On Solving the initial value problem y(t) , e⁻²¹ dy/dt =y⁻¹(1-e⁻²t); y(0) = 0 , we get the solution is y² = e^(2t) - 2t - 1 .
The function is : e⁻²¹ dy/dt =y⁻¹(1-e⁻²t) ;
⇒ e^(-2t)dy/dt = (1/y)(1-e⁻²t) ..because y⁻¹ = 1/y ;
⇒ ydy = e^(2t)[1-e^(-2t)) dt ;
⇒ ydy = (e^(2t) - 1)dt ;
now integrating both sides of the problem ;
⇒ y²/2 = [e^(2t)/2 - t]+c ;
Now we know that initial value : y(0) = 0 ;
Substituting y(0)= 0 , we get ;
⇒ 0²/2 = [e⁰/2 - 0]+c ;
⇒ c = -1/2 ;
So , the solution is y²/2 = [e^(2t)/2 - t] - 1/2 .
it can be written as : y² = e^(2t) - 2t - 1 .
Therefore , the solution of the initial value problem is y² = e^(2t) - 2t - 1 .
Solve the following initial value problems for y(t) by antidifferentiation or by aseparation of variables : e⁻²¹ dy/dt =y⁻¹(1-e⁻²t); y(0) = 0 .
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How many kg in 40 lb?
The number of kilogram in 40 lb would be 18.1437.
What is the difference between pounds and kilograms?A pound is an imperial unit used to measure bulk or weight. A kilogram is a metric measuring unit. The letters lb and lbm stand for pounds. Kilo or kg are used to denote kilograms. 0.4535 kilograms make up one pound.
In both the British imperial system and the United States' customary system, weight is measured in pounds. Measuring a person's weight is one common application of pounds.
The weight of a kilogram is 2.2046 pounds. We convert kilograms (kg) to pounds (lb) using the formula 1 kg = 2.2 lb. By multiplying by 2.2, we may convert a kilogram to a pound. We divide by 2.2 to change a pound into a kilogram.
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3) Determine the slope of the line that contains the given points!
(-6,10) and (-12,-10). (1 pt)
A) 0
B)10/3
C)undefined
D)-10/3
Answer:
B
Step-by-step explanation:
Δy = -10-10= -20
Δx = -12-(-6) = -6
-20/-6= 10/3
what 26789 divide 43
A parabola can be drawn given a focus of (-7, 9) and a directrix of y = 11. Write
the equation of the parabola in any form.
The equation of the parabola with focus at (-7,9) and directrix at y = 11 is given as follows:
(x + 7)² = -4(y - 10)
How to obtain the equation of the parabola?The equation of a vertical parabola is given as follows:
(x - h)² = 4p(y - k)
In which:
(h,k) are the coordinates of the vertex.y = k - p are the coordinates of the directrix.(h, k + p) are the coordinates of the focus.A parabola can be drawn given a focus of (-7, 9), hence:
h = -7.k + p = 9.Directrix of y = 11, hence:
k - p = 11.
Adding the equations of the y-coordinate of the focus and of the directrix, the value of k is obtained as follows:
2k = 20
k = 20/2
k = 10.
Hence the value of p is of:
p = k - 11
p = -1.
Meaning that the equation is:
(x + 7)² = -4(y - 10)
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What is the rule for an exponential graph?
One significant mathematical function that has the form is the exponential function, f(x) = [tex]$$a^x[/tex].
What is meant by exponential graph?If f(x) = [tex]$$a^x[/tex], where x is the input variable and is expressed as an exponent, is the formula for an exponential function. In addition to being dependent on the exponential function, the exponential curve also depends on the value of x. One significant mathematical function that has the form is the exponential function. f(x) = [tex]$$a^x[/tex].
The four fundamental characteristics of exponential functions are their y-intercept, horizontal asymptote, domain (the range of x values at which the function occurs), and constant growth factor, b.
Calculating the exponential growth or decay of a set of given data is done using an exponential function. According to the power to the power rule, "If the base increased to a power is being raised to another power, then the two powers are multiplied and the base remains the same."
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Can I please get help with this?
Answer:
Step-by-step explanation:
its number 3
tv screens are measured on the diagonal. if we have a tv-cabinet that is 66 inches long and 54 inches high, how large a tv could we put in the space (leave 2-inches on all sides for the edging of the tv)? round your answer to the nearest tenth.
Using Pythagoras' theorem, we can conclude that we can put a 79.65 inches TV in the TV cabinet.
We have been given that a TV -cabinet is 64 inches long and 52 inches high.
After leaving 2 inches on all sides, our new dimensions would be:
Length = 66 - 2 - 2 = 66 - 4 = 62 inches
Height = 54 - 2 - 2 = 54 - 4 = 50 inches
Using Pythagoras' theorem, we can find the diagonal of the television
Diagonal² = 62² + 50²
Diagonal² = 3844 + 2500
Diagonal² = 6344
Take square root of both sides:
Diagonal = √6344
Diagonal = 79.65 inches
Hence, we can put a 79.65 inches TV
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or the students in kendra's grade voted to select a guest speaker. 20% of the students voted for a famous athlete. if there are 85 students in kendra's grade, how many students voted for the athlete?
There will be 17 students voted for the famous athlete.
Athlete Speaker Vote CountYou can calculate this by multiplying the number of students in the grade (85) by the percentage who voted for the athlete (20% or 0.20).
85 x 0.20 = 17
The method used here is called "Percentage calculation." The method of percentage calculation is generally applicable to many situations where you want to find the proportion of a number relative to another number. It can be used to solve problems in various fields such as mathematics, finance, statistics, and more.
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Alice watched two films at the cinema. The first film was 1; hours long and the second was 2} hours long. a Work out the total length of the two films. Alice drove to the cinema. She arrived 10 minutes before the first film began and had to wait for half an hour between the two films. She left immediately after the second film finished. Car park tickets can be bought in multiples of 1 hour. b How many hours of parking did Alice need to buy?
Answer:
4
Step-by-step explanation:
1h
2hrs
10 mins before
wait 30mins
total: 3h 40mins
so has to buy 4hrs
Answer:
she has to pay for 3 hours and 40 minutes worth of parking so 4 or 3 if its rounded or not
Step-by-step explanation:
The members of a population have been numbered 1-341.
A sample of size 5 is to be taken from the population, using systematic random sampling. Complete the below using the table.
Random Number Table- 03184 61921 87377
97729 79151 33433
Procedure for Systematic Random Sampling
First, divide the population size by the sample size and round the result down to the nearest whole number, m.
Then, use a random-number table or a similar device to obtain a number, k, between 1 and m.
Finally, select for the sample those members of the population that are numbered k, kplus+m, kplus+2m,
Apply the procedure to determine the sample (that is, the numbers corresponding to the members of the population that are included in the sample), using the provided random-number table. To use the random-number table, Start at the two-digit number at the top left, read down the column, up the next, and so on.
The value of k for this sample is?
(Type a whole number.)
The sample is ?
(Type whole numbers. Use a comma to separate answers asneeded.)
b. Suppose that the random sample chosen from the random number table is 22 number chosen from the random number table is 22 (that is k=22) Determine the sample.
The sample is-
The sample is 3, 71, 139, 207, and 275.
The procedure for systematic random sampling involves first dividing the population size by the sample size and rounding the result down to the nearest whole number, m. This value of m is known as the sampling interval. For the given population size of 341 and sample size of 5, the value of m is 68.
Next, a random number, k, between 1 and m is chosen. The given random-number table contains the values 03184, 61921, 87377, 97729, and 79151. Reading the two-digit number at the top left, we get 03, which is equal to 3. Therefore, k = 3.
Finally, the sample is taken from the population in intervals of m. In this case, the sample consists of members of the population numbered 3, 71, 139, 207, and 275. Therefore, the sample is 3, 71, 139, 207, and 275.
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Name a pair of adjacent angles in this figure. N
Answer:
Step-by-step explanation:
angleNOP AND anglePOQ
anglePOQ AND angleQOR
The segment joining a vertex to the middle of
the opposite side of a triangle is called the
Select one:
O a. angle bisector
O b. altitude
c. perpendicular bisector
O d. median
In this figure, a || b || c and m/5 = 155°
What is m/3 ?
25°
65°
155°
I don't know.
25 Degres it is a obtuse angle using the dewy decimal system
Answer:
The person above me is correct
25
Step-by-step explanation:
Which item loads onto the same component as P1Q45?O PIQ42 O P1Q7O O P2Q23O none of the above
None of the aforementioned goods loads upon P1Q45. This is so that they cannot be loaded onto the same amount since each item is linked to a different one.
None of the aforementioned goods loads upon P1Q45. This is so that they cannot be loaded onto the same component since each item is linked to a different one. For instance, P1Q45 is connected to a particular component, like a printer, whereas P1Q7 is connected to a different component, like a monitor. Likewise, P2Q23 is connected to a third element, such a scanner. Therefore, it is not possible to load these items onto the same component as P1Q45. Furthermore, each of the three objects would need to be loaded separately into the component even if they were all linked to the same one. This is due to the fact that for the component to work effectively, each item needs to be put onto it securely and accurately. The answer to the question is therefore none of the aforementioned options.
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.Most of Conservative Casey’s money is invested in a savings account that pays 1%
interest a year, but some is invested in a risky stock fund that pays 7% a year. Casey’s
total initial investment in the two accounts was $10000. At the end of the first year, Casey
received a total of $250 in interest from the two accounts. Find the amount initially invested
in each
The amount Casey invested in the certificate of deposit is; $60,000.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Assume that
0.01c - 0.02s = $250---equation 1
c + s = $10,000 ------ equation 2
Where: c = amount invested in the certificate of deposit
s = amount invested in the savings account
Now Multiply equation 2 by 0.01:
0.01c + 0.01s = 100 equation 3
Subtract equation 3 from equation 1:
0.01s = 100
Divide both sides of the equation by 0.01:
s = 100 / 0.01
s = 10,000
Substitute for s in equation 2:
c + 10,000 = 70,000
c = 70,000 - 10,000
c = 60,000
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find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 5x5, y = 5x, x ≥ 0; about the x-axis
The volume of the solid obtained by rotating the region bounded by the curves y = 5[tex]x^5[/tex] and y = 5x about the x-axis is -(8π/21) cubic units.
We have,
To find the volume of the solid obtained by rotating the region bounded by the curves y = 5[tex]x^5[/tex] and y = 5x about the x-axis, we can use the method of cylindrical shells.
The region bounded by the curves is between x = 0 and x = 1.
Let's consider an infinitesimally thin strip of width dx at a distance x from the y-axis.
The height of this strip will be the difference between the two curves:
(5[tex]x^5[/tex]) - (5x).
The circumference of the shell at this distance x is 2πx (since we are rotating about the x-axis).
Therefore,
The volume of this infinitesimally thin shell is given by:
dV = (2πx) x [(5[tex]x^5[/tex]) - (5x)] x dx.
To find the total volume, we integrate this expression over the interval [0, 1]:
V = ∫(0 to 1) (2πx) x [(5[tex]x^5[/tex]) - (5x)] dx.
Simplifying the expression inside the integral:
V = 2π ∫(0 to 1) [(5[tex]x^6[/tex]) - (5x²] dx.
Integrating term by term:
V = 2π [([tex]x^7[/tex])/7 - (x³)/3] evaluated from 0 to 1.
Substituting the limits of integration:
V = 2π [(([tex]1^7[/tex])/7 - (1³)/3) - (([tex]0^7[/tex])/7 - (0³)/3)].
Simplifying:
V = 2π [(1/7 - 1/3) - (0 - 0)].
V = 2π [(3 - 7)/21].
V = 2π (-4/21).
V = -(8π/21).
Therefore,
The volume of the solid obtained by rotating the region bounded by the curves y = 5[tex]x^5[/tex] and y = 5x about the x-axis is -(8π/21) cubic units.
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alice is holding up the top vertex of a triangular banner attached to the ground by two anchors on the bottom vertices. what is the area of the banner of alice reaches her arm up above the ground and the anchors on the bottom are apart?
Let's call the length of the bottom side of the triangular banner "b". When Alice reaches her arm up above the ground, the height of the banner changes from its original height of "h" to a new height of "h'". The area of the banner can be calculated using the formula:
A = (b * h') / 2
The new height "h'", can be calculated using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse).
In this case, the two shorter sides are the original height "h" and the difference between the length of Alice's arm and the original height, which we will call "d". The longest side is the distance between the two anchors, which we will call "a".
So:
h^2 + d^2 = a^2
We can solve for "d" using this equation:
d = sqrt(a^2 - h^2)
And then we can find "h'" using:
h' = h + d
So the area of the banner can be calculated as:
A = (b * (h + sqrt(a^2 - h^2))) / 2
The solution assumes that the banner is a right triangle, with one vertex at the top, one vertex at the bottom, and a straight side along the ground connecting the two bottom vertices.
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Three boys shared D 10,500.00 in the ratio 6:7: 8. Find the largest share.
Answer:
Step-by-step explanation:
let the common ratio be x.
boy 1 share= 6x
boy 2 share= 7x
boy 3 share= 8x
-------------------------------
21x= 10500.00
=> x= 10500/21
x= 500
6 x 500= $3000
7x 500= $3500
8 x 500= $28000
therefore, boy 3 has the largest share of $28000.
Four research teams each used a different method to collect data on how fast a new iron skillet rusts. Assume that they all agree on the sample size and the sample mean (in days). Use the (confidence level; confidence interval) pairs below to select the team that has the smallest sample standard deviation
The smallest sample standard deviation
Confidence Level: 95%; Confidence Interval: 42 to 48.
How to interpret the confidence interval?Assume that x ± y represents the confidence interval at P% for the values of some parameter.
In other words, the parameter's projected value is P% likely to fall within the range.
[x - y, x + y]
Data on how quickly a brand-new iron skillet rusts were gathered by four research teams using various techniques.
Assume that everyone is in agreement with the sample size and sample mean (in days).
Choose the team with the smallest sample standard deviation using the (confidence level; confidence interval) pairs below.
Then we have
= 48 - 42 = 6
Then we have
= 6/2
=3, which is smallest
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The question you have uploaded is seems to be incomplete, the complete question is
A. Confidence Level: 99.7%; Confidence Interval: 40 to 40
B. Confidence Level: 95%; Confidence Interval: 40 to 50
C. Confidence Level: 68%; Confidence Interval: 43 to 47
D. Confidence Level: 95%; Confidence Interval: 42 to 48
Kendra watches the moon change from a new moon to a full moon. Which of the following descriptions is accurate? (Select all that apply.)
Responses
The moon is waxing.
The moon is waxing.
The moon is waning.
The moon is waning., ,
The moon appears to get smaller.
The moon appears to get smaller.
The moon appears to get bigger.
The moon appears to get bigger.
The moon does not change.
The correct description is that moon is waxing.
Which of the following descriptions is accurate?The theory used in this question is the lunar cycle, which is the process by which the moon changes its shape and illumination over the course of a month.
The waxing phase of the lunar cycle is when the moon is gradually getting bigger and more illuminated.
The waning phase is when the moon is gradually getting smaller and less illuminated.
The moon is waxing:
This is an accurate description because when the moon changes from a new moon to a full moon, it is said to be waxing.
This means that the moon is gradually getting bigger, and its illuminated side is increasing.
This process is called the waxing phase of the moon's cycle.
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While playing his favorite video game, Damien sees that his character has leveled up to 70% of the maximum ranking. If he played for 56 hours to get to 70%, how many total hours will he need to play to achieve 100% rank
Answer:
Step-by-step explanation:
If Damien can get to 70% maximum ranking in 56 hours, then we can make this equation:
0.7x(representing 70%)=56 (Amount of time Damien has played)
0.7x=56
Divide 0.7 on both sides we get:
x=80
Damien will have to play 80 hours to get to 100% Rank.
what is the anwser= $200
Figure A
Save
Store
Leff's
Store
Low
Pricer
= $200
Figure B
Save
Store
Leff's
Store
Low
Pricer
In Figure A, how much did Save Store sell?
Save store sold 100/3.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
In figure A there are 12 stores
Now each store sells 200/12
If save store is 2
Save store sells =200/12×2
=100/3
Hence, save store sold 100/3.
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Simplify the expression please. See image for problem
Answer:
answer is 1
Step-by-step explanation:
12-y/6y-36
and other you can see by photo
The differential equation xydx + (x^2 + y^2)dy = 0 is Select the correct answer.
a. exact with solution x^2y/2 + y^3/3 =c b. exact wiih solution x^2y/2 + y^2/2 = c c. exact with solution x^2y/2 + y^3/3+c d. not d: not exact but having an integrating factor x c e. not exact but having an integrating factor y
The correct answer is option is option d) not exact but having an integrating factor x c e.
Integrating factor is defined as the function which is selected in order to solve the given differential equation. It is most commonly used in ordinary linear differential equations of the first order. When the given differential equation is of the form; dy/dx + P(x) y = Q(x)
We have, (x2+y2)dy= -xydx
⇒dxdy= -(x2+y2xy)
Substitute y=vx
⇒ - dxdy=v+xdxdv
⇒v+xdxdv= -(1+v2v)
⇒ xdxdv= -(1+v2v−v)
= -(−1+v2v3)
⇒v31+v2dv =xdx
Integrating both sides we get, −2v21+logv= logx-logc, where c is constant
⇒−2v21+log(cvx)=0
⇒y=cex2/2y2
Now using y(1)=1⇒c=e−1/2
Also y(x0)=e
⇒e=e−1/2+x02/2e2⇒1=−1/2+x02/2e2
⇒x02=3e2
⇒x0=[tex]\sqrt{3}[/tex]e
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What is the weight in lbs of a 75-kg person?
Hence, we can say that the weight of a person of 75 Kg in lbs will be equal to 165.3465lbs.
Define weight?The weight of an object is the force acting on it due to gravity in science and engineering.Weight is defined as a vector quantity in some standard textbooks, as the gravitational force acting on the object.Others define weight as a scalar quantity, the magnitude of gravity.We know that the conversion factor for lbs to kg is
1 kg = 2.20462lbs
Now, to convert 75 Kg into lbs, we need to multiply the 75 with the conversion factor. That is,
75kg = 75×2.20462lbs = 165.3465lbs
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Paul wins 1500metres in 4,67metres .(c) write down his average in metres per minutes correct to: (I) The nearest Whole number ( ii ) One decimal place ( iii ) Two decimal places ( iv ) Three significant figures
Answer:
(I) The nearest whole number is 317.5 meters per minute.
(ii) One decimal place is 317.5 meters per minute.
(iii) Two decimal places is 317.47 meters per minute.
(iv) Three significant figures is 317 meters per minute.
Note: To find the average velocity, divide the distance traveled by the time it took to travel that distance. 1500 meters / 4.67 minutes = 322.2 m/min. But since you want the answer rounded to different degrees, you can round the answer accordingly.
Es.
3
e
5. Andrew says that 60 is the greatest whole
number that rounds to 60. Is Andrew
correct? Explain your reasoning
Andrew is correct because 60 is the highest whole number that can round to 60. Any number higher than 60 will round up to a higher number. For example, 61 will round up to 70, and 62 will round up to 70. Therefore, 60 is the greatest whole number that rounds to 60.
The highest whole number is infinity, as there is no limit to how high a number can be. Whole numbers are all the numbers that are greater than or equal to 0, including 0 itself. The highest whole number is therefore infinity, as this is the highest possible number.
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the manager of a supermarket tracked the amount of time needed for customers to be served by the cashier. after checking with his statistics professor, he concluded that the checkout times are exponentially distributed with a mean of 5 minutes. what propotion of customers require more than 10 minutes to check out? proportion
Approximately 86.5% of customers will be served in less than 10 minutes and only 13.5% of customers will take more than 10 minutes to check out.
Exponential Checkout Time ProportionTo find the proportion of customers who take more than 10 minutes to check out, we need to calculate the cumulative distribution function (CDF) of an exponential distribution at 10 minutes and subtract it from 1. The CDF for an exponential distribution with mean (lambda) 5 minutes is given by:
CDF = 1 - e^(- λ * x)
Plugging in λ = 0.2 (1/mean) and x = 10, we get:
CDF = 1 - e^(-0.2 * 10) = 1 - e^(-2) = 1 - 0.135 = 0.865
So, approximately 86.5% of customers will be served in less than 10 minutes and only 13.5% of customers will take more than 10 minutes to check out.
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What is 32(4x+6) in simplified form
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{ASSUMING:}[/tex]
[tex]\mathsf{\dfrac{3}{2}(4x + 6)}[/tex]
[tex]\huge\textbf{If so, distribute \boxed{\rm{\bf \dfrac{3}{2}}} within the}\\\\\huge\textbf{parentheses}[/tex]
[tex]\mathsf{\dfrac{3}{2}(4x + 6)}[/tex]
[tex]\mathsf{= \dfrac{3}{2}(4x) + \dfrac{3}{2}(6)}[/tex]
[tex]\mathsf{= \dfrac{3}{2}\times \dfrac{4}{1}x + \dfrac{3}{2} \times \dfrac{6}{1}}[/tex]
[tex]\mathsf{= \dfrac{3\times4}{2\times1}x +\dfrac{3\times6}{2\times1}}[/tex]
[tex]\mathsf{= \dfrac{12}{2}x +\dfrac{18}{2}}[/tex]
[tex]\mathsf{= 6x + 9}[/tex]
[tex]\huge\textbf{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{6x + 9}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Write equations for the vertical and horizontal lines passing through the point (8, 0)
