The general solution of the given nonhomogeneous equation is [tex]y(t)=c_{1} e^{-t} +c_{2}e^t-t[/tex]
When the vector of constants to the right of the equals sign is not zero, an equation system is said to be non-homogeneous. A broad description of the solutions to a non-homogeneous system is presented in this solution.
General solution for the equation: [tex]y''-y'=t[/tex] , [tex]yp(t)=-t[/tex]
Consider the equation [tex]y''-y'=t[/tex]. The corresponding homogeneous equation has the associated auxiliary equation [tex]r^2-1=0[/tex] which has [tex]r= -1[/tex] and [tex]r=1[/tex] as solutions.
The solution of an n[tex]^{th}[/tex]-order differential equation or difference equation depends on an algebraic equation of degree n called the characteristic equation (or auxiliary equation) in mathematics.
Hence the general solution for a homogeneous equation is [tex]y(t)=-t+c_{1}e^t+c_{2}e^-t[/tex]
Combining the general solution [tex]y(t) = c_{1}e^t+c_{2}e^t[/tex] of [tex]y"-y'=0[/tex] with the particular solution [tex]y_{p}(t)=-t[/tex] of [tex]y"-y'=t[/tex], we find that the general solution to [tex]y"-y'=t[/tex] is [tex]y(t)=c_{1}e^-t+c_{2}e^t-t[/tex]
The general solution of the given nonhomogeneous equation is [tex]y(t)=c_{1} e^{-t} +c_{2}e^t-t[/tex]
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Riley invested $5,100 in an account paying an interest rate of 7\tfrac{3}{4}7 4 3 % compounded quarterly. Ryan invested $5,100 in an account paying an interest rate of 7\tfrac{1}{4}7 4 1 % compounded daily. After 7 years, how much more money would Riley have in her account than Ryan, to the nearest dollar?
Answer: 257
257 in delta math
Step-by-step explanation:
After 7 years, Riley would $441.5 more have in her account than Ryan.
What is compound interest?Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.
Given that Riley invested $5,100 in an account paying an interest rate of [tex]7\tfrac{3}{4}[/tex]% compounded quarterly. Ryan invested $5,100 in an account paying an interest rate of [tex]7\tfrac{1}{4}[/tex] % compounded daily, we need to find that after 7 years how much more money would Riley have in her account than Ryan,
[tex]A = P(1+r/n)^{nt[/tex]
Where A = amount
P = principal
r = rate
n = number of times the amount is compounded and t = time
Riley = compounded quarterly,
[tex]A = P (1 + r / 4)^{4t[/tex]
[tex]A = 5100(1+0.019375)^{4(7)}\\\\A = 5100(1.019375)^{28}\\\\\\[/tex]
[tex]A = 8728.13[/tex]
Therefore, in 7 years Riley has $8728.13.
Ryan = compounded daily,
[tex]A = P (1 + r / 365)^{365t[/tex]
[tex]A = 5100(1 + 0.00019)^{356(7)}\\\\A = 5100(1.00019)^{2555}\\\\A = 8286.64[/tex]
Therefore, in 7 years Ryan has $8286.64.
Riley will have $441.5 more.
Hence after 7 years, Riley would $441.5 more have in her account than Ryan.
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1900 is deposited into a savings account. Interest is compounded annually. After 1 year, the value of the account is 1957. After 2 years, the value of the account is 2015.71. This scenario can be represented by an exponential function of the form f(x)=1900(b)^2 , where is the amount in the savings account, and x is time in years. What is the value of b?
Answer:
1.03
Step-by-step explanation:
2015.71 = 1900(b)^2
44.896659 = 43.588989 * b
44.896659/ 43.588989 = b
1.0300000 = b
Recall ; for an exponential distribution :
b In the equation = 1 + r ; where, r = rate
b = 1 + r
1.0300000 = 1 + r
r = 1.0300000 - 1
r = 0.03
Hence, the value of b in the equation is 1.03
Claire has 8 cards: 4 red cards and 4 blue cards. She draws 3 cards from the set at random. What is the probability that all 3 cards are red?
Answer: 1/14 assuming cards are nut returned back in deck
Step-by-step explanation: first is red P(1. R) = 4/8 = 1/2
Second red P(2. R) = 3/7 and P(3. R) = 2/6 = 1/3.
Multiply probabilities , you get 1/14
Answer:
4/56 simplified is 1/14
Step-by-step explanation:
nCr(8,3) = 56
4 (the number of red cards there are) / 56 = 1/14
someone please help me out on this problem
Answer:
[tex]x^{2}[/tex]+[tex]y^{2}[/tex]=9
Step-by-step explanation:
the equation for graphed circles centered at (0, 0) is
[tex]x^{2}[/tex]+[tex]y^{2}[/tex]=[tex]r^{2}[/tex]
and 3 is r (the radius)
A tourist standing on the New York City coast sees the Statue of Liberty, which is 305 feet tall. She must tilt her head 9 degrees upwards to look at its head. How far away is she from the base of the statue? Round your answer to the nearest whole foot.
Given:
Height of the Statue of Liberty = 305 feet
Angle of elevation = 9 degrees
To find:
The between the tourist and the Statue of Liberty.
Solution:
Using the given information, draw a figure as shown below.
In a right triangle,
[tex]\tan \theta=\dfrac{Perpendicular}{Base}[/tex]
In the triangle ABC,
[tex]\tan 9^\circ=\dfrac{305}{x}[/tex]
[tex]x=\dfrac{305}{\tan 9^\circ}[/tex]
[tex]x=1925.6942[/tex]
[tex]x\approx 1926[/tex]
Therefore, the tourist is standing 1926 feet from the Statue of Liberty.
radius of a cone with a volume of 100.48 yds3 and a height of 6 yds
Answer:
r = 4
Step-by-step explanation:
Volume of a cone:
V = πr²(h/3)
Given:
V = 100.48
h = 6
π = 3.14
Work:
V = πr²(h/3)
100.48 = r²(3.14)(6/3)
100.48 = r²(3.14)(2)
100.48 = r²6.28
r² = 100.48/6.28
r² = 16
[tex]\sqrt{r^2} =\sqrt{16}[/tex]
r = 4
Pls help me, and do not send links. Thanks
i uploaded a vid on this here
https://www.you tube.com/watch?v=dQw4w9WgXcQ
(28 divided 7 + 6 divided 3) x 1/2
Answer:
3
Step-by-step explanation:
28/7=4
6/3=2
4+2=6
6*1/2=3
Paraenthies
Exponets
Mulitplication
Divide
Add
Subtract
What flavor of ice cream would you pick?
Chocolate Vanilla Neither
Children
40
Teens 12
16
45
Adults 55
54
22
15
10
The table shows the results of a survey on the preferred flavor of ice cream. Based on this survey, what is the probability that an adult
prefers chocolate ice cream?
A)
55
52
B)
55
54
c)
55
107
D)
55
119
Answer:
I'm pretty sure the answer is C
I could be wrong tho
I need help on this now. Please.
Answer:
science is the answer
Step-by-step explanation:
becuse
Answer:
She answered fastest in social studies.
Step-by-step explanation:
Hope that helps
i need help asap pls and no links
Answer:
D
Step-by-step explanation:
I took chemistry so I know
8 2/3 + (-2 1/12)=
what would that be
Answer:
307/12
(Decimal: 25.583333)
Step-by-step explanation:
Heart if this helped
Select the correct answer.
What is the height, x, of the equilateral triangle?
an equilateral triangle with the angles labeled as 60 degrees and a side length of 14 inches, the height labeled as x
Answer:
x = [tex]7\sqrt{3} [/tex] inches
Step-by-step explanation:
- 2021 Edmentum
The height x of the equilateral triangle is 7√3 inches.
What is an Equilateral triangle?Equilateral triangles are triangles that have all their sides and angles equal to each other. The three angles are 60 degrees each.
Therefore,
The side length of the equilateral triangle is 14 inches.
Therefore, To find the height of the triangle using the Pythagoras theorem.
c² = a² + b²
14² - 7² = b²
b² = 196 - 49
b² = 147
b = 7√3
Hence, The height x of the equilateral triangle is 7√3 inches.
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Help me please! This is due today!
Answer:
the question is fillped i can not see the questions
Step-by-step explanation:
Find the interest rate for a bank account that earned $81.60 in interest over 4 years and that had a principal of $510
Answer:
[tex]si = \frac{p \times t \times r}{100} \\ 81.60 = \frac{510 \times 4 \times r}{100} \\ 8160 = 2040r \\ r = \frac{8160}{2040} \\ r = 4\%[/tex]
8.2.AP-7
B
Find the measure of side c.
a = 26 m
C
C=
m (Round the answer to the nearest whole number.)
Answer:
c ≈ 40
Step-by-step explanation:
Using the sine ratio in the right triangle
sin40° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{26}{c}[/tex] ( multiply both sides by c )
c × sin40° = 26 ( divide both sides by sin40° )
c = [tex]\frac{26}{sin40}[/tex] ≈ 40 ( to the nearest whole number )
find the slope-intercept equation of the line that passes through (-7,2) and had a slope of 0
Answer: Y=0x+b
Step-by-step explanation:
Y=mx+b is what we need to set it to.
Since we already know the slope, we can go ahead and find the y-intercept to complete the equation
(-7,2), here -7 is the x and 2 is the y value
y=mx+b
plug all the known information now and solve for b (y-intercept)
y is 2, m (slope) is 0, x is -7
2=0(-7)+b
2=0+b
2=b
y=0x+2 or simply y=2
Answer:
y = 2
Step-by-step explanation:
The line is a horizontal line thru (-7, 2)
Equation: y = 2
This is my question for now
Answer:
V = 540cm3 (E)
Step-by-step explanation:
Area of a square:
A = a2
Perimeter of a Square
P = 4a
Polygon diagonals of a square
q = √(2a2) = a√2
Side of a Square
a = √A
a = P/4
a = q / √2
Square Calculations
Calculate q, P, A | Given a
Given the length of a side calculate the diagonal, area and perimeter
q = a√2
A = a2
P = 4a
Calculate a, P, A | Given q
Given the diagonal length calculate the side length, perimeter, and area
a = q / √2
P = 4a
A = a2
Calculate a, q, A | Given P
Given the perimeter calculate the side length, diagonal, and area
a = P/4
q = a√2
A = a2
Calculate a, q, P | Given A
Given the area calculate the length of the sides, diagonal, and the perimeter
a = √A
q = a√2
P = 4a
7/15 multiplied by 5/6
Answer:
The answer will be 35/36
Answer:
[tex]\frac{7}{18}[/tex]
Step-by-step explanation:
[tex]\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}[/tex]
If a / b = 2 / 5 , then , b / a = 5 / 2
True
False
Answer:
false
Step-by-step explanation:
Answer:
false
Step-by-step explanation:
An archeologist used the functions below to model the changing populations of two ancient cities as they grew in size. Compare the populations by finding and interpreting the average rates of change over the interval [0,40].
Answer:
The answer is "6.3 and 5.25"
Step-by-step explanation:
Please find the complete question in the attached file.
Throghout the question the calculated points are:
[tex](0,0) , \ \ (40,252) \\(0,0) , \ \ (40,210) \\[/tex]
Formula for Calculating slope:
[tex]M=\frac{y_2-y_1}{x_2-x_1}[/tex]
For First point slope:
[tex]M=\frac{252-0}{40-0}=\frac{252}{40}= 6.3 \ \frac{people}{mi^2}[/tex]
For second point slope: [tex]M=\frac{210-0}{40-0}=\frac{210}{40}=\frac{21}{4}= 5.25 \ \frac{people}{mi^2}[/tex]
Solve each equation. List any restrictions. Check your solutions.
12/x+11=17
Help me ♀️
Hehdhxjjbduc eirbdudbdu
Answer:
slope = 1
y - intercept = (0.-4)
Hong reads 7 1/2 chapters in 3 1/8 hours.
Find the length of a diagonal of a square with a side of 10. Round your answer to the nearest hundredth.
please please help it's timed!
determine the value of y, if x is 7.
[tex]y=x^2-1[/tex]
Answer:
y = 48
Step-by-step explanation:
Plug in 7 for x:
y = x² - 1
y = (7)² - 1
Simplify. Remember to follow the order of operations, PEMDAS.
PEMDAS stands for:
Parenthesis
Exponents (& roots)
Multiplication
Division
Addition
Subtraction
~
First, solve the power, then subtract:
y = (7)² - 1
y = (7 * 7) - 1
y = (49) - 1
y = 48
48 is your value for y.
~
NEED HELP PLEASE. NO LINKS OR U WILL B REPORTED. WILL GIVE POINTS AND THE BRAINLIEST. THANKS!!
In a robotics competition, a robot must be built with a specific
maximum starting height, width, and depth. In order to meet the
height requirements, a robot must fit in the judge's plexi-glass box.
The box is a rectangular prism that has a surface area of 1 728 in”, a
width of 15 inches, and a length of 18 inches. The Mad Hatter robot
is 17.75 inches tall in its starting position. Does the Mad Hatter
meet the height requirement?
To serve 1 person at a local restaurant, it takes 10 minutes. To sene 5 people, it takes 18 minutes. Write and solve an equation to find the number it will take to serve a party of 8.
Answer:8x5=10-x
Step-by-step explanation:
Please answer both questions, thanks!
Answer: your welcome lol
Step-by-step explanation:
The point (3,2) reflected in the x-axis is (
,
).
Question 2
b. Reflect (3,2) in the y-axis.
The point (3,2) reflected in the y-axis is (
,
).
Answer:
the answers below:
1: (3,-2)
2: ( -3,2)