Answer:
The distance-time graph of the journey would be as follows:
From 8am to 8:01am, the car travels 0 miles (at 8am, it leaves London)
From 8:01am to 9:01am, the car travels 60 miles (at a constant speed of 60mph)
From 9:01am to 9:31am, the car travels 0 miles (the driver takes a break of 30mins)
From 9:31am to 12:51pm, the car travels 140 miles (at a constant speed of 70mph)
The graph would be a line with a slope of 60 for the first hour, a flat line for the 30 minutes break, and then a line with a slope of 70 for 2 hours and 20 minutes.
Note: Since we don't have a time-scale and time unit, this graph is just a representation of the pattern of the journey, and the actual values are not accurate.
Find the general solution of the given differential equation.
(x + 1) dy/dx + (x + 2)y = 2xe?x
y=
Give the largest interval I over which the general solution is defined. (Think about the implications of any singular points.)
(??, ?)
(0, 1)
(?1, ?)
(0, ?)
(??, 1)
Determine whether there are any transient terms in the general solution. (Enter the transient terms as a comma-separated list; if there are none, enter NONE.)
Solve the given initial-value problem. Give the largest interval I over which the solution is defined.
xy' + y = ex, y(1) = 8
y =
I
=
Solve the given initial-value problem. Give the largest interval I over which the solution is defined.
Ldi/dt + Ri = E, i(0) = i0, L, R, E, i0 constants
i =
I =
The whole response to the specified differential equation. (x + 1) dy/dx + (x + 2) y = 2xe is equal to y1(x), y2(x), f(x), and W(y1, y2), where dx = (ex)(1/2 e2x) = 1/ 2 e3x.
what is solution ?fixing a problem by an action or process; providing a solution explanation. an assortment of variable values that satisfy an equation, specifically Any value of a variable in an equation that fulfills the equality, that is, makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation equal, is the solution. Finding the solution(s) to an equation is what it means to solve it. The percentage of a solute in the solvent is one way to express a solution's concentration. the ratio of the mass of the solute to the mass of the solution
given
The characteristic equation is: r2 − 3r + 2 = 0
Factor: (r − 1)(r − 2) = 0
r = 1 or 2
So the general solution of the differential equation is y = Aex+Be2x
So in this case the fundamental solutions and their derivatives are:
Find the particular solution using the formula:
yp(x) = −y1(x)∫ y2(x)f(x) /W(y1, y2) dx + y2(x)∫ y1(x)f(x) /W(y1, y2) dx
4. First we solve the integrals:
∫ y2(x)f(x) / W(y1, y2) dx
= ∫ e2xe3xe3x dx
= ∫e2xdx
= 1 / 2 e2x
So:
−y1(x)∫ y2(x)f(x) / W(y1, y2) dx = −(ex)( 1/2 e2x) = − 1 / 2 e3x
the whole response to the specified differential equation. (x + 1) dy/dx + (x + 2) y = 2xe is equal to y1(x), y2(x), f(x), and W(y1, y2), where dx = (ex)(1/2 e2x) = 1/ 2 e3x.
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______ is a set of tools which helps in organizing, presenting information, and extracting meaning fromraw data.
Answer:
Data analytics. Data analytics is a set of tools which helps in organizing, presenting information, and extracting meaning from raw data.
Pls mark me as brainliest :)
How do you know if an absolute value graph opens up or down?
An absolute value graph is a V-shaped graph that opens either upwards or downwards, depending on the equation. To determine if an absolute value graph opens up or down, you need to examine the value of the constant k in the equation. If k is positive, the graph opens upwards and if k is negative, the graph opens downwards.
The general form of an absolute value equation is y = |x| + k, where k is a constant. The graph of this equation will open upwards if k > 0, and downwards if k < 0.
For example, if the equation is y = |x| + 2, the graph will open upwards and will have vertex at the point (0, 2)
On the other hand, if the equation is y = |x| - 2, the graph will open downwards and will have vertex at the point (0,-2)
The vertex of the graph is the point where the graph changes direction. The x-coordinate of the vertex is always 0 and the y-coordinate is the value of k.
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what is the value of L? 5L-6-7L=8
Answer:
L = -7
Step-by-step explanation:
5L - 6 - 7L = 8
combine like terms
5L - 7L - 6 = 8
-2L - 6 = 8
add 6 to both sides
-2L = 14
divide by -2
L = -7
lim x-> ∞ (sinh(x)/e^x)
Answer: [tex]\lim_{x \to \infty} (\frac{sinh(x)}{e^x})[/tex][tex]= 0[/tex]
Step-by-step explanation:
[tex]\lim_{x \to \infty} (\frac{sinh(x)}{e^x})[/tex]
[tex]\lim_{n \to \infty} \frac{sinh(\infty)}{e^(\infty)}[/tex]
As x approaches infinity, the exponential term e^x becomes much larger than the hyperbolic sine function sinh(x), so the entire expression sinh(x)/e^x becomes very close to zero.
Therefore, the limit of the expression as x approaches infinity is 0:
a basket contains 15 apples, of which two are rotten. a sample of three apples is selected at random. in how many ways can two rotten apples be chosen?
There are 6 ways to choose two rotten apples out of a sample of three.
What is algebra ?
Algebra is a branch of mathematics in which letters and symbols are used to represent numbers and quantities in equations and formulas. Algebraic concepts include the manipulation of equations and formulas using the rules of arithmetic, the solution of equations, and the study of the properties and behaviors of functions.
There are two rotten apples out of 15 total apples, so the probability of choosing a rotten apple is 2/15. The probability of choosing two rotten apples out of a sample of three is (2/15) * (1/14) * (3 choose 2) = (2/455) * 3 = 6/455. So there are 6 ways to choose two rotten apples out of a sample of three.
Hence , There are 6 ways to choose two rotten apples out of a sample of three.
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On a coordinate plane, a red line, labeled g of x, begins on a negative slope, crosses the x-axis at (negative 2, 0), the y-axis at (0, negative 2), and crosses the x-axis on a positive slope at (2, 0). A straight blue line with a negative slope, labeled f of x, crosses the y-axis at (0, 2) and the x-axis at (2, 0).
Which statement is true regarding the functions on the graph?
f(2) = g(2)
f(0) = g(0)
f(2) = g(0)
f(0) = g(2)
Which is the first error that Tomas made?
Tomas substituted the 3 for x when he should have substituted 6 for x.
Tomas added 6 to both sides of the equation instead of subtracting 6.
Tomas should have written the equation as .
Tomas substituted 3 for x when he should have substituted 3 for y.
The correct statement regarding the two functions in this problem is given as follows:
f(2) = g(2).
How to solve a system of equations graphically?The graphic solution of a system of equations is given by the point of intersection of all the equations that compose the system.
The points through which each function passes in this problem are given as follows:
g(x) = (-2,0), (0, -2) and (2,0).f(x) = (0,2) and (2,0).
The point that is common to both function is given as follows:
(2,0).
Meaning that the two functions intersect at x = 2, which is the solution to the system of equations, also meaning that they have the same numeric value at x = 2.
The fact that the two functions have the same numeric value at x = 2 means that the correct statement is given as follows:
f(2) = g(2).
Which is the first statement.
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(complete solution)
can someone help me here please thank you everyone! lovelots
Answer:
The expression a2+a4+a6+a8+......a20 can be written in sigma notation as:
∑ a(2n) where n = 1 to 10
To expand this summation, we can substitute in the values of n and evaluate the series:
a(21) + a(22) + a(23) + ... + a(210) = a2 + a4 + a6 + ... + a20
The expression (-1) + 2 +(-3) + 4 + (-5) ....+(-25) can be written in sigma notation as:
∑ (-1)^n*n where n = 1 to 25
To expand this summation, we can substitute in the values of n and evaluate the series:
(-1)^11 + (-1)^22 + (-1)^33 + ... + (-1)^2525 = -1 + 2 - 3 + 4 - 5 +... - 25
Note that the series (-1)^n*n is an alternating series, where the signs of the terms alternate between positive and negative. This series has no closed form solution, but we can evaluate them by adding and subtracting each term.
Answer:
[tex]\displaystyle \sum_{n=1}^{10} a_{(2n)}[/tex]
[tex]\displaystyle \sum_{n=1}^{25} n (-1)^{n}[/tex]
Step-by-step explanation:
Part ISigma notation means the sum of the series.
Given series:
a₂ + a₄ + a₆ + a₈ + ... + a₂₀Therefore:
First term is a₂Second term is a₄Third term is a₆So each term is a₂ₙ
Therefore, the expression in sigma notation is:
[tex]\displaystyle \sum_{n=1}^{10}a_{(2n)}[/tex]
Given series:
(-1) + 2 + (-3) + 4 + (-5) + ... + (-25)The absolute value of each term of the series is n.
The signs of each term alternate between negative and positive.
Therefore, the expression in sigma notation is:
[tex]\displaystyle \sum_{n=1}^{25} n (-1)^{n}[/tex]
Part IIThe expansion of each summation has been given in Part I.
However, the full expansions are:
[tex]\displaystyle \sum_{n=1}^{10} a_{(2n)}=a_2+a_4+a_6+a_8+a_{10}+a_{12}+a_{14}+a_{16}+a_{18}+a_{20}[/tex]
[tex]\displaystyle \sum_{n=1}^{25} n (-1)^{n}=(-1)+2+(-3)+4+(-5)+6+(-7)+8+(-9)+10+(-11)+12+\\\phantom{wwwwwwww}(-13)+14+(-15)+16+(-17)+18+(-19)+20+(-21)+22+\\\\\phantom{wwwwwwww}(-23)+24+(-25)[/tex]
Part IIIThe evaluation of each series is:
[tex]\displaystyle \sum_{n=1}^{10} a_{(2n)}=a_2+a_4+a_6+a_8+a_{10}+a_{12}+a_{14}+a_{16}+a_{18}+a_{20}[/tex]
[tex]\displaystyle \sum_{n=1}^{25} n (-1)^{n}=-13[/tex]
if f(x) = 3x²+5x, then find f(2)
Answer: 22
Step-by-step explanation:
f(2)=3*2^2+5*2
=3*4+10
=12+10
=22
mrs. johnson leaves on a trip planning to travel 24 mph.how fast must his son james travel to overtake himin 5 horus, if he starts 2.5 horus after his father?
Mr. Johnson leaves on a trip planning to travel with speed of 24 mph. His son leaves 2.5 hours after him. To catch his father in 5 hours, James must travel at 36 mph.
The relation between distance and speed is given by:
distance = speed x time.
In this case:
Ms' Johnson's speed = 24 mph
Mr Johnson's time = 2.5 + 5 = 7.5 hours
His travelled distance = 7.5 x 24 = 180 miles.
His son's time = 5 hours ( since he starts 2.5 hours after Mr Johnson left.)
He must catch distance of 180 miles in 5 hours. Therefore, his speed must be:
speed = distance / time
speed = 180 / 5 = 36 mph.
Hence, hisr son's speed is 36 mph.
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PLEASE HELP ASAP THERE ARE 3 QUESTIONS!!!!!! CORRECT ANSWER GETS BRAINLLEST!!! WORTH 100 POINTS. PLEASE HELP!!!!!!!!!!!!!!!!!!!!
Case 2
The quadratic equation x² - 14 · x + 48 = 0 have the following roots: x₁ = 6 and x₂ = 8. (Correct choice: B)
Case 3
We need to add + 64 to both sides. (Correct choice: B)
Case 4
We need to add + 16 to both sides. (Correct choice: C)
How to use completing the square method
In this problem we find three cases of quadratic equation that are not perfect square trinomials, these equations can be rewritten partially in that form by algebra properties. Completing the square offers a quick method to determine the roots of quadratic equations with integer coefficients. Now we proceed to determine the solutions corresponding to each case:
Case 2
x² - 14 · x + 48 = 0
x² - 14 · x + 49 = 1
(x - 7)² = 1
x - 7 = ± 1
x = 7 ± 1
The roots of the quadratic equation x² - 14 · x + 48 = 0 are x₁ = 6 and x₂ = 8, respectively.
Case 3
x² - 16 · x = - 21
x² - 16 · x + 64 = 64 - 21
(x + 8)² = 43
The first step consists in adding both sides by + 64.
Case 4
x² - 8 · x = 0
x² - 8 · x + 16 = 16
(x - 4)² = 16
The first step consists in adding both sides by + 16.
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Based on the information below, what are the values of x and y of the solution to the system of equations used to create the information?
?
my guess would be to pick the THIRD ONE
3
x=9.5 y= -2.0
What are the solutions of 3x² 6x 2 0?
There are two solutions for equation [tex]3x^2-6x+2=0[/tex] are [tex]1+\frac{1}{\sqrt{3}} , 1-\frac{1}{\sqrt{3}}[/tex].
and solutions are irrational solutions.
Every nth degree equation has a total of 'n' real or hypothetical roots. The polynomial [tex]f (x)[/tex] is exactly divisible by ([tex]x -a[/tex] ), which means that ([tex]x -b[/tex] ) is the factor of the provided polynomial [tex]f(x)[/tex].
The theory of equations in algebra refers to the study of algebraic equations, which are equations defined by polynomials. Any expression with one or more terms is considered to be a polynomial. Knowing when an algebraic problem has an algebraic solution was a major challenge in the theory of equations.
Here solution of equation:
[tex]3x^2-6x+2=0\\3x^2-6x+2+1-1=0\\3x^2-6x+3=1\\3(x^2-2x+1)=1\\3(x-1)^2=1\\x=1+\frac{1}{\sqrt{3}} , 1-\frac{1}{\sqrt{3}}[/tex]
So here two solutions are presented for given equation.
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Circle O shown below has a radius of 9 inches. To the nearest tenth of an inch,
determine the length of the arc, x, subtended by an angle of 81°.
9 inches
10=81°
Answer:
[tex]\boxed{12.7\;inches}[/tex]
Step-by-step explanation:
For a circle of radius r, the circumference is given by the expression
C = 2πr
So for this circle of radius 9", the circumference is 2 x π x9 = 18π
The entire circle covers a total angle of 360°
If there is a sector of the circle that is subtended by an angle Ф, then the length of that arc will be Ф/ 360 x C
Here Ф = 81°
So length of arc is
[tex]\dfrac{81}{360} \times 18 \pi\\\\\\\textrm {Using a calculator this works out to }\\\\[/tex]
[tex]\dfrac{81}{360} \times 18 \pi = 12.72345\\\\[/tex]
Rounded to the nearest tenth of an inch this would be
[tex]\boxed{12.7\;inches}[/tex] ANSWER
Taylor and Raimi each earn an hourly wage. Taylor earns $308 for working 14 hours. Raimi earns $288 for working 12 hours. Which statement is true?
Answer:
Raimi earns more per hour than Taylor.
Step-by-step explanation:
At a market, a pear cost bc and an apple cost 5 ¢ less than a pear. Mrs Ravi bought 5 pears and an apple. (a) (b) Find the total amount in cents Mrs Ravi paid in terms of b. If each pear cost 60 c, how much did Mrs Ravi pay? Leave your answer in cents.
Answer:
$355
Step-by-step explanation:
if each pear is 60c and apples are 5c less...
60×5=300
300+55=355
because 60-5=55
Andre is going to buy a new couch. His current couch is 90 inches long. The new couch he is looking at is 25% less than that. How long is the new couch?
Answer:
Step-by-step explanation:
90 inches
10%=9 inches
5%=4.5 inches
5x5=25
4.5 inches x5=22.5 inches
90-22.5=67.5
the new couch is 67.5 inches long
Vera wants to graph a line that passes through (0, 2) and has a slope of StartFraction 2 Over 3 EndFraction. Which points could Vera use to graph the line? Select three options.
The equation of the line is y = (2/3)x + 2, having a y intercept of 2 and slope of 2
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
The slope intercept form of a linear equation is:
y = mx + b
Where m is the slope (rate of change) and b is the y intercept.
The equation of a line with slope m passing through (x₁, y₁) is:
y - y₁ = m(x - x₁)
The line that passes through (0, 2) and has a slope of 2/3, hence:
y - 2 = (2/3)(x - 0)
y = (2/3)x + 2
The equation of the line is y = (2/3)x + 2
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I WILL GIVE BRAINLEY TO PERSON WHO ANSWERS!! (Correctly) HELP
Answer:
it's the second
Step-by-step explanation:
i did this before and it was the second one
1. Describe the end-behavior of the polynomial: f(x) = -2x4 - 3x³ +3x-5
A) f(x) → -∞, as x → -∞
f(x) →∞, as x → ∞
B) f(x) → ∞, as x → -∞
f(x) →∞, as x → ∞
C) f(x) →-∞, as x →-∞
f(x) →∞, as x → ∞
D) f(x) →∞, as x →-∞
f(x) →-∞, as x → ∞
5) Use the graph of f shown to find the x-values (if any) at which f is not continuous.
A) 3
B) 2
C) 2,-3
D) 0
E) None of these
The end-behavior of the polynomial is:
A) f(x) → -∞, as x → -∞
f(x) →∞, as x → ∞
What in mathematics is a polynomial?
The only operations used in a polynomial are addition, subtraction, multiplication, and non-negative integer exponentiation. In mathematics, variables are occasionally referred to as indeterminates. An example of a polynomial with a single variable x is x2 4x + 7.
The leading term of the polynomial is -2x⁴, which is negative for negative x and positive for positive x. As x approaches negative infinity, -2x⁴ approaches negative infinity, so the entire polynomial approaches negative infinity. Similarly, as x approaches positive infinity, -2x⁴ approaches positive infinity, so the entire polynomial approaches positive infinity.
Therefore, the end-behavior of the polynomial is:
f(x) → -∞, as x → -∞
f(x) →∞, as x → ∞
E) None of these
The polynomial is continuous for all real values of x. The only way for a polynomial to not be continuous is if there is a hole or a vertical asymptote in its graph. Since the graph of a polynomial is a smooth curve, there are no holes or vertical asymptotes, so the polynomial is continuous for all real values of x.
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Boris runs 7 miles in 50 minutes. At the same rate, how many miles would he run in 75 minutes
Answer: 10.5 miles
Step-by-step explanation:
What is the DIFFERENCE in rates between the 2 people below:
The difference in rates between the 2 peoples is 2.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
John y=5x
For sally we have to find the equation
m=28-14/4-2
m=14/2=7
14=7(2)+b
b=0
So for Sally y=7x
Hence, the difference in rates between the 2 peoples is 2.
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GDP Gross Domestic Product (GDP) is a measure of a country’s wealth. Indonesia had an estimated GDP in 2017 of 1,020,515,000,000. Madagascar had an estimated GDP of 10,372,000,000 in 2017. About how many orders of magnitude as great is Indonesia’s GDP?
The number of Empire State building‑height stacks of dimes required is 589,008.
What is the height of the Empire State building?The height of the Empire States Building including the antenna is 1,454 feet.
here, we have,
The height of a stack of 100 dimes is 5.3 inches.
The value of a stack of 100 dimes is 10 dollars.
The 2017 U.S. gross domestic product (GDP) = 19,390,604,000 dollars.
Number of stacks of dimes needed = $19,390,604,000 / $10 = 1,939,060,400 stacks of 100 dimes
Height of 1,939,060,400 stacks of 100 dimes in feet = 1,939,060,400 x 5.3/12
Height of 1,939,060,400 stacks of 100 dimes in feet = 856,418,343.3 feet
Number of Empire State building‑height stacks of dimes = 856,418,343.3 / 1,454
Number of Empire State building‑height stacks of dimes = 589,008
In conclusion, the number of Empire State building‑height stacks of dimes required is obtained from the height of the Empire State building and the height of a stacks of 100 dimes.
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can y’all help me pleaseee
Answer:
5. False.
Look at the graph.
Every one day, the cost jumps $30 instead of $60.
Therefore, it is false.
6. True.
Like I said, Every one day, the cost jumps $30.
So when x increases by 1, y increases by 30.
So, y = 30x is correct.
7. False.
Use the equation in the 6th question.
y = 30x.
Put x = 7.
You get y = 210, not 200.
So. it is false.
8. True
Again, same thing.
Use the equation in the 6th question.
y = 30x.
Put x = 9.
You get y = 270.
So the statement is correct.
Pls mark as brainliest for no apparent reason. Cheers
Question
The understanding of history is molded by primary and secondary
sources. Describe how primary and secondary sources impact one's
understanding of the War of 1812 and its aftermath.
A mathematics class is given the following trinomial to factor using the grouping method. 6x2 + 11x - 10 Which of the following students has correctly identified the first step towards factoring this trinomial correctly
The factorise form of the trinomial 6x² + 11x - 10 is (3x - 2)(2x + 5).
How to factorise polynomial?Trinomials is a polynomial that has three terms. Let's factorise the trinomial by grouping as follows:
6x² + 11x - 10
The grouping method can be used to factor polynomials whenever a common factor exists between the groupings.
Hence, let's find the factor of 6x² + 11x - 10
6x² + 11x - 10
let's find two numbers we can multiply to get -60 and add to get 11.
6x² + 15x - 4x - 10
3x(2x + 5) - 2(2x + 5)
Hence,
(3x - 2)(2x + 5)
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Find the area enclosed by the curve x=t^2-2t , y = √t and the y axis.
The area enclosed by the curve x = t² - 2t, y = √(t), and the y-axis is 0.754 square units.
First, find the value of t at x = 0
x = t² - 2t
⇒ t² - 2t = 0
⇒ t(t - 2) = 0
Therefore, t = 0, t = 2.
Derivative of area, dA/dy
dA/dy = (0 - x)
dA = (0 - x) × dy
Since the curve has a negative x in this region.
y = √t (given)
dy/dt = (1/2)/√t
dA = [0 - (t² - 2t)] [(1/2)/√t]dt
dA = [2t - t²]/[(1/2)/√t]dt
dA = [[tex]t^{1/2}[/tex] - (1/2)[tex]t^{3/2}[/tex]]dt
Integrating to obtain A,
A = (2/3)[tex]t^{3/2}[/tex] - (1/5)[tex]t^{5/2}[/tex]
Now apply the limits t = 0 to t = 2
Area = [(2/3)[tex]2^{3/2}[/tex] - (1/5)[tex]2^{3/2}[/tex]] - [0]
Area = √[2(4/3 - 4/5)]
Area = √[2(8/15)]
Area = √(16/15)
Area = 0.754
Thus, the area enclosed by the given curves is 0.754 square units.
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10.
(15x - 7)
х
37°
11.
Check the picture below.
Find the Taylor polynomial T3(x) for the function f centered at the number a.
f(x) = x + e−x, a = 0
T3(x)=?
T3(x) = x - x^2/2 + x^3/6.
The Taylor polynomial of degree 3 for the function f(x) = x + e^-x centered at a = 0 is given by:
T3(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3
= 1 + (-1 + 1)x + (e^-0 - (-1)(-1)e^-0)x^2/2! + (0 + (-1)(-1)(-1)e^-0)x^3/3!
= x - x^2/2 + x^3/6
So T3(x) = x - x^2/2 + x^3/6.
An infinite sum of words that are expressed in terms of a function's derivatives at a single point is known as the Taylor series or Taylor expansion of a function in mathematics.
The nth Taylor polynomial of the function is a polynomial of degree n that is created by the partial sum of the first n + 1 terms of a Taylor series. Approximations of a function made by Taylor polynomials get generally better as n rises. Quantitative estimates of the mistake brought about by the use of such approximations are provided by Taylor's theorem. If a function's Taylor series is converging, its total is the upper bound of the Taylor polynomials' infinite sequence. A function's Taylor series sum may not match.
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Pls help very urgent Write the rule for the linear function. Remember a function rule is written using f(z). 4 2- -2 2 X
