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1. Consider the vector field ? (1, y) = yî+xj. a) Use the geogebra app to sketch the given vector field, F. b) Find the equation of the flow lines. c) Sketch the flow lines for different values of th
Answers
The required equation is y = Ce^t where C = ±e^C2.
Given (1, y ) = y i + x j.
To find the equation of flow lines, solve the system of differential equation.
That implies
dx/dt = 1. --(1)
dy/dt = y. ----(2)
Integrating the first equation with respect to t gives,
x = t + c1
Integrating the second equation with respect to t gives,
ln|y| = t +c2.
Applying the exponential function to both sides, we have,
|y| = e^(t+c2)
Considering the absolute value, we get
case 1: y>0
y = e^(t+c2)
y = e^t × e^c2
Case - 2 y< 0
y = -e^(t +c2)
y = -e^t × e^c2
By combining both the cases,
y = Ce^t where C = ±e^C2.
This represents the general equation of the flow lines.
Hence, the required equation is y = Ce^t where C = ±e^C2.
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Related Questions
HELP
if a+1 is divisible by 3 prove that 4+7a is divisible by 3 too
Answers
Answer:
Step-by-step explanation:
Assume there exists integer k such that 3k=a+1.
4+7a
=7a+4
=7(a+1)-3
=7(3k)-3
=3(7k-1)
This implies that if there exists integer k such that 3k=a+1 then there is integer 7k-1 such that 3(7k-1)=4+7a
Explain to Malik why the logic that made him think the midpoint was (6,2) is almost right I had to extend his thinking to use the coordinates of the endpoint to get the midpoint of (-3,6)
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well, the way I'd put it is, 6 and 2 are a good cardinal pair to move about to get the midpoint, however the midpoint location uses an ordinal pair, so if we move 6 units over the horizontal and 2 units upwards toward the slanted line, we'd end up at our ordinal location for the midpoint of (-3 , 8). So in essence, if we move half the base and half the height, that's where our ordinal pair is.
GEOMETRY
The solid portion of the graph represents the relationship between the width of a rectangle in centimeters x and the area of the rectangle in centimeter squared y. Find and interpret any symmetry in the graph of the function
Answers
Based on symmetry, area of rectangle is same when width is number less or greater than x=5
Compare the rates of change of the following equation and table.
y = 8x
x y
2 22
4 44
6 66
8 88
A.
The rate of change of the table is equal to the rate of change of the equation.
B.
The rate of change of the table is greater than the rate of change of the equation.
C.
The rate of change of the table is less than the rate of change of the equation.
D.
There is not enough information to determine the rates of change.
Answers
The price of an item was reduced by 35 percent . The original price was $33. What is the price of the item now?
Answers
Answer:
11.55
Step-by-step explanation:
What is 5 to the 2nd power, times 5 to the 3rd power, times 5 to the 4th power? This is urgent!
Answers
Answer: 1953125
Step-by-step explanation: multiply 25 times 125 then multiply all of that by 625. It may be a big number but Im pretty sure it's right. Hope this helps.
Answer:
5 to the 2nd power = 25
5 to the 3rd power = 125
5 to the 4th power = 625
Step-by-step explanation:
All you have to do is multiply 5 by itself by what the number is. 5 to the 2nd power is 5 times 5, which is 25.
Three scientists want to estimate the mean weight of fish in the same lake. To do this, each scientist randomly chose 4 fish from the lake and recorded their weights. The samples are shown below. Do not round your answers.
Answers
SOLUTION:
Case: Averages
Method:
Sample 1
Mean
\(\begin{gathered} m=\frac{3+3+7+4}{4} \\ m=4.25 \end{gathered}\)Sample 2
Mean
\(\begin{gathered} m=\frac{6+3+8+2}{4} \\ m=\frac{19}{4} \\ m=4.75 \end{gathered}\)Sample 3
Mean
\(\begin{gathered} m=\frac{2+4+8+5}{4} \\ m=\frac{19}{4} \\ m=4.75 \end{gathered}\)b) Range of sample means:
R = 4.75 - 4.25
R = 0.5
c)
The following statements are valid:
i) The closer the range of the sample mean is to 0. The more confident they can be in their estimate
iii) The mean of the sample mean will tend to be a much better estimate than a single sample mean.
Final answers:
a)
SAMPLE 1. m = 4.25
SAMPLE 2. m = 4.75
SAMPLE 3. m = 4.75
b) Range = 0.5
c)
i) The closer the range of the sample mean is to 0. The more confident they can be in their estimate
iii) The mean of the sample mean will tend to be a much better estimate than a single sample mean.
A point P has coordinates (-8, -2). What are its new coordinates after reflecting point P across the x-axis?
Answers
Answer:
(-8,2)
Step-by-step explanation:
This is because when you reflect a point across the x-axis, the x-coordinate fo the point remains the same and the y-coordinate's sign gets switched.
(x,y) --> (x,-y)
(-8,-2) --> (-8,2)
HELPPP THANKS ILL GIVE BRAINLIEST! no links
Answers
Answer:
2, 10, 0, 4
Step-by-step explanation:
"regrouping 1 tenth into 10 hundredths" is taking one of those green tenth sticks and dividing it into 10 hundredth squares. That means that you have 2 wholes, 2 tenths (remaining green sticks), and 10 hundredths (because the only hundredths you have are the ones you got from that tenth you regrouped).
After crossing them out, you have 2 wholes, 0 tenths (because you only had 2 before), and 4 hundredths (because you crossed out 6 of the 10, 10-6=4).
Hope I could help you!
A cube made of an unknown material has a height of 9 cm. The mass of this cube is 3,645 grams. Calculate the density of this cube given this information. Hint: a cube has equal sides
Answers
Answer:
Step-by-step explanation:
Volume of the cube = s^3
s = 9cm
V = 9 * 9 * 9
V = 729 cm^3
d = mass / volume
d = 3645 / 729
d = 5 grams / cm^3
3
3
Use exponent rules to explain why (√5)³ = √√5³.
Answers
Answer:
see image
Step-by-step explanation:
Use new exponent rules like:
A power raised to a power is the product of the powers. (power to a power, times the exponents)
and,
Square root is a half power. (Converting radicals to fractional exponents)
Also, you can multiply in any order, like since you learned multiplying (example: 2×6 is the same as 6×2)
see image.
Here's the plan:
Change the radical to a 1/2 exponent. Now 3 and 1/2 are both exponents. Rearrange the order. Rewrite in radical form again.
see image.
The proof of the equation (√5)³ = √(5³) is given below.
What is an exponent?Exponentiation is one of the mathematics operation.
Let mᵃ, where m and a are the real numbers.
And m is multiplied by a times to itself.
So, a is the exponent of m.
Given:
A radical equation,
(√5)³ = √(5³).
LHS = (√5)³
Simplifying,
(√5)³ = {(5\()^{1/2}\)}³
= \(5^{3/2}\)
= √(5³)
= RHS.
Therefore, (√5)³ = √(5³).
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The complete question:
Simplify and prove the equation (√5)³ = √(5³) by using exponent rules.
I don't understand. but I think the screenshot will be useful
Answers
Answer:
a) 7, 10, 13, 16, ..., 34
Step-by-step explanation:
I'll only solve part a and you'll be able to do part b.
You're given:
3n+4
to find the first four terms, just plug in n = 1, 2, 3, 4 into n.
for n=1: 3(1)+4 = 7
for n=2: 3(2)+4 = 10
for n=3: 3(3)+4 = 13
for n=4: 3(4)+4 = 16
as you might guess, to find the 10th term, you plug in n=10.
for n=10: 3(10)+4 = 34
1. 5 2 1 4 0 0 7 2 8 1 m m 7 m 5 m A. 3656 D. 2739 B. 1841 E.5418 C. 3556
Answers
Given statement solution is :- We cannot find the missing value from the given options (3656, 2739, 1841, 5418, or 3556).
The given sequence is: 5 2 1 4 0 0 7 2 8 1 m m 7 m 5 m A.
To find the missing value, let's analyze the pattern in the sequence. We can observe the following pattern:
The first number, 5, is the sum of the second and third numbers (2 + 1).
The fourth number, 4, is the sum of the fifth and sixth numbers (0 + 0).
The seventh number, 7, is the sum of the eighth and ninth numbers (2 + 8).
The tenth number, 1, is the sum of the eleventh and twelfth numbers (m + m).
The thirteenth number, 7, is the sum of the fourteenth and fifteenth numbers (m + 5).
The sixteenth number, m, is the sum of the seventeenth and eighteenth numbers (m + A).
Based on this pattern, we can deduce that the missing values are 5 and A.
Now, let's calculate the missing value:
m + A = 5
To find a specific value for m and A, we need more information or equations. Without any additional information, we cannot determine the exact values of m and A. Therefore, we cannot find the missing value from the given options (3656, 2739, 1841, 5418, or 3556).
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Simplify the expression below by rationalizing the denominator. When typing your answer be sure to be careful and include the correct signs. Keep in mind that the variables a,b,c,d, e and f can represent a product of a number and a variable. \frac{\sqrt[]{8}}{1-\sqrt[]{3z}} simplifies to \frac{a\sqrt[]{b}+c\sqrt[]{d}}{e- \sqrt[]{f}} Our value for a is AnswerOur value for b is AnswerOur value for c is AnswerOur value for d is AnswerOur value for e is AnswerOur value for f is Answer
Answers
Given:
\(\frac{\sqrt[]{8}}{1-\sqrt[]{3z}}\)Simplife:
\(\begin{gathered} =\frac{\sqrt[]{8}}{1-\sqrt[]{3z}} \\ =\frac{\sqrt[]{8}}{1-\sqrt[]{3z}}\times\frac{1+\sqrt[]{3z}}{1+\sqrt[]{3z}} \\ =\frac{\sqrt[]{8}+\sqrt[]{24z}}{1-\sqrt[]{9z^2}} \\ =\frac{2\sqrt[]{2}+2\sqrt[]{6z}}{1-\sqrt[]{9z^2}} \end{gathered}\)The given simplifies equation is:
\(\frac{a\sqrt[]{b}+c\sqrt[]{d}}{e-\sqrt[]{f}}\)After the compare the both inequality:
a=2
b=2
c=2
d=6
e=1
f=9
Which equation represents the relationship between x and y in the table
y = x
y = x - 4
y = x - 8
y = x/5
Answers
Susan needs to buy 3 helium balloons. She can buy individual balloons for $2.75 each, or a 3-pack of balloons for $7.80. How much will Susan save per balloon if she buys a 3-pack instead of individual balloons?
Answers
Answer:
15
Step-by-step explanation:
8.25 minus 7.80 is 0.45 45 divided by 3 is 15 so the answer is 15
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Answers
Answer: A)10 B)14 C) 12 D)10
Step-by-step explanation:
You would cross multiply and divide! So for part A you would multiply 2x55 which equals 110 then divide that by 11 and get 10. You then repeat that for each part!
Mr. Smith started the school year with 26 students in his class. If x students moved out of his class, which expression represents the number of students left in the class?
The answers:
x + 26
x - 26
26 - x
26 + x
Please help me quickly before 11
Answers
Answer:
26-x
Step-by-step explanation:
If he started with 26 learners he lost x. Imagine x was a value of 5. To get the learners left you will have to subtract the numbers he lost from 26
Josie wants to determine the winner of an SCA election. Which measure should she use?
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Not sure what you mean by measure but the person with the most votes usually wins an election so I would say "maximum".
In PQR, PQ || ST. Given that RP=30, RS=9,and RT=12, find RQ
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In PQR, PQ || ST. Given that RP=30, RS=9,and RT=12, The length of rq is 12 units..
if pq is parallel to st, then we can use the property of parallel lines to find the value of rq. specifically, we can use the following proportionality theorem:
(1) rp/rq = rs/st
we are given that rp = 30, rs = 9, and rt = 12. we can use these values to solve for st:
st = rs * (rt/rp) = 9 * (12/30) = 3.6
now we can substitute these values into equation (1) and solve for rq:
30/rq = 9/3.6
multiplying both sides by rq and simplifying, we get:
rq = 30 * 3.6 / 9 = 12
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what is the difference
Answers
Answer:
what is question of this you asked
Twelve more than half of a number is equal to the number
Answers
So, twice the number (2x) is 12 greater than than the half of the number.
So the equation will be like,
2x=12+x/2
Solving this further,
2x=(24+x)/2
=> 4x=24+x
=>4x-x=24
=>3x=24
=>x=8..
So the number is "8".
Can somone help me with this will mark u brainliest
Answers
The simplest radical form of √(11/(x + 4)) when x is 16 is; ¹/₁₀√55
How to simplify surds in radical form?Surds are actually the expressions of the number, and often use radicals. Meanwhile, the radical is just the symbol used to express the square root.
We are given the expression of the surd as;
√(11/(x + 4))
We want to solve this for when x = 16. Thus, we plug in 16 for x in the surd to get;
√(11/(16 + 4))
= √(11/20)
Now, we can rewrite the fraction in the bracket to have the denominator as a perfect square by multiplying both numerator and denominator by 5 to get;
√(55/100)
Square root of 100 is 10 and as such we now have;
√(55/100) = ¹/₁₀√55
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Data analysis and probability unit test
Answers
Students should be able to apply these concepts and tools in real-world situations, such as calculating the probability of winning a game or analyzing data from a scientific Experiment.
The probability is a measure of the possibility of an event happening. It is expressed as a fraction or decimal between 0 and 1, or as a percentage between 0% and 100%. Probability can be used to determine the likelihood of an event happening or not happening.
Data analysis is the process of analyzing data to extract valuable insights from it. It involves examining data sets to uncover trends, patterns, and relationships that can be used to make informed decisions. Data analysis is an important tool in many fields, including business, finance, and science.
The data analysis and probability unit test assesses students' understanding of these concepts and their ability to apply them in real-world situations.
The test typically includes questions that require students to use probability to determine the likelihood of an event happening or not happening, as well as questions that ask students to analyze data sets to extract valuable insights.In order to prepare for the data analysis and probability unit test, students should review the key concepts and formulas related to probability, such as the addition rule, the multiplication rule, and the complementary rule.
They should also practice analyzing data sets using tools like histograms, scatter plots, and box plots, and should be familiar with key concepts like mean, median, and mode.
Finally, students should be able to apply these concepts and tools in real-world situations, such as calculating the probability of winning a game or analyzing data from a scientific experiment.
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what is -2(3x+12y-5-17x-16y+4) simplifyed
Answers
Answer: 28x+8y+2 .
= -2 (-14x-4y-1)
= 28x + 8y + 2
Step-by-step explanation:
Answer: 28x + 8y + 2
Step-by-step explanation:
-2(3x+12y-5-17x-16y+4)
= -2(3x-17x+12y-16y-5+4)
= -2(-14x-4y-1)
= -2(-14x) -2(-4y) -2(-1)
= 28x+8y+2
A 22-year old college student sets up an IRA (individual retirement account) with an APR of 6%. They deposit $55 into the account each month and plan on retiring at age 65. (Simplify your answers and round to two decimal places.) a. The IRA will contain at retirement.
Answers
The IRA (individual retirement account) of a 22-year-old college student, who deposits $55 into the account each month, will have a total balance at retirement. To calculate this, we need to consider the time period, the monthly deposit, and the annual percentage rate (APR).
The student plans on retiring at age 65, which means the IRA will have 65 - 22 = 43 years to grow. Since the student deposits $55 each month, we can calculate the total number of deposits over the 43-year period: 43 years * 12 months/year = 516 deposits.
To calculate the total balance at retirement, we need to consider the growth of the account due to the APR. The annual growth rate is 6%, which can be expressed as 0.06 in decimal form. To calculate the monthly growth rate, we divide the annual growth rate by 12: 0.06/12 = 0.005.
Using the formula for the future value of an ordinary annuity, we can calculate the total balance at retirement:
FV = PMT * [(1 + r)^n - 1] / r
Where:
FV = future value (total balance at retirement)
PMT = monthly deposit ($55)
r = monthly interest rate (0.005)
n = number of deposits (516)
Plugging in these values into the formula:
FV = 55 * [(1 + 0.005)^516 - 1] / 0.005
Calculating this equation, the IRA will contain $287,740.73 at retirement.
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A cyclist rode at an average speed of 15 mph for 30 miles. how long was the ride? responses 0.5 hours 0.5 hours 1 hour 1 hour 2 hours 2 hours 3 hours
Answers
A cyclist rode at an average speed of 15 mph for 30 miles.
It will take 2 hours to cover 30 miles so option (C) is correct.
What are the ratio and proportion?
The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given that,
A cyclist rode at an average speed of 15 mph for 30 miles.
So,
15 miles ⇒ hour
Multiply by 2
2 hours ⇒ 30 miles.
Hence "It will take 2 hours to cover 30 miles".
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Help me with Math plz
Answers
2y=-6
=2
The answer is 2
Answer:
14
Step-by-step explanation:
2(4)-2(-3)
8-(-6)
8+6
14
Simplify to a single power of 5: 5^8/5^6
Answers
Answer:
5^8/5^6 = 5^(8-6) = 5^2 = 25. Therefore, 5^8/5^6 simplified to a single power of 5 is 25.
Step-by-step explanation:
Answer:
the answer for that is 5^6-3 = 5^3 = 125
Step-by-step explanation:
Keiko made a shirt using 5/8 yards of green fabric and 1/4 yards of blue fabric. How many yards of green fabric did Keiko use? Write your answer as a fraction in simplest form
Answers
Keiko used 5/8 yards of green fabric to make the shirt.
To arrive at this answer, we first need to recognize that the question is asking for the amount of green fabric used, and that there are two types of fabric being used - green and blue. The amounts of each fabric are given as fractions of a yard.
To find the amount of green fabric used, we simply need to look at the fraction given for the green fabric, which is 5/8 yards. This means that Keiko used five-eighths of a yard of green fabric. It is already in its simplest form, so the answer is 5/8 yards.
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