Answer:
[tex]F(t,y)=(2+7e^t)y+3(1-t)e^t +C[/tex]
Step-by-step explanation:
You have the following differential equation:
[tex]e^t(7y-3t)dt+(2+7e^t)dy=0[/tex]
This equation can be written as:
[tex]Mdt+Ndy=0[/tex]
where
[tex]M=e^t(7y-3t)\\\\N=(2+7e^t)[/tex]
If the differential equation is exact, it is necessary the following:
[tex]\frac{\partial M}{\partial y}=\frac{\partial N}{\partial t}[/tex]
Then, you evaluate the partial derivatives:
[tex]\frac{\partial M}{\partial y}=\frac{\partial}{\partial t}e^t(7y-3t)\\\\\frac{\partial M}{\partial t}=7e^t\\\\\frac{\partial N}{\partial t}=\frac{\partial}{\partial t}(2+7e^t)\\\\\frac{\partial N}{\partial t}=7e^t\\\\\frac{\partial M}{\partial t} = \frac{\partial N}{\partial t}[/tex]
The partial derivatives are equal, then, the differential equation is exact.
In order to obtain the solution of the equation you first integrate M or N:
[tex]F(t,y)=\int N \partial y = (2 +7e^t)y+g(t)[/tex] (1)
Next, you derive the last equation respect to t:
[tex]\frac{\partial F(t,y)}{\partial t}=7ye^t+g'(t)[/tex]
however, the last derivative must be equal to M. From there you can calculate g(t):
[tex]\frac{\partial F(t,y)}{\partial t}=M=(7y-3t)e^t=7ye^t+g'(t)\\\\g'(t)=-3te^t\\\\g(t)=-3\int te^tdt=-3[te^t-\int e^tdt]=-3[te^t-e^t][/tex]
Hence, by replacing g(t) in the expression (1) for F(t,y) you obtain:
[tex]F(t,y)=(2+7e^t)y+3(1-t)e^t +C[/tex]
where C is the constant of integration
What’s the correct answer for this?
Answer:
XY = 5268
Step-by-step explanation:
XY = XZ (originating from the same point)
85b+83=91b-283
85b-91b=-283-83
-6b=-366
Dividing both sides by -6
b = 61
Now
XY = 85b+83
= 85(61)+83
= 5268
Solve x-6y=17 for y, please help
Answer:
y = x/6 - 17/6
Step-by-step explanation:
x - 6y = 17
<=>6y = x - 17
<=> y =x/6 - 17/6
Hope this helps!
There are 4, 6, and 7 points on three lines. How many quadrilaterals is it possible to create with given points as vertices?
Answer:
Step-by-step explanation:If you choose any 3 of the 7 vertices, you can connect them with lines to create a unique triangle.
So, the question becomes "In how many different ways can we select 3 vertices from 7 vertices?"
Since the order in which we select the 3 vertices does not matter, we can use COMBINATIONS.
We can select 3 vertices from 7 vertices in 7C3 ways.
A bowl of cold gazpacho soup is warming to room temperature.the temperature difference between the soup and the room decreases by 5% every minute. What will the temperature difference be in 5 minutes if it is currently 16°C
Answer:
The temperature difference in 5 minutes will be 12.38ºC
Step-by-step explanation:
The difference in temperature after t minutes is given by the following equation:
[tex]T(t) = T(0)(1-r)^{t}[/tex]
In which T(0) is the initial temperature and r is the decrease rate, as a decimal.
Decreases by 5% every minute.
This means that [tex]r = 0.05[/tex]
What will the temperature difference be in 5 minutes if it is currently 16°C
This is T(5) when [tex]T(0) = 16[/tex]
So
[tex]T(t) = T(0)(1-r)^{t}[/tex]
[tex]T(t) = 16(1-0.05)^{t}[/tex]
[tex]T(t) = 16*(0.95)^{t}[/tex]
[tex]T(5) = 16*(0.95)^{5} = 12.38[/tex]
The temperature difference in 5 minutes will be 12.38ºC
Mr. Patel is photocopying lab sheets for his first period class. A particle of toner carrying a charge of 4.0 * 10^9 C in the copying machine experiences an electric field of 1.2 * 10^6 N/C as it’s pulled toward the paper. What is the electric force acting on the toner particle?
Answer:
4.8 * 10^15 Newton
Step-by-step explanation:
Electric field is electric force created by a unit charge. Mathematically it is defined as
Electric field = electric force /charge in coulomb _____(1)
given
Electric field = 1.2 * 10^6 N/C
charge = 4.0 * 10^9 C
substituting above value in equation 1 we have
1.2 * 10^6 N/C = electric force/4.0 * 10^9 C
=> 1.2 * 10^6 N/C * 4.0 * 10^9 C = electric force
=> electric force = 4.8 * 10^15
Thus, electric force acting on the toner particle is 4.8 * 10^15 Newton
The augmented matrix of a system of equations has been transformed to an equivalent matrix in​ row-echelon form. Using​ x, y, and z as​ variables, write the system of equations corresponding to the following matrix. If the system is​ consistent, solve it.
left bracket Start 3 By 3 Matrix 1st Row 1st Column 1 2nd Column 2 3rd Column 2 2nd Row 1st Column 0 2nd Column 1 3rd Column negative 3 3rd Row 1st Column 0 2nd Column 0 3rd Column 1 EndMatrix Start 3 By 1 Table 1st Row 1st Column 4 2nd Row 1st Column 9 3rd Row 1st Column negative 2 EndTable right bracket
1 2 2
0 1 −3
0 0 1
4
9
−2
Which of the following system of equations corresponds to the given​ matrix?
A.
x plus 2 y plus 2 zx+2y+2z
equals=44
y minus 3 zy−3z
equals=99
z
equals=minus−22
B.
2 x plus 2 y2x+2y
equals=44
negative 3 y−3y
equals=99
z
equals=minus−22
C.
2 x plus 2 y plus 4 z2x+2y+4z
equals=1
negative 3 y plus 9 z−3y+9z
equals=1
minus−z
equals=1
D.
x
equals=44
2 x plus y2x+y
equals=99
2 x minus 3 y plus z2x−3y+z
equals=minus−22
Select the correct choice below and fill in any answer boxes in your choice.
A.
The solution set is
StartSet nothing EndSet{}.
​(Type an ordered​ triple.)
B.
The solution is the empty set.
Answer: The system of equations is:
x + 2y + 2 = 4
y - 3z = 9
z = - 2
The solution is: x = -22; y = 15; z = -2;
Step-by-step explanation: ONe way of solving a system of equations is using the Gauss-Jordan Elimination.
The method consists in transforming the system into an augmented matrix, which is writing the system in form of a matrix and then into a Row Echelon Form, which satisfies the following conditions:
There is a row of all zeros at the bottom of the matrix;The first non-zero element of any row is 1, which called leading role;The leading row of the first row is to the right of the leading role of the previous row;For this question, the matrix is a Row Echelon Form and is written as:
[tex]\left[\begin{array}{ccc}1&2&2\\0&1&3\\0&0&1\end{array}\right][/tex][tex]\left[\begin{array}{ccc}4\\9\\-2\end{array}\right][/tex]
or in system form:
x + 2y + 2z = 4
y + 3z = 9
z = -2
Now, to determine the variables:
z = -2
y + 3(-2) = 9
y = 15
x + 30 - 4 = 4
x = - 22
The solution is (-22,15,-2).
What is 8 times as many as 3 is
Answer:
24?
Step-by-step explanation:
The following table shows a proportional relationship between www and zzz.
www zzz
181818 222
454545 555
818181 999
Write an equation to describe the relationship between www and zzz.
Answer:
z=1/9w
Step-by-step explanation:
Equation w = 9z best describes the proportional relationship between w and z.
Data has been given
w = 18 45 81
z = 2 5 9
proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense that are they directly proportional or inversely proportional to each other.
Clearly from the data as z increases w increases so it implies w is directly proportional to z.
w ∝ z
w = kz - - - - - - (1)
Where k is proportionality constant.
From data put w = 18 and z = 2
18=k*2
k=18/2
k=9
put k in equation w =kz
w = 9z
It shows that w is directly proportional to z by the constant of proportionality 9.
Thus equation w = 9z best describes the proportional relationship between w and z.
Learn more about proportionality here:
https://brainly.com/question/22620356
#SPJ2
4 10
- = -
7 X
What's the value of x
Answer: [tex]x = \frac{35}{2}[/tex] or [tex]x = 17.5[/tex]
Step-by-step explanation:
[tex]\frac{4}{7} = \frac{10}{x}[/tex]
[tex]\frac{4x}{4} = \frac{70}{4}[/tex]
[tex]x = \frac{35}{2}[/tex]
or [tex]x = 17.5[/tex]
A city has a total budget of $10 million per year. It brings in $3.5 million per year
in revenues other than property taxes. Therefore, the city must generate $6.5
million in property taxes to balance its budget. The net assessed valuation of all
property in that city is $825 million. What is the percent tax rate necessary to
generate the $6.5 million? Only use two decimal places and do not round.
Answer:
0.78%
Step-by-step explanation:
The percentage tax rate required is t such that ...
825t = 6.5 . . . . . milliions of dollars
t = 6.5/825
As a percentage, ...
t = 6.5/825 × 100% = 0.7878...% ≈ 0.78%
_____
Comment on rounding
Ordinarily, this value would be rounded to 0.79%. Property tax rates are often expressed in mils, or dollars per thousand. In that form, the tax rate would be 7.88‰ when rounded to two decimal places.
find the difference
8ab^3 square root ac^2-14ab^3 squareroot ac^2
Answer:
-6ab^3sqrtac^2 option b
Step-by-step explanation:
i just did it
Answer:
Step-by-step explanation:
How do you create and solve equations in one variable given a real-world situation?
Answer:
by finding something to factor it by
Answer:
1) first eliminate constant (number without variable) you eliminate constant by doing the inverse operation (if constant is being added, then subtract) (if constant is being subtracted, then add it)
ex: if x+9=32
subtract 9 from both sides to get rid of it
x=23
2) if there is another constant but this constant is being multiplied/divided then do the opposite operation to remove it
you could multiply by 3 on both sides:
x+9=69
x=60
pls halp me TwT im l
confused since quarantine happened reee
lateral area
surface area
volume
Answer:
22 is the answer but which country are you from
Answer:
22
Step-by-step explanation:
(Old Final Exam Problem-A2011) A right circular cone of height h and base radius r has total surface area S consisting of its base area plus its side area, leading to the formula: S= π r2 + π r r2+h2 Suppose you start out with a cone of height 8 cm and base radius 6 cm, and you want to change the dimensions in such a way that the total surface area remains the same. Suppose you increase the height by 15/100. In this problem, use tangent line approximation to estimate the new value of r so that the new cone has the same total surface area. The estimated value of r =
Answer:
5.972 cm
Step-by-step explanation:
Using implicit differentiation, we have ...
0 = (2πr +π(√(r^2+h^2) +r^2/√(r^2+h^2))·dr/dh +πrh/√(r^2+h^2)
For the given values of r and h, this is ...
0 = (12π +π(10 +36/10))dr/dh +48π/10
dr/dh = -4.8/(12+13.6) = -0.1875
Then the tangent line is ...
r = -0.1875(h -8) +6
__
For a height of 8 +15/100 = 8.15, the estimated value of r is ...
r = -0.1875(8.15 -8) +6 = -0.1875(0.15) +6 = 5.971875
The estimated value of r is 5.972 cm.
4x + 3y - z = -6
6x - y + 3z = 12
8x + 2y + 4z = 6
Answer:
(x, y, z) = (1, -3, 1)
Step-by-step explanation:
Any number of calculators and/or web sites can be used to solve this system of equations. It can be helpful to familiarize yourself with your graphing calculator's capabilities in this area. The solution from one such site is shown below:
(x, y, z) = (1, -3, 1)
__
Both y and z show up in these equations with coefficients that have a magnitude of 1. This means you can easily use one of those equations to create a substitution for y or for z.
Using the first equation to write an expression for z, we have ...
z = 4x +3y +6
Substituting that into the second and third equations gives ...
6x -y +3(4x +3y +6) = 12 ⇒ 18x +8y = -6
8x +2y +4(4x +3y +6) = 6 ⇒ 24x +14y = -18
Now, we can subtract 4 times the first equation from 3 times the second to eliminate x:
3(24x +14y) -4(18x +8y) = 3(-18) -4(-6)
10y = -30
y = -3
Substituting into the first equation (of the equations in x and y), we have ...
18x +8(-3) = -6
18x = 18
x = 1
Finally, substituting into the equation for z gives ...
z = 4(1) +3(-3) +6 = 1
The solution is (x, y, z) = (1, -3, 1).
___
The equations can also be solved using Cramer's rule, elimination, matrix methods, and other means. When solving by hand, the method of choice will often depend on what you're familiar with and what the coefficients are.
72 candies are devided between ahmad, zara and bilal in the ratio 3:4:5,find the number of candies that each person will receive
Answer:
6*3 = 18 candies - Ahmad
6*4 = 24 candies - Zara
6*5 = 30 candies - Bilal
Step-by-step explanation:
3+4+5= 12 parts
72 : 12 = 6 candies is one part
6*3 = 18 candies - Ahmad
6*4 = 24 candies - Zara
6*5 = 30 candies - Bilal
If the terminal ray of β lies in the fourth quadrant and sin (β) = -√3/3 determine cos(β) in simplest form.
I really appreciate your help, please help.
Thank you
God bless
Answer:
cos(β) = √6/3
Step-by-step explanation:
Given β lies in the fourth quadrant and sin (β) = -√3/3
we know that the trigonometry formula
sin²(β)+cos²(β) = 1
cos²(β) = 1- sin²(β)
cos²(β) = 1- ( -√3/3)²
= [tex]1-\frac{3}{9} } } =\frac{6}{9}[/tex]
cos(β) = √6/9 = √6/3
we Know that β lies in the fourth quadrant so cos(β) is Positive
cos(β) = √6/3
What 4 1/2 meters equal to
Answer:
4 1/2 meters is equal to 4.5
Step-by-step explanation:
This is the correct answer to 4 1/2 meters. :)
what are the square units?
Answer:
my butt
Step-by-step explanation:
my poop
dxhfhdjdjsjajalalalalqlqlqlalalal
A sample of size =n72 is drawn from a population whose standard deviation is =σ25. Part 1 of 2 (a) Find the margin of error for a 95% confidence interval for μ. Round the answer to at least three decimal places. The margin of error for a 95% confidence interval for μ is . Part 2 of 2 (b) If the sample size were =n89, would the margin of error be larger or smaller?
Answer:
a) margin of error ME = 5.77
b) Margin of error becomes smaller
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
x+/-ME
Where margin of error ME = zr/√n
a)
Given that;
Mean = x
Standard deviation r = 25
Number of samples n = 72
Confidence interval = 95%
z(at 95% confidence) = 1.96
Substituting the values we have;
ME = 1.96(25/√72)
ME = 1.96(2.946278254943)
ME = 5.774705379690
ME = 5.77
b)
For n = 89
ME = 1.96(25/√89)
ME = 1.96(2.649994700015)
ME = 5.193989612031
ME = 5.19
5.19 is smaller than 5.77 in a) above. So,
Margin of error becomes smaller
simplify the expression 2\3(-4)-(1/6-8/6
Answer:
1/8
Step-by-step explanation:
Answer:
When you simplify it, you get the answer of 1.
Step-by-step explanation:
Order of operation rules are required that you multiply and divide before you carrying out addition and/or subtraction.
So, simplify 2/3 / (-4) first, obtaining -1/6.
Now, you have -1/6 - 1/6 + 8/6, which combines to 1 or 6/6.
How many pounds of a 23% zinc alloy must be mixed with a 42% zinc alloy to make 516 pounds of a 37.25% zinc alloy?
Answer:
(A)129 Pounds
Step-by-step explanation:
Let x be the number of 23% zink alloy
Therefore:
Since the total result is 516 pounds
The number of pounds of 42% zink alloy =516-x pounds
We then have the resulting equation:
0.23x+0.42(516-x)=0.3725*516
0.23x+216.72-0.42x=192.21
Colect like terms
0.23x-0.42x=192.21-216.72
-0.19x=-24.51
Divide both sides by 129
x=129 pounds
Therefore, the number of pounds of 23% zink alloy that must be mixed is 129 pounds.
Find the area of the shape shown below.
4
4
8
2
Two shaped are merged so
One is square and the other is trapezoid so,
AREA OF SQUARE=4*4
=16
AREA OF TRAPEZOID=(2+4)x4/2
So,rhe answer will be
12+16=28
HOPE IT IS HELPFUL
Answer: 28 units^2
Step-by-step explanation:
You basically have a square and a trapezoid merged together
4*4=16 for the square
(2+4)*4/2=12 for the trapezoid
so
12+16=28 is your answer
Flow meters are installed in urban sewer systems to measure the flows through the pipes. In dry weatherconditions (no rain) the flows are generated by waste-water from households and industries, together withsome possible drainage from water stored in the topsoil from previous rainfalls. In a study of an urbansewer system, the following values were obtained for flowrates during dry weather conditions:
423.6, 487.3, 453.2, 402.9, 483.0, 477.7, 442.3, 418.4, 459.0
Assume that the flow rates are normally distributed.
a. Construct a 98% two-sided confidence interval for the standard deviation of the flow rate under dry weather conditions.
b. Explain, only using words, the meaning of the CI you determined in (a).
Answer:
a) [tex]\frac{(8)(30.23)^2}{20.09} \leq \sigma^2 \leq \frac{(8)(30.23)^2}{1.65}[/tex]
[tex] 363.90 \leq \sigma^2 \leq 4430.80[/tex]
Now we just take square root on both sides of the interval and we got:
[tex] 19.08 \leq \sigma \leq 66.56[/tex]
b) For this case we are 98% confidence that the true deviation for the population of interest is between 19.08 and 66.56
Step-by-step explanation:
423.6, 487.3, 453.2, 402.9, 483.0, 477.7, 442.3, 418.4, 459.0
Part a
The confidence interval for the population variance is given by the following formula:
[tex]\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}[/tex]
On this case we need to find the sample standard deviation with the following formula:
[tex]s=sqrt{\frac{\sum_{i=1}^8 (x_i -\bar x)^2}{n-1}}
And in order to find the sample mean we just need to use this formula:
[tex]\bar x =\frac{\sum_{i=1}^n x_i}{n}[/tex]
The sample deviation for this case is s=30.23
The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:
[tex]df=n-1=9-1=8[/tex]
The Confidence interval is 0.98 or 98%, the value of [tex]\alpha=0.02[/tex] and [tex]\alpha/2 =0.01[/tex], and the critical values are:
[tex]\chi^2_{\alpha/2}=20.09[/tex]
[tex]\chi^2_{1- \alpha/2}=1.65[/tex]
And replacing into the formula for the interval we got:
[tex]\frac{(8)(30.23)^2}{20.09} \leq \sigma^2 \leq \frac{(8)(30.23)^2}{1.65}[/tex]
[tex] 363.90 \leq \sigma^2 \leq 4430.80[/tex]
Now we just take square root on both sides of the interval and we got:
[tex] 19.08 \leq \sigma \leq 66.56[/tex]
Part b
For this case we are 98% confidence that the true deviation for the population of interest is between 19.08 and 66.56
What’s the correct answer for this?
Answer:
C: x = 10
Step-by-step explanation:
PO = QR (so having equal central angles)
Now
4x-11 = 2x+9
4x-2x = 9+11
2x = 20
Dividing both sides by 2
x = 10
Answer:
x=10
Step-by-step explanation:
2x+9=4x-11
-2x -2x
9=2x-11
+11 +11
20=2x
:2 :2
x=10
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order or formula (5), as instructed, to ?nd a second solution y2(x)
y"+2y'+y=0; y1=xe^-x.
Answer:
[/tex]y2=e^(-x)[/tex]
Step-by-step explanation:
CHECK THE ATTACHMENT BELOW FOR DETAILED EXPLANATION
Please help me figure this one out!
Answer:
7
Step-by-step explanation:
∑ᵢ₌₁³ (4 × (½)ⁱ⁻¹)
This is the sum of the first 3 terms of the sequence.
The first 3 terms are:
4 × (½)¹⁻¹ = 4
4 × (½)²⁻¹ = 2
4 × (½)³⁻¹ = 1
So the sum is:
∑ᵢ₌₁³ (4 × (½)ⁱ⁻¹) = 4 + 2 + 1 = 7
I need 6th question in the paper
Answer:
8
Step-by-step explanation:
[tex] a = 1 - \sqrt{2} [/tex]
[tex] (a - \dfrac{1}{a})^3 = [/tex]
[tex] = (\dfrac{a^2}{a} - \dfrac{1}{a})^3 [/tex]
[tex] = (\dfrac{a^2 - 1}{a})^3 [/tex]
[tex] = (\dfrac{(a + 1)(a - 1)}{a})^3 [/tex]
[tex] = (\dfrac{(1 - \sqrt{2} + 1)(1 - \sqrt{2} - 1)}{a})^3 [/tex]
[tex]= (\dfrac{(2 - \sqrt{2})(-\sqrt{2})}{1 - \sqrt{2}})^3[/tex]
[tex]= (\dfrac{(-2\sqrt{2} + \sqrt{2}\sqrt{2}}{1 - \sqrt{2}})^3[/tex]
[tex]= (\dfrac{2 - 2\sqrt{2}}{1 - \sqrt{2}})^3[/tex]
[tex]= (\dfrac{2(1 - \sqrt{2})}{1 - \sqrt{2}})^3[/tex]
[tex] = 2^3 [/tex]
[tex] = 8 [/tex]
Can someone help me with the answer
Answer:
D. 129°
Step-by-step explanation:
Angles XZY and XZV form a linear pair, so are supplementary.
angle XZV = 180° -51° = 129°
If a coin is flipped 10 times, what is the best prediction possible for the number of times it will land on tails
Answer:
5 times
Step-by-step explanation:
There is a 1/2 (50%) chance each time it is flipped that it will land on heads. Therefore, if flipped 10 times, 1/2 of 10 is 5