Solve the initial value problem. dy dx Ex4(y – 2), y(0) = 6
Answers
This equation represents the solution to the given initial value problem.
\(1/4 * e^{(4(y - 2))} = x + 1/4 * e^{(16)}\)
To solve the initial value problem, we'll separate variables and integrate both sides.
Starting with the given differential equation:
\(dy/dx = e^{4(y - 2)}\)
Separating variables:
\(e^{(4(y - 2))} dy = dx\)
Integrating both sides:
\(\int e^{(4(y - 2))} dy = \int dx\)
To integrate \(e^{4(y - 2)}\), we can use the substitution u = 4(y - 2), du = 4dy:
\(1/4 \int e^u du = x + C\)
Integrating \(e^u\) gives us:
\(1/4 * e^u = x + C\)
Substituting back u = 4(y - 2):
\(1/4 * e^{(4(y - 2))} = x + C\)
Now, applying the initial condition y(0) = 6, we can solve for C:
\(1/4 * e^{(4(6 - 2))} = 0 + C\)
\(1/4 * e^{(4(4))} = C\)
\(1/4 * e^{(16)} = C\)
Therefore, the solution to the initial value problem is:
\(1/4 * e^{(4(y - 2))} = x + 1/4 * e^{(16)}\)
This equation represents the solution to the given initial value problem.
To know more about initial value problem, refer here:
https://brainly.com/question/17613893
#SPJ4
Related Questions
Solve the following equation for x: 2x^2 - 3 = 47
With explanation plz ion wanna go summer school
Answers
Answer:
Step-by-step explanation:
2x²-3=47
2x²=47+3
x²=50/2=25
x=±√25=±5
Answer:
x = ±5
Step-by-step explanation:
2x^2 - 3 = 47
Add 3 to each side
2x^2 - 3+3 = 47+3
2x^2 = 50
Divide each side by 2
2x^2 = 50/2
x^2 = 25
Take the square root of each side
sqrt(x^2) = sqrt(25)
x = ±5
Sally invests £8000 in a savings account.
The account pays 2.8% compound interest per year.
Work out the value of her investment after 4 years.
Give your answer to the nearest penny.
Answers
After four years, the investment is worth £8934.34.
How does compound interest work?The interest you earn on interest is known as compound interest. For instance, if you start with $100 and it generates 5% interest annually, you will conclude the first year with $105 in your account. You'll have $110.25 after the second year is over.
We employ the formula approach to determine the entire amount,
A = P(1+r)^n
The amount invested, or principal(P), is £8,000.
Interest rate r is 2.8%, or 0.028.
n = 4 years have passed.
Now, immediately enter these values into the formula, A = P(1+r)n.
A = 8000 * (1 + 0.028) ^ 4
= 8000 * 1.028 ^ 4
= 8934.34
Consequently, the investment's value after four years is £8934.34.
To read more about compound interest
https://brainly.com/question/28020457
#SPJ9
a tukey multiple comparison is performed to compare the means of 5 populations. how many confidence intervals will be obtained?
Answers
There will be 10 confidence intervals obtained in a Tukey multiple comparison of 5 populations.
In a Tukey multiple comparison, the confidence intervals are constructed to compare the means of all pairs of groups. To calculate the number of confidence intervals, we use the following formula:
C = n(n-1)/2
Where C is the number of confidence intervals, and n is the number of groups. In this case, there are five populations being compared, so n=5. Plugging this into the formula, we get:
C = 5(5-1)/2 = 10
Each confidence interval will provide information about the difference between the means of two groups, with a certain level of confidence. These confidence intervals can be used to identify which pairs of groups have significantly different means.
To learn more about confidence intervals click on,
https://brainly.com/question/28213446
#SPJ4
Solve the following expressions. Write your answer in scientific notation. 13. (6.125×10 3
)×(2.345×10 4
) 14. (6.125×10 3
)×(2.345×10 −4
) 15. 3700.13×(6.04×10 4
) 16. (6.2×10 4
)/(0.4×10 −5
)
Answers
13) The scientific notation is 1.4354125 * 10⁸. 14) The scientific notation is 1.4354125 * 10⁻¹. 15) The scientific notation is 22366.0992. 16) The scientific notation is 1.55 * 10¹⁰.
Let's solve the given expressions and write the answers in scientific notation:
13) \((6.125*10^3) * (2.345*10^4)\)
To multiply the numbers in scientific notation, we multiply the coefficients and add the exponents:
\((6.125 * 2.345) * (10^3 * 10^4) = 14.354125 * 10^(3 + 4) = 14.354125 * 10^7 = 1.4354125 * 10^8\)
\(= 1.4354125 * 10^8\)
14) \((6.1258*10^3) * (2.345*10^{-4})\)
To multiply the numbers in scientific notation, we multiply the coefficients and add the exponents:
\((6.125 * 2.345) * (10^3 * 10^{-4}) = 14.354125 * 10^{3 - 4} = 14.354125 * 10^{-1} = 1.43541258* 10^{-1}\)
\(= 1.4354125 * 10^{-1}\)
15) \(3700.13 * (6.04*10^4)\)
To multiply a decimal number and a number in scientific notation, we simply multiply the decimal by the coefficient of the scientific notation:
3700.13 × 6.04 = 22366.0992
Since the answer does not need to be expressed in scientific notation, the result is 22366.0992.
= 22366.0992
16) \((6.2*10^4) / (0.4*10^{-5})\)
To divide numbers in scientific notation, we divide the coefficients and subtract the exponents:
\((6.2 / 0.4) * (10^4 / 10^{-5}) \\= 15.5 * 10^{4 - (-5}) \\= 15.5 * 10^9 \\= 1.55 * 10^{10}\\= 1.55 * 10^{10}\)
For more details about scientific notation
https://brainly.com/question/19625319
#SPJ4
A rectangular region is removed from another rectangular region to create the shaded region shown below. Find the area of the shaded region.
7 yd
11 yd
4 yd
8 yd
Answers
The area of the shaded region is 60 square units.
What is Area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.
To find the area of the shaded region, we need to subtract the area of the rectangular region that was removed from the larger rectangular region.
The area of the larger rectangle is:
11 x 8 = 88
The area of the rectangle that was removed is:
7 x 4 = 28
So, the area of the shaded region is:
88 - 28 = 60
Therefore, the area of the shaded region is 60 square units.
Learn more about Area here:
https://brainly.com/question/27683633
#SPJ7
jolene has a 85% average on her quizzes, and 98% average on her homework, and a 89% average on her tests. quarter gardes are composed of 25% from quizzes, 25% from homework, and 50% from tests. if during the quarter she has taken 9 quizzes, 32 homeworks and 2 tests, what is the minimum score she needs in her next test to have an A in the class?
Answers
Answer:
415
Step-by-step explanation:
if there are 5 arithmetic means betweeen 5 and b.the last term is 25 then find the value of b
Answers
Answer:
b = 21
Step-by-step explanation:
If there are 5 arithmetic means between 5 and b and the last term is 25, then we can find the value of b by using the formula for the nth term of an arithmetic sequence:
a_n = a_1 + (n - 1)d
where a_n is the nth term, a_1 is the first term, n is the number of terms, and d is the common difference.
We know that there are 5 arithmetic means between 5 and b. Therefore, there are 7 terms in total (including 5 and b). We also know that the last term is 25. So we have:
a_7 = 25 a_1 = 5 n = 7
We can use these values to solve for d:
a_n = a_1 + (n - 1)d 25 = 5 + (7 - 1)d d = 4
Now that we know d, we can find b by using the formula for the fifth term:
a_5 = a_1 + (5 - 1)d a_5 = 5 + (4)(4) a_5 = 21
Therefore, b = 21.
Solve the inequality. −5x+27>2 Which answer represents the solution set?
Answers
Answer:
x<5
Step-by-step explanation:
We solve this question as if it was an equation but keep the sign an inequality sign this will be flipped when you divide both sides.
-5x+27>2
Subtract 27 from both sides:
-5x+27-27>2-27
-5x>-25
Divide both sides by -5 AND FLIP THE SIGN:
-5x/-5<-25/-5
x<5
If we substitute 5 into the inequality it will not be true but if you do any number below 5 it will work.
Therefore x<5 is the correct answer
Which line L has a slope of zero?
Answers
It is horizontal and therefore the slope is zero
Answer:
D
Step-by-step explanation:
GradientA Gradient is also called a slope of a line, which represents how steep a line is.
Formula of slope: Vertical difference ÷ Horizontal difference
For a slope to be zero, the line must be horizontal.
SolutionBased on the question given, we can deduce that D is a horizontal line and therefore the slope is zero.
if speed varies inversely as the time it takes to drive and kris takes 5 hours driving at 55 mph, what speed will martin need to drive if he wants to take 512hours
Answers
The speed that will martin need to drive, if he wants to take the 512 hours is 0.537 mph.
What does proportionality's constant look like?Students determine the rate of change, often referred to as the constant of proportionality (k = y/x), which is the consistent ratio between two proportional values (y/x) indicated by the symbol k, which may be a positive rational integer. The x value and the y value are directly proportional, as in the equation y = kx.
Speed and travel time vary in opposite directions.,
So v ∝ 1/t.
speed = v
time = t
So
=> v = k/t, k=constant of proportionality.
Since it takes Kris 5 hours when driving at 55 mph,
=> v = 55mph and t = 5 hours.
=> 55 = k/5
by doing cross multiply
=> k = 55*5
=> k = 275
Hence, to calculate for Martin to drive for 5 hours, we will take k = 275 and t = 5 into v = k/t
=> v = 275/512
=> v = 0.537 mph
To know more about constant of proportionality visit:
https://brainly.com/question/22620356
#SPJ4
Which polynomial function gets larger and larger in the negative direction as x gets larger and larger in the
negative direction?
Answers
Answer:
The first one
Step-by-step explanation:
The first one because the largest exponent is odd and its coefficent is positive
This equation shows how the total amount of paper Scott's office has recycled depends on the number of weeks since they started the new recycling plan. p = 12w The variable w represents the number of weeks the office has been on the new recycling plan, and the variable p represents the total kilograms of paper recycled. How many weeks will it take Scott's office to recycle a total of 12 kilograms of paper?
Answers
Answer:
1 week
Step-by-step explanation:
Given:
p = 12w
Where,
w = number of weeks the office has been on the new recycling plan
p = total kilograms of paper recycled.
How many weeks will it take Scott's office to recycle a total of 12 kilograms of paper?
Find w when p = 12
p = 12w
12 = 12w
Divide both sides by 12
w = 12/12
= 1
w = 1 week
(1+sinA+cosA)^2 = 2(1+sinA) (1+cosA)
Answers
Answer:
Step-by-step explanation:
\(L.H.S = 1^2+Sin^2A+Cos^2A+2SinA+2CosA+2SinACosA\\ \{(a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ca\}\\ = 1 + (Sin^2A+Cos^2A) + 2SinA+2CosA+2SinACosA \\ \{Sin^2A+Cos^2A=1\}\\ = 1 + 1 + 2SinA+2CosA+2SinACosA \\ = 2(1 + SinA+CosA+SinACosA)\\ = 2(1^2 + (SinA+CosA).1+ SinACosA )\\ \{x^2+(a+b)x + ab = (x+a)(x+b)\} \quad here \quad x=1\\ = 2(1+SinA)(1+CosA).\\\)
1. Solve for the unknown in each triangle. Round each answer to the nearest tenth.
Answers
The values of the missing sides are;
a. x = 35. 6 degrees
b. x = 15
c. x = 22. 7 ft
d. x = 31. 7 degrees
How to determine the valuesTo determine the values, we have;
a. Using the tangent identity;
tan x = 5/7
Divide the values
tan x = 0. 7143
x = 35. 6 degrees
b. Using the Pythagorean theorem
x² = 9² + 12²
find the square
x² = 225
x = 15
c. Using the sine identity
sin 29= 11/x
cross multiply the values
x = 11/0. 4848
x = 22. 7 ft
d. sin x = 3.1/5.9
sin x = 0. 5254
x = 31. 7 degrees
Learn more about trigonometric identities at: https://brainly.com/question/7331447
#SPJ1
Angles 1 and 2 are supplementary. Angle 2 is 1/5 the size of angle 1. What are the degree measurements of each angle?
Answers
Answer:
the stated ratio means that of the 180 degrees involving two supplementary angles, the smaller angle is one sixth of that whole. Thus the smaller angle measures 30 degrees & the larger measures 150 degrees.
Step-by-step explanation:
In triangle xyz, m∠y = 45.43° and m∠z = 38.7°. determine the measure of the exterior angle to ∠x. 44.57° 51.3° 75.75° 84.13°
Answers
Answer:
\(84.13^{\circ}\)
Step-by-step explanation:
By the exterior angle theorem, the answer is \(m\angle y+m\angle z=84.13^{\circ}\).
Answer:
Step-by-step explanation:
USE THE EXTERIOR ANGLE THEROME!
FIRST
THE FOMULA
a+b=c
y+z=x
now we have to add y and z
45.43 + 38.7
which gives us 84.13!
1. If m=1/2 and b=-4, what is the equation of the line?
Answers
Answer:
y=1/2x-4
Step-by-step explanation:
What number is halfway between 4 and 20?
Answers
Answer:
4....20. 12 is halfway
Step-by-step explanation:
5 19
6 18
7 17
8 16
9 15
10 14
11 13
12
Homework: Compound Probability (With Replacement)
You have a jar or marbles in front of you with the following colors, 7 Red, 12 Blue, 6 Green, and 9 White. What is the probability of selecting a red marble and then a white marble with replacement?
Answers
Answer:
C
Step-by-step explanation:
Help I forgot! How do you find slope? I have the change, but need the slope!
Answers
Answer:
(y2 - y1)/(x2-x1)
Step-by-step explanation:
if you have 2 points (x1,x2) and (y1,y2), just plug it in the formula for slope m
m = (y2 - y1)/(x2-x1)
HELP CHOOSE THE CORRECT ANSWER
Answers
Answer:
D.) I multiplied 4x3x5 because there is 3 on one side four on the other and 5 going up and down
Step-by-step explanation:
Hope this helps have a good day:)
in a toy store, the ratio of the dolls to teddy bears is 9:3. If the store has 240 dolls, how many teddy bears are in the store?
Answers
If the ratio is 9 to 3 and there are 240 dolls divide 240 by 3 which equals 80
:)
In 2012, gallup asked participants if they had exercised more than 30 minutes a day for three days out of the week. Suppose that random samples of 100 respondents were selected from both vermont and hawaii. From the survey, vermont had 65. 3% who said yes and hawaii had 62. 2% who said yes. What is the value of the sample proportion of people from vermont who exercised for at least 30 minutes a day 3 days a week?.
Answers
in the sample of 100 respondents from Vermont, 65.3% of them reported exercising for at least 30 minutes a day for three days out of the week.
The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week can be calculated as:
sample proportion = 65.3% = 0.653
what is minute?
In this context, "minute" likely refers to the amount of time spent exercising per day. Specifically, the survey asked if participants had exercised "more than 30 minutes a day for three days out of the week."
To learn more about minute visit:
brainly.com/question/15600126
#SPJ11
find the slope of a line that passes through the points (2,-1) and (4,7)
Answers
Answer:
if I did it correctly then it is y= 1/4x-9/4
Step-by-step explanation:
Can I get an answer to these? I feel asleep during a zoom class and I didn't hear what he said and now I'm confused.
Answers
PLEASE PLEASE PLEASE HELP
Answers
Answer:
FDE = 116 degrees
Step-by-step explanation:
If FDE and CDE are supplementary, then their total would be 180 degrees. Thus, we can set up the following equation:
CDE + FDE = 180
3x + 10 + 6x + 8 = 180
9x + 18 = 180
9x = 162
x = 18
Now that we know "x = 18", we can find the measurement of FDE:
FDE
6x + 8
6(18) + 8
116
In ΔMNO, m∠M = 57° and m∠N = 75°. Which list has the sides of ΔMNO in order from shortest to longest?
Answers
Answer: Choice B
MN, NO, OM
Refer to the diagram below
=====================================================
Explanation:
M = 57 and N = 75 are the two given angles.
Angle O is the missing angle of the triangle.
Recall that for any triangle, the three inside angles always add to 180
M+N+O = 180
57+75+O = 180
132+O = 180
O = 180-132
O = 48
Angle O is 48 degrees.
Note: be sure not to mix up the letter 'oh' with the number zero. Unfortunately, they look very similar.
-------------------------
We know the following three angles of this triangle
M = 57N = 75O = 48As a rule, the smallest side is always opposite the smallest angle. The smallest angle is O = 48, and the side opposite that is MN.
Also, the largest side is always opposite the largest angle. The largest angle is N = 75, and the side opposite that is OM
-------------------------
In short, we found that MN is the smallest side and OM is the longest side.
That must mean side NO is placed in the middle of MN and OM
So that's how we get get the answer of MN, NO, OM which is choice B.
Refer to the diagram below.
Which transformation of Figure A results in Figure A′?
Answers
A reflection across the y-axis.
What is transformation rule?A translation transformation rule describes how to move an object in the plane without changing its shape, size, or orientation. A reflection transformation rule describes how to flip an object across a line or plane. A scaling transformation rule describes how to change the size of an object by multiplying its coordinates by a scalar factor. A rotation transformation rule describes how to rotate an object around a fixed point by a certain angle.
From the graph, we can see,
The coordinates of the figure A are (-2, 0), (-2, 3) and (-5, 2)
The coordinates of the figure A' are (2, 0), (2, 3) and (5, 2)
The reflection across the y-axis, according to the rule is: \((x, y)\) → \((-x, y)\)
We can see, the y-coordinates stay the same values, while the x-coordinates will have the opposite values.
Therefore, the reflection across the y-axis.
To know more about reflection across the axis, visit:
https://brainly.com/question/24696463
#SPJ1
Which pair of numbers is relatively prime?
O 7 and 21
O4 and 15
O 6 and 9
O9 and 27
Answers
Reason:
Relatively prime numbers have a GCF of 1. The largest factor they have in common is 1. Another term for "relatively prime" is "coprime".
7 and 21 have a GCF of 7, which means they are not relatively prime. We can eliminate choice A off the list. Choice C and choice D are a similar situation.
h(x)=x2-x;h(5) find function
Answers
Answer:
h(5) = 20
Step-by-step explanation:
Assume that '2' is an exponent.
So the question for you should be:-
\( \displaystyle \large{h(x) = {x}^{2} - x}\)
We want to find h(5); we substitute x = 5 in.
\( \displaystyle \large{h(x) = {5}^{2} - 5}\)
5^2 is 5•5 = 25.
\( \displaystyle \large{h(x) = 25 - 5} \\ \displaystyle \large{h(x) = 20}\)
Therefore, h(5) is 20.