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].
Write an equation in slope intercept form and in standard form for the line passing through (4,9) and perpendicular to x=-6
Answer:
Input work is the work done on a machine as the input force acts through the input distance. This is in contrast to output work which is a force that is applied by the body or system to something else. Output work is the work done by a machine as the output force acts through the output distance.Jan 15, 2020 hwgsvsd d jxvsd
dvsud sgsgs hsysvdudbd dvyd dhsgtsjd vsytwgsud gsyfwuyebdbhys. dusgcejd b
plzzzz help me!!!
Find the total cost to the nearest cent.
$49.95 pair of shoes; 5% tax
Answer:
49.95+2.4975(the 5% tax)
Step-by-step explanation:
=52.4475 dollars
Answer:
$52.4475
Step-by-step explanation:
5/100×49.95=249.75
249.75÷100=2.4975
2.4975+49.95=52.4475
What is 19,067 divided by 43
Answer:
443.418604651
Step-by-step explanation:
Thank you for the points!
!!!Plz help!!!Which notation shows that Pis a function of X?
A. Pox
B. P(x)
C. x.P
O D. x(P)
Answer:
the answer is that B .P(X)
8. Robert has $50 000 in the bank. Belinda has $5 000. Compare how much money they
have using (a) subtraction and (b) division. Write your answers as sentences.
explain how you would use integer tiles to find the quotient of -15 and 3
Answer:
Start with 15 negative tiles. Separate the tiles into 3 equal groups. Each group will have 5 negative tiles, so -15 divided by 3 is -5.
Step-by-step explanation:
What is the equation for trying to solve slope ?
Answer:
slope =
Step-by-step explanation:
Complete the equation that represents the total value of the nickels and p pennies
Answer:
Answers below
Step-by-step explanation:
Equation
Let's call:
p = number of pennies Janesa has in her pocket
n = number of nickels Janesa has in her pocket
She has 24 coins in total, thus:
[tex]p + n=24\qquad\qquad [1][/tex]
Since each penny is worth $0.01 and each nickel is worth $0.05, and Janesa has $1 in total:
[tex]0.01p+0.05n=1[/tex]
Multiplying by 100:
[tex]p+5n=100\qquad\qquad [2][/tex]
A. Completing the equation:
[tex]5n+p=100[/tex]
B.
From [1]:
[tex]p=24-n[/tex]
Substituting into [2]:
[tex]24-n+5n=100[/tex]
Simplifying:
[tex]24+4n=100[/tex]
Rearranging:
[tex]4n=100-24=76[/tex]
[tex]n=76 / 4= 19[/tex]
[tex]p=24-19=5[/tex]
B. There are 5 pennies in Janesa's pocket
C. Since each penny is worth $0.01, the total value of pennies is 5*$0.01=$0.05
The total value of the pennies is $0.05
D. The total value of the nickels is 19*$0.05 = $0.95
E. Jackson should say she has 19 nickels and 5 pennies
janesa has 24 coins in her pocket worth exactly $1.00. she tells her younger brother jackson that he can have the coins if he correctly guesses how many of each coin she has. she gives him the hint that there are only nickels and pennies. complete the equation that represents the total value of the nickels and p pennies 5( blank ) + p = 100 The type of coins that Janessa has = nickels and pennies.
Janessa has a total number of 24 coins
The sum of the nickels and pennies = $1.00
Let us represent the number of nickels as x
The number of pennies as y
If 2.2x10^6 - 4.3x10^5 what does this equal
Answer:
If the decimal is being moved to the left, the exponent will be positive. 1.77×10 ...
Step-by-step explanation:
Answer:
The answer is 1,770,000
Step-by-step explanation:
[tex]2.2 \times 10 {}^{6 } - 4.3 \times 10 {}^{5} [/tex]
1. Orders of Operation. Exponents come first before multiplication. So do the exponents first.
2.2×1,000,000-4.3×100,000
2. Order of Operation. Mutilpication comes before subtraction.
2,200,000-430,000
3. Subtract
1,770,000
Given x and y are integers, explain why the product of the expression and it's conjunct will always be an integer
Answer:
If neither of the two real numbers is zero, then their product is also not zero Suppose also that x is a real number that satisfies the equation The " / " symbol does not always give you a result of an integer, so be careful.pkek, and any other expression for n as a product of prime numbers is identical to this except,.
Step-by-step explanation:
For this module's assignment review the following. 1. A student randomly guesses the answers to a four-question true-or-false quiz. The observation is the student's answer for each question. Write out the sample space. (Use T = true and F = false) 2. At Aunt Edna's Diner, a customer can choose from 5 appetizers, 7 entrees, 4 side dishes, and 6 desserts. How many different meals can be made by selecting one item from each course? 3. Compute gC3. 4. Compute 9P3-
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Answer:
tttt, tttf, ttft, ttff, tftt, tftf, tfft, tfff fttt, fttf, ftft, ftff, fftt, fftf, ffft, ffff84084504Step-by-step explanation:
1. The sample space is all 16 possible sequences of T or F of length 4:
tttt, tttf, ttft, ttff, tftt, tftf, tfft, tfff fttt, fttf, ftft, ftff, fftt, fftf, ffft, ffff
__
2. The number of possibilities is the product of the numbers of choices at each stage:
5 × 7 × 4 × 6 = 840 . . . different meals
__
3. 9C3 = 9!/(3!·6!) = 84
__
4. 9P3 = 9!/6! = 504
I have no idea what to do, i need the answer!!!
Answer:
y = -x - 6
Step-by-step explanation:
From point A, to get to point C, you would need to go down 2 and right 2 which is -2/2 and -2/2 is the same thing as -x.
The y-intercept is -6 because the line goes thorough -6 in the y axis.
Hope this helps and pls do mark me brainliest if you can:)
Max pays a flat rate of $85 for his cell phone. He is also charged $0.15 for every text that he sends. His cell phone bill can be no more than the amount he has budgeted for it each month. If x represents the number of texts and y represents his budgeted amount, which inequality represents Max's cell phone budget each month? (3 points)
a $0.15x + $85 ≥ y
b $0.15x + $85 ≤ y
c $0.15x - $85 ≥ y
d $0.15x - $85 ≤ y
Callista used 10% off coupon to purchase a band t-shirt from Hot Topic . If the shirt cost $21.00, what is the discount in dollars?
Answer:
The discount is 2.1 dollars
Select all angles of symmetry.
Answer:
B,C,F
Step-by-step explanation:
what is le 2+2?
im -2 years old
Answer: The answer is 4
Step-by-step explanation: and FYI nobody is -2 years old
Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.)f(x) = 3 â 48x + 4x2, [5, 7]
Answer:
Step-by-step explanation:
The given equation is:
f(x) = 3 - 48x + 4x² [5,7]
where; f(x) is continous and derivable in [5,7]
f'(x) = -48x + 8x
f(5) = 3 - 48(5) + 4(5)² = -137
f(7) = 3 - 48(7) + 4(7)² = -137
Thus, it satisfies the hypotheses of Rolle's Theorem
f'(x) = f'(c) = 0
-48 + 8c = 0
c =48/8
c = 6
a pump moves 42 gallons in 7 minutes
Answer:
The correct answer is 6
Step-by-step explanation:
Divide 42 divided by 7 to get 6.
Answer:
What is the question?
Step-by-step explanation:
The pump moves 6 gallons in 1 minute
Divide 42 by 7 = 6
But I don't know the question so I can't tell you the best correct answer.
I just took a guess at what you wanted
ILL GIVE BRAINLIEST!!! The average of x+6, 6x+2, and 2x+7 is 4x-7. What is x?
Answer:
yStep-by-step explanation:
Find the present value of an annuity due that pays $4000 at the beginning of each quarter for the next 7 years. Assume that money is worth 6.2%, compounded quarterly. If $90,000 is invested in an annuity that earns 5.4%, compounded quarterly, what payments will it provide at the end of each quarter for the next 7 1/2 years?
Answer:
Step-by-step explanation:
From the first question:
We are to find PV of the annuity.
Using the formula:
Present value of Annuity = Annuity Amount × Present Value Annuity Factor i.e. PVAF (n , r)
Where , Annuity Amount = $4,000
n = No. of periods = 7 years × 4 quarters per year = 28 periods but since the first payment is at beginning of the quarter, Then, n = 27 when considered for PVAF
r = 6.2% / 4 quarters = 1.55%,
PVAF(n0,r) when first payment is at beginning of n i.e. n0 = 1 + { [1-(1+r)^ -n0 ]/r }
= 1 + { [1-(1+0.0155)^ {-27}]/0.0155 }
= 1 + [ (1 - 0.66015 ) ] / 0.0155]
= 1 + 21.926
= 22.926
PVAF(28,1.55%) = 22.926
Thus , Present Value of Annuity = $4,000 × 22.926 = $91704.00
2. Present value of Annuity due = Annuity Amount × Present Value Annuity Factor i.e. PVAF (n , r)
Present Value of Annuity = $90,000
n = No. of periods = 7.5 years × 4 quarters per year = 30 periods
r = 5.4% / 4 quarters = 1.35%,
PVAF(n,r) = [1-(1+r)^-n]/r
PVAF(n,r) = [1-(1+0.0135)^ -30]/0.0135
PVAF(30,1.35%) = (1 - 0.6688)/0.0135
PVAF(30,1.35%) = 0.3312/0.0135
PVAF(30,1.35%) = 24.53
Hence ;
$90,000 = Annuity Amount × 24.53
Annuity amount = $90,000/24.53 = $3,668.48
Which linear function is represented by the graph?
O f(x) = -2x + 1
O f(x) = -1/2x + 1
O f(x) = 1/2x + 1
O f(x) = 2x + 1
Answer:
The answer is B
Step-by-step explanation:
Find the quotient. 3,482 ÷ 9 = *
Answer:
386.8
Step-by-step explanation:
pretty sure thats it
Answer:
386.8888 .. ...
Step-by-step explanation:
3482/9
Selma uses a jogging trail that runs through a park near her home. The trail is a loop that is of a mile long. On Monday, Selma ran the loop in of an hour. What is Selma’s unit rate in miles per hour for Monday’s run?
In this activity, you will use the common denominator method to calculate a unit rate that involves fractions. Answer the questions that follow to calculate Selma’s unit rate in miles per hour.
part A. According to the question, the unit rate is to be expressed in which units?
Part B. Now, write Selma’s jogging rate as a complex fraction. A complex fraction is one whose numerator, denominator, or both are fractions. Be sure to include units in your answer.
Part C. Find the least common denominator of the two fractions from part B. To do this, list and compare the first five multiples of the denominators. The smallest number that appears in both lists is the least common denominator. Show your work.
Part D
Answer:
a) Her rate is 1 mile per hour for Monday’s run
b) 0.447 m/second
c) In fraction 20467m/180000 seconds
Step-by-step explanation:
Speed = distance / time = 1 mile/ 1 hour
= 1 mile per hour
Her rate is 1 mile per hour for Monday’s run
part A. According to the question, the unit rate is to be expressed in miles per hour units.
Part B.
Speed = distance / time = 1 mile/ 1 hour
= 1 mile per hour
But 1 mile = 1609.34 m
and 1 hour = 3600 seconds
There fore
1 mile/ 1 hour = 1*1609.34/ 1*3600 seconds
= 0.447 m/second
Part C.
1 mile/ 1 hour =1609.34/ 3600 seconds
= 1609.34 * 100/100 * 1/3600 ( multiplying and dividing by 100 to remove the decimal)
= 160934/360000
= 20467m/180000 seconds
The first five multiples of 1 are 2,3,4,5,6,7,8, 9......
The LCM of 1 and 1 is 1
Elvira used 4 cups of grape juice, 15 cups of cranberry juice, and 2 1 / 2 cup of pineapple juice to make punch. One liter is
approximately equal to 4.23 cups.
Which measurement is closest to the number of liters of punch Elvira made?
PLEAS HELP FAST!!!!!!!!!!!!!!
Answer: Point D
Step-by-step explanation: Point D is at 3 and 3/4.
I think the answer is point D
Which system of inequalities can model Gabrielle’s situation, where x represents batches of brownies and y represents batches of cookies?
Answer:
2x + 2y ≤ 20
x + 3y ≤ 2
Step-by-step explanation:
this is the correct answer i got on my assignment-------
The system of inequalities can model Gabrielle’s situation is x + 2y ≤ 20
and 3x + 2y ≤ 21.
What are inequalities?The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.
It follows from the task content, that the inequalities which can be used to model Gabrielle's situation be determined.
By setting variables as follows; batches of brownies = x and batches of cookies = y
Brownie:
Sugar = 1 cup
Eggs = 2
x + 2y ≤ 20
Cookie:
Sugar = 3 cups
Eggs = 2
3x + 2y ≤ 21
To learn more about inequality visit:
brainly.com/question/25275758
#SPJ2
Gabrielle is baking large batches of brownies and cookies to share with her friends and family. Among other ingredients, her brownie recipe calls for 1 cup of sugar and 2 eggs and her cookie recipe calls for 3 cups of sugar and 2 eggs. Gabrielle has 20 eggs and 21 cups of sugar, and she would like to know how many batches of brownies and cookies she can bake without getting more of these ingredients. Part A Question Which system of inequalities can model Gabrielle’s situation, where x represents batches of brownies and y represents batches of cookies?
The income from the spanish club bake sale was $465. Expense for the sale totlaed $50. Using integer addition find the total profit or loss from the bake sale
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Answer:
profit: $415
Step-by-step explanation:
Profit = Income - Expense
= $465 - 50
= $415
The profit from the bake sale was $415.
__
If you consider the above subtraction not to be "integer addition," then the equation you want to evaluate is ...
profit = $465 + (-50) = $415
Subtraction is the same as addition of the opposite.
If ƒ (x ) = 3x2 - x, find ƒ (-2).
Answer:
f(-2) is 14.
Step-by-step explanation:
We have been given the function:
We have to find f(-2)
That means put x= -2 in the given function we get:
After simplification we will get:
After further simplification we will get the required result:
Hence, ƒ (-2) is 14
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = t2 + 35, y = ln(t2 + 35), z = t; (6, ln(36), 1)
Answer:
Attached below is the detailed solution
answer : x(t), y(t), z(t) = ( 6 + t/6, In (36) + t/18, 1 + t )
Step-by-step explanation:
x = [tex]\sqrt{t^2 + 35 }[/tex] , y = In(t^2 + 35 ), Z = t;(6, ln(36), 1)
Determine the parametric equations for the tangent line to the curve with the above given parametric equations
attached below is the detailed solution
Please help me. What’s the answer ?
Answer:
D
Step-by-step explanation:
D