) consider the initial value problem y′−5y=15t+3et,y(0)=y0 y′−5y=15t+3et,y(0)=y0 (a) solve the initial value problem. (enter y0 for y0y0). y(t)y(t)= equation editorequation editor (b) determine the value of y0y0 that separates solutions that grow positively as t→[infinity]t→[infinity] from those that grow negatively.
Answers
Answer:
a)value attached below
b)Yo = [tex]\frac{-27}{20}[/tex]
Step-by-step explanation:
A) solving initial value problem
[tex]y' - 5y = 15t + 3e^t[/tex]
y(0) = yo
hence the solution of the initial value problem : y(t)
Y(t) =
Attached below is the detailed solution
B) Yo = [tex]\frac{-27}{20}[/tex] separates the solutions as
t →∞
this is because when y(t) < [tex]\frac{-27}{20} y(t) tends to inifiniy[/tex]
y(t) > [tex]\frac{-27}{20} y(t) tends to inifinity[/tex]
Related Questions
A package of floor tiles contains 22 one-foot-square tiles. Find how many packages
should be bought to cover a square ballroom floor whose side measures 66 feet Note:
Partial packages cannot be bought
Answers
So therefore your answer would be 3 packages!
Answer:
Step-by-step explanation:
66 times 66 for area is 4356 then 4356 divided by 22 is 217.8 so 218
DeShawn her $21 to spend on two pencils after buying them he has $17 how much did each pencil cost
Answers
Find the value of x in the triangle shown below. Help ASAP please!! :)
Answers
This is an isosceles triangle. The two angles opposite the two equal sides are equal. With this knowledge, we now know that the angles are 61, 61, x.
We also know that the sum of all the angles of a triangle is equal to 180 degrees.
61 + 61 + x = 180.
Combine like terms.
122 + x = 180
Subtract 122 from both sides.
x = 58 degrees
Sosa received $90 in gift cards to Coffee Crazee and each drink she purchases costs $4.75. Sosa also received $75 in gift cards to Fran's Frappes and each drink she purchases cost $3.25. How many drinks will Sosa have to purchase in order to have the same amount remaining on the gift cards from both shops? * 33
Answers
Answer:
90 -4.75x = 75 -3.25x
90-75= 4.75x-3.25x
x= 10
Step-by-step explanation:
Answer:
10 drinks
Step-by-step explanation:
We can set up an equation to find the amount of drinks needed, x.
[tex]90-4.75x = 75-3.25x[/tex]
Now let’s solve for x by isolating it on one side of the equation.
Subtract 75 from both sides:
[tex]15 - 4.75x = -3.25x[/tex]
Add 3.25x to both sides:
[tex]15-1.5x=0[/tex]
Add 1.5x to both sides:
[tex]15 = 1.5x[/tex]
Divide both sides by 1.5:
[tex]x = 10[/tex]
Hope this helped!
-6x+8y-10x-8y
Show and explain work
Answers
Answer:
Simplify the expression.
−16x
Step-by-step explanation:
Select the decimal that is equivalent to 2/3
Answers
Answer:
0.66666667 or 0.6
Step-by-step explanation:
if you put [tex]\frac{2}{3}[/tex] in a calculator and convert it, it would display
0.6666 with infinite sixes.
you can also write it as:
0.6
ps ;; you would do this for any fraction, then round it.
Find the midpoint of the segment with the following endpoints.
(8,5) and (0, -1)
Answers
Answer:
(4,2)
Step-by-step explanation:
[tex]Midpoint =\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)\\\\\left(x_1,\:y_1\right)=\left(8,\:5\right),\:\\\left(x_2,\:y_2\right)=\left(0,\:-1\right)\\\\=\left(\frac{0+8}{2},\:\frac{-1+5}{2}\right)\\\\= (\frac{8}{2} , \frac{4}{2} )\\\\Simplify\\=\left(4,\:2\right)[/tex]
Answer:
(4,2)
Step-by-step explanation:
you know why
Find the area of a triangle with a 21 cm base and 4 cm height
Answers
Answer:
42 cm^2
Step-by-step explanation:
Base = 21 cm
Height = 4 cm
Area = [tex]\frac{base\times height}{2}[/tex]
Substitute values into the given equation
[tex]A = \frac{21\times 4}{2} \\\\A = \frac{84}{2} \\\\A = 42cm^2[/tex]
the unit digit of square of the square of the number 42 is
Answers
A cube has a surface area of 54 square centimeters, what is the side length?
Answers
Answer:
9cm
Step-by-step explanation: i think. ah
Answer:
3 cm³
Step-by-step explanation:
Formula a =√(A/6)
a = edge
A = Surface Area
a = √(54/6) = 3
im doing the zero product propety and some factoring for a hw assignment but these ones i cant figure out x² - 2x - 35= 0
3x² + 14x - 5 = 0
offering brainliest
Answers
Answer:
(x-7)(x+5) for the first one. ( 3 x − 1 ) ( x + 5 ) = 0 for the second.
Step-by-step explanation:
what is 75.3% of 1394
Answers
Answer:
1049.682 is 75.3% of 1394 or as a fraction is 1049 341/500
Step-by-step explanation:
1394/x=100/75.3
(1394/x)*x=(100/75.3)*x - we multiply both sides of the equation by x
1394=1.32802124834*x - we divide both sides of the equation by (1.32802124834) to get x
1394/1.32802124834=x
1049.682=x
x=1049.682
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{1049.682}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{75.3\% \: of \: 1394}[/tex]
Convert 75.3 percent into fraction
To convert a percentage to a fraction, divide it by 100
[tex] \dashrightarrow{ \sf{ \frac{75.3}{100} \times 1394}}[/tex]
Calculate
[tex] \dashrightarrow{ \boxed{ \sf{1049.682}}}[/tex]
Hope I helped!
Best regards! :D
how to solve the following quadratic equations; 2L, m, o, 3a and g
Answers
Answer:
Please see the attached pictures for full solution.
2.
Scientists estimate that the distribution of the life span of the Galápagos Islands giant tortoise is
approximately normal with mean 100 years and standard deviation 15 years. Based on the estimate, which
of the following is closest to the age of a Galápagos Islands giant tortoise at the 90th percentile of the
distribution?
Answers
Answer:
119.2
Step-by-step explanation:
Given the following :
Mean (m) = 100 years
Standard deviation (sd) = 15 years
closest to the age of a Galápagos Islands giant tortoise at the 90th percentile of the
distribution?
Obtain the Zscore for 90th percentile (0.90) on the z table = 1.28
Zscore = (X - mean) / standard deviation
1.28 = (X - 100) / 15
1.28 × 15 = X - 100
19.2 = X - 100
19.2 + 100 = X
X = 119.2
Using the normal distribution, it is found that an age of 119 years is closest to the 90th percentile.
-------------------
Normal Probability Distribution
The z-score formula is used, which, in a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. Each z-score has a p-value associated, which represents the percentile of X.-------------------
Mean of 100 means that [tex]\mu = 100[/tex]Standard deviation of 15 means that [tex]\sigma = 15[/tex]The 90th percentile is X when Z has a p-value of 0.9, so X when Z = 1.28.Thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 100}{15}[/tex]
[tex]X - 100 = 15(1.28)[/tex]
[tex]X = 119.2[/tex]
An age of 119 years is closest to the 90th percentile.
A similar problem is given at https://brainly.com/question/15686085
Someone please help.
Answers
-3x+2<8 answer this equation
Answers
Answer:
x>-2
Step-by-step explanation:
-3x+2<8
Subtract 2 from each side
-3x+2-2<8 -2
-3x < 6
Divide each side by -3. remembering to flip the inequality
-3x/-3 >6/-3
x>-2
Move constant to the right side and change its sign
-3x<8-2
Subtract the numbers
-3x<6
Divide both sides of the inequality by -3 and flip the inequality sign
X>-2
Brainliest?
Graph the function rule.
y = 3x + 3
Answers
Answer:
On the y axis (the vertical line titled y) graph a point at 3, then from there rise 3 and walk 1 and plot a point. keep doing this until you can graph a line.
Step-by-step explanation:
hope this helps :)
Chase watched a movie about aliens who never stop growing. Every alien is 10 centimeters tall at birth and grows exactly 8 centimeters each year.
Let y represent the number of years since birth and h represent the alien's height in centimeters.
Complete the equation that represents the relationship between y and h.
y h
5 50
6 58
7 66
8 74
h=y+
Answers
Answer:
Step-by-step explanation:
Let the height (the dependent variable) be h.
Let the independent variable (x) be y
h = 8y + 10
So at birth, these creatures are 10 cm long. At each birthday, they are another 8 cm.
Take the fifth year which is where the table begins.
y= 8*5 + 10
y = 40 + 10
y = 50 cm which is exactly what you got.
BC = 4x + 2 AB = 8x + 8 and AC = 22 Find BC
Answers
Answer:
BC = 6.8
Step-by-step explanation:
The distance from A to B, then from B to C, is the same distance as from A to C.
Thus,
AB + BC = AC
AB = 8x + 8
BC = 4x + 2
AC = 22
AB + BC = AC
(8x + 8) + (4x + 2) = 22
Expanding the parenthesis:
8x + 8 + 4x + 2 = 22
8x + 4x + 8 + 2 = 22
12x + 12 = 22
Subtracting 12 from both sides:
12x = 10
Dividing both sides by 12:
x = 10/12 = 1.2
x = 1.2
We're looking for BC. As we know,
BC = 4x + 2
Let's now put in x = 1.2 into this equation:
BC = 4x + 2
BC = 4 * 1.2 + 2
Since 4 * 1.2 is 4.8:
BC = 4.8 + 2
BC = 6.8
Answer: BC = 6.8
X = 18 is a solution to this equation X + 79 = 98 Question 4 options: True False
Answers
X=19 so it is false
Answer:
false
Step-by-step explanation:
Find the coordinates of the midpoint of a segment with the given endpoints (7,0) and (2,4)
Answers
Answer:
[tex]MP= (4.5,2)[/tex] another way of writing [tex]MP= (\frac{9}{2}, 2)[/tex]
Step-by-step explanation:
[tex]MP= (\frac{x_1+x_2}{2})(\frac{y_1+y_2}{2})[/tex]
[tex]MP= (\frac{7+2}{2})(\frac{0+4}{2})[/tex] 7+2=9 0+1=1
[tex]MP= (\frac{9}{2})(\frac{2}{2})[/tex] MP= (4.5,2)
The coordinates of the mid - point of XY will be - M(4.5, 2)
We have two coordinate points - X(7, 0) and Y(2, 4).
We have to find the coordinates of the mid - point of the line segment XY.
What is Mid - Point Theorem?It states that a line with endpoint coordinates as - [x(1), y(1)] and
[x(2), y(2)] has its mid - point at the coordinates -
[tex]$x(m) =\frac{x(1)+x(2)}{2}[/tex]
[tex]$y(m) = \frac{y(1)+y(2)}{2}[/tex]
According to question, we have -
Assume that the coordinates of Mid - Point = M(h, k)
Coordinates of X= (7, 0)
Coordinates of Y= (2, 4)
Using the Mid - Point formula -
h = [tex]\frac{7+2}{2}[/tex] = 4.5
and
k = [tex]\frac{0+4}{2}[/tex] = 2
Hence, the coordinates of the mid - point of XY will be - M(4.5, 2)
To solve more questions on Mid - points, visit the link below -
brainly.com/question/25377004
#SPJ2
answer for p=2l+2w for l
Answers
Answer:
[tex]I=\frac{p-2w}{2}[/tex]
Step-by-step explanation:
[tex]p=2I+2w\\\\p-2w=2I+2w-2w\\\\p-2w=2I\\\\\frac{p-2w}{2}= I[/tex]
A football team loses 8 yards on each of 4 consecutive plays. Find the total change in yards from where the team started. pls help fgkogijriojg
Answers
Answer:-32
Step-by-step explanation:
You times the two numbers and add a negative sign in front of it
8 would be a negative in this situation and 4 would be a positive. So the problem would look like this:
-8 x 4 = ?
For this particular problem, we would do 8 x 4 which would equal 32. Then we would try to find which one has the greater absolute value.
Absolute Value:
4 = 4
-8 = |8|
Since -8 has the greater absolute value, the answer would be negative.
The Answer: -32
what is 2 time 30000
Answers
Answer:
60000
Step-by-step explanation:
Answer:
60,000
Step-by-step explanation:
2 times 30,000 is 60,000
property operation of 6 { 2.7 + 4 }=6{ 4 + 2.7 }
Answers
The definition of Reflexive property:
The same thing should appear on both sides on the equation.
I hope this helps! :)
Place commas in the number 4978.
Answers
Answer:
4,978 because after 3 digits you have to put a coma
Answer:
4,978
Step-by-step explanation:
[tex] {3}^{a} = \frac{1}{9} [/tex]
[tex] {3}^{b} = 9 \sqrt{3} [/tex]
[tex] {3}^{c} = \frac{1}{ \sqrt{3} } [/tex]
Work out the value of a + b + c
Answers
a) -2
b) 5/2
c) -1/2
a = -2
b = 5/2
c = -1/2
Step by step explanation:
which property of equality is if 4m + n = 7 and n = 3 then, 4m + 3 = 7
Answers
Answer:
m = 1
Step-by-step explanation:
4 x 1 + 3 = 7
Answer: Addition property
Step-by-step explanation:
In the equation 4m + n = 7 , it indicates that n is 3, which means 3 has been added to it to get 4m + 3 = 7 so 3 has been added on each side.
HELP ME ASAP PLEASE!!!!!!!!!1
Answers
Find the distance between (-12, 1) and (12, -1) *
Answers
Answer:
[tex]d = 2\sqrt{145}[/tex]
Step-by-step explanation:
Use the Distance Formula to help you determine the distance between the two following points ( [tex](-12, 1)[/tex] and [tex](12, -1)[/tex] ):
-Distance Formula:
[tex]d = \sqrt{(x_{2} - x_{1}) ^2 + (y_{2} - y_{1})^2}[/tex]
(where [tex]( x_{1}, y_{1})[/tex] represents the first point, and [tex](x_{2}, y_{2})[/tex] represents the second point)
-Apply the following points to the equation:
[tex]d = \sqrt{(12 + 12) ^2 + (-1 - 1)^2}[/tex]
[tex]( x_{1}, y_{1})[/tex] = [tex](-12, 1)[/tex]
[tex](x_{2}, y_{2})[/tex] = [tex](12, -1)[/tex]
-Solve the equation:
[tex]d = \sqrt{(12 + 12) ^2 + (-1 - 1)^2}[/tex]
[tex]d = \sqrt{(24)^2 + (-2)^2}[/tex]
[tex]d = \sqrt{576 + 4}[/tex]
[tex]d = \sqrt{580}[/tex]
[tex]d = 2\sqrt{145}[/tex]
Therefore, the distance is [tex]2\sqrt{145}[/tex].