Answers
The solution to the initial value problem is determined as y = e³ˣ.
Form auxiliary equationThe auxiliary equation is determined as follows;
y'' - 7y' + 12y = 0
m² - 7m + 12 = 0
m² - 3m - 4m + 12 = 0
m(m - 3) - 4(m - 3) = 0
m = 3 or 4
[tex]y = c_1e^{3x} + c_2e^{4x}\\\\y(0) = 1\\\\1 = c_1e^{3\times 0} + c_2e^{4\times 0}\\\\1 = c_1 + c_2 \ --(i)\\\\y' = 3c_1e^{3x} + 4c_2e^{4x}\\\\y'(0) = 3\\\\3 = 3c_1e^{3\times 0} + 4c_2e^{4\times 0}\\\\3 = 3c_1 + 4c_2 \ \ --(ii)[/tex]
solve (i) and (ii)
3 = 3c₁ + 4(1 - c₁)
3 = 3c₁ + 4 - 4c₁
3 = -c₁ + 4
c₁ = 1
c₂ = 0
[tex]y = e^{3x}[/tex]
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Related Questions
Does anyone know the correct answer.
Answers
Answer:
The answer is B
Please help me! Thanks.
Answers
Answer: Answer:
The perimeter of the polygon are
PQ = 5
RS = 5
PR = √74 = 8.60
QS = √74 = 8.60
QR = 7
Step-by-step explanation:
To calculate the perimeter of a polygon, polygon is like a coordinate with points, to find the length, we use this formula
d = √(x _2 - x_1)^2 + (y_2 - y_1)^2
Let's start from the first two vertices P ( 0 , 4) and Q(5 , 4)
x_1 = 0
y_1 = 4
x_2 = 5
y_2 = 4
PQ = √ ( 5 - 0)^2 + ( 4 - 4)^2
= √ 5^2 + 0^2
= √ 25
= 5
Between R( 5 , -3) and S ( 0 , -3)
x_1 = 5
y_1 = -3
x_2 = 0
y_2 = -3
RS = √ ( 0 - 5)^2 + ( -3 - (-3))^2
= √( -5)^2 + ( -3 + 3)^2
= √ 25 + 0
= √ 25
= 5
Between P( 0 , 4) and R (5 , -3)
x_1 = 0
y_1 = 4
x_2 = 5
y_2 = -3
PR = √( 5 - 0)^2 + ( -3 - 4)^2
= √ 5^2 + (-7)^2
= √ 25 + 49
= √ 74
= 8.60
Between Q ( 5 , 4) and S(0 ,-3)
x_1 = 5
y_1 = 4
x_2 = 0
y_2 = -3
QS = √ ( 0 - 5)^2 + ( -3 - 4)^2
= √ -5^2 + -7^2
= √ 25 + 49
= √ 74
= 8.60
Between Q( 5,4) and R(5 , -3)
x_1 = 5
y_1 = 4
x_2 = 5
y_2 = -3
QR = √ (5 - 5)^2 + ( -3 - 4)^2
= √ 0^2 + (-7)^2
= √ 0 + 49
= √ 49
= 7
Step-by-step explanation:
x+14/x=-9
Help please and if possible could someone be so kind as to make a step by step please
Answers
Answer:
X = 1.4
Step-by-step explanation:
x + 14/x = -9
x + 14 = -9x
x + 9x = -14
10x = -14
X = -14/10
X = -1.4
Of the following fractions: 1/4, 7/9, 7/12, and 9/16, which is the largest?
Answers
Answer:
1/4, 7/8, 7/12, 9/16
LCM of 4,8,12,16 = 48
1/4= 1×12/4×12= 12/48
7/8= 7×6/8×6= 42/48
7/12= 7×4/12×4= 28/48
9/16= 9×3/16×3= 27/48
hence, 7/8 is the largest fraction. I hope it helps ya!!
The largest fraction is 7/8.
What is Least Common Multiple?Least Common Multiple is defined as the smallest number that is a multiple of two or more numbers.
Given fractions,
1/4, 7/8, 7/12, 9/16
LCM of 4,8,12,16 = 48
1/4= 1×12/4×12= 12/48
7/8= 7×6/8×6= 42/48
7/12= 7×4/12×4= 28/48
9/16= 9×3/16×3= 27/48
Since the largest will be the fraction
NUMERATOR > DENOMINATOR
Hence, the largest fraction is 7/8.
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Please show how you solved
Answers
Answer:
x = 7 degrees
Step-by-step explanation:
The unlabelled angle at M PLUS 12x + 24 = 180
then the unlabelled interior angle is 180 - (12x+24)
The sum of the interior angles then = 180
80 + 4x + 180-(12x+24) = 180
236 -8x = 180
x = 7
Find the distance between the points (-20,6) and (-20,-14)
Answers
Answer:
20.00 units
Step-by-step explanation:
The distance between two points with coordinates
(-20,6) and (-20,-14) is:
20.00 units
(results are in decimal form, rounded to the nearest 100th)
Fabian mixes orange juice with 4 cans of pineapple juice to make punch. Each can of pineapple juice holds 2 liters. He makes a total of 19 liters of punch.
How many liters of orange juice did Fabian use to make the punch?
A.
9 L
B.
11 L
C.
13 L
D.
15 L
Answers
Step-by-step explanation:
Total= 19
Each holds 2 litres .
So it means, 19 -4= 15
You need 15 litres of oranges.
If f(x) = x + 1 and g(x) = 2x – 7, which expression is equivalent to [f o g](3)? (3 + 1)(2(3) –7) 2(3)2 – 6 2(3 + 1) – 7 (2(3) – 7) + 1
Answers
Answer:
Solution
-1
f
x=
1
-X+
2
Step-by-step explanation:
f(x=2x-7
Solving Steps
y=2x-7
Interchange the variables
x=2y-7
Swap the sides
2y-7=X
Move the constant to the right
2y=X+7
Divide both sides
1
y=
>+*.
7
2
Solution
-1
f
x=
1
-X+
2
A cone has a height of 8 yards and a radius of 3 yards. What is its volume?
Use ≈ 3.14 and round your answer to the nearest hundredth.
cubic yards
Submit
Answers
The volume of the given cone.
Solution:[tex]\large\boxed{Formula:V= \frac{1}{3}\pi{r}^{2}h}[/tex]
[tex]\large\boxed{\red \pi \red = \red 3 \red . \red 1 \red 4}[/tex]
Let's solve!
Substitute the values according to the formula.
[tex]V= \frac{1}{3}×3.14×{3}^{2}×8[/tex]
[tex]\large\boxed{V= 75.36 \: {yd}^{3}}[/tex]
Therefore, the volume of the given cone is 75.36 cubic yards.
What fraction is equivalent to 046464646
Answers
Answer:
46/99
explanation shown in the picture
The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of 50 business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow. 6, 4, 6, 8, 7, 7, 6, 3, 3, 8, 10, 4, 8 7, 8, 7, 5, 9, 5, 8, 4, 3, 8, 5, 5, 4 4, 4, 8, 4, 5, 6, 2, 5, 9, 9, 8, 4, 8 9, 9, 5, 9, 7, 8, 3, 10, 8, 9, 6 Develop, a, 95%, confidence, interval, estimate, of, the, population, mean, rating, for, Miami.
Answers
Using the t-distribution, it is found that the 95% confidence interval for the population mean rating for Miami is (5.73, 6.95).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 50 - 1 = 49 df, is t = 2.0096.
Considering the given sample, the other parameters are given as follows:
[tex]\overline{x} = 6.34, s = 2.16, n = 50[/tex]
Hence, the bounds of the interval are:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 6.34 - 2.0096\frac{2.16}{\sqrt{50}} = 5.73[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 6.34 + 2.0096\frac{2.16}{\sqrt{50}} = 6.95[/tex]
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Select the correct answer from each drop-down menu.
Alice is playing checkers against a computer and has won 8 games out of the 12 she's played so far.
Alice must win the next ✓consecutive games to reach a winning percentage of 80%. After that, losing
will bring her winning percentage down to 50%.
consecutive games
Answers
She must win the next 8 consecutive games to get 80% and after that loose the next 12 games to get to 50%.
How to find the probability of winning?
She has won 8 out of 12 days. Thus, percentage of winning is;
P(winning) = 8/12 * 100%
P(Winning) = 75%
To arrive at 80% winning, it means that the number of extra consecutive games she must win is;
(8 + x)/(12 + x) = 80/100
10(8 + x) = 8(12 + x)
80 + 10x = 96 + 8x
2x = 16
x = 8
Thus, she must win the next 8 consecutive games to get 80%.
For her to get to 50% after that, it means that;
(16 - x)/(20 - x) = 50/100
(16 - x)/(20 - x) = 1/2
2(16 - x) = 20 - x
32 - 2x = 20 - x
x = 12
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Using horizontal strip, determine the area of the region bounded by curves x² + 4y - 8 = 0 and x =
2y
Answers
The Area of the region bounded by curves = 9 sq.units.
What is Area ?Area is the space occupied by a two dimensional figure on a two dimensional space coordinate.
The two curves given are
x² + 4y - 8 = 0 and x =2y
Convert the two equation so ‘x’ is the dependent variable.
y = -(1/4) x² +2 and y = (1/2)x
Find the limit by the intersection point of both the graph
so (-4, 2) and (2, 1)
The x-values of the line are greater so subtract the parabola:
A = ∫ (1/2)x - (-(1/4) x² +2 ) in the limits of (-4 and 1)
The Area = 9 sq.units.
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only answer if you know (no guesses) no spams! :)
Answers
Answer:
3/4
Step-by-step explanation:
I actually took this quiz a day ago!
solve u^2 = -4, where u is a real number. Simplify your answer as much as possible.
will mark brainliest if correct
Answers
Answer:
2i and -2i
Step-by-step explanation:
I'll change u to x to be easier to understand.
x^2 = -4
sqrt(x^2) = sqrt(-4)
sqrt(-4) = 2i, or -2i
I NEED HELP NOWWWW PLSSS
From this data, how many male, female, adult, and baby moose do you predict are in the park?
Elk Mountain Goat Deer Moose
Male 105 71 42 52
Female 120 93 63 34
Adult 173 103 72 58
Baby 52 61 33 28
Answers
The data shows that the number of male, female, adult, and baby moose that are in the park will be 52, 34, 58, and 28 respectively.
What is data?It should be noted that data simply means the facts and statistics that are given which are used for analysis.
In this case, the data shows that the number of male, female, adult, and baby moose that are in the park will be 52, 34, 58, and 28 respectively. This can be seen from the information in the table.
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pls help it’s the last day of school
Answers
Answer:
12.56ftcube
Step-by-step explanation:
if V=(3.14×1^2)×4= 3.14 ×4=12.56
Mary's total bill for a used car is $2,700.00. If she pays an equal amount each month for an entire year, how much will she have to pay each month?
Answers
Answer:
$225
Step-by-step explanation:
When Mary pays the cost in 12 equal payments, each is 1/12 of the total amount.
__
1/12 × $2700 = $225
Mary will have to pay $225 each month.
53 POINTS. Which expression gives the distance between the points (7, -2) and (3, -1)?
A.√4² +3²
B.√4² +1²
C. 10² +3²
D.√10² + 1²
Answers
the formula for distance between points is:
Distance = sqrt((x2-x1)^2 + (y2-y1)^2)
Using the points given:
Sqrt((3-7)^2 + (-1 - -2)^2)
Sqrt(-4^2 + 1^2)
None of the answer have a -4 but I think it should be B. Since it is the closest. Did you forget a negative sign when typing??
answer B.
help please! thank you so much
Answers
Answer:
4 units ...................
2x-y=3, x=-2y-2 solve for substitution
Answers
Answer:
-1.25
Step-by-step explanation:
2x - 7 = 3
x = -2y - 2
3 + 7 = 2x
x = 5
5 = -2y - 2
5 = -4y
5 = -4 times y
-
a. The velocity, v, of an object is moving in a medium at time t is given by
t = √ 30² +50+2 du. Evaluate t.
+
Answers
The value of "t" in the given expression for the velocity of the object moving in the medium is t = u³ + 2.5u² + 2u.
Velocity of the object moving in the medium
The velocity of the object moving in the medium is given as;
t = ∫(3u² + 5u + 2)du
the value of t is obtained by integrating the function as follows;
t = (3u³)/3 + (5u²)/2 + 2u
t = u³ + 2.5u² + 2u
Thus, the value of "t" in the given expression for the velocity of the object moving in the medium is t = u³ + 2.5u² + 2u.
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GIVEN F(x) = 4/x , FIND THE FOLLOWING VALUES.
1. x= 0
2. x= 2
3. x= 1
4. x = 2x
Answers
Answer: x = 0 the equal sign has to have a line going through it.
The denominator must not equal 0. So the domain is x = 0 the equal sign has to have a line going through it.
4 GET EVE ⠀ Directions:
Answers
Answer:
not a solution.. simple not needed to explain too
The equation of this circle is (x +
)2 + (y +
)2 =
.
Answers
Answer:
x2 + y2 = r2, and this is the equation of a circle of radius r whose center is the origin O(0, 0). The equation of a circle of radius r and center the origin is x2 + y2 = r2.
I think this is the answer.
TYPES OF CARS WORKED ON German cars 25% Other 10% American 50% Japanese 15% These are the types of cars worked on in the auto service.
6) What is the probability that the next car worked on will be Japanese or German?
7) If the mechanics work on 6,000 cars next year, how many cars would probably be Japanese?
I really would appreciate help on this! Thank you
Answers
Answer:
6) 40%7) 900 carsStep-by-step explanation:
German 25%
Other 10%
American 50%
Japanese 15%
……………………………………………
6) the probability that the next car worked on
will be Japanese or German :
p(J∪G) = p(J) + p(G) = 15% + 25% = 40%.
…………………………………………………………
7) the probable number of Japanese cars :
[tex]6000\times \frac{15}{100} = 900[/tex]
What is the solution to the system of equations graphed below?
Answers
realmente no lo se bro per necesito completar este paso
6230000 in standard form
Answers
Answer:
6.23*10^6
Step-by-step explanation:
in standard form, it should be written as x*10^n, and x is only allowed from 1-9, so
1) write the first number and add a decimal point(.) and copy down the numbers behind the first number (DO NOT WRITE 0):
6.23
2) check how many numbers are they behind the first number
6230000
~~~~~~
in here, it's 6numbers, so 10^6
3) all in all, your answer is
6.23*10^6
What the equation of the line that passes through the points (-4, 3) and is parallel to y = ½ x - 7?
Answers
The equation of the parallel line is: y = 1/2x + 5.
What is the Equation of Parallel Lines?The slope (m) of parallel lines are the same.
Given the equation, y = 1/2x - 7, the slope (m) is 1/2. Therefore, the slope of the line that passes through (-4, 3) would be m = 1/2.
To find the y-intercept (b), substitute m = 1/2 and (x, y) = (-4, 3) into y = mx + b.
3 = 1/2(-4) + b
3 = -2 + b
3 + 2 = b
5 = b
b = 5
Substitute m = 1/2 and b = 5 into y = mx + b:
y = 1/2x + 5
The equation is: y = 1/2x + 5.
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Which number is the largest 1.2 x 10^4, 4.5 x 10^-3,3.8x10^3,7.5^3
Answers
1.2x10^4
Step-by-step explanation:
2.
negative exponent means it's a fraction so
4.5x10^-3 is 1/4500 or 0.0045 so
it's a very small number
1.
^4 means means move the decimal 4 spots
12×10^4 = 12,000
3.
^3 means move the decimal 3 spots
3.8 x 10^3 =
3800
4.
7.5x10^3 =
7500