Answer:
The answer to the question is
The longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution is (-∞, 4)
Step-by-step explanation:
To apply look for the interval, we divide the ordinary differential equation by (t-4) to
y'' + [tex]\frac{3t}{t-4}[/tex] y' + [tex]\frac{4}{t-4}[/tex]y = [tex]\frac{2}{t-4}[/tex]
Using theorem 3.2.1 we have p(t) = [tex]\frac{3t}{t-4}[/tex], q(t) = [tex]\frac{4}{t-4}[/tex], g(t) = [tex]\frac{2}{t-4}[/tex]
Which are undefined at 4. Therefore the longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution, that is where p, q and g are continuous and defined is (-∞, 4) whereby theorem 3.2.1 guarantees unique solution satisfying the initial value problem in this interval.
The existence and uniqueness theorems for ODEs determine that the longest interval where the initial value problem has a unique and twice-differentiable solution is (0, 4), avoiding discontinuities at t=0 and t=4.
Explanation:The initial value problem provided is a second-order linear ordinary differential equation (ODE) of the form:
t(t-4)y"+3ty'+4y=2, with initial conditions y(3)=0 and y'(3)=-1.
To determine the longest interval in which the solution is guaranteed to be unique and twice-differentiable, we need to consider the existence and uniqueness theorems for ODE's, which are predicated on the functions of the equation being continuous over the interval considered. Here, the coefficients of y" and y' are t(t-4) and 3t respectively. The problematic points occur where the coefficient of y" is zero because it will make the equation not well-defined, which occurs at t=0 and t=4. Therefore, the longest interval around the initial condition t=3 that avoids these points is (0, 4). Within this interval, the coefficients are continuous, and hence, the conditions for the existence and uniqueness of the solution are satisfied.
Write an equation in slope-intercept form of the line satisfying the given conditions. The line passes through (minus1,3) and is parallel to the line whose equation is y equals 2 x plus 1.
Answer:
y = 2x + 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 2x + 1 ← is in slope- intercept form
with slope m = 2
Parallel lines have equal slopes, thus
y = 2x + ← is the partial equation of the parallel line
To find c substitute (- 1, 3) into the partial equation
3 = - 2 + c ⇒ c = 3 + 2 = 5
y = 2x + 5 ← equation of parallel line
i can't fail this class plz helppppppp
Which of the following are ordered pairs for the equation y = -1/3x - 6?
(0,-6) (3,-7) (-3,5)
(0,-6) (3,-7) (-3,-5)
(0,-6) (3,7) (-3,-5)
(0,6) (3,7) (-3,-5)
Answer:
2nd option (B)
Step-by-step explanation:
(0,-6) works
(3,-7) works
(-3,-5) works
This means the answer is B
The probability that a randomly selected car will be in an accident in the next year in a particular country is 0.0467. If four cars are randomly selected, find the probability that at least one has an accident during the coming year. Round to 4 decimals.
To find the probability that at least one of four cars has an accident, calculate the probability that no cars have accidents and subtract from 1. The probability is approximately 0.1785 after rounding to four decimal places.
Explanation:The probability that at least one of four randomly selected cars will be in an accident in the next year can be found by using the complement rule. The complement of at least one car being in an accident is that no cars are in an accident. We can calculate the probability of no accidents occurring and then subtract from 1 to find the desired probability.
First, we calculate the probability of a single car not being in an accident. This is 1 - 0.0467 = 0.9533. We then raise this probability to the power of four to represent all four independent events (four car selections): (0.9533)4.
Probability of no accidents = 0.95334 ≈ 0.8215 (rounded to four decimals).
Now, we subtract this from 1 to find the probability that at least one car has an accident in the coming year.
Probability at least one accident = 1 - Probability of no accidents = 1 - 0.8215 = 0.1785 (rounded to four decimals).
The width of a rectangular prism is six times its length. The height is five times its length. If its length is m units, what is m units; what is the volume of the prism?
Answer:
[tex]30m^3[/tex] cubic units.
Step-by-step explanation:
Let m represent length of the rectangular prism.
We have been given that the width of a rectangular prism is six times its length, so width of the prism would be [tex]6m[/tex].
We are also told that the height is five times its length, so height of the prism would be [tex]5m[/tex].
We know that volume of rectangular prism is height times width times length.
[tex]\text{Volume of rectangular prism}=lwh[/tex]
[tex]\text{Volume of rectangular prism}=m\cdot 6m\cdot 5m[/tex]
[tex]\text{Volume of rectangular prism}=30m^3[/tex]
Therefore, the volume of the given rectangular prism would be [tex]30m^3[/tex] cubic units.
A line segment that has both endpoints on the circumference
Answer:
A chord
Step-by-step explanation:
By the definition of a chord, it is a line segment whose endpoints lie on the circle, (and in this case circle is meant by the set of points equidistant from a center point, or as an algebraic term: circumference)
Dont skip plz i need yall help
Answer: B) 1 and -3
Step-by-step explanation:
On a Quadrant Plane:
Q1: (+,+)
Q2: (-,+)
Q3: (-,-)
Q4: (+,-)
Answer:
B
Step-by-step explanation:
because the 4th quadrant is positive and negative which option B is the only one that has that option in the same order . HOPE THIS HELPED!
Teddy called the movie theater to find out how much tickets cost for him and his seven friends to go to the new hero movie. He remembered that the total was $60 if they go to the early movie but not how much each ticket is. Select which equation can be used so that he can tell his friends how much money the
Answer:
7.5
Step-by-step explanation:
If 8 people are going to the movie theater including Teddy, then we have to divide 60 by 8 which equals 7.5.
Molly made 3,600 mL3{,}600 \text{ mL}3,600 mL3, comma, 600, start text, space, m, L, end text of tea for a party, and she served the tea divided equally in 12121212 cups. How many liters of tea did Molly put in each cup?
Answer:
0.3 liters
Step-by-step explanation:
Molly made 3600mL of tea for a party.
The tea was served equally in 12 cups.
We are to determine how many liters of tea Molly put in each cup.
Total Volume of Tea = 3600mL
Number of Cups=12
Volume Per Each Cup = 3600/12 = 300mL
Next, we convert our Volume Per Each Cup from mL to Liters
1000 Milliliter = 1 Liter
300 Milliliter =[tex]\frac{300}{1000}[/tex] liters =0.3 liters
Molly put 0.3 liters of tea in each cup.
A certain computer loses half of its value every two years. If the value of the computer after 3 years is 425, what was the initial value of the computer
To solve this problem, we can use the concept of exponential decay, where the value of the computer decreases by half every two years. Let's denote the initial value of the computer as [tex]\( V_0 \)[/tex]. After the first two years, its value will be [tex]\( \frac{1}{2}V_0 \)[/tex], after another two years (total of 4 years), its value will be [tex]\( \frac{1}{4}V_0 \)[/tex], and after three years, its value will be [tex]\( \frac{1}{8}V_0 \).[/tex]
Given that after three years its value is $425, we can set up the equation:
[tex]\[ \frac{1}{8}V_0 = 425 \][/tex]
Now, let's solve for [tex]\( V_0 \):\[ V_0 = 425 \times 8 \]\[ V_0 = 3400 \][/tex]
So, the initial value of the computer was $3400.
Can someone please explain this problem to me idk what I am doing wrong and can you draw the problem for me thanks
Answer:
you're not doing anything wrong
Step-by-step explanation:
In order for cos⁻¹ to be a function, its range must be restricted to [0, π]. The cosine value that is its argument is cos(-4π/3) = -1/2. You have properly identified cos⁻¹(-1/2) to be 2π/3.
__
Cos and cos⁻¹ are conceptually inverse functions. Hence, conceptually, cos⁻¹(cos(x)) = x, regardless of the value of x. The expected answer here may be -4π/3.
As we discussed above, that would be incorrect. Cos⁻¹ cannot produce output values in the range [-π, -2π] unless it is specifically defined to do so. That would be an unusual definition of cos⁻¹. Nothing in the problem statement suggests anything other than the usual definition of cos⁻¹ applies.
__
This is a good one to discuss with your teacher.
help help help help
Which of the following is 2x(x-7)(x+3)/6x³(x+3)(x-5) simplified?
Cannot be simplified
(x-7)/3x(x-5)
2x(x-7)/6x³(x-5)
(x-7)/3x²(x-5)
Yes it can be, it will be a fraction
Answer:
[image]
Step-by-step explanation:
follow the steps provided in the picture
Technician A says that a MAF sensor is a high-authority sensor and is responsible for determining the fuel needs of the engine based on the measured amount of air entering the engine. Technician B says that a cold wire MAF sensor uses the electronics in the sensor itself to heat a wire 20 degrees below the temperature of the air entering the engine. Who is right
Answer: Both Technicians are correct
Step-by-step explanation: Technician A talked about the functions of a MAF sensor which is to determine the fuel need of the engine based on the of air entering the engine.
Technician B talked about types of MAF sensor employed in vehicles and how they function
Point M is the midpoint of AC , find the coordinates of the missing endpoint when you are given one endpoint, and the coordinates of the midpoint. M(0, 5.5) and C(-3, 6).
Step-by-step explanation:
Here, given the line segment is AC.
Let us assume the coordinates of the point A = (p,q)
The point M (0,5.5) is the mid point of line segment AC.
By Mid-Point Formula:
The coordinates of the mid point M of segment AC is given as:
[tex](0,5.5) = (\frac{p + (-3)}{2} ,\frac{q+ (6)}{2})\\\implies \frac{p + (-3)}{2} = 0 , \frac{q+ (6)}{2} = 5.5\\\implies p = 0 + 3 = 3, q = 5.5 (2) - 6 = 11-6 = 5\\\implies p = 3, q = 5[/tex]
So, the coordinates of the point A is (3,5)
A company is going to make an oil container in the shape of a cylinder. As shown below, the container will have a height of 8m and a diameter of 12m. The container will be made from steel (including its top and bottom). Suppose the total cost of the steel will be $17,408.16. How much will the steel cost per square meter? Use 3.14 for π, and do not round your answer.
For the cylinder whose surface area is 527.52 square meter, the total steel cost per square meter is $33.
The following information given in the question:
Height of the cylinder = 8 m
Diameter of the cylinder = 12 m
And the total cost of the steel = $17,408.16
We have to find the steel cost per square meter.
We know the radius is half of the diameter.
So, the radius (r) of the cylinder = 12/2 = 6 m
[tex]\text{Cost per square meter} = \dfrac{\text{total cost}}{\text{total surface area}}[/tex]
Surface area of the cylinder is calculated by the following formula:
Total surface area= 2πr(r+h)
=2×(3.14)×6(6+8)
=527.52 square meter
That means the steel cost for the 527.52 square meter is $17,408.16 (given in the question)
So, Cost per square meter = [tex]\dfrac{17,408.16}{527.52 }[/tex]
The steel cost of per square meter = $33
Hence, the steel cost of per square meter will be $33.
Learn more about surface area of the cylinder here:
https://brainly.com/question/28575608
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A box contains three coins: two regular and one fake one-sided coin (P(H) = 1) You pick a coin at random and toss it. What is the probability that it lands tails up? You pick a random coin and after tossing get H. What is the probability that the coin is not fake?
Answer:
0.50
Step-by-step explanation:
Given that a box contains three coins: two regular and one fake one-sided coin (P(H) = 1) You pick a coin at random and toss it.
Probability of selecting any one coin = 1/3
The coins are regular 1, regular 2 , fake
P for head 0.5 0.5 1
Probability for head = [tex]\frac{1}{3} (1+0.5+0.5) = 0.6667[/tex]
using total probability theorem for mutually exclusive and exhaustive)
Probability that coin is not fake/head = [tex]\frac{0.5+0.5}{1+0.5+0.5} \\= 0.5[/tex]
Bonita Industries sells radios for $50 per unit. The fixed costs are $645000 and the variable costs are 60% of the selling price. As a result of new automated equipment, it is anticipated that fixed costs will increase by $215000 and variable costs will be 50% of the selling price. The new break-even point in units is:
Answer:
The new break even point in units = 34400 units
Step-by-step explanation:
Fixed cost ( F ) = $ 645000
Selling price ( s )= $ 50
Variable Cost ( v ) = [tex]\frac{60}{100}[/tex] × 50 = 30
Break Even Quantity ( [tex]x_{BEP}[/tex] ) = [tex]\frac{F}{s - v}[/tex]
⇒ [tex]x_{BEP}[/tex] = [tex]\frac{645000}{50 - 30}[/tex]
⇒ [tex]x_{BEP}[/tex] = [tex]\frac{645000}{20}[/tex]
⇒ [tex]x_{BEP}[/tex] = 32250 units
Now the new fixed cost ( [tex]F_{1}[/tex] ) = $ 645000 + $ 215000 = $ 860000
Selling price ( s )= $ 50
Variable Cost ( v ) = [tex]\frac{50}{100}[/tex] × 50 = $ 25
Break Even Quantity ( [tex]x_{BEP}[/tex] ) = [tex]\frac{F_{1} }{s - v}[/tex]
⇒ [tex]x_{BEP}[/tex] = [tex]\frac{860000}{50 - 25}[/tex]
⇒ [tex]x_{BEP}[/tex] = 34400 units
Therefore, The new break even point in units = 34400 units
In the library at lenape elmentary school, there are 3/8 as, many fiction books as there are nonfiction books. There are 44 books in school library. How many booka are fiction books
Answer:
12 fiction books.
Step-by-step explanation:
Let b represent number of non-fiction books.
We have been given that in the library at Lenape elementary school, there are 3/8 as many fiction books as there are nonfiction books. So number of fiction books would be [tex]\frac{3}{8}x[/tex].
We are also told that there are 44 books in school library. We can represent this information in an equation as:
[tex]x+\frac{3}{8}x=44[/tex]
Let us solve for x.
[tex]\frac{8x}{8}+\frac{3}{8}x=44[/tex]
[tex]\frac{8x+3x}{8}=44[/tex]
[tex]\frac{11x}{8}=44[/tex]
[tex]\frac{11x}{8}\cdot \frac{8}{11}=44\cdot\frac{8}{11}[/tex]
[tex]x=4\cdot 8[/tex]
[tex]x=32[/tex]
Therefore, there are 32 non fiction books in the library.
Number of fiction books would be [tex]\frac{3}{8}x\Rightarrow \frac{3}{8}*32=3*4=12[/tex]
Therefore, there are 12 fiction books in the library.
A plane can fly 520 miles in the same time as it takes a car to go 200 miles. If the car travels 80 mph slower than the plane, find the speed of the plane.
Answer: the speed of the plane is 130 mph
Step-by-step explanation:
Let x represent the speed of the plane. If the car travels 80 mph slower than the plane, then the speed of the car would be (x - 80) mph.
Time = Distance/speed
plane can fly 520 miles in the same time as it takes a car to go 200 miles. This means that the time it takes the plane to fly 520 miles is
520/x
Also, the time it takes the car to drive 200 miles is
200/(x - 80)
Since the time is the same, it means that
520/x = 200/(x - 80)
Cross multiplying, it becomes
520(x - 80) = 200 × x
520x - 41600 = 200x
520x - 200x = 41600
320x = 41600
x = 41600/320
x = 130 mph
Point w is located at -2 and 3 on a coordinate plane point w is reflected over the x axis to create point w point w is then reflected over the y axis to create point w what ordered pair describes the location of point w
Answer:
w(2,-3)
Step-by-step explanation:
the initial coordinates of point w are w(-2,3), to differentiate the different coordinates of w we will place sub-indexes (according to the graph)
the point w is reflected over the x axis to create point w₁(-2,-3) point w is then reflected over the y axis to create point w₂(2,-3)
The DeMarco hotel has 500 rooms available for sale. For Monday night the hotel’s occupancy is 60%. What is the number of rooms the hotel has available to sell for Monday night? 100 200 250 300
Answer:
200 rooms are available to sell.
Step-by-step explanation:
Given,
Total number of rooms for Monday night = 500,
Occupancy percentage for Monday night = 60%,
Thus, the remaining rooms available for Monday Night
= (100-60)% of total rooms
= 40% of 500
[tex]=\frac{40\times 500}{100}[/tex]
[tex]=\frac{20000}{100}[/tex]
= 200
Therefore, there are 200 rooms available to sell for Monday night.
Suppose the position of an object moving in a straight line is given by s (t )equals 4 t2+ 5 t+ 5. Find the instantaneous velocity when t equals 2. What expression can be used to find the instantaneous velocity at the given time?
Answer:
[tex] v(t) = 8t +5[/tex]
And that represent the instantaneous velocity at a given time t.
And then we just need to replace t =2 in order to find the instantaneous velocity and we got:
[tex] v(t=2) = 8*2 + 5 = 16+5 = 21[/tex]
Step-by-step explanation:
For this case we have the position function s(t) given by:
[tex] s(t) = 4t^2 + 5t+5[/tex]
And we can calculate the instanteneous velocity with the first derivate respect to the time, like this:
[tex] v(t) = s'(t)= \frac{ds}{dt}[/tex]
And if we take the derivate we got:
[tex] v(t) = 8t +5[/tex]
And that represent the instantaneous velocity at a given time t.
And then we just need to replace t =2 in order to find the instantaneous velocity and we got:
[tex] v(t=2) = 8*2 + 5 = 16+5 = 21[/tex]
HELPPPPPPP HELP HELP HELP HELP
Using the distance formula, d = √(x2 - x1)2 + (y2 - y1)2, what is the distance between point (-5, -2) and point (8, -3) rounded to the nearest tenth?
10.3 units
12.6 units
1 unit
13 units
Answer:
13 units
Step-by-step explanation:
Im doin this in class to so i got you
the equation would be d=(8-(-5))2-(-3-(-2))2
Next solve in the parenthesis 13 power of 2 +-1 power of 2
Then do the powers 169+1
d=170
Then you square 170 which is 13.03840481
That simplifies to 13
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2/3 of the students study a language 2/5 of the students study french Find the ratio of students who study french to students who do not study french.
Answer:
Therefore the ratio of students who study french to students who do not study french is 4:11.
Step-by-step explanation:
Given that [tex]\frac2 3[/tex] of the students study a language. [tex]\frac2 5[/tex] of the students study french.
Consider total number of student be x.
The number of student who study language [tex]= \frac2 3\times x[/tex]
Again [tex]\frac2 5[/tex] of the students study french.
The number of student who study french [tex]= \frac2 3\times x\times \frac25[/tex]
[tex]=\frac{4}{15}x[/tex]
The number of student who do not study french
[tex]=x-\frac{4}{15}x[/tex]
[tex]=\frac{x(15-4)}{15}[/tex]
[tex]=\frac{11x}{15}[/tex]
Therefore the ratio of students who study french to students who do not study french is
[tex]=\frac{4}{15}x:\frac{11}{15}x[/tex]
=4:11
Answer:
(2/3)(300)= 200, study a language. Of those, 2/5, so (2/5)(200)= 80, study French. The other 300- 80= 220 students do not study French. The ratio of students who study French to those who do not is 80 to 220 which can be reduced to 8 to 22 and then 4 to 11.
There are twice as many flute players as there are trumpet players. If there are n flute players write an expression to find how many trumpet players there are.
Answer:
there are n flute players so that means that you have a n amount of flute players.
Step-by-step explanation:
You would need n flute players to play ou would have n trumpet players
1/5+1/7+3/21 the answer is
Answer:
17/35Step-by-step explanation:
We need to get all the fractions with a common denominator before we can solve the problem.
The only fractions that have a common multiple are 1/7 and 3/21, so we'll add these first and then add 1/5.
1/7 = 3/21
Add
[tex]\frac{3}{21} + \frac{3}{21} =\frac{6}{21}[/tex]
6/21 = 30/105
1/5 = 21/105
[tex]\frac{30}{105} + \frac{21}{105} = \frac{51}{105}[/tex]
Simplify
[tex]\frac{51}{105} / \frac{3}{3} =\frac{17}{35}[/tex]
ANSWER: 17/35I'm always happy to help :)
50 POINTS Find the perimeter of the polygon if B = D
Answer:
92 cm
Step-by-step explanation:
2[ (2×11.5) + 10.5 + 12.5 ]
92
The vertex of this parabola is at (2, -4). Which of the following could be its equation?
A.y = 2(x - 2)2 + 4
B.x = 2(y + 4)2 + 2
C.x = 2(y - 4)2 + 2
D.y = 2(x - 2)2 - 4
Answer:
The answer to your question is letter B
Step-by-step explanation:
Data
Vertex = (2, -4)
Process
From the image we know that it is a horizontal parabola that opens to the right so the equation must be
(y - k)² = 4p(x - h)
Let 4p be 1
- Substitution
(y + 4)² = (x - 2)
- Solve for x
(y + 4)² = x - 2
- Result
x = (y + 4)² + 2
The answer is letter B, because of the signs.
plz dont skip me help me
In which quadrant would point (12, 18) be located?
Quadrant IV
Quadrant II
Quadrant I
Quadrant III
Answer:
it's Quadrant 1 because both of he cordnates
Step-by-step explanation:
Let f(x)=15/(1+4e^(-0.2x) )
What is the point of maximum growth rate for the logistic function f(x)? Show all work.
Round your answer to the nearest hundredth
Answer:
6.93
Step-by-step explanation:
f(x) = 15 / (1 + 4e^(-0.2x))
f(x) = 15 (1 + 4e^(-0.2x))^-1
Taking first derivative:
f'(x) = -15 (1 + 4e^(-0.2x))^-2 (-0.8e^(-0.2x))
f'(x) = 12 (1 + 4e^(-0.2x))^-2 e^(-0.2x)
f'(x) = 12 (1 + 4e^(-0.2x))^-2 (e^(0.1x))^-2
f'(x) = 12 (e^(0.1x) + 4e^(-0.1x))^-2
Taking second derivative:
f"(x) = -24 (e^(0.1x) + 4e^(-0.1x))^-3 (0.1e^(0.1x) − 0.4e^(-0.1x))
Set to 0 and solve:
0 = -24 (e^(0.1x) + 4e^(-0.1x))^-3 (0.1e^(0.1x) − 0.4e^(-0.1x))
0 = 0.1e^(0.1x) − 0.4e^(-0.1x)
0.1e^(0.1x) = 0.4e^(-0.1x)
e^(0.1x) = 4e^(-0.1x)
e^(0.2x) = 4
0.2x = ln 4
x = 5 ln 4
x ≈ 6.93
Graph: desmos.com/calculator/zwf4afzmav
The point of maximum growth rate for the logistic function f(x) is at (7.5, 7.926).
What is exponential function?Exponential function → An exponential equation is given by - y = eˣ.Graph → The graph of y = eˣ is upward-sloping, and increases faster as {x} increasesGiven is the function f(x) as follows -
f(x) = 15/(1+4[tex]$e^{-0.2x}[/tex] )
The given logistic function is -
f(x) = 15/(1+4[tex]$e^{-0.2x}[/tex] )
The inflection point represents the time of most rapid growth. After the inflection point, the growth rate declines, reaches the limiting value. The inflection point occurs at half of the carrying capacity. This is the level of maximum growth.The equation for a logistic model is N = {K/1 + b[tex]$e^{-rt}[/tex]}. The constant {K} is the carrying capacity. It is the limiting value of N. The inflection point occurs at N = K/2.So, we can say that at {x} = N = 15/2 = 7.5, the point of maximum growth exists. At {x} = 7.5, the value of {y} = 7.926. Refer to the graph of the function attached.
Therefore, the point of maximum growth rate for the logistic function f(x) is at (7.5, 7.926).
To solve more questions on exponential equations, visit the link below -
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A parallelogram with an area of 211.41m^2 has a base that measures 24.3m find its height
Step-by-step explanation:
[tex]height \: of \: {\parallel}^{gm} \\ \\ = \frac{area \: of \: {\parallel}^{gm} }{base} \\ \\ = \frac{211.41}{24.3} \\ \\ = 8.7 \: m[/tex]