of each group who can solve the problem.
(iii) She gives each student a pretest. She then randomly divides the class into two groups. One group receives computer-based instruction. The other group receives traditional instruction without computers. After instruction, each student takes a post-test. The teacher compares the improvement in scores (post-test minus pretest) in the two groups.
(iv) The teacher uses a combination of traditional methods and computer-based instruction. She asks students which they liked better. She wants to determine if the majority prefer the computer-based instruction."
The sum, s, of 4 consecutive odd integers can be represented by the equation s = 4n â 12. what does n represent?
The variable n represents the smallest of the four integers.
How to interpret what n represents?The given parameters are
Number of consecutive odd integers = 4
Sum of consecutive odd integers= s
Where
S = 4n - 12
The variable n represents the smallest of the four integers.
In the sense that, the consecutive odd integers are
n, n + 2, n + 4 and n + 6
Hence, the variable n represents the smallest of the four integers.
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Which of the following segments is a diameter of o
Answer:
Segment UF
Step-by-step explanation:
Diameter is a line that passes through the center and meets the circumference at opposite ends.
Segments OF and WO are radii, and segment WM is a chord.
I don’t know what the second part of the question means
Answer:
Hello!
independent variable: variable in an experiment that is changed e.g. a plant's exposure to light
dependent variable: variable in an experiment that is measured e.g. a plant's height
The question is just asking to identify these variables.
Hope this helps! Feel free to ask further questions if need be.
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 10 N acts on a certain object, the acceleration of the object is 5 meters per second². If the acceleration of the object becomes 4 meters per second², what is the force?
Answer:
8
Step-by-step explanation:
F=ma
10=5m
4m=10*4/5
4m=8
So the answer is 8
Beau Thai has a rectangular mirror with a length of 6 inches and a width of 10 inches.
a) How much ribbon could Beau wrap around the outside of the mirror?
b) What is the area of Beau Thai's mirror?
a. Amount needed to wrap the outside of the rectangular mirror around = 32 inches.
b. Area of the Beau Thai's rectangular mirror around = 60 square inches.
What is the Area of a Rectangle?Area of a rectangle = (l)(w), where l is the length and w is the width of the rectangle.
What is the Perimeter of a Rectangle?Perimeter of a rectangle = 2(l + w), where l is the length and w is the width of the rectangle.
a. The amount of ribbon that can be used to wrap the outside of the mirror around can be determined by using the formula for the perimeter of a rectangle.
Length of rectangular mirror = 6 inches
Width of rectangular mirror = 10 inches
Perimeter = 2(6 + 10)
Perimeter = 2(16)
Perimeter = 32 inches
Amount needed to wrap the outside of the rectangular mirror around = 32 inches.
b. The area of Beau Thai's rectangular mirror can be determined by using the formula for the area of a rectangle.
Length of rectangular mirror = 6 inches
Width of rectangular mirror = 10 inches
Area = (6)(10)
Area = 60 square inches
Area of the Beau Thai's rectangular mirror around = 60 square inches.
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ABCD is a square.
Square A B C D is shown. A diagonal is drawn from point A to point C. The measure of angle B A C is question mark.
What is the measure of angle BAC?
30°
45°
60°
90°
Since ABCD is a square, and AC is the diagonal of the square, therefore, then, angle BAC would be Option B. 45°
What is square?A square is known as a quadrilateral with four interior angles of 90° each, and four equal sides.
Properties of a square include
The interior angles are equal to 90°All the sides are congruent or equal The opposite sides are parallel The diagonals of the square bisect each other at 90 degreesThe two diagonals are equalAngle BAC is half the angle of the diagonal
= 90/2 = 45°
Thus, since ABCD is a square, and AC is the diagonal of the square, therefore, then, angle BAC would be Option B. 45°
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What is the area of triangle pqr? round to the nearest tenth of a square unit. 70.5 square units 111.3 square units 185.4 square units 222.5 square units
The area of the triangle pqr is 111.3 square units
How to determine the triangle area?The complete question is added as an attachment
The area is calculated as:
[tex]A= 0.5 ab\sin(C)[/tex]
So, we have:
[tex]A= 0.5 * 12 * 20 * \sin(68)[/tex]
Evaluate the product
A= 111.3
Hence, the area of the triangle pqr is 111.3 square units
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x - 3y = 9, complete the ordered pair (12, ).
Answer:
(12,1)
Step-by-step explanation:
We know that ordered pairs are in the format of (x,y).
This means in that (12, __) 12 is our x coordinate. Plugging 12 into the equation as x we get:
[tex]12-3y=9\\-3y=9-12\\-3y=-3\\y=1[/tex]
Therefore our answer is (12,1) as we plug y back into our coordinate (x,y).
Answer:
(12,1)
Step-by-step explanation:
In the ordered pair, x=12
plug 12 back in the equation
12-3y=9
-3y=-3
3y=3
y=1
Factor this polynomial.
-3x²-5x-2
A. (-3x+2)(x+1)
B. (3x-2)(x-1)
C. (3x+2)(x-1)
D. -1(3x+2)(x+1)
Answer: D. -1(3x+2)(x+1)
Step-by-step explanation: First, use the F.O.I.L. method (First, Outer, Inner, Last). Then combine all your like terms. After, multiply the whole outcome by negative one. So, 3[tex]x^{2}[/tex] turns into -3[tex]x^{2}[/tex]; 5x turns into -5x; and 2 is -2. BOOM! you got the exact right answer.
according to the graph, what is the value of the constant in the equation below?
Answer:
3
Step-by-step explanation:
height = constant * width
let's rearrange this equation
constant = height/width
let's pick several points as a proof
15/5 =3
6/2 =3
1.5/0.5 = 3
hope this helps you!!
slope and y intercept?
Answer:
slope: -1/3
Y-intercept: 0
Step-by-step explanation:
The line crosses the y-axis at 0, and the pibe decreases by 1 down and goes to the side by 3, using rise over tu it would be -1/3
I hope it helps! Have a great day!
Pan~
Answer:
Slope: -1/3
Y-intercept: 0
Step-by-step explanation:
I hope it helps! Have a great day!
bren~
Determine the value of x that would make quadrilateral lmno a parallelogram. 3 9 11 18
The correct answer is x = 9
What is a parallelogram in math?
A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal). A quadrilateral with equal sides is called a rhombus, and a parallelogram whose angles are all right angles is called a rectangle.Diagonals of a parallelogram bisect each other.
For quadrilateral LMNO to be a parallelogram, LP must equal PN, and OP must equal PM.
Set OP equal to PM and solve for x.
PM = OP
3x - 9 = 18
Add 9 to both sides.
3x = 27
Divide both sides by 3.
x = 9
Therefore, the value of x = 9
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The complete question is -
Determine the value of x that would make quadrilateral LMNO a parallelogram.
3
9
11
18
Answer: x=9
Step-by-step explanation:
Can someone help me on this pls? It’s urgent, so ASAP (it’s geometry)
Write formal proofs using LA Theorem.
Given the parameters in the diagrams, we have;
4. ∆ABC ≈ ∆DEF by ASA
5. UW ≈ XZ by CPCTC
6. QR ≈ TR by CPCTC
How can the relationship between the triangles be proven?4. The given parameters are;
<B = <E = 90°
AB = DE Definition of congruency
<A = <D Definition of congruency
Therefore;
∆ABC ≈ ∆DEF by Angle-Side-Angle, ASA, congruency postulate5. Given;
XY is perpendicular to WZ
UV is perpendicular to WZ
VW = YZ
<Z = <W
Therefore;
∆UVW ≈ ∆XYZ by Angle-Side-Angle, ASA, congruency postulate
Which gives;
UW is congruent to XZ, UW ≈ XZ, by Corresponding Parts of Congruent Triangles are Congruent, CPCTC6. Given;
PQ is perpendicular to QT
ST is perpendicular to QT
PQ ≈ ST
From the diagram, we have;
<SRR ≈ <PRQ by vertical angles theorem;
Therefore;
∆QRP ≈ ∆TRS by Side-Angle-Angle, SAA, congruency postulate
Which gives;
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A square sandbox has sides of length 9 ft and a depth of 1 ft. If sand costs $5 / cubic foot, how much will it cost to fill the sandbox with sand?
The cost spent on fill the box with sand is 405$.
According to the statement
we have given a square sandbox with length 9 ft and depth of 1 ft.
and the rupees of sand per cubic ft is $5
then
Now, we have to find the volume of sandbox with the given length and depth.
So, for this purpose we use Volume formula
V = (a)^3
V = 9*9*1
V = 81 cubic feet
And the cost of sand per cubic feet is $5.
then
The cost of sand for 81 cubic per feet is calculate by multiplication formula then
Total cost of sand = 81*5
Total cost of sand = 405$
So, The cost spent on fill the box with sand is 405$.
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PLEASE HELP ME AS SOON AS POSSIBLE
The parent function of g(x) = |x - 7| +6 is f(x) = |x|
How to determine the parent function?The function is given as:
g(x) = |x - 7| +6
The above function is an absolute function, and the parent function is f(x) = |x|
Hence, the parent function of g(x) = |x - 7| +6 is f(x) = |x|
The reflectionWhen f(x) is reflected across the x-axis, we have:
f'(x) = -|x|
When f(x) is reflected across the y-axis, we have:
f'(x) = |x|
Stretching and CompressionWhen f(x) is stretched horizontally by a factor k
g'(x) = |kx|
When f(x) is stretched vertically by a factor k
g'(x) = k|x|
Horizontal ShiftWhen f(x) is shifted horizontally by k units
f'(x) = |x ± k|
Vertical ShiftWhen f(x) is shifted vertical by k units
f'(x) = |x| ± k
See attachment for the graph of g(x)
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Can someone help me with these problems and show work please !!
Answer:
I have just wrote answers
The average age of 4 children is 15 yrs . if the ages of their parents are added , their average age is 25 .find the age of their father if he is 4 yrs older than is wife
The age of the father is 57 years old
Calculating mean of a populationTotal age = Average age x Population
Average of the four children = 15
Population = 4
Total age of the four children = 15 x 4
Total age of the four children = 60 years
If the parents are added:
Population = 6
Average age = 25
Total age = 25 x 6
Total age = 150 years
Total age of the parents = 150 - 60
Total age of the parents = 110 years
The father is 4 years older than his wife
Let the age of the father be x
The age of the wife = x - 4
x + x - 4 = 110
2x = 114
x = 114/2
x = 57
Therefore, the age of the father is 57 years old
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Use the drop-down menus to complete the proof. by the unique line postulate, you can draw only one segment,
The reflection of BC over I is shown below.
What is reflection?A reflection is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is known as the reflection's axis (in dimension 2) or plane (in dimension 3). A figure's mirror image in the axis or plane of reflection is its image by reflection.See the attached figure for a better explanation:
1. By the unique line postulate, you can draw only one line segment: BC
Since only one line can be drawn between two distinct points.2. Using the definition of reflection, reflect BC over l.
To find the line segment which reflects BC over l, we will use the definition of reflection.3. By the definition of reflection, C is the image of itself and A is the image of B.
Definition of reflection says the figure about a line is transformed to form the mirror image. Now, the CD is the perpendicular bisector of AB so A and B are equidistant from D forming a mirror image of each other.4. Since reflections preserve length, AC = BC
In Reflection the figure is transformed to form a mirror image.Hence the length will be preserved in case of reflection.Therefore, the reflection of BC over I is shown.
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The question you are looking for is here:
C is a point on the perpendicular bisector, l, of AB. Prove: AC = BC Use the drop-down menus to complete the proof. By the unique line postulate, you can draw only one segment, Using the definition of, reflect BC over l. By the definition of reflection, C is the image of itself and is the image of B. Since reflections preserve , AC = BC.
The graph below shows the height of an object that has been launched off a 45 foot high wall. Approximately what is the maximum height this ball will reach?
A) 4.6 feet
B) 45 feet
C) 2 feet
D) 109 feet
The maximum height of the ball that is displayed by the graph is: D. 108 feet.
What is a Graph?A graph is a statistical diagram that displays the relation between two variables. One of the variables is plotted on the x-axis (horizontal axis) against the other variable on the y-axis (vertical axis).
The variable on the x-axis (horizontal axis) is the input, while the variable on the y-axis (vertical axis) is the output.
Considering the given graph in the image above, we have the following variables:
On the x-axis (horizontal axis): time which is the input
On the y-axis (vertical axis): height of the ball which is the output.
Thus, the peak of the line represents the maximum height the ball reaches. The maximum height which is the peak is approximately 109 feet.
Therefore, the maximum height is: D. 109 feet.
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Answer:
109 feet
Step-by-step explanation:
just took the lesson
help! what do i do
In quadrilateral LMNO, LO ∥ MN.
Quadrilateral L M N O is shown.
What additional information would be sufficient, along with the given, to conclude that LMNO is a parallelogram? Check all that apply.
ML ∥ NO
ML ⊥ LO
LO ≅ MN
ML ≅ LO
MN ⊥ NO
The additional information which would be sufficient to conclude that LMNO is a parallelogram is; ML ∥ NO, LO ≅ MN, and ML ≅ LO.
What information renders LMNO a parallelogram?The condition for a quadrilateral to be a parallelogram is that; the opposite pairs must be parallel and consequently opposite pairs are congruent as they have equal length measures.
On this note, it can be concluded that the additional information which would be sufficient are; ML ∥ NO, LO ≅ MN, and ML ≅ LO.
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(A.) ML ∥ NO,
(C.) LO ≅ MN.
Have a great day and hydrate!! <3
A square has an area of 49 square inches. how long are its sides
Answer:
Step-by-step explanation:
We know that,
Area of a square = l^2
so in this case, we form an equation:
l^2=49 square inches
Now taking square root on both sides
[tex]\sqrt{l}[/tex]^2=[tex]\sqrt{49}[/tex]
l=7 inches
so each side is 7 inches
Hope that helps
Answer:
7 inStep-by-step explanation:
A square has an area of 49 square inches. how long are its sides
A = l²
inverse formula
l = √A
l = √49
l = 7 in
When calculating correlation and regression both sets of data must be __________
When calculating correlation and regression both sets of data must be Statistical.
According to the statement
we have to find the type of data when we calculate the correlation and regression both sets.
so, The difference between these two statistical measurements is that correlation measures the degree of a relationship between two variables (x and y), whereas regression is how one variable affects another.
And when we calculate both then data sets must be a statistical data. because correlation summarizing direct relationship between two variables and regression predict or explain numeric response. So, without statistical data this is not possible to calculate correlation and regression both sets.
so, When calculating correlation and regression both sets of data must be Statistical.
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For every 5 employees there must be 3 supervisors. if there are a total company size of 160 people how many supervisors are needed
Answer:
Step-by-step explanation: