Answer:
Step-by-step explanation:
Actually its
Andy spends $ 13.20
Emily will spend 23.40
HOPE IT HELPS!!!!!!!!!!
Find the general solution of y''' + 9y'' + y' − 111y = 0 if it is known that y1 = e−6x cos(x) is one solution.
Answer:
[tex]\mathbf{y(x) = \dfrac{(c_1 + c_2) \ cos (x)}{e^{6x} }+ \dfrac{i(c_1 -c_2) \ sin (x)}{e^{6x}}+ c_3e^{3\ x}}[/tex]
Step-by-step explanation:
The objective of this question is to solve:
[tex]\dfrac{dy(x)}{dx}+ 9\dfrac{d^2y(dx)}{dx^2}+\dfrac{d^3y(x)}{dx^3}-111y(x) = 0 :[/tex]
Suppose the general solution is proportional to [tex]e^{\lambda x}[/tex] for [tex]\lambda[/tex] is constant; Then:
Let's replace [tex]y(x) = e^{\lambda\ x}[/tex] into the above equation:
i.e.
[tex]\dfrac{d^3}{dx^3}(e ^{\lambda x} )+ 9 \dfrac{d^2}{dx^2}(e ^{\lambda x} ) + \dfrac{d}{dx}(e ^{\lambda x} )- 111 \ e ^{\lambda x} = 0[/tex]
To Replace:
[tex]\dfrac{d^3}{dx^3}(e ^{\lambda x} )[/tex] with [tex]\lambda^3 e ^{\lambda x }[/tex]
[tex]\dfrac{d^2}{dx^2}(e ^{\lambda x} ) \ with \ \lambda^2 e^{\lambda\ x}[/tex]
[tex]\dfrac{d}{dx}(e ^{\lambda x} ) \ with \ \lambda e ^{\lambda \ x}[/tex]
Thus;
[tex]\lambda^3 e ^{\lambda x }[/tex] + [tex]9 \lambda^2 e^{\lambda\ x}[/tex] + [tex]\lambda e ^{\lambda \ x}[/tex] - 111 [tex]e ^{\lambda \ x}[/tex] = 0
[tex]e ^{\lambda \ x} (\lambda ^3 + 9 \lambda ^2 + \lambda - 111 )= 0[/tex]
∴
In as much as [tex]e^{ \lambda x}\neq 0[/tex] for any finite [tex]\lambda[/tex]; Then:
[tex]\lambda ^3 + 9 \lambda ^2 + 111 = 0[/tex]
By Factorization:
[tex](\lambda - 3) ( \lambda ^2 + 12 \lambda + 37) = 0[/tex]
[tex]\lambda = -6 + i \ or\ \lambda = -6 - i \ or \ \lambda = 3[/tex]
However;
The root [tex]\lambda = -6 \pm i[/tex] yield;
[tex]y_1 = (x) = c_1 e ^ {(-6+i)x}[/tex]
[tex]y_2 (x) = c_2e^{(-6-i)x}[/tex]
The root [tex]\lambda = 3[/tex] yield;
[tex]y_3(x) = c_3 e^{3x}[/tex]
∴
The general solution is:
[tex]y(x) = y_1(x) + y_2(x) + y_3(x) = \dfrac{c_1}{c^{(6-i)}x}+\dfrac{c_2}{c^{(6+i)}x}+ c_3e^{3x}[/tex]
Using Euler's Identity ;
[tex]e^{\alpha+i \beta} = e^\alpha \ cos (\beta ) + i \ e^\alpha \ sin ( \beta)[/tex]
[tex]y(x) = c_1 ( \dfrac{cos (x) }{e^{6x}}+ \dfrac{i \ sin x }{e^{6x} }) + c_2 ( \dfrac{cos (x)}{e^{6x}}- \dfrac{-i \ sin (x)}{e^{6x}})+c_3 e^{3x}[/tex]
[tex]\mathbf{y(x) = \dfrac{(c_1 + c_2) \ cos (x)}{e^{6x} }+ \dfrac{i(c_1 -c_2) \ sin (x)}{e^{6x}}+ c_3e^{3\ x}}[/tex]
(3+sqrt-16)(6-sqrt-64)
Answer:
12i + 9
Step-by-step explanation:
Since sqrt of negative numbers cannot exist, they are numbers followed by the letter I.
sqrt -16=4i
sqrt -64=8i
3 and 6 cannot be grouped with them, so you would add these two
3+6=9
8i+4i=12
I believe this would be the answer:
12i + 9.
Answer:
18-32i
Step-by-step explanation:
(3+sqrt(16i)(6-sqrt(64i)
= 18-32i
This table gives a few (x, y) pairs of a line in the coordinate plane. What is the y-intercept of the line?
Answer:
The Y-intercept is the Y value when X = 0.
Find the change in X:
-56 to -42 = 14
-42 to -28 = 14
The X value changes by 14.
For every change in X the Y change:
66-58 = 8
58-50 = 8
For X to get from -28 to 0 would be 2 more changes:
-28 +14 = -14
-14 + 14 = 0
2 more changes of Y would be:
50-8 = 42
42-8 = 34
So when X = 0, Y = 34
The Y-intercept would be (0,34)
Step-by-step explanation:
like if it helps <3
10) Sarah is 3 years older than her sister Mary.
Together their ages add up to 23. How old is Mary?
Answer:
20
Step-by-step explanation:
20 - 3
Sarah is 3 years older so 23 is going to be subtracted.
Which expression is a prime polynomial, x^3-1, x^2+1, x^3+1, x^2-1
Answer:
[tex]x^2+1[/tex] cannot be factored, thus it's a prime polynomial
Step-by-step explanation:
A prime number or expression cannot be factored in any factor different from 1 and the number or expression itself.
One of the following expressions is prime. The rest of them can be factored.
[tex]x^3-1[/tex] is the difference of two cubes. It can be factored as:
[tex]x^3-1=(x-1)(x^2+x+1)[/tex]
[tex]x^3+1[/tex] is the sum of two cubes. It can be factored as:
[tex]x^3+1=(x+1)(x^2-x+1)[/tex]
[tex]x^2-1[/tex] is the difference of two squares. It can be factored as:
[tex]x^2-1=(x-1)(x+1)[/tex]
[tex]\mathbf{x^2+1}[/tex] cannot be factored, thus it's a prime polynomial
I would really appreciate some help. Thanks!
Seth has game and education apps on his tablet. He noticed that he has 5 game apps for every 2 education apps. Which of the following is another way to write this ratio?
A. 2:3
B. 2:5
C. 3:2
D. 5:2
Answer:
D
Step-by-step explanation:
the question says that he has 5 to 2 and if you put it in a fraction you cant reduce it so therefore the answer has to be 5:2
Answer:
D. 5:2
Step-by-step explanation:
He has 5 games so 5: for every 2 school apps so 5:2
David has 574 cereal bars that he wants to fit in bags of 10 and bags of 8. The number of bags of 8 is 2 more than the number bags of 10. How many bags of 8 and 10 can david pack the cereal bar into
Answer: lol have the same question
Step-by-step explanation:
Text a friend and write a clear set of instructions on how to find a ratios amount
Answer:
Hi ___
A ratio is created from two numbers it can also be a fraction.
To find a ratio you have to have 2 numbers
You can take these 2 numbers and divide them so they are a unit ratio
For example 3:6 can be reduced to 1:3
Step-by-step explanation:
Hope this helps please give brainliest
At 7:00 one Summer morning Harry and Hermione hopped into their speedy more motorboat and left Hogwarts dock. They arrived at Dumbledore Wharf 35 minutes later. During the busy summer months a car ferry departs from Dumbledore wharf every five minutes. Tourists crowd onto the ferry for the 55 minute ride to Hogswarts dock. If Harry and Hermione followed the route that the car ferries take, how many car ferries did they see on their trip?
9514 1404 393
Answer:
19
Step-by-step explanation:
If we assume that the car ferries start at or before 6:05, and each 5 minutes thereafter, and if we count the ferries at the dock on either end, the total number seen is the number of ferries encountered in ...
55 +35 = 90 . . . minutes
That is, it is the number already in transit when they leave, plus the number that start while they are traveling.
That's 90/5 +1* = 19 ferries.
_____
The attached diagram can give an idea. Each up-sloping line represents a ferry in-transit. The left side is Dumbledore Wharf; the right side is Hogwarts dock. Each horizontal unit represents the distance traveled by a ferry in 5 minutes. Each vertical unit represents a 5-minute interval.
The down-sloping line represents the motorboat travel. The dots at either end of the latter line represent car ferries that are at the dock, just arriving or just-departing. Altogether, there are 17 places where the lines cross, in addition to the boats at the docks.
__
* the +1 is because the number of points defining intervals is 1 more than the number of intervals.
12x + 7 < -11
OR
5.2 – 8 > 40
Answer:
x < - 3/2 or x > 48/5 (option a in your list of answers)
Step-by-step explanation:
We solve for x in each inequality:
12 x + 7 < -11
subtract 7 from both sides:
12 x < - 11 - 7
12 x < -18
divide both sides by 12 to isolate "x" on the left:
x < - 18 / 12
simplify a common factor 6 in numerator and denominator on the right:
x < - 3 / 2
Now the other inequality:
5 x - 8 > 40
add 8 to both sides:
5 x > 40 + 8
5 x > 48
divide both sides by 5:
x > 48 / 5
So the answer is:
x < - 3/2 or x > 48/5
which coincides with answer a) in your list.
the value of x in logx(9/63)=1/2 is
Answer: x = 7/2
Step-by-step explanation: u juss simplify 1/2 x 7 to 7/2 so x = 7/2
The value of x in logarithmic equation [tex]log_{10}x(\frac{9}{63} )=\frac{1}{2}[/tex] is [tex]1000\sqrt{10}[/tex].
What is a logarithmic equation?
"A logarithmic equation is an equation that involves the logarithm of an expression containing a variable."
Given logarithmic equation
[tex]log_{10}x(\frac{9}{63} )=\frac{1}{2}[/tex]
⇒ [tex]log_{10}x(\frac{1}{7} )=\frac{1}{2}[/tex]
⇒ [tex]log_{10}x=\frac{1}{2}({7} )[/tex]
⇒ [tex]log_{10}x=\frac{7}{2}[/tex]
⇒ [tex]x = 10^{\frac{7}{2} }[/tex]
⇒ [tex]x = 10^{3+\frac{1}{2} }[/tex]
⇒ [tex]x = 10^{3}[/tex] × [tex]10^{\frac{1}{2} }[/tex]
⇒ [tex]x = 1000\sqrt{10}[/tex]
The value of [tex]x = 1000\sqrt{10}[/tex]
Hence, the value of x in logarithmic equation [tex]log_{10}x(\frac{9}{63} )=\frac{1}{2}[/tex] is [tex]1000\sqrt{10}[/tex].
Learn more about logarithmic equation here
https://brainly.com/question/14406114
#SPJ2
how many number of subsets in set D
Answer: A proper subset is a subset that is not identical to the original set—it contains fewer elements. You can see that there are 16 subsets, 15 of which are proper subsets. Listing the sets is fine if you have only a few elements.
Quickkkk!!!!!!!! Help
Answer:
2143
Step-by-step explanation:
At Sakaro's Sushi, you can get 18 wraps for $30.06 What is the price for 1 wrap?
Answer: $1.67
Let's make an equation for the problem. To find the price for each sushi roll, divide the price by the number of sushi rolls.
30.06 ÷ 18 = 1.67
3 people take 90mins to water a garden how long does it take 6 people
Answer:
hope it is helpful
Step-by-step explanation:
mark as branlist
^ ^
State the domain of the relation (1,2,3,3,4,5) (-3,-1,1,2,3)
Please help I would appreciate
Answer:
the 1st 2nd and 5th since if there is even one negative in the fraction it makes the whole fraction negative
What is the image of point (-3,-1) under a reflection in the origin?
Answer:
3,1
Step-by-step explanation:
A.(-2,3)
B.(-2,-3)
C.(2,3)
D.(4,3)
Jon used 64.4 cups of flower to make 8 loaves of bread. How much flower did he use for each loaf?
Answer:
8.05 cups per loaf
Step-by-step explanation:
divide 64.4 and 8
equation
64.4÷8=8.05
Rewrite the following using the GCF and Distributive properly ?
63 + 27
The toco toucan, the largest member of the toucan family, possesses the largest beak relative to body size of all birds. This exaggerated feature has received various interpretations, such as being a refined adaptation for feeding. However, the large surface area may also be an important mechanism for radiating heat (and hence cooling the bird) as outdoor temperature increases. Here are data for beak heat loss, as a percent of total body heat loss, at various temperatures in degrees Celsius:
Temperature (degrees Celsius) 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Percent heat loss from beak 35 36 38 28 41 43 55 46 39 54 45 58 60 56 62 67
a. The equation of the least-squares regression line for predicting beak heat loss, as a percent of total body heat loss from all sources, from temperature is: _____ (Use decimal notation. Give your answer to four decimal places.)
b. Use the equation to predict (
±
0.01) beak heat loss, as a percent of total body heat loss from all sources, at a temperature of 25 degrees Celsius.
c. What percent (
±
0.01) of the variation in beak heat loss is explained by the straight-line relationship with temperature?
d. Find the correlation r (
±
0.001) between beak heat loss and temperature.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
Temperature (degrees Celsius) : 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Percent heat loss from beak : 35 36 38 28 41 43 55 46 39 54 45 58 60 56 62 67
Using an online regression calculator ; the regression equation obtained is :
ŷ = 2.0927X + 0.6029
X = independent variable
Y = predicted variable
2.0927 = slope
0.6029 = intercept
B.) temperature = 25
ŷ = 2.0927(25) + 0.6029
= 52.9204
C.) the explained variance is the value of the coefficient of determination (R²) which is the square of the correlation Coefficient
0.8785² = 0.7718
D.) the correlation Coefficient r is 0.8785 using the Coefficient of regression calculator
Find the value of
5x^2 if x = -3.
Step-by-step explanation:
5x²
If x = 3
Then,
5(3)²
= 5×9
= 45
The fraction model below shows the steps that a student performed to find a quotient. Which statement best interprets the quotient? There are fraction 6 and 1 over 4 two-thirds in fraction 4 and 1 over 6.
a. There are fraction 6 and 1 over 4 five and one-sixths in fraction 2 over 3.
b. There are fraction 8 and 1 over 6 two-thirds in fraction 5 and 1 over 6.
c. There are fraction 8 and 1 over 6 five and one-sixths in fraction 2 over 3.
Answer:
C. D. E. or 3. 4. 5.
Step-by-step explanation:
A coral reef grows 0.14 m every week. How much does it grow in 14 weeks? Write your answer in millimeters.
Answer:
0.14*14= 1.96
Step-by-step explanation:
Must multiply 0.14 times 14 for the answer.
If two different integers between 1 and 100 inclusive are chosen at random, what is the probability that the difference of the two numbers is 15
Answer: 17 / 990
Step-by-step explanation:
To obtain the probability of the question above :
Find the count of number pairs whose difference gives is 15 in the range (1 to 100).
Also find the count of all distinct number pair differences
Number pair which have a difference of 15 = 85
Total distinct number pair differences = 4950
Probability = required outcome / Total possible outcomes
P(difference of 15) = 85/4950 = 17/990
The regular admission price for an amusement park is $72. For a group of 15, or more, the admission price is reduce by $25 per person. How many people need to be in a group to save $500?
=========================================
Explanation:
x = number of people
Without the discount, each person pays $72, so the total cost is 72x dollars if x people go through the gate individually.
Now applying the group discount, those x people pay 72-25 = 47 dollars each. Meaning the total cost is now 47x. Keep in mind that [tex]x \ge 15[/tex] in order for the discount to kick in.
Subtracting the two amounts leads to 72x-47x = 25x. It is not a coincidence that we get a coefficient of 25 here.
Set this equal to 500 and solve for x
25x = 500
x = 500/25
x = 20
------------
If x = 20 people attend individually, then they pay 72*x = 72*20 = 1440 dollars.
If 20 people go as one group, they pay 47x = 47*20 = 940 dollars
We have a savings of 1440-940 = 500 dollars. This confirms the answer.
All 20 people must go as one group if they want to save $500.
A simple index of three socks have opening values on day 1 and day 8 as shown in the table below. What is the rate of change of this simple index over one week? Round your answer to the nearest tenth
Answer: -7.7%
Step-by- A P E X
If a =
3
5
, b = 3, c = 1, d = 5, which equality is true?
A)
d
a
=
b
c
B)
a
b
=
c
d
C)
b
a
=
c
d
D)
a
d
=
b
c
Answer:
could you give a picture of the problem. cause I may be able to help but I cant really understand the question with what you typed
Answer:
D
Step-by-step explanation:
just took this test
Helppp me plssss! ASAP
Answer:
140 ft.
Step-by-step explanation:
first find the area of the rectangle
16 x 8 = 128
Area: 128
then find the area of the triangle
Base: 4
Height: 6
Area: 12
Then all u need to do is add
12 + 128 = 140