Answer:c
Step-by-step explanation:
C. 5, 13,12, 67,23, right angle
Find the solution of the differential equation that satisfies the given initial condition. xy' + y = y2, y(1) = −5
Answer: [tex]y=\dfrac{5}{5-6x}[/tex]
Step-by-step explanation:
The given differential equation: [tex]xy' + y = y^2[/tex]
[tex]\Rightarrow\ xy'=y^2-y[/tex]
[tex]\Rightarrow\ \frac{1}{y^2-y}y'\:=\frac{1}{x}\\\\\Rightarrow\ \dfrac{1}{y(y-1)}\dfrac{dy}{dx}=\frac{1}{x}\\\\\Rightarrow\dfrac{y-(y-1)}{y(y-1)}dy=\dfrac{1}{x}dx\\\\\Rightarrow\dfrac{1}{(y-1)}dy+\dfrac{1}{y}dy=\dfrac{1}{x}dx[/tex]
Integrate both sides , we get
[tex]\int\dfrac{1}{(y-1)}dy+\int\dfrac{1}{y}dy=\dfrac{1}{x}dx\\\\\Rightarrow\ \ln(y-1)-\ln y=\ln x+c\ \ \ \ (i)[/tex]
At x=1 , y=-5 (given)
[tex]\ln(-5-1)-\ln -5=\ln 1+c\\\\\Rightarrow\ \ln (-6)-\ln(-5)=0+c\\\\\Rightarrow\ \ln(\dfrac{-6}{-5})=c\\\\\Rightarrow\ \ln(\dfrac{6}{5})=c[/tex]
[tex][\ \ln a+\ln b=\ln ab ,\ \ \ \ \ \ln a-\ln b=\ln\dfrac{a}{b}\ ][/tex]
Put value of x in (i), we get
[tex]\ln(y-1)-\ln y=\ln x+\ln (\dfrac65)\\\\\Rigtarrow\ \ln (\dfrac{y-1}{y})=\ln(\dfrac{6}{5}x)[/tex]
[tex]\Rightarrow\ 1-\dfrac{1}{y}=\dfrac{6}{5}x\Rightarrow\ \dfrac{1}{y}=1-\dfrac{6}{5}x\\\\\Rightarrow\ \dfrac{1}{y}=\dfrac{5-6x}{5}\\\\\Rightarrow\ y=\dfrac{5}{5-6x}[/tex]
hence, the required solution: [tex]y=\dfrac{5}{5-6x}[/tex]
The solution to the differential equation
[tex]xy'+y=y^2[/tex]
given the initial condition [tex]y(1)=-5[/tex] is [tex]y=\frac{5}{5-6x}[/tex]
Given the differential equation
[tex]xy'+y=y^2[/tex]
We can rearrange it as follows:
[tex]x\frac{dy}{dx}+y=y^2\\\\x\frac{dy}{dx}=y^2-y\\\\\frac{1}{y^2-y}\frac{dy}{dx}=\frac{1}{x}\\\\\frac{1}{y^2-y}dy=\frac{1}{x}dx[/tex]
Factoring the denominators of the LHS, and decomposing into partial fractions, we get
[tex]\frac{1}{y(y-1)}dy \implies \frac{1}{(y-1)}dy+\frac{1}{y}dy[/tex]
The final rearranged equation is
[tex]\frac{1}{(y-1)}dy+\frac{1}{y}dy=\frac{1}{x}dx[/tex]
Integrating both sides;
[tex]\int\frac{1}{y-1} dy +\int\frac{1}{y}dy=\int\frac{1}{x}dx\\\\ln(y-1)-ln(y)=ln(x)+c\\\\ln(\frac{y-1}{y})=ln(x)+c[/tex]
(We made of a law of logarithms on the last line to simplify the equation)
The initial condition [tex]y(1)=-5\implies y=-5 \text{ when }x=1[/tex]
Substituting into the general solution we got earlier
[tex]ln(\frac{y-1}{y})=ln(x)+c\\\\ln(\frac{-5-1}{-5})=ln(1)+c\\\\ln(\frac{-6}{-5})=ln(1)+c \\\\(\text{since }ln(1)=0)\\\\ln(\frac{-6}{-5})=c\\\\ln(\frac{6}{5})=c[/tex]
Substituting the value of [tex]c[/tex] back into the general solution
[tex]ln(\frac{y-1}{y})=ln(x)+c\\\\ln(\frac{y-1}{y})=ln(x)+ln(\frac{6}{5})\\\\ln(\frac{y-1}{y})=ln(\frac{6x}{5})\\\\\frac{y-1}{y}=\frac{6x}{5}[/tex]
When [tex]y[/tex] is made the subject of the formula
[tex]y=\frac{5}{5-6x}[/tex]
Therefore, the solution that satisfies the initial condition [tex]y(1)=-5[/tex] is [tex]y=\frac{5}{5-6x}[/tex]
Learn more about solving differential equations here: https://brainly.com/question/4537000
Can you guys help me find the supplements for question 6
Answer:
d
Step-by-step explanation:
i looked it up
How do you write expanded from for 0.68 with decimals
Answer:
0.6 + 0.08
Step-by-step explanation:
3/4of 16/27/23/14+12/18 using bodmas rule
Select the correct answer.
Each side of a square is
(st
5) units. Which expression can be used to represent the area of the square?
22 - 50 - 10
I2 – 50 + 10
2 – 100 - 25
22 - 10x + 25
Answer:
D.) x²-10x+25 sq. units
Step-by-step explanation:
The question is not properly written. The question should have been:
If each side of a square is (x-5) units, which expression can be used to represent the area of the square.
Area of a square = L² where:
L is the length of the square
Given
L = x-5
Required
Area of the square
Substitute the given function into the formula to get the required as shown:
Area of the square = (x-5)²
Expand
A(x) = (x-5)(x-5)
A(x) = x(x)-5x-5x-5(-5)
A(x) = x²-10x-25
Hence the area of the square is (x²-10x+25)sq. units. Option D is correct.
PLEASE PLEASE HELP ME I WILL GIVE BRAINLIEST
options box one:
graph a
Graph B
Options for box two:
1. appears to decrease more
2. Is less
3. Decreases less
4. Appears to decrease less
5. Decreases more
Answer:
1) graph b
2)appears to decrease more
Step-by-step explanation:
Helpppppp ASAP!!!!!!!
Answer:
x=2
Step-by-step explanation:
According to a 2018 survey by Bankrate, 20% of adults in the United States save nothing for retirement (CNBC website). Suppose that twenty-one adults in the United States are selected randomly. What is the probability that more than five of the selected adults save nothing for retirement
Answer:
0.769296
Step-by-step explanation:
The desired probability can be calculated from binomial probability distribution because there are 21 independent trials and probability of success(saving nothing for retirement) 0.2 remains same for each trial. Here, n=21 and p=0.20. We want to compute P(X>5).
The pdf of binomial distribution is
P(X=x)=nCx(p)^x(1-p)^(n-x)
P(X>5)=1-P(X≤5)
P(X≤5)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)
P(X=0)=21C0*(0.2)^0*(1-0.2)^(21-0)=0.009223
P(X=1)=21C1*(0.2)^1*(1-0.2)^(21-1)=0.048423
P(X=2)=21C2*(0.2)^2*(1-0.2)^(21-2)=0.121057
P(X=3)=21C3*(0.2)^3*(1-0.2)^(21-3)=0.191673
P(X=4)=21C4*(0.2)^4*(1-0.2)^(21-4)=0.215632
P(X=5)=21C5*(0.2)^5*(1-0.2)^(21-5)=0.183287
P(X≤5)=0.009223+0.048423+0.121057+0.191673+0.215632+0.183287
P(X≤5)=0.769296
P(X≤5) can also be computed by using excel function BINOM.DIST(5,21,0.2,TRUE) which results in
P(X≤5)=0.769296.
The probability that more than five of the selected adults save nothing for retirement is; P(X > 5) = 0.239928
We are told that 20% of adults in the US save nothing for retirement. Thus;
p = 20% = 0.2
21 adults are selected randomly. Thus;
n = 21
Probability that more than five of the selected adults save for retirement is gotten from formula for binomial probability distribution which is;
P(X = x) = nCx × p^(x) × (1 - p)^(n - x)
Thus;
P(X > 5) = 1 - P(X ≤ 5)
Where;
P(X ≤ 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)
P(X = 0) = 21C0 × 0.2^(0) × (1 - 0.2)^(21 - 0) =
0.009223
Using online binomial probability calculator, we can find the remaining as;
P(X = 1) = 0.048423
P(X = 2) = 0.121057
P(X = 3) = 0.191673
P(X = 4) = 0.215632
P(X = 5) = 0.183287
Thus;
P(X ≤ 5) = 0.048423 + 0.121057 + 0.191673 + 0.215632 + 0.183287
P(X ≤ 5) = 0.760072
Thus;
P(X > 5) = 1 - 0.760072
P(X > 5) = 0.239928
Read more about binomial probability distribution at; https://brainly.com/question/24239758
Are the statements true or false?
Select True or False for each statement.
Statement True False
1/ 4 · 3/ 4 = 3 /4 · 1/ 4
3/4÷2/5=2/5÷3/4
false false false false false
Answer:
no the first on is true and the last one is false
Step-by-step explanation:
If m<3 =54°. find each measure.
Answer/Step-by-step explanation:
Given:
m<3 = 54°
m<2 = right angle
a. m<1 + m<2 + m<3 = 180° (angles in a straight line)
m<1 + 90° + 54° = 180° (substitution)
m<1 + 144° = 180°
m<1 = 180° - 144°
m<1 = 36°
b. m<2 = 90° (right angle)
c. m<4 = m<1 (vertical angles)
m<4 = 36° (substitution)
d. m<5 = m<2 (vertical angles)
m<5 = 90°
e. m<6 = m<3 (vertical angles)
m<6 = 54°
f. m<7 + m<6 = 180° (same side interior angles)
m<7 + 54° = 180° (substitution)
m<7 = 180 - 54
m<7 = 126°
g. m<8 = m<6 (alternate interior angles are congruent)
m<8 = 54°
h. m<9 = m<7 (vertical angles)
m<9 = 126°
i. m<10 = m<8 (vertical angles)
m<10 = 54°
j. m<11 = m<4 (alternate interior angles are congruent)
m<11 = 36° (substitution)
k. m<12 + m<11 = 180° (linear pair)
m<12 + 36° = 180° (substitution)
m<12 = 180° - 36°
m<12 = 144°
l. m<13 = m<11 (vertical angles)
m<13 = 36°
m. m<14 = m<12 (vertical angles)
m<14 = 144° (substitution)
What is the answer for 8
Answer:
no they share the same y value for two different x values
HELPPPP PLZZZ ASAPPP!!!Look at the illustration of four letters from the American Manual Alphabet. Decide whether the description of the letter is a good definition. If not,
choose a counterexample.
The letter I is formed by sticking up the smallest finger and folding all the other fingers into the palm of your hand with the thumb folded over them.
The letter J is a counterexample
The letter y is a counterexample
The letter A is a counterexample
This is a good definition
while keeping your hand still
Answer: I think it’s J, because the picture is also holding the smallest finger up (the pinky) and the rest of the fingers are folded inside the palm of the hand and the thumb is folded over them, I hope this helps!!
Step-by-step explanation:
The letter J is a counter example. Option a is correct.
Letters of alphabet to be determine.
Alphabets are the sets of letters from A to Z.
Here, the little finger is up and all the finger is folded and the thumb folded over the three finger implies its 'J'.
Thus, the letter J is a counter example.
Learn more about alphabets here:
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Participants in a psychology expirement
were able to memorize an average of M Words in
T minutes, where M is -0.00lt3 and T is 0.1t2 Find the
average
number of words memorized in 10min.
Answer:
11 words
Step-by-step explanation:
The question is poorly formatted.
The right relationship between M and t is given as:
M = −0.001t³ + 0.1t²
Required
Solve for M when t = 10
To do this, substitute 10 for t
So,we have:
M = −0.001t³ + 0.1t²
M = -0.001 * 10³ + 0.1 * 10²
M = -0.001 * 1000 + 0.1 *100
M = 1 + 10
M = 11
11 words in 10 minutes
A triangular flag has an area of 462 square feet. The base is 14 feet. What is the height?
Answer: 66ft
Step-by-step explanation:
A=1/2bh
462=1/2(14)(h)
462=7h
66=h
0.079times what equals 7.9
Answer:
100
Step-by-step explanation:
PLEASE help. Will give brainliest.
Answer:
y=5
x=10 and
z=2
Step-by-step explanation:
since they are equivalance then,
for
triangle ABC and triangle DFE
AB=DF,BC=FE and AC= DE
So, AB=DF
8y-20= 4y
or, y=5
Then, BC= FE
2x+5=x+15
or, x=10
and
AC=DE
3z+9=10z-5
or, z= 2
hope u got ut.
The triangles are parallel thus their sides are equal to each other peer to peer.
So ;
[tex]x + 15 = 2x + 5[/tex]
Subtract sides -5
[tex]x + 15 - 5 = 2x + 5 - 5[/tex]
[tex]x + 10 = 2x[/tex]
Subtract sides -x
[tex]x - x + 10 = 2x - x[/tex]
[tex]x = 10[/tex]
_________________________________
[tex]4y = 8y - 20[/tex]
Subtract sides -8y
[tex]4y - 8y = 8y - 8y - 20[/tex]
[tex] - 4y = - 20[/tex]
Negatives simplifies
[tex]4y = 20[/tex]
Divided sides by 4
[tex] \frac{4}{4}y = \frac{20}{4} \\ [/tex]
[tex]y = 5[/tex]
_________________________________
[tex]10z - 5 = 3z + 9[/tex]
Plus sides 5
[tex]10z - 5 + 5 = 3z + 9 + 5[/tex]
[tex]10z = 3z + 14[/tex]
Subtract sides -3z
[tex]10z - 3z = 3z - 3z + 14[/tex]
[tex]7z = 14[/tex]
Divided sides by 7
[tex] \frac{7}{7}z = \frac{14}{7} \\ [/tex]
[tex]z = 2[/tex]
_________________________________
And we're done....♥️♥️♥️♥️♥️
Translate the given phrase into an algebraic expression and simplify if possible: the product of −4 and 16
Answer: -4 x 16, -48
Step-by-step explanation:
word phrase: -4 x 16
symplified = -48
product means multiply
Unit 4: Lesson 9: Parallel and Perpendicular Lines Unit Test Parallel and Perpendicular Lines does anyone have the answers for this 13 question test ??
Answer:
I need these answers and the ones he put in in the comments are all wrong
Which situations can represent the expression n+ 2? Check all that apply.
Ramya's grade increased by two points
the difference between Escher's highest score and two
the number of chapters Wally read plus two more
O two fewer than the maximum number of absences Ellie is allowed
two added to Allison's age.
the sum of Mikel's height and two
Answer:
Yes: Ramya's grade increased by two points
No: the difference between Escher's highest score and two
Yes: the number of chapters Wally read plus two more
No: O two fewer than the maximum number of absences Ellie is allowed
Yes: two added to Allison's age.
Yes: the sum of Mikel's height and two
Step-by-step explanation:
If it says yes, it is because it was adding 2. If it says no, it was either subtracting 2 or any other form of math other than adding 2.
Answer:
A,C,E,F
Step-by-step explanation:
Just shortening it up! The person above me is correct, though. Don't forget to make them brainliest (if you want to of course)! Major Big brain moment... lol!
Answer answered by Jordan
Stay Safe <3
↖(^ω^)↗
(-82)+(-47)-(+33)do u all know this answer
Answer:
-157
Step-by-step explanation:
Answer: -162
Hope this helps you
Step-by-step explanation:
subtract and add
A human gene carries a certain disease from the mother to the child with a probability rate of 39%. That is, there is a 39% chance that the child becomes infected with the disease. Suppose a female carrier of the gene has four children. Assume that the infections of the four children are independent of one another. Find the probability that all four of the children get the disease from their mother. Round to the nearest thousandth.
Answer:
[tex]Probability = 0.023[/tex]
Step-by-step explanation:
Given
Represent the given probability with P(Gene)
[tex]P(Gene) = 39\%[/tex]
[tex]Children = 4[/tex]
Since all 4 children get the disease, the required probability is calculated as thus:
[tex]Probability = P(Gene)^4[/tex]
[tex]Probability = 39\%^4[/tex]
Convert % to decimal
[tex]Probability = 0.39^4[/tex]
[tex]Probability = 0.02313441[/tex]
[tex]Probability = 0.023[/tex] Approximated
GIVING 30 POINTS
need it RN
Which equation represents a line which is perpendicular to the line
5x + 4y = -24?
Nancy has 192 golf balls.
How many dozen golf balls does she have?
Answer:
16
Step-by-step explanation:
192/12=16
hope this helps :3
if it did pls mark brainliest
Answer:16
192/12 equals 16
the height h(t) of a trianle is increasing at 2.5 cm/min, while it's area A(t) is also increasing at 4.7 cm2/min. at what rate is the base b(t) chaging when the height h=15cm and the area A= 130cm2
Answer:
The base of the triangle decreases at a rate of 2.262 centimeters per minute.
Step-by-step explanation:
From Geometry we understand that area of triangle is determined by the following expression:
[tex]A = \frac{1}{2}\cdot b\cdot h[/tex] (Eq. 1)
Where:
[tex]A[/tex] - Area of the triangle, measured in square centimeters.
[tex]b[/tex] - Base of the triangle, measured in centimeters.
[tex]h[/tex] - Height of the triangle, measured in centimeters.
By Differential Calculus we deduce an expression for the rate of change of the area in time:
[tex]\frac{dA}{dt} = \frac{1}{2}\cdot \frac{db}{dt}\cdot h + \frac{1}{2}\cdot b \cdot \frac{dh}{dt}[/tex] (Eq. 2)
Where:
[tex]\frac{dA}{dt}[/tex] - Rate of change of area in time, measured in square centimeters per minute.
[tex]\frac{db}{dt}[/tex] - Rate of change of base in time, measured in centimeters per minute.
[tex]\frac{dh}{dt}[/tex] - Rate of change of height in time, measured in centimeters per minute.
Now we clear the rate of change of base in time within (Eq, 2):
[tex]\frac{1}{2}\cdot\frac{db}{dt}\cdot h = \frac{dA}{dt}-\frac{1}{2}\cdot b\cdot \frac{dh}{dt}[/tex]
[tex]\frac{db}{dt} = \frac{2}{h}\cdot \frac{dA}{dt} -\frac{b}{h}\cdot \frac{dh}{dt}[/tex] (Eq. 3)
The base of the triangle can be found clearing respective variable within (Eq. 1):
[tex]b = \frac{2\cdot A}{h}[/tex]
If we know that [tex]A = 130\,cm^{2}[/tex], [tex]h = 15\,cm[/tex], [tex]\frac{dh}{dt} = 2.5\,\frac{cm}{min}[/tex] and [tex]\frac{dA}{dt} = 4.7\,\frac{cm^{2}}{min}[/tex], the rate of change of the base of the triangle in time is:
[tex]b = \frac{2\cdot (130\,cm^{2})}{15\,cm}[/tex]
[tex]b = 17.333\,cm[/tex]
[tex]\frac{db}{dt} = \left(\frac{2}{15\,cm}\right)\cdot \left(4.7\,\frac{cm^{2}}{min} \right) -\left(\frac{17.333\,cm}{15\,cm} \right)\cdot \left(2.5\,\frac{cm}{min} \right)[/tex]
[tex]\frac{db}{dt} = -2.262\,\frac{cm}{min}[/tex]
The base of the triangle decreases at a rate of 2.262 centimeters per minute.
The equations of sides of a triangle are 2x-3y+5=0, 2x+y=7 and 2x+5y=3. Find the coordinates of the vertices.
Answer:
Vertices A B y C
A ( 2 , 3 ) B ( -1 , 1 ) C ( 3, 1 )
Step-by-step explanation:
We have to solve a two-equation system, by pair of equations as follows
equation (1) 2x - 3y + 5 = 0
equation (2) 2x + y -7 = 0
Solving this system we find let´s say vertex A
0x - 4y +12 = 0 y = 3
Then x ?
2x - 3y + 5 = 0
2x - 9 + 5 = 0 ⇒ 2x = 4 x = 2
Then vertex A ( 2 , 3 )
From equation (1) and (3)
2x - 3y + 5 = 0
2x + 5y - 3 = 0
Agan subtracting (1) - (2)
0x -8y + 8 = 0
y = 1 and
2x + 5y = 3
2x + 5 = 3
2x = -2
x = -1
Vertex B ( -1 , 1 )
Finally from equation (2) and (3) we get the third vertex C
2x + y - 7 = 0
2x + 5y - 3 = 0
0x -4y -4 = 0
y = 1
2x + y = 7
2x + 1 = 7
2x = 6
x = 3
C ( 3 , 1 )
The triangular arrangement of numbers shown is known as Pascal's triangle. Use inductive reasoning to find the 6 missing numbers.
Answer:
1 5 10 10 5 1
Step-by-step explanation:
The complete question has been attached as an image.
Looking at the triangle, we see a pattern. The first level we have 1, in the next level we have 1 1, the next evel we have 1 2 1, the next level we have 1 3 3 1 and so on. From here, we see that to get the numbers of the next level, we have to write 1 as the first number, then add 1 to the next number after it in the previous level to get the second number in the next level then add the second number of the previous level to the next number beside it to get the third number in the next level and so on until you get to the last number before 1 in the previous level, add that number to 1 to get the second to the last number in the next level and finally put 1 as the last number in the next level. Now, we have
1 4 6 4 1
1 5 10 10 5 1
And that is the required set of numbers.
K^2+k=0 what does k=
Answer:
k = K^2
Step-by-step explanation:
Subtract K^2 from both sides of the equation.
A robot can complete 7 tasks in 2/3 hour. Each task takes the same amount of time. How long does it take the robot to complete one task? How many tasks can the robot complete in one hour?
Answer:
a. is 2/21 hours to complete one task
b. is 10 1/2 tasks in one hour
Robot takes 2/21 hour to complete the task.
In one hour, robot complete 21/2 task.
What is ratio?Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
Time taken to complete 7 tasks = 2/3 hours.
To find the time taken to complete one task and tasks that completed in one hour,
Use ratio method,
7 tasks take = 2/3 hours
1 task takes = 2/(3 x 7) = 2 / 21 hours.
In 2/3 hours = 7 tasks completed,
1 hour = 21/2 tasks.
In one hour, 21/2 tasks can be completed.
To know more about Ratio on:
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8(3x-2)-8x=9(2x-6) find x
Answer:
x=19
Step-by-step explanation:
8(3x-2)-8x=9(2x-6) Distribute.
24x-16-8x=18x-54 Combine like terms.
16x-16=18x-54 Subtract 16x from both sides (getting rid of a variable first
-16x -16x is easier).
-16=2x-54 Add 54 to both sides.
+54 +54
38=2x Divide both sides by 2.
/2 /2
19=x
Hope this helps!! Have a great day ^^
what is the slope of the line that passes through (37, -9) and (36, 81)
Answer:
m= -90 is your answer
Step-by-step explanation:
For future reference, you should try using Symbolab, it works really well and I use it ALL the time!