Answer:
a=-30
Step-by-step explanation:
Find the solution of the second-order linear differential equation that satisfies the given initial conditions. y'' + 6y' + 9y = 0 y(0) = 0 y'(0) = 1
Answer:
The solution of this differential system is [tex]y(x) = x\cdot e^{3\cdot x}[/tex].
Step-by-step explanation:
This second-order differential equation is homogeneous and linear of the form:
[tex]y'' + p\cdot y' +q\cdot y = 0[/tex] (1)
Where:
[tex]p[/tex] - First-order constant coefficient, dimensionless.
[tex]q[/tex] - Zero-order constant coefficient, dimensionless.
Whose characteristic polynomial is:
[tex]\lambda^{2}+p\cdot \lambda + q = 0[/tex] (2)
Where [tex]\lambda[/tex] contains the roots associated with the solution of the differential equation.
If we know that [tex]p = 6[/tex] and [tex]q = 9[/tex], the roots of the characteristic equation are, respectively:
[tex]\lambda^{2}+6\cdot \lambda + 9 = 0[/tex]
[tex](\lambda +3)\cdot (\lambda + 3) = 0[/tex]
Which means that [tex]\lambda_{1} = \lambda_{2} = 3[/tex] and the solution of the differential equation is of the form:
[tex]y(x) = e^{3\cdot x}\cdot (c_{1}+c_{2}\cdot x)[/tex] (3)
Where [tex]c_{1}[/tex] and [tex]c_{2}[/tex] are integration constants.
The first derivative of the equation above is:
[tex]y'(x) = 3\cdot e^{3\cdot x}\cdot (c_{1}+c_{2}\cdot x)+c_{2}\cdot e^{3\cdot x}[/tex] (4)
Now, if we get that [tex]y(0) = 0[/tex] and [tex]y'(0) = 1[/tex], then the system of equations to the solved is:
[tex]c_{1} = 0[/tex] (3b)
[tex]c_{1}+c_{2} = 1[/tex] (4b)
The solution of this system is: [tex]c_{1} = 0[/tex], [tex]c_{2} = 1[/tex]. Therefore, the solution of this differential system is [tex]y(x) = x\cdot e^{3\cdot x}[/tex].
a city depatment uses an average of 25 10cent,35 15 cent and 350 20 cent postage stamps each day.the total cost of stamps used by the department in a 5 day period is
What's 15/45 written as a fraction in simplest form
A. 3/15
B.13
C.53
D. 153
Answer:
None of the above
Step-by-step explanation:
15/45=1/3
Answer:
None of those options lol
Step-by-step explanation:
But the answer is 1/3
Suppose that a population of bacteria triples every hour and starts with 700 bacteria.
(a) Find an expression for the number n of bacteria after t hours.
(b) Estimate the rate of growth of the bacteria population after 1.5 hours.
Answer:
(a) An expression for the number n of bacteria after t hours is n(t)=700*[tex]3^{t}[/tex]
(b) The rate of growth of the bacteria population after 1.5 hours is 3,996 number of bacteria per hour.
Step-by-step explanation:
An exponential function is one in which the independent variable x appears in the exponent and has a constant a as its base. Its expression is:
f(x)=aˣ
being a real positive.
When 0 <a <1, then the exponential function is a decreasing function and when a> 1, it is an increasing function.
An exponential function allows us to refer to phenomena that grow faster and faster, such as population growth.
In that case, the formula used to model the growth of a population is given by:
P(t)=P0*[tex]a^{t}[/tex]
where the function P (t) grows exponentially and represents the quantity of the population at time t; a represents the constant of growth or decrease and P0 represents the initial population at time zero.
In this case:
P0=700a=3Replacing, you get:
P(t)=700*[tex]3^{t}[/tex]
An expression for the number n of bacteria after t hours is n(t)=700*[tex]3^{t}[/tex]
The derivative of this function P (t) is:
n'(t)=700*ln(3)*[tex]3^{t}[/tex]
and reflects the growth rate of the bacteria population.
So, the rate of growth of the bacteria population after 1.5 hours is:
n(1.5)=700*ln(3)*[tex]3^{1.5}[/tex]
Solving, you get:
n(1.5)≅ 3,996
The rate of growth of the bacteria population after 1.5 hours is 3,996 number of bacteria per hour.
What is the estimate of the sum of 165, 123, 376 and 134 using front end estimation? A. 600 B. 700 C. 800 D. 900
Answer:
A.
Step-by-step explanation:
Sorry, just unexplainable thinking.
At a carnival, Tammy bought 9 packs of 17 tickets each. She has used 36 of the tickets so far. How many tickets does she have left?
Answer: 117 tickets left
Step-by-step explanation:
Nolan bought 7 packs of
Starbursts, x. He had a
total of 98 individual
Starbursts, y Determine
the constant of
proportionality and write
a linear equation to
represent the
relationship
14
Divide 98 by 7, you get 14.
This is how many starburst are in each packet.
Please could you show the working out as well:)
Answer:
( [tex]\frac{6}{7}[/tex] - [tex]\frac{1}{3}[/tex] ) is closer to [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\frac{2}{15}[/tex] + [tex]\frac{1}{3}[/tex] = [tex]\frac{2 + 5}{15}[/tex] = [tex]\frac{7}{15}[/tex]
[tex]\frac{6}{7}[/tex] - [tex]\frac{1}{3}[/tex] = [tex]\frac{18-7}{21}[/tex] = [tex]\frac{11}{21}[/tex]
[tex]\frac{7}{15}[/tex] , [tex]\frac{1}{2}[/tex] , [tex]\frac{11}{21}[/tex]
LCD (2, 15, 21) = 210
[tex]\frac{98}{210}[/tex] , [tex]\frac{105}{210}[/tex] , [tex]\frac{110}{210}[/tex]
105 - 98 = 7
110 - 105 = 5 ⇒ [tex]\frac{11}{21}[/tex] is closer to [tex]\frac{1}{2}[/tex] ⇒ ( [tex]\frac{6}{7}[/tex] - [tex]\frac{1}{3}[/tex] ) is closer to [tex]\frac{1}{2}[/tex]
Select the expression equivalent to (-133–15)-(-9x + 16).
А
4x - 31
B
--4x + 1
с
-4x - 31
D
-22x-31
given that a=2 and b=3, what is (ab)^2
Answer:
(ab)² = 36
Step-by-step explanation:
Plug in 2 for a and 3 for b:
(2·3)²
Multiply 2 and 3:
6²
Square the number:
36
WHats 100000000000000 x 1000000000000000000000
Answer:
1e+35
Step-by-step explanation:
An engineer is building a bridge that should be able to hold a maximum weight of 1 ton. He builds a model of the bridge that is exactly 4 times smaller than the actual bridge. 16 ounces = 1 pound. 2,000 pounds = 1 ton. If a test of the model shows that it holds 8,000 ounces, will the bridge hold 1 ton?
fill in thw blanks please extra points:)
Answer:
First blank- 32000 ounces
Second blank- 2000 pounds
Yes the bridge can hold 1 ton.
Step-by-step explanation:
The ratio of the scale of the model to the real bridge = 1:4
The test model shows the model can take 8000 ounces
The real bridge will therefore take 8000 x 4 = 32000 ounces
16 ounces = 1 pound
32000 ounces = x pounds
==> = 32000/16 = 2000 pounds
2000 pounds = 1 ton
therefore the bridge holds 1 ton
Answer:
First blank- 32000 ounces
Second blank- 2000 pounds
Yes the bridge can hold 1 ton.
Step-by-step explanation:
The ratio of the scale of the model to the real bridge = 1:4
The test model shows the model can take 8000 ounces
The real bridge will therefore take 8000 x 4 = 32000 ounces
16 ounces = 1 pound
32000 ounces = x pounds
==> = 32000/16 = 2000 pounds
2000 pounds = 1 ton
therefore the bridge holds 1 ton
Please help with my homework
It's 65. Because you add the other angles and get 90+25 and get 115. 180 -115 = 65.
Answer:
c=65°
Step-by-step explanation:
180-90=90
90-25=65
hopefully this helps :)
The slope- intercept form of the equation of a line is y = mx + b. When the formula is solved for m, the result is
1. y-x/b
2. y - bx
3. y-b/x
4. x/y - b
A cart weighing 60 lb is placed on a ramp inclined at 15° to the horizontal. The cart is held in place by a rope inclined at 60° to the horizontal, as shown in the figure. Find the force that the rope must exert on the cart to keep it from rolling down the ramp. (Round your answer to one decimal place in lbs.)
I assume you ignore friction. The cart is held in equilibrium, so the net force on the cart is zero.
There are 3 forces acting on the cart:
• weight (magnitude w, pointing down)
• normal force (mag. n, pointing perpendicular to the ramp)
• tension in the rope (mag. t, pointing 60º from the horizontal, or equivalently 60º - 15º = 45º from the parallel direction)
Split up the forces into horizontal and vertical components. We have
• horizontal:
t cos(60º) + n cos(105º) = 0
• vertical:
n sin(105º) + (-w) = 0
(the normal force has a direction of 105º from the horizontal because it's perpendicular to the ramp, so it forms an angle of 90º with the ramp, plus the 15º inclination of the ramp itself)
We're given that w = 60 lb, so
n sin(105º) = 60 lb
n ≈ 62.1 lb
Solve for t :
t cos(60º) = -n cos(105º)
t = -n cos(105º)/cos(60º)
t ≈ 32.2 lb
Eight sports fans were asked to count the number of baseball
caps and the number of basketball jerseys in their collection.
Create a scatter plot that represents the data that is shown in the
table. The x-axis represents number of baseball caps and the y-
axis represents the number of basketball jerseys.
Answer:
what grade are you in?
Step-by-step explanation:
what is 25+30 pleas help me
Please help me I don’t understand stand it
What is the result of 72 divided by 12? 6 8 9 12
Answer:
the answer is 6
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
Hope this helps!!!!!!
12 yd/min =________ft/s
Answer:
you need yarn
Step-by-step explanation:
3fts times 12 is equal to=kuha ka calculator
Answer: 12 yd/min = 0.6 ft/seconds.
Because: 36/60 = 36 1/60 = 6 1/10 = 3/5 = 0.6
A monthly budget with expenses is shown.
MONTHLY BUDGET
for a family of three
in San Antonio, Texas
Rent
$870
Food
$550
PR Child care
$375
Transportation
$480
Utilities
$400
Insurance
$235
Savings
$400
Taxes
$290
Monthly total
Which equation can be used to determine y, the minimum amount of money a family must earn to meet the requirements of this budget for one year?
y = 3600 x 12
y = 3600 + 7
y = 3600 x 4
y = 360052
Answer:
[tex]y = 3600 * 12[/tex]
Step-by-step explanation:
Given: Breakdown of Monthly Budget
Required
Determine the equation that shows minimum earnings in a year
First, we need to get the sum of the given list of budgets:
[tex]Budget = 870 + 550 + 375 + 480 + 400+235+400 + 290[/tex]
[tex]Budget = 3600[/tex]
The are 12months in a a year; So, the yearly budget (y) is:
[tex]Yearly\ Budget = Monthly\ Budget * Duration[/tex]
[tex]Yearly\ Budget = 3600* 12[/tex]
i.e.
[tex]y = 3600 * 12[/tex]
i need help on this question
PLZ HELP I BEG U!!!!!! ILL MARK U BRAINLIEST
Create a story using the inequality symbols , ≤,≥,≠ . the story must be creative, detailed, coherent, and written clearly. it does not have to be solely math related.
Answer:
T_T said to 个_个: Hallo, I am so happee!!!
Step-by-step explanation:
Plz mark as Brainliest!
A bacteria culture contains 1500 bacteria initially and doubles every hour. Find a function N that models the number of bacteria after t hours. Write out how many bacteria there will be for t = 0, 1, 2, etc. and think about how you are getting those values.
Answer: N(t) = (2^t)*1500
Step-by-step explanation:
Let's define the hour "zero" as the initial population.
So if N(t) is the number of bacteria after t hours, then:
N(0) = 1500.
Now, we know that the population doubles every hour, so we will have that after one hour, at t = 1
N(1) = 2*1500 = 3000
after two hours, at t = 2.
N(2) = 2*(2*1500) = (2^2)*1500
After three hours, at t = 3
N(3) = 2*(2^2)*1500 = (2^3)*1500
So we already can see the pattern, the number of bacteria after t hours will be:
N(t) = (2^t)*1500
jim koslo earns $156,200 annually as a plant manager. He is married and supports 3 children. The state tax rate in his state is 3.55% of taxable income. What ammount is withheld yearly for state income tax?
Answer:
44
Step-by-step explanation:It's 44 because 156,200 divided by 3.55=44.
If jim koslo earns $156,200 annually as a plant manager. The state tax rate in his state is 3.55% of taxable income. then 5545.1 is the amount is withheld yearly for state income tax
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
jim koslo earns $156,200 annually as a plant manager.
The state tax rate in his state is 3.55% of taxable income.
We need to find the amount is withheld yearly for state income tax
We need to find 3.55% of 156200
First we have to convert 3.55% to decimal by dividing with 100
3.55/100=0.0355
Now multiply 0.0355 with 156200
0.0355×156200
5545.1
Hence 5545.1 is the amount is withheld yearly for state income tax.
To learn more on Percentage click:
https://brainly.com/question/28269290
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evaluate the expression when x=4/5 and y=-2/9: 3y-x
Answer:
-2/15
Step-by-step explanation:
Select all the statements that are true for the graph shown.
Submarines descent graph of a diagonal line on a coordinate plane going down and to the right with Time in seconds on the x-axis and Height above Sea Level in feet on the y-axis. The line begins at the origin and passes through point 4 comma negative 12.
The relationship is proportional.
The rate of change is −32
The rate of change is −83
The relationship is linear.
The equation of the line is y = –3x.
Answer:
The relationship is proportional.
The relationship is linear.
The equation of the line is y = –3x.
Step-by-step explanation:
The line in the question passes through origin and (4,-12).
The rate of change of the line is
[tex]m=\dfrac{-12-0}{4-0}\\\Rightarrow m=\dfrac{-12}{4}\\\Rightarrow m=-3[/tex]
The rate of change of the line or slope of the line is -3
Equation of the line is given by
[tex](y-0)=-3(x-0)\\\Rightarrow y=-3x[/tex]
This means that the relationship is linear.
If we take any value of x then there will be only one value of y this means that the relationship is proportional.
So the following statements are true
The relationship is proportional.
The relationship is linear.
The equation of the line is y = –3x.
Answer:
Step-by-step explanation:
Proportional
Linear
Equation of line is y=-3x
Clara’s school awarded 1900 raffle tickets as incentives. The principal will draw one winning ticket. The winner will receive an iPad pro. Clara received 5 tickets for good attendance, 4 for making the honor roll, and 8 for tutoring other students.
What is the probability that one of Clara’s tickets will be selected by the principal? (write your answer as a %, once it is in % form round to the hundredths place)
Answer:
0.89%
Step-by-step explanation:
Given that :
Total number of raffle tickets = 1900
Total number of Clara's tickets (5 + 4 + 8) = 17
Probability that one of Clara's tickets will be picked :
Probability = (required outcome / Total possible outcomes)
Required outcome = total number of Clara's ticket
Total possible outcomes = total number of raffle tickets
Hence,
P(picking one of Clara's tickets) = 17 / 1900
17 / 1900 = 0.0089473
0.0089473 * 100%
= 0.8947%
= 0.89%
x/4-6=2 simplify the following two step equation
Answer:
First, collect the like terms by one side
x/4=2+6
x/4=8
Then, criss-cross it, which means multiply 4 with 8
x=4×8
x=32
Step-by-step explanation:
I hope this is the answer to your question, if it helped you, please give me brainliest
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I need the answers to number 2 and 4 asap
Answer:
2.Matrices and Linear Algebra. 2.1 Basics. Definition 2.1.1. A matrix is an m × n array ... aij = 0 i = j. (1b) A diagonal matrix A may be denoted by diag(d1,d2,... ,dn) ... space of A. With r1 (A),...,rm (A) denoting the rows of A the row space
4.Introduces reflections in the x- and y-axes. Demonstrates the ... This leaves us with the transformation for doing a reflection in the y-axis. For this transformation, I'll switch ... Many textbooks don't get any further than this. If these are all the rules ...