Q.1 Determine whether y = (c - e ^ x)/(2x); y^ prime =- 2y+e^ x 2x is a solution for the differential equation Q.2 Solve the Initial value problem ln(y ^ x) * (dy)/(dx) = 3x ^ 2 * y given y(2) = e ^ 3 . Q.3 Find the general solution for the given differential equation. (dy)/(dx) = (2x - y)/(x - 2y)
Answers
(Q.1)
[tex]y = \dfrac{C - e^x}{2x} \implies y' = \dfrac{-2xe^x-2C+2e^x}{4x^2} = \dfrac{-xe^x-C+e^x}{2x^2}[/tex]
Then substituting into the DE gives
[tex]\dfrac{-xe^x-C+e^x}{2x^2} = -\dfrac{2\left(\dfrac{C-e^x}{2x}\right) + e^x}{2x}[/tex]
[tex]\dfrac{-xe^x-C+e^x}{2x^2} = -\dfrac{C-e^x + xe^x}{2x^2}[/tex]
[tex]\dfrac{-xe^x-C+e^x}{2x^2} = \dfrac{-C+e^x - xe^x}{2x^2}[/tex]
and both sides match, so y is indeed a valid solution.
(Q.2)
[tex]\ln\left(y^x\right)\dfrac{\mathrm dy}{\mathrm dx} = 3x^2y[/tex]
This DE is separable, since you can write [tex]\ln\left(y^x\right)=x\ln(y)[/tex]. So you have
[tex]x\ln(y)\dfrac{\mathrm dy}{\mathrm dx} = 3x^2y[/tex]
[tex]\dfrac{\ln(y)}y\,\mathrm dy = 3x\,\mathrm dx[/tex]
Integrate both sides (on the left, the numerator suggests a substitution):
[tex]\dfrac12 \ln^2(y) = \dfrac32 x^2 + C[/tex]
Given y (2) = e ³, we find
[tex]\dfrac12 \ln^2(e^3) = 6 + C[/tex]
[tex]C = \dfrac12 \times3^2 - 6 = -\dfrac32[/tex]
so that the particular solution is
[tex]\dfrac12 \ln^2(y) = \dfrac32 x^2 - \dfrac32[/tex]
[tex]\ln(y) = \pm\sqrt{3x^2 - 3}[/tex]
[tex]\boxed{y = e^{\pm\sqrt{3x^2-3}}}[/tex]
(Q.3) I believe I've already covered in another question you posted.
Related Questions
Complete the Similarity statement below only if the triangles are similar.
Answers
find the equation of the sides of an isosceles right angled triangle whose vertex is (-2,-3) and the base is on the line x=0
Answers
Answer:
AC:y=x-1 CB:y=-x-5 AB:x=0
Step-by-step explanation:
Consider the triangle. The base AB is on the line x=0, the vertex C is (-2,-3)
The side AC is equal to BC. The angle ACB is 90 degrees. If the base is on the line x=o, it is on the axis Y.Explore the distance from the point C to the AB
c(-2,-3), the distance to the axis Y is equal to the modul of the coordinate x (-2), it is 2. The coordinates of point projected by the point C to the axis Y is N(0,-3). The modul of the height is 2, the height of the isosceles triangle to the base is the bisectrix, so the angle BCA is 90/2=45degrees, CBA is 180-90-45=45 degrees too
the heigt CN is equal to side NB, NB=2
Suppose B is (0,y) (x=0 because the base is on this line)
THe modul of the vector NB is equal to sqrt ((0-0)^2+(y+3)^2)= 2
modul (y+3)= 2
y=-1 or y=-5
(0,-1), (0,-5) - two points, one of them (suppose B) is (0,-5) when A is (0,-1) (A is remote from the point N on the same distance with B, because AB is the median too)
Find CB and AC
Use the equation for AC
(x-0)/(-2-0)= (y+1)/(-3+1)
x/-2= (y+1)/-2
x=y+1
y=x-1
For CB
(x-0)/ (-2-0)= (y+5)/ (-3-(-5))
x/-2= (y+5)/2
-x=y+5
y=-x-5
Larissa is ordering nachos at a restaurant, and the server tells her that she can have up to four toppings: ground beef, black beans, refried beans, and sour cream. Since she cannot decide how many of the toppings she wants, she tells the server to surprise her. If the server randomly chooses which toppings to add, what is the probability that Larissa gets just refried beans and sour cream
Answers
Answer:
0.0625
Step-by-step explanation:
Given that :
Number of toppings = 4 (ground beef, black beans, refried beans, and sour cream)
The probability of choosing any particular topping at random from the four is :
Probability = required / total possible outcomes
Hence, P = 1 / 4 = 0.25
Hence, the probability of choosing : getting refried bean and sour cream :
P(refried bean) = 1/4
P(sour cream) = 1/4
P(refried bean and sour cream) = 1/4 * 1/4 = 1/16 =
0.0625
Suppose that a group of 10 people join a weight loss program for 3 months. Each person's weight is recorded at the beginning and at the end of the 3-month program. To test whether the weight loss program is effective, the data should be treated as:
Answers
To test the effectiveness of the weight loss program, a PAIRED SAMPLE test distribution is used.
The weight loss data collated for the program for both the beginning and end of the program period was obtained with one subject or person having two separate readings, these shows that the samples are NOT INDEPENDENT.
When performing a test which involves DEPENDENT or MATCHED samples, whereby means of two measurements taken from the SAME subject are involved, a PAIRED SAMPLE TEST DISTRIBUTION IS ADOPTED.
Therefore, the effectiveness of the weight loss programme will be accurately evaluated using a PAIRED SAMPLE TEST.
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x and y are related.
х
-2
-1
0
1
2
3
y
-4
-4.5
-5
-5.5
-6
-6.5
y = -0.5x + [?]
Enter the answer that belongs in [?].
Answers
Answer:
-5
Step-by-step explanation:
y = -0.5x + [?]
The equation is put in slope intercept form
slope intercept form: y = mx + b
where m = slope and b = y intercept
We want to find the y intercept.
the y intercept is the value of y when x = 0
looking at the table when x = 0, y = -5 so the y intercept is -5.
In other words -5 belongs in [?]
You have fit a regression model with two regressors to a data set that has 20 observations. The total sum of squares is 1000 and the model (regression) sum of squares is 750. What is the adjusted R-squared value for this model
Answers
Answer:
Hence the adjusted R-squared value for this model is 0.7205.
Step-by-step explanation:
Given n= sample size=20
Total Sum of square (SST) =1000
Model sum of square(SSR) =750
Residual Sum of Square (SSE)=250
The value of R ^2 for this model is,
R^2 = \frac{SSR}{SST}
R^2 = 750/1000 =0.75
Adjusted [tex]R^2[/tex] :
[tex]Adjusted R^2 =1- \frac{(1-R^2)\times(n-1)}{(n-k-1)}[/tex]
Where k= number of regressors in the model.
[tex]Adjusted R^2 =1-(19\times 0.25/((20-2-1)) = 0.7205[/tex]
Harrison has 20 tasks on to do list he has completed 5%. How many tasks has he completed?
Answers
Answer:
1 task
Step-by-step explanation:
100%=20 tasks
5%=1 task
1 +32-10 divided by 2
Answers
Step-by-step explanation:
1+32-10 ÷21+32-533-528Hope it is helpful to youThe value of the numerical expression 1 + 32 – 10 ÷ 2 will be 28.
What is Algebra?Algebra is the study of graphic formulas, while logic is the interpretation among those signs.
The numerical expression is given below.
⇒ 1 + 32 – 10 ÷ 2
According to the PEMDAS rule, the computation wrapped in quotes or the parenthesis comes first in the sequence of operation.
This rule is used to solve the equation in a proper and correct manner.
PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction.
⇒ 1 + 32 – (10 ÷ 2)
Simplify the numerical expression, then the expression will be
⇒ 1 + 32 – 5
⇒ 33 – 5
⇒ 28
Then the value of the numerical expression 1 + 32 – 10 ÷ 2 will be 28.
More about the Algebra link is given below.
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Find the area of the plot of land shown below.
Answers
9514 1404 393
Answer:
3070.06 square inches
Step-by-step explanation:
The area of the left triangle can be found using Heron's formula:
s = semiperimeter = (53+71+58)/2 = 91
area = √(s(s -53)(s -71)(s -58)) = √2282280 ≈ 1510.72
The area of the right triangle can be found using the trig formula ...
area = 1/2ab·sin(C)
area = 1/2(55)(71)sin(53°) ≈ 1559.34
Then the total area is ...
1510.72 +1559.34 = 3070.06 . . . . . square inches
Use the distributive property to write an
expression that is equivalent to each expression. If
you get stuck, consider drawing boxes to help
organize your work.
D. 8(-x-1/2)
e. -8(-x-3/4y+7/2
Answers
Answer:
D. -8x-4
E. 8x+6y-28
Step-by-step explanation:
D. 8(-x-1/2) = -8x-4
E. -8(-x-3/4y+7/2 = 8x+6y-28
Is -8 an irrational number?
yes or no
Answers
no bc it is not no no no no no no no
On his recent free-throw attempts, Lamar made 4 shots and missed 6 shots. Considering this
data, how many of his next 20 free-throw attempts would you expect Lamar to miss?
Answers
Answer:
12 free throw attempts
Step-by-step explanation:
First, find what percent of free throw attempts he misses:
6/10
= 0.6
So, he misses 60% of the time. Multiply 20 by 0.6 to find how many you would expect Lamar to miss out of 20 attempts:
20(0.6)
= 12
So, you would expect Lamar to miss 12 free throw attempts
represent (-12)+(-8)+14 on a number line
Answers
Answer:
-6
Step-by-step explanation:
(-12)+(-8)= -20
-20+14= -6
please help me asapp
Answers
Answer:
C. 12, 8, 5
Step-by-step explanation:Side lengths of any triangle must conform to the triangle inequality theorem, which says that the sum of the lengths of any of the two sides of the triangle is greater than the length of the third side.
This means:
a + b > c
a + c > b
b + c > a
Let's check each of the options to see which set are possible lengths for a triangle:
A. 6, 5, 11
6 + 11 > 5 ===> 17 > 5
5 + 11 > 6 ===> 16 > 6
6 + 5 > 11 ===> 11 > 11 (INCORRECT. Does not confirm to tye theorem)
Therefore, this set cannot be possible side lengths for a triangle.
B. 8, 1, 2
8 + 1 > 2 ===> 9 > 2
1 + 2 > 8 ===> 3 > 8 (INCORRECT)
8 + 2 > 1 ===> 10 > 1
This set cannot be possible side lengths for a triangle.
C. 12, 8, 5
12 + 8 > 5 ===> 20 > 5
8 + 5 > 12 ===> 13 > 12
12 + 5 > 8 ===> 17 > 8
All are correct, therefore these are possible side lengths for a triangle.
Many individuals over the age of 40 develop intolerance for milk and milk-based products. A dairy has developed a line of lactose-free products that are more tolerable to such individuals. To assess the potential market for these products, the dairy commissioned a market research study of individuals over 40 years old in its sales area. A random sample of 250 individuals showed that 86 of them suffer from milk intolerance. Based on the sample results, calculate a 90% confidence interval for the population proportion that suffers milk intolerance. Interpret this confidence interval. a) First, show that it is okay to use the 1-proportion z-interval. b) Calculate by hand a 90% confidence interval. c) Provide an interpretation of your confidence interval. d) If the level of confidence was 95% instead of 90%, would the resulting interval be narrower or wider
Answers
Answer:
a) To show that we can use the 1 proportion z-interval, we know that 250 ( size sample) is big enough to approximate the binomial distribution ( tolerance-intolerance) to a normal distribution.
b) See step by step explanation
CI 90 % = ( 0,296 ; 0,392)
c) We can support that with 90 % of confidence we will find the random variable between this interval ( 0,296 ; 0,392)
d) the CI 95 % will be wider
Step-by-step explanation:
Sample Information:
Sample size n = 250
number of people with milk intolerance x = 86
p₁ = 86 / 250 p₁ = 0.344 and q₁ = 1 - p₁ q₁ = 0,656
To calculate 90 % of Confidence Interval α = 10% α/2 = 5 %
α/2 = 0,05 z(c) from z-table is: z(c) = 1.6
Then:
CI 90 % = ( p₁ ± z(c) * SE )
SE = √ (p₁*q₁)/n = √ 0,225664/250
SE = 0,03
CI 90 % = ( 0,344 ± 1,6* 0,03 )
CI 90 % = ( 0,344 - 0,048 ; 0,344 + 0,048)
b) CI 90 % = ( 0,296 ; 0,392)
a) To show that we can use the 1 proportion z-interval, we know that 250 ( size sample) is big enough to approximate the binomial distribution ( tolerance-intolerance) to a normal distribution.
c) We can support that with 90 % of confidence we will find the random variable between this interval ( 0,296 ; 0,392) .
d) CI 95 % then significance level α = 5 % α/2 = 2.5 %
α/2 = 0,025 z(c) = 1.96 from z-table
SE = 0,03
And as 1.96 > 1.6 the CI 95 % will be wider
CI 95% = ( 0,344 ± 1.96*0,03 )
CI 95% = ( 0,344 ± 0,0588 )
CI 95% = ( 0,2852 ; 0,4028 )
Find the area.
2 cm
6 cm
4 cm
Answers
Answer:
A=1/2(a+b)h
A=1/2(2cm+4cm)6cm
A=1/2×6cm×6cm
A=18cm²
HELLO PLEASE HELP??
which equation represents the circle described? 1. the radius is 2 units 2. the center of the circle is at (5,-6) (x+5)^2+ (y- 6)^2 =4
(x - 5)^2 + ( y + 6)^2 = 4
(x + 5)^2 + (y - 6)^2 =2
(x - 5)^2 + (y + 6)^2 =2
Answers
Answer:
(x-5)^2 + (y+6)^2 = 4
Step-by-step explanation:
The equation of a circle is given by
(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
(x-5)^2 + (y- -6)^2 = 2^2
(x-5)^2 + (y+6)^2 = 4
44,587 plus what equals 65,000
Answers
Let the missing number be x.
=> x + 44587 = 65000
=> x = 65000 - 44587
= 20413
Ans.= The missing number will be 20413.
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The number of cubic feet of water in a curved container can be approximated by V=0.95h^2.9 find the amount of water in the container when h=8 feet round to the nearest tenth
Answer choices:
A. 0.9
B. 358.4
C. 395.1
D. 314.9
Answers
Answer:
C. 395.1
Step-by-step explanation:
Substitute the value for x:
[tex]V=0.95(8)^{2.9}\\V=395.1[/tex]
6. If the following fractions were converted to decimals, which one would result in a repeating decimal?
A. 3/7
B. 1/9
C. 3/4
D. 5/11
Answers
Find the formula for the geometric sequence 1, 5, 25, 125, .
Answers
To check our formula, we can find the 5th term. a5 = 1 * 5^5-1. This gives us 625. If we look at our last term provided, the 4th term, 125 * 5 is 625.
A tire manufacturer has a 60,000 mile warranty for tread life. The company wants to make sure the average tire lasts longer than 60,000 miles. The manufacturer tests 250 tires and finds the mean life for these tires to be 64,500 miles.What is the alternative hypothesis being tested in this example
Answers
Answer:
The alternative hypothesis being tested in this example is that the tire life is of more than 60,000 miles, that is:
[tex]H_1: \mu > 60,000[/tex]
Step-by-step explanation:
A tire manufacturer has a 60,000 mile warranty for tread life. The company wants to make sure the average tire lasts longer than 60,000 miles.
At the null hypothesis, we test if the tire life is of at most 60,000 miles, that is:
[tex]H_0: \mu \leq 60,000[/tex]
At the alternative hypothesis, we test if the tire life is of more than 60,000 miles, that is:
[tex]H_1: \mu > 60,000[/tex]
Which of the following numbers is divisible by 6?
3,246
9,787
8,752
5,967
Answers
Answer: 3246/6= 541
if u wanna know if a # is divisible by 6 or not, see if the # is divisible by 2 or 3. if it works for both, then it is divisible by 6
help me please please plewse
Answers
The answer would be D.
Answer: D
Step-by-step explanation:
Pretend that C is 12, pi is 3, and d is 4. 4=3/12, 4=3*12, 4=12-3, or 4=12/3? The only one that works is that last one, so the and is D: d=C/pi
Which equation would have real zero(s) corresponding to the x-intercept(s) of the graph below?
Answers
Answer:
Choice A.
[tex]y = - {2}^{x} + 4[/tex]
Step-by-step explanation:
Use graphing calculator
Answer:
Choice A.
Step-by-step explanation:
Select the line segment.
O A.
P
OB.
R
S
Ос.
M
N
OD.
G
H
Answers
Answer: Choice A
Explanation: A segment (or line segment) is whenever we have two endpoints connected with a straight line. It does not go on forever in either direction.
Answer:
Step-by-step explanation:
B is a ray. One of its ends is stationary.
C is an arc which means it bends
D is a line.
That means that A is the answer. Both its ends are stationary.
-3x > 12
What is the value of x? Use substitution to support your answer.
Answers
Answer:
x < -4
Step-by-step explanation:
-3x > 12
----- ----
-3 -3
12 ÷ -3 = -4
Which means:
x < -4
(The sign changes because the equation is divided by a negative number)
Hope this helped.
Answer:
x <-4
Step-by-step explanation:
-3x > 12
Divide each side by -3. remembering to flip the inequality
-3x/-3 > 12/-3
x <-4
please help! Here are the shopping times(in minuts) of nine shoppers at a local grocery store. complete the grouped frequency distribution for the data. in the distribution, the frequency of a class is the number of shopping times in that class.( Note that we are using a class width of 6.)
Answers
Answer:
The shopping time (in minutes) of the nine shoppers are:
15, 16, 18, 20, 22, 25, 27, 28, 29 (just to make it easier to read, I rearranged everything from least to greatest.)
We can see, that 3 shoppers shopped for 15-20 minutes.
And, 3 shoppers shopped for 21-26 minutes.
And finally, 3 shoppers shopped for 27-32 minutes.
So the answer for all 3 of the boxes is 3.
Let me know if this helps.
A composite figure is made up of one simple figure.
True or
False
Answers
Answer:
False
Step-by-step explanation:
A composite figure would be any irregular shapes and can be made up of multiple shapes
Estimate the mean exam score for the 50 students in Prof. Burke's class.
Score
f
40 but less than 50
21
50 but less than 60
39
60 but less than 70
40
70 but less than 80
34
80 but less than 90
28
Total
162
Group of answer choices
65.56
63.78
64.89
62.34
Answers
The mean of the exam score is 65.56
The given exam data is as follows;
Possible Score range ----------- frequency (f) -------- score (x) -----------(fx)
40 - 50 ------------------------- 21 ------------------- -----45 -------------- 945
50 - 60 --------------------------- 39------------------------55 ---------------2145
60 - 70 ----------------------------- 40---------------------- 65 ---------------- 2600
70 - 80 ------------------------------ 34 --------------------- 75 ----------------- 2550
80 - 90 ------------------------------ 28 --------------------- 85 ---------------- 2380
Note:[tex]score (x) = \frac{sum \ of \ the \ range }{2} , \ example \ \frac{40+49.99}{2} \approx 45[/tex]
The sum of the frequency (f) = 162
The sum of fx, ∑fx = 10620
The mean of the exam score:
[tex]\bar x = \frac{\Sigma fx }{\Sigma f} = \frac{10620}{162} = 65.56[/tex]
Therefore, the mean of the exam score is 65.56
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