Therefore , the solution of the given problem of function comes out to be it is compatible with P(J(y)) = 1/3J(y) +4.
What is meant by the word function?Math is a science that studies numbers, their variants, math and the tissues in the area, shapes, and both their real and possible locations. 'Function' refers to the relationship between a set of inputs, which each have a corresponding output. A function is a relationship between inputs in which each input yields a single variable, distinct output.
Here,
Given:
The quantity of paintings is returned by the function P, which accepts a number of months as an argument.
The function J returns the number of weeks in a year after accepting an undefined parameter.
P(weeks annually) = P(J(y)) seems to be the composites function that will provide the annual number of paintings.
Choice C is compatible with P(J(y)) = 1/3J(y) +4.
Therefore , the solution of the given problem of function comes out to be it is compatible with P(J(y)) = 1/3J(y) +4.
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While on vacation you visit a canyon. you shout at the far wall and the sound returns after 6.00 seconds. the speed of sound that day was 345 m (about the height of the empire state building)/s. how far was it to the far side of the canyon? the sound you made had a frequency of 600 hz. what was its wavelength? what was the period?
The distance travelled is 1035 meters, The period T is 1.67m/s and The wavelength is 0.575 meters.
What is wavelength?Because sound is a wave, we can use the proper definitions of the terms to derive the relationship between the wavelength, frequency, and speed of a wave. The wavelength is the distance travelled by the wave in one time period of its cycle, whereas the frequency is the number of cycles per second.
Formula used:
Speed = Distance/time
Frequency of wave = 1/Time period of the wave
Wavelength = Distance travelled by the wave in one time period
Given,
a)The distance travelled is 2d,
where d is the distance to the wall
Thus d = 345 × 6/2= 1035 m
b)The frequency is 600 Hz thus the period T = 1/f= 1.67ms
c)The wavelength λ = Velocity/Frequency
= 345/600
= 0.575 meters
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Chloe is trying to find three consecutive, positive integers such that six times the largest is equal to the twice sum of the two smaller integers.
set up an equation that models the numbers chloe is trying to find
An equation that models the numbers is x, x+1, x + 2
The term equation is known as a condition on a variable such that two expressions in the variable have equal value
Here we know that Chloe is trying to find three consecutive, positive integers such that six times the largest is equal to the twice sum of the two smaller integers.
Then the given parameters are written as the three consecutive positive numbers Chloe is trying to find are x, x+1, x + 2
Here we have the conditions of the three positive numbers are written as,
=> 6 × (x + 2) = 2 × (x + x + 1)
Now, we have to check if the three consecutive numbers can be 4, 5, and 6 by substituting the values as written as,
=> x + 2 = 6
=> x + 1 = 5
Then the value of x is 4
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a chef uses 800g from a 5kg bag of flour.What percentage of the flour is left?
Answer:
80% of the flour is left.
Answer:
I hope may answer is correct! I am sorry if it is not!
The chef used 800g out of a 5kg bag of flour, so the amount of flour left is 5,000g - 800g = 4,200g. To find the percentage of flour left, divide the amount of flour left by the total amount of flour and multiply by 100: (4,200g / 5,000g) * 100 = 84%. So 84% of the flour is left.
find the value of p q and r
The value of p, q, and r cannot be found without more information about what the variables represent and any equations or relationships that they may be a part of.
Please provide more context or information about the problem you are trying to solve.
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Solve for X, Leave in simplest radical
We know,
[tex] \cos(angle) = \frac{base}{hypotenuse} [/tex]
Here, the angle is 45°. Base = x, Hypotenuse = √10
We know,
[tex] \cos(45) = \frac{1}{ \sqrt{2} } [/tex]
Therefore,
[tex] \cos(45) = \frac{x}{ \sqrt{10} } \\ = > \frac{1}{ \sqrt{2} } = \frac{x}{ \sqrt{10} } \\ = > x = \frac{ \sqrt{10} }{ \sqrt{2} } = \sqrt{5} [/tex]
Answer:
√5
Hope it helps.
The area of two similar triangles are 18cm^2 and 8cm^2. ONe of the sides of the first triangle is 4.5cm. What is the length of the corresponding side of the other triangle.
Answer:
If two triangles are similar, the ratio of their corresponding side lengths is the same as the ratio of their areas.
We know that the area of the first triangle is 18 cm^2, and the area of the second triangle is 8 cm^2. So, the ratio of their areas is 18/8 = 9/4
We also know that one of the sides of the first triangle is 4.5 cm.
So the ratio of the corresponding side of the second triangle to the first triangle is:
(length of corresponding side of second triangle) / 4.5 = 9/4
We can cross-multiply and solve for the length of the corresponding side of the second triangle:
4.5 * (9/4) = 9 * (9/4) / 4 = 9 * 2.25 / 4 = 20.25 / 4 = 5.0625 cm
So, the length of the corresponding side of the second triangle is 5.0625 cm.
(03.05 MC)
A moon's elliptical orbit around a planet is modeled by the equation 225x2 +576y2 = 176,400, where distance is measured in megameters
(Mm). If the planet is the center of the orbit's path, what is the maximum distance between the planet and its moon?
As, the moon has an elliptical orbit around a planet, the maximum distance between the planet and its moon is 88.54 Mm.
What is an elliptical orbit?
When an object moves around another object in an oval shaped path (ellipse), it is known to be revolving in an elliptical orbit.
The standard form of the equation of an ellipse with center at the origin (0,0) and x - axis major axis is given by
x²/a² + y²/b² = 1
Now,
Given that a moon's elliptical orbit around a planet is modeled by the equation 225x² + 576y² = 176,400, where distance is measured in megameters (Mm). and the planet is the center of the orbit's path.
Since the equation of the path is the equation of an ellipse, we write it in standard form
As standard form of the equation of an ellipse with center at the origin (0,0) and x - axis major axis is
x²/a² + y²/b² = 1 (1) where
a = vertex of major axis and
b = vertex of minor axis
So, converting 225x² + 576y² = 176,400 into standard form, we have
225x² + 576y² = 176,400
225x²/1764,000 + 576y²/1764,000 = 176,400/1764,000
x²/7840 + y²/3062.5 = 1 (2)
Comparing equation (2) with (1), we have that
a² = 7840 and b² = 3062.5
⇒ a = √7840 = 88.54 and
⇒ b = √3062.5 = 55.34
Since a = 88.54 is greater than b = 55.34, so, a is the major axis, and the maximum distance between the planet and its moon is 88.54 Mm
So, the maximum distance between the planet and its moon is 88.54 Mm
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Since the moon's has an elliptical orbit around a planet, the maximum distance between the planet and its moon is 88.54 Mm
How to find the maximum distance between the planet and its moon?
Given that a moon's elliptical orbit around a planet is modeled by the equation 225x² + 576y² = 176,400, where distance is measured in megameters (Mm). and the planet is the center of the orbit's path.Since the equation of the path is the equation of an ellipse, we write it in standard form.Equation of ellipse in standard formThe standard form of the equation of an ellipse wth center at the origin (0,0) and x - axis major axis is given byx²/a² + y²/b² = 1 (1) where
a = vertex of major axis and
b = vertex of minor axis
o, converting 225x² + 576y² = 176,400 into standard form, we have
225x² + 576y² = 176,400
225x²/1764,000 + 576y²/1764,000 = 176,400/1764,000
x²/7840 + y²/3062.5 = 1 (2)
Comparing equation (2) with (1), we have that
a² = 7840 and b² = 3062.5
⇒ a = √7840 = 88.54 and
⇒ b = √3062.5 = 55.34
Since a = 88.54 is greater than b = 55.34, so, a is the major axis, and the maximum distance between the planet and its moon is 88.54 Mm
So, the maximum distance between the planet and its moon is 88.54 Mm
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The grid below contains the $16$ points whose $x$- and $y$-coordinates are in the set $\{0,1,2,3\}$:A square with all four of its vertices among these $16$ points has area $A$. What is the sum of all possible values of $A$
Therefore, 24 square units are the answer to the surface area problem that has been given.
What would this surface area actually mean?Shape is a term used to express how much total area a material's surface takes up. Surface area of a three-dimensional shape is determined by its surrounds added together. Surface area refers to a multi-total shape's surface area covering. A cube with five rectangular sides has a volume of water equal to the sum of the areas of each face. Alternately, you can get the box's dimensions by using the following formula: Surface (SA) equals twice twice twice twice.
Here,
The height of the square in the example is 5-2 = 3.
The base of the provided square is composed of units => 7 -(-1) units => 8 units.
The given square therefore contains an area equal 8 * 3 = 24 square units.
The preceding area problem must therefore be solved using 24 square units.
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Please help (leave answers in terms of pi.)
1. The area of the shaded part = 95π
2. The area of the half circle = 12.5π
3. the distance of the bicycle = 0.0675/π inches
4. The diameter of the circle = 9 unit
radius = 4.5
area = 20.25π unit²
What is area of a circle?A circle is simply a round shape that has no corners or line segments. It is a closed curve shape in geometry. The points of circle are at a fixed distance from the center.
The area of a circle = πr²
1. Area of the shaded part = area of big circle - area of small circle
= 12²π - 7²π
= 144π - 49π
= 95π
2. area of semi circle = 1/2πr²
= 1/2×5²× π
= 25π/2
= 12.5π unit²
3. The distance moved by the biycle =
S = tetha/r
tetha = 2π×100 = 200π
S = 200π/13.5
S = 14.8π inches
4. c = πd
c = 9π
d = 9
r =d/2 = 9/2 = 4.5
Area = 4.5²π
A = 20.25π unit²
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What is a formula for the nth term of the
given sequence?
an = 125(³)¯n
an = 125(³)n-1
125 (-/-)¹-1
An
=
75, 45, 27...
An =
125 (5) n
Answer:
Step 1: The nth term of an arithmetic sequence is given by an = a + (n – 1)d. So, to find the nth term, substitute the given values a = 2 and d = 3 into the formula. Step 2: Now, to find the fifth term, substitute n = 5 into the equation for the nth term.
Determine the slope of a line perpendicular to -3x + 5y = 20
The slope of the original line is 3/5.
What is the slope?
The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).
The slope of a line perpendicular to another line can be found by taking the negative reciprocal of the slope of the original line.
To find the slope of the original line, we need to convert the equation to the slope-intercept form (y = mx + b), where m is the slope.
To convert, we'll isolate y:
-3x + 5y = 20
5y = 3x + 20
y = (3/5)x + 4
The slope of the original line is 3/5. The slope of the line perpendicular to this line would be the negative reciprocal of this slope, or -5/3.
Hence, The slope of the original line is 3/5.
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Over the past year, becky has enjoyed 7 of the 9 movies recommended by her local newspaper. she wants to design a spinner she can use to simulate this situation and predict the probability that she will enjoy each of the next 5 movies the paper recommends.
how should becky divide her spinner to best simulate this situation?
Over the past year, Becky has enjoyed watching 7 out of the 9 movies recommended by her local newspaper. She aims to design a spinner that she can use to simulate this scenario and predict the probability that she will be going to enjoy each of the next 5 movies recommended by the newspaper. Becky should divide her spinner into 9 equal-sized sections in order to best simulate this situation.
Becky enjoyed 7 of the 9 movies So the probability of enjoying movies = 7/9Becky needs to divide her spinner into 9 equal-sized divisions where7 divisions are indicators of the movies she enjoyed2 divisions are indicators of the movies she did not like.Hence, Becky should divide her spinner into 9 equal-sized sections in order to best simulate this situation.
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Given a right triangle, find the measures of all of the angles, if one angle is a right angle (90 degrees) and the measure of the second angle is six less than seven times the measure of the third angle. This is represented by the equation 7x - 6 x
The measurements of all the angles, if one angle is a right angle (90 degrees), and the second angle's measurement is six times smaller than the third angle's measurement of 180 degrees.
As per the data given in the above question are as bellow,
The data provided are as bellow.
The known angle (90) a pronumeral of r.
give the second angle (the one with all the subtraction) a pronumeral or x.
The third angle the pronumeral of y
x = 7y - 6
90 + x + y = 180
90 + 7y - 6 + y = 180
90 + 8y - 6 = 180
90 + 8y =186
8y = 96
y = 12.
the third angle is 12
so 12 + 90 = 102
the second angle must equal 88 to make it to 180
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Note the correct question is as bellow,
Given a right triangle, find the measures of all of the angles, if one angle is a right angle (90 degrees) and the measure of the second angle is six less than seven times the measure of the third angle. This is represented by the equation x=7y - 6
a conical water tank with vertex down has a radius of 10 ft at the top and is 24 ft high. if water flows into the tank at a rate of 20 ft3/min, how fast is the depth of the water increasing when the water is 16 ft de
The rate of increase of the depth of the water is 6.67 ft/min.
First, calculate the volume of the water tank:
Volume = (1/3) πr²h
Volume = (1/3) × 3.14 × 10² × 24
Volume = 7,040 ft³
Now calculate the rate of increase of the depth of the water:
Rate of increase of the depth = (Flow rate of water into tank / Volume of tank)
Rate of increase of the depth = (20 ft³/min / 7,040 ft³)
Rate of increase of the depth = 0.0028 ft/min
Finally, calculate the rate of increase of the depth of the water when the water is 16 ft deep:
Rate of increase of the depth = (Flow rate of water into tank / Volume of water)
Rate of increase of the depth = (20 ft³/min / 4,096 ft³)
Rate of increase of the depth = 0.0049 ft/min
Therefore, the rate of increase of the depth of the water when the water is 16 ft deep is 0.0049 ft/min, which is equivalent to 6.67 ft/min.
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Can anyone figure this out for me please?
Answer:
simple 5×-5 the answer divide by -5
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
-15
Step-by-step explanation:
im thinking +[-15] and [-15] are the same thing
What is the domain and range for this function?
10) statement: "two triangles with corresponding congruent angles are congruent." is this statement true or false? *
10) explain your answer to number 9. (statement: "two triangles with corresponding congruent angles are congruent." why is this true or false?) *
The statement, "two triangles with corresponding congruent angles are congruent," is true.
According to the Triangle Congruence Postulate, if two triangles have three pairs of corresponding congruent angles, then the triangles are congruent.
This means that if two triangles have three pairs of corresponding congruent angles, all six angles are congruent and the triangles are exactly the same size and shape.
Thus, the statement, "two triangles with corresponding congruent angles are congruent," is true.
Congruence is determined by the congruence of angles, sides, and the overall shape of the triangle. If two triangles have the same angles and sides, then they are considered to be congruent.
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Solve for X, Leave in simplest radical
The value of x using trigonometry is √6.
What is trigonometry ?The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.
The area of mathematics known as trigonometry examines the link between the ratios of a right-angled triangle's sides to its angles. Trigonometric ratios, such as sine, cosine, tangent, cotangent, secant, and cosecant, are employed to analyze this connection.
The measurement of angles and issues relating to angles are covered in the fundamentals of trigonometry. Trigonometry has three fundamental operations: sine, cosine, and tangent. The cotangent, secant, and cosecant are three crucial trigonometric functions that may be derived from these three fundamental ratios or functions. These functions serve as the foundation for all the key ideas in trigonometry.
In the triangle base = [tex]\sqrt{2}[/tex] and height as x
The value of the angle is [tex]60\x^{o}[/tex]
so tanθ = tan[tex]60\x^{o}[/tex]
[tex]\frac{height }{base} = tan60\x^{o} \\[/tex]
⇒ x = √3 * √2
⇒ x = √6
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a plane can fly 3750 km in 3 hours with the wind. the plane takes 5 hours to travel the same distance aganist the same wind speed. find the rate of the plane in still air. find the speed of the wind
The rate of the plane in still air is 1,000 kph and the speed of the wind is 250 kph. The result is obtained by using elimination and substituting method.
Elimination and Substitution MethodTo eliminate equations, we can either add or subtract the equations. Substitution is substituting the value of one variable in the other equation.
A plane can travel:
3750 km in 3 hours with the wind.The same distance in the first trip against the same wind speed in 5 hours.Find the rate of the plane in still air and the speed of the wind!
Let's say
v = the rate/speed of the plane in still airw = the speed of the windThe speed of the plane with the wind is
v + w = 3750 km/3 h
v + w = 1250 kph ... (equation 1)
The speed of the plane against the wind is
v - w = 3750 km/5 h
v - w = 750 kph ... (equation 2)
Eliminate the equation 1 and 2!
v + w = 1250
v - w = 750 +
2v = 2000
v = 1000 m/s
Substitute the value of v in equation 1!
v + w = 1250
1000 + w = 1250
w = 1250 - 1000
w = 250 m/s
Hence, the speed of the plane when there is no wind and the speed of the wind respectively are 1000 m/s and 250 m/s.
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y=x+6
y=2x+7
solve system by using equal values method
Answer:
(- 1, 5 )
Step-by-step explanation:
y = x + 6 → (1)
y = 2x + 7 → (2)
since both equations have y on the left side, then equate the right sides
2x + 7 = x + 6 ( subtract x from both sides )
x + 7 = 6 ( subtract 7 from both sides )
x = - 1
substitute x = - 1 into either of the 2 equations for y
substituting into (1)
y = x + 6 = - 1 + 6 = 5
solution is (- 1, 5 )
Step-by-step explanation:
We would make these two equations equal to each other since both equations are in y= form
[tex](x + 6) = (2x + 7)[/tex]
Now to get numbers on one side and X's on the other.
Let's start by subtracting 6 from both sides
[tex]x = 2x + 1[/tex]
Next we can subtract 2X
[tex] - x = 1[/tex]
Last but not least, we can divide by -1 to reverse the signs
[tex]x = - 1[/tex]
Parallelogram AB'C'D' was obtained by dilating parallelogram ABCD using the center if dilation.
A. What was the scale factor of the dilation?
B. How many congruent copies of ABCD can fit inside of AB’C’D’?
C. If the original area was 12 square units, what is the dilated area of AB’C’D’?
Answer:
A) 2, B) 4, C) 48--------------------------------
Part AThe scale factor is 2, since each side is twice the initial length.
Part BThere are 4 congruent copies, as we can see on the picture.
Part CThe dilated area is 12*4 = 48 square units, since the area is the product of two dimensions, each dimension is twice the initial value therefore the area is 2*2 = 4 times greater.
Find fx (1,0) and fy (1,0) and interpret these numbers as slopes for the following equation: f( x,y)= sqrt(4-x^2-4y^2) fx(1,0)= fy (1,0)=
The value of fx(1, 0) equal to -(1/√(3)) and fy(1, 0) is equal to -20/√3.
To find fx(1, 0) and fy(1, 0), we need to take the partial derivative of the given equation with respect to x and y respectively, and then evaluate the derivatives at the point (1,0).
First, we have f(x, y) = √(4 - x² - 4y²)
To find fx(1, 0), we'll take the partial derivative of f(x, y) with respect to x:
fx(x, y) = ∂f/∂x = -(x/√(4 - x² - 4y²))
Therefore, fx(1, 0) = -(1/√(4 - 1² - 4×0²)) = -(1/√(3))
fx(1, 0) = -(1/√(3))
To find fy(1,0), we'll take the partial derivative of f(x, y) with respect to y:
fy(x, y) = ∂f/∂y
= -2y/√(4 - x² - 4y²)
Therefore, fy(1, 0) = -20/√(4 - 1² - 4×0²) = -20/ √3
These numbers, fx(1, 0) and fy(1, 0), can be interpreted as slopes of the equation. The slope in this case represents the rate of change of the function in the x and y directions. A negative value for fx(1,0) means that as x increases by a small amount, the function value decreases by a small amount, while a value of 0 for fy(1,0) means that as y increases by a small amount, the function value does not change.
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4,1234-123 =. ??????
Answer:41,111
Step-by-step explanation:4-3=1 3-2=1 2-1=1 bring the 1 down and bring the 4down to and you got your answer
the manager of an online shop wants to determine whether the mean length of calling time of its customers is significantly more than 3 minutes. a random sample of 100 customers was taken. the average length of calling time in the sample was 3.1 minutes with a sample standard deviation of 0.5 minutes. at a 0.05 level of significance, it can be concluded that the mean of the population is:
The null hypothesis is that the population mean is equal to 3 minutes. The calculated p-value from the sample data is 0.28, which is higher than the 0.05 significance level.
not significantly more than 3 minutes.
The null hypothesis is that the population mean is equal to 3 minutes. The calculated p-value from the sample data is 0.28, which is higher than the 0.05 significance level. Therefore, we cannot reject the null hypothesis and conclude that the mean of the population is not significantly more than 3 minutes.
1. The null hypothesis is that the population mean is equal to 3 minutes.
2. A sample of 100 customers was taken, with an average length of calling time of 3.1 minutes and a sample standard deviation of 0.5 minutes.
3. The p-value from the sample data is 0.28, which is higher than the 0.05 significance level.
4. Therefore, we cannot reject the null hypothesis and conclude that the mean of the population is not significantly more than 3 minutes.
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Which statement is incorrect
A. A triangle with three congruent sides is equiangular
B. The Isosceles Triangle Theorem can be applied to Equilateral Triangles
C. The Measure of each angle of an Equlateral Triangle is 120 degrees
D. The Triangle with 3 Congruent sides is equilateral.
Answer: C
Step-by-step explanation: a triangle has a measurement of 180 degrees not 120
the answer is c the measure of each angle of an Equlateral triangle in 120 °
x³ = x² + 20x how do you solve this by factoring?
Answer:
Factors of x are 0, 5, and -4.
Step-by-step explanation:
⇒ x³ = x² + 20x
⇒ x³ - x² - 20x = 0
⇒ x (x² - x - 20) = 0
⇒ x ( x² - 5x + 4x - 20) = 0
⇒ x ( x ( x - 5) + 4 ( x - 5)) = 0
⇒ x (x - 5) (x + 4) =0
⇒ x = 0, 5, and -4
Answer: x = 5
x = -4
x = 0
Step-by-step explanation:The first term is, x2 its coefficient is 1 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -20
Step-1 : Multiply the coefficient of the first term by the constant 1 • -20 = -20
Step-2 : Find two factors of -20 whose sum equals the coefficient of the middle term, which is -1 .
-20 + 1 = -19
-10 + 2 = -8
-5 + 4 = -1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and 4
x2 - 5x + 4x - 20
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-5)
Add up the last 2 terms, pulling out common factors :
4 • (x-5)
Step-5 : Add up the four terms of step 4 :
(x+4) • (x-5)
Which is the desired factorization A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well. Solving x2-x-20 = 0 by Completing The Square .
Add 20 to both side of the equation :
x2-x = 20
Now the clever bit: Take the coefficient of x , which is 1 , divide by two, giving 1/2 , and finally square it giving 1/4
Add 1/4 to both sides of the equation :
On the right hand side we have :
20 + 1/4 or, (20/1)+(1/4)
The common denominator of the two fractions is 4 Adding (80/4)+(1/4) gives 81/4
So adding to both sides we finally get :
x2-x+(1/4) = 81/4
Adding 1/4 has completed the left hand side into a perfect square :
x2-x+(1/4) =
(x-(1/2)) • (x-(1/2)) =
(x-(1/2))2
Things which are equal to the same thing are also equal to one another. Since
x2-x+(1/4) = 81/4 and
x2-x+(1/4) = (x-(1/2))2
then, according to the law of transitivity,
(x-(1/2))2 = 81/4
We'll refer to this Equation as Eq. #4.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x-(1/2))2 is
(x-(1/2))2/2 =
(x-(1/2))1 =
x-(1/2)
Now, applying the Square Root Principle to Eq. #4.2.1 we get:
x-(1/2) = √ 81/4
Add 1/2 to both sides to obtain:
x = 1/2 + √ 81/4
Since a square root has two values, one positive and the other negative
x2 - x - 20 = 0
has two solutions:
x = 1/2 + √ 81/4
or
x = 1/2 - √ 81/4
Note that √ 81/4 can be written as
√ 81 / √ 4 which is 9 / 2
It can be helpful to classify a differential equation, so that we can predict the techniques that might help us to find a function which solves the equation. Two classifications are the order of the equation -- (what is the highest number of derivatives involved) and whether or not the equation is linear .
Therefore , r its derivation are not present. The dependent variable does not have a transcendental function.
What does the word function mean?Numbers and their variants, math and nearby tissues, shapes and their real positions, as well as potential placements, are all studied in mathematics. The term "function" describes the connection between a group of inputs, each of which has a corresponding output. An input-output relationship is called a function when each input results in a single, unique output. A realm and a city or municipality, or scope, are assigned to each function.
Here,
Given : (1+y²)(d²y/dt²)+t(dy/dt)+y=et
The second derivative is the highest derivative in this fractional derivative (). As a result, this differential equation has an order of 2.
The dependent variable's product and its derivative are present, indicating linearity.
The differential equation is hence non-linear.
Second order nonlinear ordinary differential equations are categorized as such.
t²(d²y/dt²)+t(dy/dt) + 2y =sint
The differential equation shown is t²(d²y/dt²)+t(dy/dt) +2y=sint
Order: This differential equation has a higher order differential equation since the largest derivative it has is.
Lack of the dependent variable's product and/or derivative indicates linearity. Higher powers of the variable or its derivation are not present. The dependent variable does not have a transcendental function.
Therefore , r its derivation are not present. The dependent variable does not have a transcendental function.
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Can some one help me with 1 2 and 4
1) The function f(x) is defined as follows: B. F(x) = -(x + 2)²(x - 2).
2) The standard definition of function f(x) is given as follows: A. F(x) = ax³ + bx² + cx + d.
4) The approximate solution to the system of equations is given as follows: A. (-3.43, 6.30).
How to define the function f(x)?The function f(x) is defined according to the Factor Theorem, with the product of the linear factors of the function, which are dependent on the roots of the functions.
The zeros of the function, along with their multiplicity, are given as follows:
x = -2, with a multiplicity of 2, as the function just touches the x-axis, not crossing.x = 2, with a multiplicity of 1.Hence the function is defined as follows:
F(x) = a(x + 2)²(x - 2).
The y-intercept is positive, meaning that:
-8a > 0.
Thus the leading coefficient a is negative, and the correct option is given by option B.
A cubic function, in which the coefficients a and d are positive, is represented as follows:
A. F(x) = ax³ + bx² + cx + d.
How to solve the system of equations?The solution to the system of equations is found through graphing, and is the point of intersection of the two functions.
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consider the following binomial experiment: a company owns 5 copiers. the probability that on a given day any one copier will break down is 0.66. what is the probability that at least 3 copiers will break down on a given day?
The probability that at least 3 copiers will break down on a given day is 0.0909.
1. Calculate the probability that 0 copiers will break down:
P(0) = (1-0.66)^5
= 0.0729
2. Calculate the probability that 1 copier will break down:
P(1) = 5 * 0.66 * (1-0.66)^4
= 0.2221
3. Calculate the probability that 2 copiers will break down:
P(2) = 5C2 * 0.66^2 * (1-0.66)^3
= 0.3088
4. Calculate the probability that 3 copiers will break down:
P(3) = 5C3 * 0.66^3 * (1-0.66)^2
= 0.2197
5. Calculate the probability that at least 3 copiers will break down:
P(at least 3) = 1 - (P(0) + P(1) + P(2))
= 0.0909
The probability that at least 3 copiers will break down on a given day is 0.0909. This was calculated by first calculating the probability of 0 copiers breaking down (P(0)) which is (1-0.66)^5, then the probability of 1 copier breaking down (P(1)) which is 5 * 0.66 * (1-0.66)^4, and then the probability of 2 copiers breaking down (P(2)) which is 5C2 * 0.66^2 * (1-0.66)^3. Finally, the probability that at least 3 copiers will break down (P(at least 3)) was calculated by subtracting the sum of P(0), P(1), and P(2) from 1. This gives us the final result of 0.0909.
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