The distance between the cities on the map is given by the equations
a) The distance of 50km = ( 1/3 ) cm
b) The distance of 280km = ( 1 13/15 ) cm
c) The distance of 142 1/2 km = ( 19/20 ) cm
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the distance on the map be represented as A
Now , the equation will be
The scale on the map is given by 1/2 cm = 75 km
So , 1 km = ( 1/2 ) / 75 cm
1 km = ( 1/150 ) cm
a)
when the distance = 50 km
The distance on the map = 50 x ( 1/150 ) cm
The distance on the map = ( 1/3 ) cm
b)
when the distance = 280 km
The distance on the map = 280 x ( 1/150 ) cm
The distance on the map = ( 1 13/15 ) cm
c)
when the distance = 142 1/2 km
The distance on the map = 142 1/2 x ( 1/150 ) cm
The distance on the map = ( 19/20 ) cm
Hence , the equation is solved
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IREADY MATH AREA QUESTIONS PLS HELP TTYYY!!
A circle has a diameter of 10 cm. A rectangle has a length of 10 cm and a width of 5 cm.
Determine how the areas of the circle and the rectangle are related.
Use the drop-down menus to describe how the areas are related.
Area of circle: A = r²
1) The rectangle's length is equal to ______of the circle,
THIS BLANKS OPTION CHOICE:
A) the radius
B) the diameter
C) the circumference
D) half the circumference
E) twice the circumference
2) while the The rectangle's length is equal to rectangle's width is equal to _______. the circle.
THE BLANKS OPTION:
A) the radius
B) the diameter
C) the circumference
D) half the circumference
E) twice the circumference
3) So, the area of the circle is _______ of the Pick of area of the rectangle.
THE BLANK ANSWER CHOICES:
A) one fifth
B) two fifths
C) one half
D) twice
Answer:
The rectangle's length is equal to the diameter of the circle.while the rectangle's width is equal to half the circumference.So, the area of the circle is approximately two times the area of the rectangle.Find the measure of angle x in the figure below: angle x⁰ angle 75⁰ 75⁰
a) 15⁰
b) 25⁰
c) 30⁰
d) 60⁰
the measure of the angle x is c)30°
Answer:
30 degrees
Step-by-step explanation:
In the bottom triangle,
Both angles are 75 degrees, so their sum is 75 + 75 = 150 degrees
The remaining angle is 180 - (sum of the two other angles)
= 180 - ( 75 + 75)
= 30 degrees
As this angle is a the vertically opposite angle to x, it will be equal to x
∴ x = 30 degrees
Consider the following input-output table. Row P Q R S
1 1 1 1 0
2 1 1 0 1
3 1 0 1 0
4 q 0 0 0
5 0 1 1 0
6 0 1 0 1
7 0 0 1 0
8 0 0 0 0
The output column, S, was created from the student ID 21444368 using the algorithm: - If ID digit n (left-to-right) is an even integer, place a 0 in S, row n (top-down) - If ID digit n (left-to-right) is an odd integer, place a 1 in S, row n (top-down) Create a similar table, but with S reflecting the result of the algorithm applied to your student ID (do this on scratch paper). On the quiz essay: 1. Record your student ID's column S as an ordered, horizontal list. For the example given, the list would be S=(0,1,0,0,0,1,0,0). 2. Write the disjunctive normal expression that would implement your student ID input/output table. Do not reduce the expression. Use the words "or." and "not" for the operators, and the letters P,Q,R, and S for the variables. For full credit show parentheses where required.
The output column, S, of the given input-output table was created from the student ID 21444368 using an algorithm where if the student ID digit is an even integer, a 0 is placed in the corresponding row of column S, and if the student ID digit is an odd integer, a 1 is placed in the corresponding row of column S.
Student ID: 81725225
P Q R S
1 1 1 0
1 1 0 1
1 0 1 1
0 1 0 0
0 0 1 1
0 1 1 0
0 0 0 1
Student ID: 81725225
P: The first digit of my student ID is 8 so it is an even integer, therefore I place a 0 in row 1 of column P.
Q: The second digit of my student ID is 1 so it is an odd integer, therefore I place a 1 in row 2 of column Q.
R: The third digit of my student ID is 7 so it is an odd integer, therefore I place a 1 in row 3 of column R.
S: The fourth digit of my student ID is 2 so it is an even integer, therefore I place a 0 in row 4 of column S.
The resulting table is:
P Q R S
1 1 1 0
1 1 0 1
1 0 1 1
0 1 0 0
0 0 1 1
0 1 1 0
0 0 0 1
The output column, S, of the given input-output table was created from the student ID 21444368 using an algorithm where if the student ID digit is an even integer, a 0 is placed in the corresponding row of column S, and if the student ID digit is an odd integer, a 1 is placed in the corresponding row of column S. The same algorithm was applied to my student ID 81725225, resulting in the table shown above.
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For the given decision algorithm, find how many outcomes are possible.
Step 1
Alternative 1: 1 outcome
Alternative 2: 5 outcomes
Step 2
Alternative 1: 4 outcomes
Alternative 2: 3 outcomes
Alternative 3: 1 outcome
The total number of outcomes that are possible are given as follows:
48 outcomes.
How to obtain the number of outcomes?The number of outcomes for each case is obtained using the Fundamental Counting Theorem, with the multiplication of the number of outcomes for each trial.
The number of outcomes in each step is given as follows:
Step 1: 1 + 5 = 6 outcomes.Step 2: 4 + 3 + 1 = 8 outcomes.Hence the total number of outcomes that are possible are obtained as follows:
N = 6 x 8
N = 48.
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identify the nominal categorical variables in this study. (select all that apply.) A. voting yes percentage B. country C. issue type D. city E. year F. there are no nominal categorical variables.
Nominal categorical data is a categorical variable with two or more values, with no order. The examples of nominal categorical data here are the issue type, country, city.
Categorical data can be divided as two as per the variables. They are nominal and ordinal. In nominal categorical data, there will be two or more data points, but they are not ranked. The hair color can be red/blond/brown/black etc. But these cannot be ranked by taking one over the other.
In ordinal categorical data, there we can assign an order on the data points. Like grading system in marks of students, size comparison like large, medium, small. Here we could rank these in order.
Year can sometimes be nominal and sometimes ordinal. It is as per the context. If we are using it to calculate time it is ordinal.
So here we could not rank of variables in country, issue type, city. So all are nominal categorical data.
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kendra has $7.35 in her purse. she needs at least $2.87 more to buy a special bead. what is the total amount, x, she needs for the bead? which inequalities can be used to represent the situation? select all that apply.
Answer:
$10.22
Step-by-step explanation:
The total amount Kendra needs for the bead is $2.87 more than the amount she currently has in her purse, which is $7.35. Therefore, x = $7.35 + $2.87 = $10.22.
The inequality that represents this situation is:
x ≥ $7.35 + $2.87
x ≥ $10.22
Another way to represent this would be:
x - $7.35 ≥ $2.87
x ≥ $10.22
Both of these inequalities represent the same thing, that x (the total amount Kendra needs for the bead) must be greater than or equal to $10.22.
Please help me with this question.
Can someone help me with question number 3 and 4 please?
3) The components of composition between two functions are [tex]f(n) = n^{2}+ 5^{n}[/tex] and g(n) = n² + 1.
4) The composition between functions g(n) = √(4 + n + √n) and h(n) = n⁴ + 8 is the function (g ° h)(n) = √[4 + n⁴ + 8 + √(n⁴ + 8)].
How to apply composition between functions
In this problem we find two cases of composition between functions, that is, a operation between two functions, so that the input of the first function (f(x)) is substituted by the entire second function (g(x)), that is:
f ° g(x) = f [g(x)]
Case 3 - If we know that [tex](f\,\circ \,g) (n) = (n^{2}+1)^{2}+5^{n^{2}+1}[/tex], then the components of the composition of functions are:
[tex]f(n) = n^{2}+ 5^{n}[/tex]
g(n) = n² + 1
Case 4 - If we know that g(n) = √(4 + n + √n) and h(n) = n⁴ + 8, then the composition between the two functions is:
(g ° h)(n) = √[4 + n⁴ + 8 + √(n⁴ + 8)]
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Find the volume of the solid generated by revolving the region bounded by the given curve and lines about the x-axis.
y=e^(x-9)
y=0, x=9, x= 10
According to the problem the volume of the solid generated by revolving the region is .
What is volume?The amount of space a thing occupies is its volume, which is expressed in cubic units. It is a three-dimensional measure of an object's size, as opposed to its length and width, which are considered two-dimensional measures. Volume is commonly used to measure the capacity of containers, such as barrels, tanks, and boxes.
This is a solid of revolution generated by revolving the region bounded by the curves y=[tex]e^{(x-9)}[/tex] and y=0 and the lines x=9 and x=10 about the x-axis. To find the volume of this solid, we can use the method of washers.
The formula for the volume of a solid of revolution generated by revolving a region bounded by two curves about the x-axis is given by:
V = π∫[tex]b a [((f(x))^{2} - (g(x))^{2}] dx[/tex]
In this problem, f(x) = [tex]e^{(x-9)}[/tex] and g(x) = 0. Thus,
V = π∫10 9 [tex]e^{(2x-18)} dx[/tex]
Integrating, we get
V = π [tex][\frac{e^{(2x-18)}}{2}] 10^{9}[/tex]
V = π(157.087 - 1.1102)/2
V = 78.488π [tex]cm^{3}[/tex] equal to the integral of the area of the region over the interval [9, 10] with respect to x.
The area of the region is equal to the integral of y from 9 to 10. Thus, the volume of the solid generated by revolving the region is equal to the double integral:
V = ∫[tex]9^{10}[/tex] ∫[tex]0^{e^{(x-9)} } dy dx[/tex]
Evaluating the integral yields:
V =∫ [tex]9^{10} e^{(x-9)} dx[/tex]
[tex]= \frac{e^{(x-9)} }{9^{10} }\\ =e^{1} -1\\ =2.718-1 =1.718[/tex]
Therefore, the volume of the solid generated by revolving the region is 1.718.
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The price for peaches at Smith’s Grocery is usually $3.60 per pound. This week, the peaches are on sale and the price for peaches is 20% less than usual. What is the price per pound of peaches this week?
Answer:
$2.88
Step-by-step explanation:
formula → 3.6 × (1 - 20%)
→ 3.6 × (1 - 0.2)
calculate sum or difference
→ 3.6 × 0.8
→ = 2.88
4. Determine the equation of the parabola with x-intercepts
a) -4 and 3, and that passes through (2, 7)
b) 0 and 8, and that passes through (-3, -6)
c) √7 and - √7, and that passes through (-5, 3)
5. Determine the equation of the parabola with vertex
a) (-2, 5) and that passes through (4, -8)
Answer:
4.
a.) -7/6 (x + 4)(x - 3) = y
b.) -6/121 (x-8)^2 = y
c.) 1/6 (x-sqrt 7)(x + sqrt 7) = y
5.
a.) -13/36 (x+2)^2 + 5 = y
Step-by-step explanation:
4. The intercept form of a quadratic equation is
[tex]y=a(x-p)(x-q)[/tex], where a is a number determining things like if the parabola opens up or down and how wide or narrow the parabola, while p and q are the x-intercepts.
Because we're given the x-intercepts and a point on the parabola, we can simply plug everything in and solve for a to find the equation of the parabola:
a.):
[tex]y=a(x-(-4))(x-3)\\y=a(x+4)(x-3)\\\\7=a(2+4)(2-3)\\7=a(6)(-1)\\7=-6a\\-7/6=a\\\\y=-7/6(x+4)(x-3)[/tex]
b.):
[tex]y=a(x-8)^2\\\\-6=a(-3-8)^2\\-6=a(-11)^2\\-6=121a\\-6/121=a\\\\y=-6/121(x-8)^2[/tex]
c.):
[tex]y=a(x-\sqrt{7})(x-(-\sqrt{7}))\\ y=a(x-\sqrt{7})(x+\sqrt{7})\\ \\ 3=a(-5-\sqrt{7})(-5+\sqrt{7})\\ 3=a(25-5\sqrt{7}+5\sqrt{7}-7)\\ 3=a(25-7)\\ 3=18a\\ 3/18=1/6=a\\ \\ 1/6(x-\sqrt{7})(x+\sqrt{7})=y[/tex]
5. The vertex form of a quadratic equation is
[tex]y=a(x-h)^2+k[/tex], where a is the same type of number as in the intercept form and (h, k) is the vertex.
Like the intercept form of the equation, we're given everything except a and thus we can plug in what we have and solve for a:
[tex]y=a(x-(-2))^2+5\\y=a(x+2)^2+5\\\\-8=a(4+2)^2+5\\-8=a(6)^2+5\\-8=36a+5\\-13=36a\\-13/36=a\\\\y=-13/36(x+2)^2+5[/tex]
The perimeter of a triangular park shown on the right is 11x-6.
What is the missing length?
Find the error and describe it
Answer:
Step-by-step explanation:
the error, based on the question, the eqution has 4 solution for the X
listed as (4, -4, -3, 1)
as X solution in verticial , put all the X value into the F(x) to find the Y valuein horizontal value
2x-y≤-3
graph the inequality
Therefore , the solution of the given problem of inequality graph comes out to be the graph of the inequality 2x - y ≤ -3 is a line that cuts through the x-y plane
What do you mean by inequality graph?An inequality graph is a graph that represents the solution set of an inequality, showing the values of the independent variable (usually represented on the x-axis) for which the inequality is true.
Here,
An inequality can be represented graphically by shading the region on a coordinate plane that satisfies the inequality. The direction of shading (above or below the line) depends on the inequality symbol.
The graph of the inequality 2x - y ≤ -3 in the x-y plane can be plotted by finding the boundary line for the inequality and shading the region that satisfies the inequality. To do this, we can start by setting the equation 2x - y = -3 and finding the x- and y-coordinates of the points on the line. Then we can plot these points and draw the line that connects them.
Next, we will determine which side of the line represents the solution set. To do this, we can pick a point that is not on the line and substitute its x- and y-coordinates into the inequality. If the inequality is true for the point, we shade the region that contains the point. If the inequality is false, we shade the region that does not contain the point.
So the graph of the inequality 2x - y ≤ -3 is a line that cuts through the x-y plane and is shaded on one side. The shaded region represents all the x- and y-coordinates that satisfy the inequality.
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what is the constant in 8b + 3.2
the length of a rectangle is (2x + 3) ft. and the width is (x - 4) ft. Find the perimeter and area in terms of x.
The perimeter of the rectangle is (6x - 2)ft and the area of the rectangle is (2x^2 - 5x - 12) square ft.
What is a rectangle?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral.
We are given that the length of a rectangle is (2x + 3) ft. and the width is
(x - 4) ft.
We know that perimeter of rectangle = 2(Length + Width)
So,
⇒Perimeter = 2(2x + 3 + x - 4)
⇒Perimeter = 2(3x - 1)
⇒Perimeter = (6x - 2)ft
We know that area of rectangle = Length * Width
So,
⇒Area = (2x + 3) * (x - 4)
⇒Area = 2x^2 - 8x + 3x - 12
⇒Area = (2x^2 - 5x - 12) square ft
Hence, the perimeter of the rectangle is (6x - 2)ft and the area of the rectangle is (2x^2 - 5x - 12) square ft.
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How do I complete this
Answer:
Point A: y = 552
Point B: y = 123
Step-by-step explanation:
y = -13x - 46
A: x = -46
y = -13(-46) - 46 ==> plugin -46 for x in y = -13x - 46
y = 598 - 46
y = 552
A: x = -13
y = -13(-13) - 46 ==> plugin -13 for x in y = -13x - 46
y = 169 - 46
y = 123
Original discount price of a puppy $169.95. Discount 45%. Tax 6%.
Answer:
99.08
Step-by-step explanation:
169.95*(1-45%)*(1+6%) = 99.08
Answer:
400.33
Step-by-step explanation:
haul price= 377.67
tax=22.66
377.67+22.66=400.33
[tex](\frac{3p}{7}+\frac{7}{6p})^2 -(\frac{3p}{7}-\frac{7}{6p})^2[/tex]
Solve with steps please
ty :)
Answer:
The expression simplifies to:
[tex](\frac{3p^2 + 49}{42p})^2 -(\frac{3p^2 - 49}{42p})^2[/tex]
Using the difference of squares identity, the expression further simplifies to:
[tex]\frac{98p}{42p^2} = \frac{98}{42p}[/tex]
Step-by-step explanation:
Lara is a wildlife researcher. They were analyzing the mean and median lengths of
7
77 fish their team had observed. The fish all had different lengths between
15
cm
15cm15, start text, c, m, end text and
33
cm
33cm33, start text, c, m, end text.
Lara found out that they were misreading the longest length. It was actually
88
cm
88cm88, start text, c, m, end text, not
33
cm
33cm33, start text, c, m, end text.
How will this length increasing affect the mean and median?
Using their concepts, we have that the mean will be increased and the median will remain constant.
What is the mean of a data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile, which is the middle value of the distribution.
The largest value is the 7th observation, therefore it will be included in the calculation of the mean.
Since this observation have an increased value, the sum of all observations will be increased while the number of observations remains constant,
So the mean will be increased.
Hence, for a distribution of 7 observations, we have that:
The first three observations are the first half.
The 4th observation is the median.
The last three observations are the second half.
Here only the last observation changes, not the fourth, hence the median remains constant.
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What’s the measure of AC?
What’s the measure of AC’
What’s the measure of C’B
The measure of AC is 12 units.
The measure of AC' is 6 units
The measure of C'B' is 10.5 units.
How to find the measure of a triangle?The midsegment of a triangle is a line connecting the midpoints between two sides of a triangle. Therefore, the segment is parallel to the third side and half of it.
Therefore, applying mid segment principle,
C'B' = 1 / 2 (21)
C'B' = 21 / 2
C'B' = 10.5 units
Hence, using mid segment principle
AC' = CC' = 6
Therefore,
AC = 6 + 6 = 12 units
using mid segment principle,
AC' = 6 units
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The function f(x) = 1.1x³-36x² +260x + 550 below models the number of discharges from the military, f(x), of active-duty gay service members under the "don't ask, don't tell years after 1994. Complete parts a and b.
The slope of the secant line is 137.
What is the rate of change of discharges between 1994 and 1995?The rate of change of discharges between 1994 and 1995 can be determined by taking the first derivative of the function, f'(x) = 3.3x² - 72x + 260. When x = 1994, the rate of change is -6. This means that the discharges decreased by 6 from 1994 to 1995.
The average rate of change of discharges from 1994 to 2000 can be determined by taking the average of the first derivative of the function for x = 1994 and x = 2000. When x = 1994, the first derivative is -6 and when x = 2000, the first derivative is 148. The average rate of change of discharges from 1994 to 2000 is therefore 71.
f(0) = 1.2 (0)3-36 (0)2+262/0)+570 = 570
+(4) = 1-2(4)3-36(4)2 +262 (4) +570 = 1118.8
Slope of the secant line = [tex]\dfrac{1118.8 - 570}{4-0}[/tex]
Slope of the secant line = 137
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Given the following information, determine which lines , if any , are parallel.State the converse that justifies your answer.
Reversed Alternate Interior Angles.The theorem states that j || k.J and K converse different internal angles.
Why do parallel angles exist?j and k angles.The Converse of Corresponding Angles Postulate leads to the expression j || k.
2Angles 2 and 5 make up the alternating inner angles of the lines j and k.Angle 2 equals Angle 5 if
Reversed Alternate Interior Angles.The theorem states that j || k.
J and K converse different internal angles.
3. Angle 3 also equals Angle 10.
The exterior angles of the lines l and m are, respectively, Angle 3 and
Angle 10.
The Converse of Alternate Exterior Angles Theorem states that angle 3 equals angle 10, so l || m.
Reversed Alternate Interior Angles.The theorem states that j || k.J and K converse different internal angles.
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A piecewise function f (x) is defined by f of x is equal to the piecewise function of 2 to the power of the quantity x plus 1 end quantity minus 3 for x is less than or equal to 2 and the quantity 10 over x for x is greater than 2
Part A: Based on the graph of f (x), what is the range? (5 points)
Part B: Determine the asymptotes of f (x). (5 points)
Part C: Describe the end behavior of f (x). (5 points)
Part A: The range of a function is the set of all possible outputs (y-values) for the given domain of the function. In this case, the domain of f(x) is all real numbers. We can find the range of f(x) by analyzing the two different parts of the piecewise function:
For x <= 2, f(x) = 2^(x+1) - 3. The minimum possible output for this function is y = -1 (when x = -1) and the maximum possible output is y = 3 (when x = 0).
For x > 2, f(x) = 10/x. The minimum possible output for this function is y = 0 (as x approaches infinity) and the maximum possible output is y = 10 (when x = 2)
So, the range of f(x) is [-1, 10].
Part B: The asymptotes of a function are the lines that the graph of the function approaches but never touches. In this case, the graph of f(x) has a vertical asymptote at x = 0, because the function is not defined at x=0.
Part C: The end behavior of a function is the behavior of the function as the input (x) approaches positive or negative infinity. In this case, the function f(x) = 10/x as x > 2, as x approaches positive infinity the output(y) approaches 0, and as x approaches negative infinity the output(y) does not exist. Therefore, the end behavior of f(x) is that it approaches 0 as x approaches positive infinity.
 When solving equations - or "undoing" the operations to get "x" by itself on one side of the equation - we use INVERSE OPERATIONS.
Match the operation with its inverse operation.
Column A
2
Addition
Multiplication
Square
Cube
Column B
a. Divide by 3
b. Cube root
Divide by 2
d. Square root
Subtraction
f.
Division
For given arithmetic operations, matching is as:
Addition - Subtraction
Multiplication - Division
Square - Square root
Cube - Cube root
What are arithmetic operations?Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.
These basic mathematical operations (+, -, ×, and ÷) we use in our everyday life. Whether we need to calculate the annual budget or distribute something equally to a number of people, for every such aspect of our life, we use arithmetic operations.
The four basic arithmetic operations in Maths, for all real numbers, are:
Addition (Finding the Sum; ‘+’)
Subtraction (Finding the difference; ‘-’)
Multiplication (Finding the product; ‘×’ )
Division (Finding the quotient; ‘÷’)
As, inverse operations inverses the actual value
Addition - Subtraction
Multiplication - Division
Square - Square root
Cube - Cube root
hence, they will be matched accordingly.
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what is the correct answer
The required meaning of the word sped is A special education student.
What is a noun?The noun is defined as any word used to identify any of class of people, places, or things are called noun.
Here,
Sped is a noun word that tends is meaning toward education, which has meaning as special education student. The plural of sped is speds while in british english sped is used as a verb past tense and past participle of speed.
Thus, the required meaning of the word sped is A special education student.
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27. (a) Verify that if c is a constant, then the function defined piecewise by So = for x =c, y(x) = (x – c)2 for x > 0 satisfies the differential equation y' = 2 y for all x (in- cluding the point x = c). Construct a figure illustrating the fact that the initial value problem y' = 2/7, y(0) = 0 has infinitely many different solutions. (b) For what values of b does the initial value problem y' = 2/y, y(0) = b have (i) no solution, (ii) a unique solution that is defined for all x?
(a) Verifying that y(x) = (x - c)^2 satisfies the differential equation y' = 2y:
To verify that the function y(x) = (x - c)^2 satisfies the differential equation y' = 2y, we can find the derivative y' and substitute it back into the equation:
y' = d/dx [(x - c)^2] = 2(x - c)
So, y' = 2y if and only if 2(x - c) = 2y, which can be simplified to x - c = y.
Therefore, y(x) = (x - c)^2 satisfies the differential equation y' = 2y for all x, including x = c.
(b) Values of b for which the initial value problem y' = 2/y, y(0) = b has no solution or a unique solution:
(i) No solution: If b = 0, the initial value y(0) = 0 and the denominator of the right-hand side of the differential equation y' = 2/y would be 0, making the equation undefined at that point. Therefore, the initial value problem y' = 2/y, y(0) = 0 has no solution.
(ii) Unique solution defined for all x: For all other values of b (b ≠ 0), the initial value problem y' = 2/y, y(0) = b has a unique solution that can be found using standard methods of solving initial value problems. This solution will be defined for all x.
The figure illustrating the fact that the initial value problem y' = 2/7, y(0) = 0 has infinitely many different solutions would show a family of curves that are all solutions to the differential equation y' = 2/7, with different starting values y(0) leading to different curves. This demonstrates that there are infinitely many different solutions to the initial value problem.
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I bet no one can do this. Find x, y, and z such that x³+y³+z³=k, for each k from 1 to 100
Answer:
It is a well-known fact that for any natural number k, there are no non-zero integers x, y, and z that satisfy x^3 + y^3 + z^3 = k, unless k = 1 or k = 8. This is known as Fermat's Last Theorem.
However, for k = 1, we have the solution (x, y, z) = (1, 0, 0) and for k = 8, we have the solution (x, y, z) = (2, −1, 1)
It's important to note that this problem is a complex mathematical problem, which was solved only by Andrew Wiles in 1994 using advanced mathematical theories such as Iwasawa theory and Galois representations.
q>d, if = 3 pls tell me the right answer
Sorry but i can't really read the writing so... Maybe try take a pic again
During her first week of work, a physical therapist estimated that therapy sessions would
last about 30 minutes each. However, the sessions take longer than expected. On one
day, the sessions lasted for 47 minutes, 53 minutes, 32 minutes, 50 minutes, and 45
minutes. How long should the physical therapist expect to spend at a therapy session?
Round to the nearest whole number.
If during her first week of work, a physical therapist estimated that therapy sessions would last about 30 minutes each. The time the physical therapist expect to spend at a therapy session is: about 45 minutes.
How to find the mean ?In order to find the expected duration of a therapy session, you can calculate the mean (average) of the durations for the five sessions.
The mean is calculated by adding the durations of all the sessions and then dividing by the number of sessions.
Mean = (47+53+32+50+45) / 5
Mean = 227/5
Mean = 45 minutes
Therefore the physical therapist should expect to spend about 45 minutes on average for each therapy session.
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