To get the number of half-lives passed, we divide the time of flight from part a by the length of a half-life, as
given in the statement of the problem:
Number of half lives = 2×10−4
1.5×10−6 ≈ 133
The fraction of remaining muons will decrease by 1/2
every half life, so the fraction after a given number N of
half-lives will be:
1/2 × 1/2 × 1/2
· · · N times · · · × 1/2 = ( 1/2)N .
This makes the fraction remaining equal to 1/2 to the power 133:
fraction remaining = ( 1/2)
133 ≈ 10−40. That’s not very many muons
First-generation quarks are what make up pions, which are mesons with no spin. An anti-down quark and an up quark are described in the quark model. In addition to vector, rho, and omega mesons, the exchange of virtual pions also explains why there is still a strong interaction between nucleons. Pions are typically created in high-energy collisions between hadrons and are not created during radioactive decay. In some matter-antimatter annihilation processes, pions are also produced.
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Note that the full question is:
Ne of the many fundamental particles in nature is the muon mu. This particle acts very much like a "heavy electron." It has a mass of 106 MeV/c^2, compared to the electron's mass of just 0.511 MeV/c^2. (We are using E = mc^2 to obtain the mass in units of energy and the speed of light c).Unlike the electron, though, the muon has a finite lifetime, after which it decays into an electron and two very light particles called neutrinos (nu). We'll ignore the neutrinos throughout this problem.
If the muon is at rest, the characteristic time that it takes it to decay is about 2.2 microseconds. Most of the time, though, particles such as muons are not at rest and, if they are moving relativistically, their lifetimes are increased by time dilation. In this problem we will explore some of these relativistic effects.
Cosmic rays are constantly raining down on the earth from outer space. (Figure 1)The majority of these cosmic rays are protons, and when upper atmosphere, they can convert into particles called pions (), which subsequently decay into muons with a characteristic lifetime of T.
Suppose that a cosmic-ray proton crashes into a nitrogen molecule in the upper atmosphere. 45 km above the earth's surface, producing a pia a muon. Assume that the pion has a velocity of 99.99% the speed of light and decays into a muon, which, owing to kinematics, has a downward velocity of 99.9943% the speed of light.
now let’s consider the effect of time dilation how far would the pion actually travel before decaying?
Help with thisss pleasseeeee
Answer: The last one; is the one closest to the keyboard.
Step-by-step explanation: Its D because after I looked at the range, I looked at the median, which is 22, and D is the only one that had that as its median. I hope this helped!
To download movies off the internet, you must pay $1.99 per movie, plus a onetime fee of $5.50. Which expression shows the total cost to download N movies?
Answer:
Step-by-step explanation:
well then the anwser is 1.99 because the one time fee is only for downloading one movie the first, but 1.99 is the money you have to pay everytime you download a movie.
6) how to get the equation show all ur steps
From the graph of the system of equations y = 3x - 8 and 6x - 2y = 10, there is no solution
What is an equation?An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.
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 slope and b is the y intercept
The slope of the line passing through points (x₁, y₁) and (x₂, y₂) is:
m = (y₂ - y₁) / (x₂ - x₁)
Given the system of equations:
y = 3x - 8 (1)
and:
6x - 2y = 10 (2)
From the graph of the equations, there is no solution
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if there must be at least one person in each table, in how many ways can 6 people be seated (a) around two tables? (b) around three tables?
There are 120 possible ways for two tables and 90 ways for 3 tables.
If we split the six people into 4/1/1, there will be (6 4) ways to select the 4 people sitting together, and 3! ways to arrange them at their table, so this gives (6 4)(3!)=15(6)=90 possibilities.
If we split the six people into 3/2/1, we will get (6 3) ways to select the 3 people sitting together, 2! ways to arrange them at their table, and (3 2) ways to select the 2 people sitting together, so this gives (6 3)⋅2⋅(3 2)=20(2)(3)=120 possibilities.
Finally, there are 120 possible ways for two tables and 90 ways for 3 tables.
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Find the length of side x in simplest radical form with a rational denominator
Check the picture below.
A colored spinner with eight equal sections is given. spinner divided evenly into eight sections with three colored blue, one red, two purple, and two yellow Using the fair spinner, determine P(less than 4) when the spinner is spun once. 0.125 0.25 0.375 0.5
The probability that less than four colours will be chosen when the spinner is spun once would be = 0.5. That is option D.
What is probability?Probability is defined as the expression that show the possible outcome of an event which is likely or unlikely to occur.
The coloured spinner is divided into = 8 colour sections
The number of blue section = 3
The number of red = 1
The number of purple section = 2
The number yellow section = 2
Therefore the probability to select 4 colour when spun once = 4/8 = 1/2 = 0.5
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the points at which the parabola intersects the x-axis
The x-intercepts or roots of the parabola are the locations where a parabola contacts the x-axis. These are the solutions to the parabola equation where the y-value is equal to zero.
What is parabola?A parabola is an open curve formed by the intersection of a right circular cone with a plane parallel to one of the cone's elements. This is known as the standard form of a quadratic function. A parabola is the graph of a quadratic function that is a U-shaped curve. A parabola is the graph of the equation y=x2 illustrated below. Parabolas are classified into three categories. There are three types of forms: vertex form, standard form, and intercept form. Each type offers a unique important characteristic for the graph. The three major forms from which we graph parabolas are known as standard form, intercept form, and vertex form. Each form will provide you with somewhat different information as well as its own set of pros and downsides.
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Tyler and Blake have rectangular pieces of paper with the same length and same width. They each cut their paper exactly in half. Tyler cuts his paper horizontally through the middle. Blake cuts his paper along a diagonal. Which student has the half piece of paper with the greater area?
The student that has the half piece of paper with the greater area is blake.
How to find the surface area of some object?Find the area that its outer surfaces possess. Sum of all those surfaces' area is the surface area of the considered object.
Given;
Tyler and Blake have rectangular pieces of paper with the same length and same width
Tyler cuts his paper horizontally through the middle
Blake cuts his paper along a diagonal
Now,
Let the length and breadth be y
Tylers half area= y*y/2=y^2/2
Blakes half area=1/2* [tex]\sqrt{3}[/tex]y*[tex]\sqrt{3}[/tex]y/2
=3y^2/4
Therefore, blakes piece of paper has more area.
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__________ is a measure of how responsive one variable is to a change in another variable.
Answer: Elasticity
Elasticity is a measure of how responsive one variable is to a change in another variable.
If 3(m + n) is even, then which of the following must also be even ?
A.m + n
B.m
C.n
D.3m
E.3n + 1
The solution is, A. m + n, must also be even .
What is Even ?A number that is divisible by 2 and generates a remainder of 0 is called an even number. Examples of even numbers are 2, 4, 6, 8, 10, etc. For example, assume you have ten chocolates. These chocolates may be divided into two groups, each having five chocolates. So, ten is an even number.
here, we have,
given that,
If 3(m + n) is even
so, we get,
3(m + n) is divisible by 2.
i.e. m+n is must ne divisible by 2.
Hence, The solution is, A. m + n, must also be even .
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3. Six square-based pyramids fit exactly onto the six faces of a cube of side 4 cm. If the volume of the object formed is 256 cm³, find the height of each of the pyramids.
The height of the pyramid is 6cm
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given that Six square-based pyramids fit exactly onto the six faces of a cube of side 4 cm.
The volume of the object formed is 256 cm³.
We need to find the height of each of the pyramids.
The total volume can be calculated as
Total volume= cube volume+6 one pyramid volume
cube volume=4³=64
pyramid volume=1/3.4²h=16/3h
64+6.16h/3=256
64+32h=256
Subtract 64 on both sides
32h=256-64
32h=192
Divide both sides by 32
h=6
Hence, the height of the pyramid is 6cm
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Find the inverse of this function f(x)=(x-2)^4 (if x ≥ 2)
Answer:
[tex]f^{-1}(x)=\sqrt[4]{x}+2 \qquad \textsf{for $x \geq 0$}[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=(x-2)^4[/tex]
The domain of the given function is restricted:
{x : x ≥ 2}Therefore, the range of the given function is also restricted:
{f(x) : f(x) ≥ 0}To find the inverse of a function, swap x and y:
[tex]\implies x=(y-2)^4[/tex]
Rearrange the equation to make y the subject:
[tex]\implies \sqrt[4]{x}=y-2[/tex]
[tex]\implies y=\sqrt[4]{x}+2[/tex]
Replace y with f⁻¹(x):
[tex]\implies f^{-1}(x)=\sqrt[4]{x}+2[/tex]
The domain of the inverse of a function is the same as the range of the original function. Therefore, the domain of the inverse function is restricted to {x : x ≥ 0}.
Therefore, the inverse of the given function is:
[tex]f^{-1}(x)=\sqrt[4]{x}+2 \qquad \textsf{for $x \geq 0$}[/tex]
Parallel lines m and n are cut by transversal t. Which ones are complementary and subblememtary and congruent?
Complementary Angles : ( ∠1 , ∠5 ) , ( ∠2 , ∠6 ) , ( ∠3 , ∠7 ) , ( ∠4 , ∠8 )
Supplementary Angles : ( ∠1 , ∠2 ) , ( ∠2 , ∠4 ) , ( ∠3 , ∠4 ) , ( ∠1 , ∠3 )
Congruent Angles : ( ∠1 , ∠5 ) , ( ∠2 , ∠6 ) , ( ∠3 , ∠7 ) , ( ∠4 , ∠8 )
What are Parallel Lines Cut by Transversal?Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.
Corresponding angles
When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position
Alternate Interior Angles
Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.
Alternate Exterior Angles
The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.
Consecutive Interior Angles
When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.
Given data ,
Let the parallel lines be represented as m and n
Now , the lines m and n are cut by the transversal line t
So , the angles are
The corresponding angles are ( ∠1 , ∠5 ) , ( ∠2 , ∠6 ) , ( ∠3 , ∠7 ) , ( ∠4 , ∠8 )
The supplementary angles are having a sum = 180°
The supplementary angles are angles in a straight line
So , ( ∠1 , ∠2 ) , ( ∠2 , ∠4 ) , ( ∠3 , ∠4 ) , ( ∠1 , ∠3 ) are supplementary angles
And , ( ∠5 , ∠6 ) , ( ∠6 , ∠8 ) , ( ∠7 , ∠8 ) , ( ∠5 , ∠7 ) are supplementary angles
The congruent angles are having the same measure
So , corresponding angles and alternate interior angles are also congruent angles
Hence , the angles are solved
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Find the rule. Solve for n
X 5 6 7 n
Y 10 12 14 20 Rule:
Answer:
n = 10
Step-by-step explanation:
2x = y
2(n)=20
n = 20/2
n = 10
3. Decide whether the polygons are similar, not similar, or not enough information is given. If similar, write a similarity statement. If not, explain why.
The solution is the given triangles are similar to each other due to S-S-S rule.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
From the given figure we get,
triangle ABC & HIJ
we get,
AC = 2* HI
AB= 2*IJ
BC = 2* HJ
so, the scale factor = 2
Hence, The solution is the given triangles are similar to each other due to S-S-S rule.
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a drawer contains a mixture of red socks and blue socks, at most 1991 in all. it so happens that, when two socks are selected randomly without replacement, there is a probability of exactly 1 2 that both are red or both are blue. what is the largest possible number of red socks in the drawer that is consistent with this data?
The largest possible number of red socks in the drawer that is consistent with this data is 990.
Let r be the number of socks that are red, and t be the total number of socks. We get:
2(r(r-1)+(t − r)(t − r − 1)) = t(t − 1)
Expanding the left hand side and the right hand side,
we get: 4r²-4rt+2t²- 2t = t²- t
And, moving terms, we will get that:
47r²-4rt + t² = t
We notice that the left side is a perfect square.
(2r-t)² = t
Thus t is a perfect square. And, the higher t is, the higher r will be. So, we should set t =44²= 1936
And, we see, 2r- 1936 (+-)44
We will use the positive root, to get that 2r -1936 = 44, 2r =1980, and r = 990
About probabilityThoughts about probability began with a question from a French nobleman named Chevalier de Mere to Pascal (1623-1662). He wants to know how the pattern of distributing betting money in a gambling game is if the game has to be stopped before it is finished. This question then became the subject of discussion between Pascal and Fermat (1601-1665), based on this discussion came the theory of probability.
Although the basics of probability initially appeared to explain problems in gambling, in its development, the concept of probability can be applied to various problems such as social problems, engineering, health, biology, industry, transportation, management, accounting, education etc.
Probability is the amount of chance (likely) that an event will occur. The amount of opportunity can be written in the form of a decimal number, fraction or percent.
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use rguroo to solve for the proportions (probabilities). a normal population has a mean and standard deviation . round answers up to four decimal places. a) the proportion of the population that is less than 18 is 0.3085 . b) the probability that a randomly chosen value is greater than 25 is 2.6667
a) The proportion of the population that is less than 18 is 0.3085.
b) The probability that a randomly chosen value is greater than 25 is 15.39%, which is not equal to 2.6667 as stated in the question.
a) To find the z-score corresponding to the value of 18, we can use the standard normal formula:
z = (18 - mu) / sigma
Where mu is the mean and sigma is the standard deviation of the population.
To find the proportion of the population that is less than 18, we can use the cumulative distribution function (CDF) of the standard normal distribution.
The CDF gives us the proportion of the population that is less than a given value.
For a standard normal distribution, we can use a standard normal table or a calculator to find the CDF.
Using the standard normal table, or a standard normal calculator,
we find that the CDF of the standard normal distribution at z = -0.6309 is 0.3085.
So, the proportion of the population that is less than 18 is 0.3085.
b) To find the z-score corresponding to the value of 25, we can use the standard normal formula:
z = (25 - mu) / sigma
Using a standard normal calculator or table,
we find that the z-score for 25 is 1.0538.
The proportion of the population that is greater than 25 is 1 - the CDF of the standard normal distribution at z = 1.0538.
Using a standard normal calculator or table, we find that the CDF of the standard normal distribution at z = 1.0538 is 0.8461.
So, the proportion of the population that is greater than 25 is 1 - 0.8461 = 0.1539.
To find the probability that a randomly chosen value is greater than 25, we can multiply 0.1539 by 100% to get 15.39%.
Therefore, the probability that a randomly chosen value is greater than 25 is 15.39%, which is not equal to 2.6667 as stated in the question.
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Example 4: Find the length of AC? D A 65° 12cm 7cm B
topic: trigonometry
Step-by-step explanation:
hope you can see the awful green
Answer:
13.14cm
Step-by-step explanation:
lets start by finding the length of AD
90 + 65=155...........180-155= 25
x/sin 25= 7/sin 90
xsin90=7sin 25
x= 2.96cm=AD
Now lets find DC
we shall find DB first;
x/sin65=7/sin90
xsin90=7sin65
x=6.34cm...=DB
Now lets use Pythagoras theorem to find DC
12²-6.34²=√103.80
DC=10.18cm
Add AD and DC
2.96+10.18= 13.14cm
AC=13.14cm
Price of a book: $18.50
Discount: 45%
Find the new price of the book after the discount. Round to the nearest cent.
#8. The half-life of a radioactive kind of tellurium
is 3 hours. How much will be left after 15 hours,
if you start with 60 grams of it?
After 15 hours there will be 1.875 grams of the radioactive tellurium.
How much will be left after 15 hours?We know that the half-life of a radioactive kind of tellurium is 3 hours.
This means that for any quantity A of that radioinuclei, after 3 hours we will have half of that amount.
Then we can write the exponential equation:
M(x) = A*(1/2)^(x/3h)
Here we start with A= 60 grams, and after 15 hours we will have:
M(15h) = 60g*(1/2)^(15h/3h)
M(15h) = 60g*(1/2)^(5) = 1.875 g
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Graph each system of Inequalities:
A graph of the system of linear inequalities is shown in the image attached below.
What is an inequality?In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:
Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).In this exercise, we would use an online graphing calculator to plot the given system of linear inequalities y > -x + 5 and y ≤ 3x -4 as shown on the graph attached below. Based on the graph (see attachment), we can logically deduce that the solution to the given inequality is the shaded region, with a point of intersection at the ordered pair (2.25, 2.75) in quadrant I.
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debate team has ten members. five members must be chosen for a particular debate. a.) in how many ways can the five be chosen if no positions are assigned to the members? b.) in how many ways can the five be chosen if each member is assigned a position from one to five? the positions signify the order in which each member will participate in the debate. c.) suppose of the ten debate team members there are only two members who may be assigned position five in the debate. any member may be assigned positions one through four. in how many ways can the five members be chosen?
In total, there are 252 ways to choose five members without assigning positions, 5 ways to choose five members with assigned positions, and 56 ways to choose five members with two members assigned to a particular position.
a.) The number of ways that the five team members can be chosen without assigning them positions is 10C5 = 252. This is calculated using the formula for combinations, which is n!/(r!(n-r)!), where n is the total number of members and r is the number to choose. In this case, n=10 and r=5, so 10!/(5!(10-5)!) = 252.
b.) The number of ways that the five team members can be chosen with assigned positions is 5!. This is because there are five positions, and each team member must occupy one of the positions. The order of the positions is irrelevant, so there is only one possible combination.
c.) The number of ways that the five team members can be chosen with the two members assigned to position five is 8C5 = 56. This is calculated using the same formula as in part a, but with n=8 since two members are already assigned to position five. 8!/(5!(8-5)!) = 56.
In total, there are 252 ways to choose five members without assigning positions, 5 ways to choose five members with assigned positions, and 56 ways to choose five members with two members assigned to a particular position.
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in convex hexagon , all six sides are congruent, and are right angles, and , , , and are congruent. the area of the hexagonal region is . find .
In a convex hexagon, if the area of the hexagonal region is 2116 (√2 + 1), then the value of AB is 46.
What is a convex hexagon?A convex hexagon is a hexagon in which all of the inner angles and all of the vertices have to be smaller than 180 degrees. There are both regular and irregular convex hexagons. Inside a convex hexagon, there are no angles. More specifically, no internal angle will exceed 180 degrees. Any internal angle which exceeds 180 degrees is concave.
Let the side length be x.
So, the diagonal BF = √(AB^2 + A F^2) = √(x^2 + x^2) = x√2.
Then, the areas of the triangles AFB and CDE in total equals (x^2 / 2) * 2, and the area of the rectangle BCEF equals x * x√2 = x^2 √2.
Now, let the equation be:
2116 (√2 + 1) = x^2√2 + x^2
And by simplifying the above equation, we will get:
2116 (√2 + 1) = x^2 (√2 + 1)
2116 = x^2
By taking root both sides, then it will be:
x = 46
Hence, the value of AB is 46.
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Although part of your question is missing, you might be referring to this full question: In a convex hexagon ABCDEF, all six sides are congruent, ∠A and ∠D are right angles. And ∠B, ∠C, ∠E and ∠F are congruent. The area of the hexagonal region is 2116 (√2 + 1). Find AB.
When this net is folded up, which two points meet X?
The points will meet x when it is folded are C or E
What is the point?A point is a location of an object by taking reference of origin, In general case we consider it at (0,0), At the origin value of both the coordinate position is considered as Zero, In simple words point indicates how much it is above or below from the coordinate axes.
Vertical distance from the x axis is known as y coordinate and horizontal distance from the y axis is known as x coordinate.
Given that,
A green colored Net,
After folding x point will meet the points = ?
When we start folding,
First step,
Side ABCD and DEFG will be folded,
C and E will meet with each other
Second Step,
Side ABCD and AGHI will be folded,
B and I will meet with each other
Third step,
Side DEFG and AGHI will be folded,
F and H will meet each other
Fourth step,
Upper portion AHI will cover the upper portion BCF of the box
X will at position of C or E
Hence, the X will meet C or E
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Which choice shows the graph of the function g (x) = -1/3f(x)?
Option A is a correct representation of the graph of the function,
g(x) = -1/3f(x).
What is the cartesian plane?When two parallel lines intersect, a two-dimensional coordinate plane called the cartesian plane is created. The horizontal line is the X-axis, while the vertical line is the Y-axis. If the sign of x is positive, the coordinate point (x, y) in the Cartesian plane indicates that the point is on the right of the origin; otherwise, it indicates that the position is on the left of the origin.
Given the graph of the function,
f(x) is the shape of a parabola so the graph is of a quadratic function.
and given g(x) = -1/3f(x)
graph of f(x) is on coordinates (0, 0), (1, 1), and (-1, 1)
so the function is f(x) = x²
so g(x) should lie in coordinates (0, 0), (1/3, -1/3), and (-1/3, -1/3)
the shape of g(x) will be the same as f(x), but due to the negative sign, the shape will be in opposite quadrants.
and g(x) is 1/3 time f(x) so the shape will evolve more as compared to g(x),
so the graph of Option A only follows the required condition.
Hence option A is correct.
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write a polynomial that represents the area of the soccer field
A polynomial that represents the area of the soccer field is 40x² + 240x + 200
What is polynomial?
A polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
The area (A) of the rectangular pitch is calculated as
A = lb ( l is the length and b the breadth )
= (10x + 10)(4x + 20)
Each term in the second factor is multiplied by each term in the first factor, that is
10x(4x + 20) + 10(4x + 20) ← distribute both parenthesis
= 40x² + 200x + 40x + 200 ← collect like terms, thus
A = 40x² + 240x + 200 ← in standard form
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PLEASEEEEE I NEED TO GRADUATE
The solution for the given expression b = √ -1 -2b is b = -1.
What is quadratic equation?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax^2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. First, there must be a term other than zero in the coefficient of x^2 (a not equal 0) for an equation to be a quadratic equation.
The expression is:
b = √ -1 -2b
Take square on both sides of the equation. The square negates the square root and we have the following expression:
b² = - 1 - 2b
b² + 2b + 1 = 0
The quadratic formula is given as:
x = - b ± √b² - 4ac ÷ 2a
Substituting the value of b = 2, a = 1 and c = 1:
x = -2 ± √4 - 4(1)(1) ÷ 2(1)
x = -2 ÷ 2
x = -1
Hence, the solution for the given expression b = √ -1 -2b is b = -1.
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CAN SOMEONE PLS HELP ME!!!!!!!!!
The trigonometric form of the complex number is,
-6+ i (-6) = 6√2( cos5pi/4 + i sin 5pi/4)
What is complex number?In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation {\displaystyle i^{2}=-1}; every complex number can be expressed in the form a + bi, where a and b are real numbers.
here, we have,
the complex number which we get from the given graph is,
-6+ i (-6)
so, a = -6
b = -6
i.e. z = √a^2+b^2
=6√2
so, we know,
The trigonometric form of a complex number:
z = |z| (cosα +i sinα)
now, cosα = a/|z|
= -1/√2
and, sinα = b/|z|
= -1/√2
so, solving we get,
α = 5pi/4
i.e. -6+ i (-6) = 6√2( cos5pi/4 + i sin 5pi/4)
Hence, The trigonometric form of the complex number is,
-6+ i (-6) = 6√2( cos5pi/4 + i sin 5pi/4)
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if the zero vector is a solution of the system , then the system is homogeneous. group of answer choices true false
True, If the zero vector is a solution of the system , then the system is homogeneous.
A system of linear equations is considered homogeneous if the zero vector (i.e., the vector with all components equal to 0) is a solution. This means that the system of equations only has the trivial solution of all variables equal to zero, but no non-trivial solutions.
A homogeneous system of linear equations is a system where all the equations have the same form and all the coefficients are proportional to each other. This means that if one equation is multiplied by a constant, the same constant must be multiplied by all the other equations in the system to maintain the homogeneous property.
The zero vector is a solution of a homogeneous system because if all the variables are equal to zero, all the coefficients in the equations are also equal to zero and the equations are satisfied. This is why the presence of the zero vector as a solution is a defining characteristic of homogeneous systems.
In contrast, a non-homogeneous system is a system where the zero vector is not a solution and there are both trivial (zero) and non-trivial (non-zero) solutions. Non-homogeneous systems are solved using different methods compared to homogeneous systems.
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At a cupcake shop, cupcakes cost $3
each. If you have no more than $42 to
spend on your birthday cupcakes, how
many can you get? Write in inequality
and solve for c, cupcake.
Answer: 14 cupcakes
Step-by-step explanation:
42 divided by 3