(a) Take the Laplace transform of both sides:
[tex]2y''(t)+ty'(t)-2y(t)=14[/tex]
[tex]\implies 2(s^2Y(s)-sy(0)-y'(0))-(Y(s)+sY'(s))-2Y(s)=\dfrac{14}s[/tex]
where the transform of [tex]ty'(t)[/tex] comes from
[tex]L[ty'(t)]=-(L[y'(t)])'=-(sY(s)-y(0))'=-Y(s)-sY'(s)[/tex]
This yields the linear ODE,
[tex]-sY'(s)+(2s^2-3)Y(s)=\dfrac{14}s[/tex]
Divides both sides by [tex]-s[/tex]:
[tex]Y'(s)+\dfrac{3-2s^2}sY(s)=-\dfrac{14}{s^2}[/tex]
Find the integrating factor:
[tex]\displaystyle\int\frac{3-2s^2}s\,\mathrm ds=3\ln|s|-s^2+C[/tex]
Multiply both sides of the ODE by [tex]e^{3\ln|s|-s^2}=s^3e^{-s^2}[/tex]:
[tex]s^3e^{-s^2}Y'(s)+(3s^2-2s^4)e^{-s^2}Y(s)=-14se^{-s^2}[/tex]
The left side condenses into the derivative of a product:
[tex]\left(s^3e^{-s^2}Y(s)\right)'=-14se^{-s^2}[/tex]
Integrate both sides and solve for [tex]Y(s)[/tex]:
[tex]s^3e^{-s^2}Y(s)=7e^{-s^2}+C[/tex]
[tex]Y(s)=\dfrac{7+Ce^{s^2}}{s^3}[/tex]
(b) Taking the inverse transform of both sides gives
[tex]y(t)=\dfrac{7t^2}2+C\,L^{-1}\left[\dfrac{e^{s^2}}{s^3}\right][/tex]
I don't know whether the remaining inverse transform can be resolved, but using the principle of superposition, we know that [tex]\frac{7t^2}2[/tex] is one solution to the original ODE.
[tex]y(t)=\dfrac{7t^2}2\implies y'(t)=7t\implies y''(t)=7[/tex]
Substitute these into the ODE to see everything checks out:
[tex]2\cdot7+t\cdot7t-2\cdot\dfrac{7t^2}2=14[/tex]
Find the sum of (5x3 + 3x2 - 5x + 4) and (8x3 -5x2 + 8x + 9)
Answer:
(5x³+3x²-5x+4) + (8x³-5x²+8x+9)
= 5x³+3x²-5x+4 +8x³-5x²+8x+9
= 5x³+8x³+3x²-5x²-5x+8x+4+9
= 13x³-2x²+3x+13
Hope this helps
if u have question let me know in comments ^_^
Find n for the arithmetic sequence for which sn=345, u1=12 and d = 5 .
Answer:
n = 10
Step-by-step explanation:
The sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = 12 and d = 5 and [tex]S_{n}[/tex] = 345, thus
[tex]\frac{n}{2}[/tex] [ (2 × 12) + 5(n - 1) ] = 345 ( multiply both sides by 2 )
n( 24 + 5n - 5) = 690 ← distribute and simplify left side
n(19 + 5n) = 690
19n + 5n² = 690 ( subtract 690 from both sides )
5n² + 19n - 690 = 0 ← in standard form
(5n + 69)(n - 10) = 0 ← in factored form
Equate each factor to zero and solve for n
5n + 69 = 0 ⇒ 5n = - 69 ⇒ n = - [tex]\frac{69}{5}[/tex]
n - 10 = 0 ⇒ n = 10
However, n > 0 , thus n = 10
(Score for Question 1: ____ of 5 points)
1. The equation of a circle is x2 + y2 - 4x + 2y - 11 = 0. What are the center and the radius of the circle?
Show your work
Answer:)
Answer:
The center of the circle:
(2, -1)
The radius of the circle:
r = 4
Step-by-step explanation:
The first step is to complete the square on both x and y:
x^2 + y^2 -4x + 2y - 11 = 0
x^2 -4x +y^2 +2y = 11
We determine c1 to complete the square on x:
c1 = (b/2)^2
c1 = (-4/2)^2 = 4
We then determine c2 to complete the square on y:
c2 = (2/2)^2 = 1
The equation of the circle is then re-written as:
x^2 -4x + 4 +y^2 +2y + 1 = 11 +4 +1
We then factorize the expressions in x and y separately:
(x-2)^2 + (y +1)^2 = 16
The center of the circle is thus:
(2, -1)
The radius is the square root of 16:
r = 4
Answer:
center : (2, -1)
radius : r = 4
Step-by-step explanation:
Examine the diagram. Triangle M P L. Angle P is 90 degrees and angle L is (4 x + 6) degrees. The exterior angle to angle M is 136 degrees. What is the value of x?
Answer:
x = [tex]10^{0}[/tex]
Step-by-step explanation:
From Δ MPL given that; <P = [tex]90^{0}[/tex], exterior angle to M = [tex]136^{0}[/tex] and <L = [tex](4x+6)^{0}[/tex].
In the triangle, the exterior angle is equal to the sum of the two adjacent interior angles. So that;
[tex]136^{0}[/tex] = [tex]90^{0}[/tex] + [tex](4x+6)^{0}[/tex]
= [tex]90^{0}[/tex] + 4[tex]x^{0}[/tex] + [tex]6^{0}[/tex]
[tex]136^{0}[/tex] = [tex]96^{0}[/tex] + [tex]x^{0}[/tex]
⇒ 4[tex]x^{0}[/tex] = [tex]136^{0}[/tex] - [tex]96^{0}[/tex]
4[tex]x^{0}[/tex] = [tex]40^{0}[/tex]
Divided both sides by 4 to have;
[tex]x^{0}[/tex] = [tex]10^{0}[/tex]
The value of x is [tex]10^{0}[/tex].
Answer:
The correct answer is in fact 10 degrees.
Step-by-step explanation:
I hope this helps!
Have a great day! :)
in the diagram,QOS and ROU are straight lines.OT is the bisector of angle UOS. Angle POQ and angle QOR are complementary angles. Find the values of x and y.pleaseeee answer sooonnn
Answer:
x=50° and y=45°
Step-by-step explanation:
x=QU(90°)-QP(40°)
x=50°
y=SU(90°)/2
y=45°
Calculate the derivative of the function. Then find the value of the derivative as specified:
f(x) = 5x + 9; f "(2)
A) f "(x) 0,f , (2)-0
B) f , (x)-9; f , (2) = 9
C)f"(x) = 5; f "(2) = 5
D) f '(x) 5x; f '(2) 10
The correct question is;
Calculate the derivative of the function. Then find the value of the derivative as specified:
f(x) = 5x + 9; f '(2)
A) f'(x) = 0; f'(2) = 0
B) f'(x) = 9; f '(2) = 9
C)f'(x) = 5; f'(2) = 5
D) f '(x) = 5x; f '(2) = 10
Answer:
Option C: f'(x) = 5 and f '(2) = 5
Step-by-step explanation:
We want to find the derivative of f(x) = 5x + 9.
Now, the derivative with respect to x will be;
f'(x) = 5
Now,we also want to find out f'(2)
This means we are to put 2 for x in the derivative function.
In the derivative function, we don't have x as we have just 5.
Thus,f'(2) = 5
Which relation is a function?
Answer:
The second graph is a function.
Step-by-step explanation:
This is the only one that passes the vertical line test.
(If there exits a vertical line which passes through more than one point, then the relation is NOT a function).
To which set of numbers does the number sqr rt-16 belong? Select all that apply
Answer:
The square root of -16 is an imaginary number and a complex number. Sqrt(-16)=4i. We use the i to indicate that the number is imaginary since there is no number that can be multiplied by itself to get a negative number (a negative times a negative is a positive, and a positive times a positive is also a positive). So the use of i tells you immediately that it's an imaginary number. You can tell the number is complex because it has both a real and an imaginary part and could be written in the form a+bi, where a is a real number and bi is an imaginary number. In this specific case, the real part (a) is 0 and the imaginary part (bi) is 4i.
Step-by-step explanation:
Given f(x) = –2x+5 find f'(x).
a f'(x)=- 5x+1.5
b.
x 5
2 2
f'(x) =
C. f'(x) = 2x-5
d.
x 5
2 2
f'(x) -- +
R
Please select the best answer from the choices provided
B.
ОООО
D
Answer: D
Step-by-step explanation:
To find the inverse function, you switch y with x and x with y. Then you solve for y.
y=-2x+5 [replace y with x and x with y]
x=-2y+5 [subtract both sides by 5]
x-5=-2y [divide both sides by -2]
(x-5)/-2=y
Now that we have our inverse function, we can rewrite it so that it matches the answer choice. D matches our answer choice the best.
A special mixed-nut blend at a store cost $1.35 per lb, and in 2010 the blend cost $1.83 per lb. Let y represent the cost of a pound of the mixed-nut blend x years after 2005. Use a linear equation model to estimate the cost of a pound of the mixed-nut blend in 2007.
Answer:
y = $1.542 per lb
Step-by-step explanation:
given data
mixed-nut blend store cost 2005 = $1.35 per lb
blend cost in 2010 = $1.83 per lb
solution
we consider here y = cost of a pound
and x year = after 2005
we will use here linear equation model
so
[tex]\frac{y - 1.35}{1.83-1.35} = \frac{x-10}{5 - 0}[/tex] .........................1
solve it we get
5y - 6.75 = .48 x
so
at 2007 year here x wil be 2
so
[tex]y = \frac{0.48 \times 2 + 6.75}{5}[/tex]
solve it we get
y = $1.542 per lb
Musah stands at the center of a rectangular field. He first takes 50 steps north, then 25 steps west and finally 50 steps on a bearing of 315°. Sketch musah's movement. How far west is musah's final point from the center?
Answer: 4.17 steps
Step-by-step explanation:
Draw a point to use as the center and then sketch 50 units north (up) and 25 units west (left) and 315° which creates a right triangle that has an angle of 360° - 315° = 45°
Use Pythagorean Theorem to find the length of the hypotenuse.
50² + 25² = hypotenuse² --> hypotenuse = 55.9 units
Since Musah only walked 50 units along the hypotenuse, he is 5.9 units from the center.
Create another right triangle using the remaining 5.9 units as the hypotenuse. You can use 45°-45°-90° rules OR sin 45° to find the horizontal distance from the center to be 4.17.
see attachment for sketch
5(y–3.8)=4.7(y–4) help help
Answer:
y = 2/3 or 0.667Step-by-step explanation:
5(y–3.8)=4.7(y–4)
Expand the terms in the bracket
That's
5y - 19 = 4.7y - 18.8
Group like terms
5y - 4.7y = 19 - 18.8
0.3y = 0.2
Divide both sides by 0.3
We have the final answer as
y = 2/3 or 0.667Hope this helps you
The dance team is selling headbands to raise
money for dance team jackets. They need
to sell 1,260 headbands. The headbands must
be divided equally among the three coaches.
Each coach is in charge of 10 dancers. If all
the headbands must be sold, how many
headbands will each dancer on the team
need to sell?
Answer:
42 headbands per dancer
Step-by-step explanation:
Selling 1260 headband
Divide by the three coaches
1260/3
420 per coach
Divide by each dancer under a coach
420/10 = 42
Each dancer must sell 42 headbands
What fraction of a pound is an ounce?
Answer:
1/16
Step-by-step explanation:
there are 16 ounces in a pound
Answer:
1/16 pounds
Step-by-step explanation:
3.85∙47.3+52.7∙3.85 PLSSSSS HELP
Answer:
385
Step-by-step explanation:
Suppose x varies directly with the square root of y and inversely with the cube root of z. What equation models this combined variation?
Answer:
[tex]\huge\boxed{x = k \frac{\sqrt{y} }{\sqrt[3]{z} }}[/tex]
Step-by-step explanation:
Given that:
1) x ∝ √y
2) x ∝ [tex]\frac{1}{\sqrt[3]{z} }[/tex]
Combining the proportionality
=> x ∝ [tex]\frac{\sqrt{y} }{\sqrt[3]{z} }[/tex]
=> [tex]x = k \frac{\sqrt{y} }{\sqrt[3]{z} }[/tex]
Where k is the constant of proportionality.
ASAP HELP WILL MARK BRAINLIEST
Answer:
c(x)=(3/4)^x
(3/4)^-2= 16/9
(3/4)^-1 =4/3
(3/4)^0=1
(3/4)^1 = 3/4
(3/4)^2= 9/16
Which quadratic equation would be used to solve for the unknown dimensions?
0 = 2w2
512 = w2
512 = 2w2
512 = 2l + 2w
Answer:
C
Step-by-step explanation:
Answer:
C: 512 = 2w2
Step-by-step explanation:
on edge
What are the solutions to the system of equations? {y=2x2−8x+5y=x−2 (3.5, 0.5) and (1, −1) (7, 5) and (0.5, −1.5) (3.5, 1.5) and (1, −1) (3.5, 1.5) and (−1, −3)
Answer:
[tex](1,-1)[/tex] and [tex](3.5,1.5)[/tex]
Step-by-step explanation:
Given
[tex]y = 2x^2 - 8x+5[/tex]
[tex]y = x - 2[/tex]
Required
Determine the solution
Substitute x - 2 for y in [tex]y = 2x^2 - 8x+5[/tex]
[tex]x - 2 = 2x^2 - 8x+5[/tex]
Collect like terms
[tex]0 = 2x^2 - 8x - x + 5 + 2[/tex]
[tex]0 = 2x^2 - 9x + 7[/tex]
Expand the expression
[tex]0 = 2x^2 - 7x - 2x+ 7[/tex]
Factorize
[tex]0 = x(2x - 7) -1(2x - 7)[/tex]
[tex]0 = (x-1)(2x - 7)[/tex]
Split the expression
[tex]x - 1 = 0[/tex] or [tex]2x - 7 = 0[/tex]
Solve for x in both cases
[tex]x = 1[/tex] or [tex]2x = 7[/tex]
[tex]x = 1[/tex] or [tex]2x/2 = 7/2[/tex]
[tex]x = 1[/tex] or [tex]x = 3.5[/tex]
Recall that
[tex]y = x - 2[/tex]
When [tex]x = 1[/tex]
[tex]y = 1 -2[/tex]
[tex]y = -1[/tex]
When [tex]x = 3.5[/tex]
[tex]y = 3.5 - 2[/tex]
[tex]y = 1.5[/tex]
Hence, the solution is;
[tex](1,-1)[/tex] and [tex](3.5,1.5)[/tex]
What happens to the probability of making a Type II error, beta,as the level of significance, alpha,decreases? Why?
Answer:
Lowering the level of significance, α increases the probability of making a Type II error, β.
Step-by-step explanation:
Lowering the level of significance, α increases the probability of making a Type II error, β.
This is because the region of acceptance becomes bigger, and it makes it less likely for one to reject a null hypothesis, when it is false, the type II error.
4/2÷4/7? plz help me
Answer:
2
Step-by-step explanation:
4/2÷4/7
= 4/2 × 7/4
= 28/14
= 2
What is the area of the house (including the drawing room, TV room, balcony, hallway, kitchen, and bedroom)?
Answer:
1256 i think
Step-by-step explanation:
Are you able to find tri-sector (equally divided by 3) rays for an arbitrary angle with straightedge-and-compass construction?
Answer:
Step-by-step explanation:
No, it is an ancient problem which has been proved to be impossible (in 1837), at least not for an arbitray angle.
However, we can trisect certain angles, such as 90 degrees, but rather than trisection, we are just constructing 30 degree angles.
For further reading, google "angle trisection"
PLEASE ANSWER!!! Brainliest to whoever answers at first!Order the following expressions by their values from least to greatest.
Answer:
-j, 0, j-k
Step-by-step explanation:
j is a positive number, so -j will be less than 0.
j is a number greater than k, so j - k will be greater than 0.
From least to greatest, the order is ...
-j, 0, j-k
Answer:
Step-by-step explanation:
convert 407 in base 8 to decimal
[tex]4\cdot8^2+0\cdot8^1+7\cdot8^0=256+7=263[/tex]
[tex]407_8=263_{10}[/tex]
36x7 please EXPLAIN the process of the multiplication plse
36×7
=252
Explaination :
First Multiply 6 and 7 we get 42 !
Write 2 and 4 will be added to the product of 3×7
We get 21 and add 4 here
So we get 252
Answer:
[tex]36 \times 7 = 252[/tex]
Step-by-step explanation:
Firstly multiply 6 with 7 you have to write 2 and take 4 carry and then multiply 7 with 3 u get 21 now add the number u carry in 21 u get ur answer. 252.
Hope it helps u mate
The local bowling alley pays you
$7.25 per hour to manage the desk.
Last week you worked 16 hours.
What is your straight-time pay?
Answer:
my straight time payment will be $116 for last week
Step-by-step explanation:
The local bowling alley pays
$7.25 per hour to manage the desk.
If worked 16 hours, my straight time payment will be
Rate= $7.25 per hour
Hour worked= 16 hours
my straight time payment = rate*hour worked
my straight time payment = 7.25*16
my straight time payment = 166.00
my straight time payment will be $116
please help solving.
Answer:
right machine first, then left.6 into left machine, then rightStep-by-step explanation:
a) Putting 6 into the first (left) machine will give an output of ...
y = √(6 -5) = √1 = 1
Putting 1 into the second (right) machine will give an output of ...
y = 1² -6 = -5
This answers the second question, but not the first question.
__
If we put 6 into the right machine first, we get an output of ...
y = 6² -6 = 30
Putting 30 into the left machine, we get an output of ...
y = √(30 -5) = √25 = 5 . . . . . the desired output.
The input must go into the right machine first, then its output goes into the left machine to get a final output of 5 from an input of 6.
__
b) The left machine cannot produce negative outputs, so achieving an output of -5 with the arrangement used in part A is not possible. (green curves in the attached graph)
However, as we have shown above, inputting 6 to the left machine first, following that by processing with the right machine, can produce an output of -5. (purple curve in the attached graph)
Musah stands at the centre of a rectangular field. He first takes 50 steps north, then 25 steps
west and finally 50 steps on a bearing of 3150
.
i. Sketch Musah’s movement [Mark 4]
ii. How far west is Musah’s final point from the centre?
Answer:
Inokkohgy8uokokj76899
-50 POINTS- (2/5) please no wrong answers for points. A) y = [tex]\frac{9}{2}[/tex] x + [tex]\frac{1}{2}[/tex] B) y = - [tex]\frac{1}{2} x + \frac{7}{2}[/tex] C) [tex]y = -4x +9[/tex] D) [tex]y=4x+15[/tex]
This problem is about creating a linear regression model.
First, we should take note of the points:
(-4,8)
(-2,4)
(-1,2)
(1,5)
(2,2)
(6,-5)
(7,6)
It's necessary to find a equation y = ax + b that brings us the least MSE (Mean Squared Error). You can calculate at hand, but I bet it is going to be tiresome.
So, basically intuitively you just need to choose a line that fits closer to the given points.
First: remember if y = ax+b, a is the slope which means if a > 0 the line is " / " and a < 0 the line is " \ ".
A) No, this equation is " / "
B) It could be this one.
C) It could be this one too.
D) Nope. " / "
B) a = -1/2
C) a = -4
You can draw those two lines and see that B) gets closer to the points.
Equation:
Y = -0.4957*X + 3.780
Answer: B)Answer:
[tex]\Large \boxed{y=-\frac{1}{2} x+\frac{7}{2} }[/tex]
Step-by-step explanation:
Using a graph,
we can see that the line y = -1/2x + 7/2 best fits for the data.
