Answers
Answer:
[tex]\displaystyle y = \sqrt{2}e^{\frac{1}{2} ln|2 + x^2|}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
|Absolute Value|FunctionsFunction NotationExponential Rule [Multiplying]: [tex]\displaystyle b^m \cdot b^n = b^{m + n}[/tex]Algebra II
Logarithms and Natural LogsEuler's number eCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Differential Equations
Separation of VariablesAntiderivatives - Integrals
Integration Constant C
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
U-Substitution
Logarithmic Integration
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y' = \frac{xy}{2 + x^2}[/tex]
[tex]\displaystyle y(0) = 2[/tex]
Step 2: Rewrite
Separation of Variables
Rewrite Derivative Notation: [tex]\displaystyle \frac{dy}{dx} = \frac{xy}{2 + x^2}[/tex][Division Property of Equality] Isolate y's: [tex]\displaystyle \frac{1}{y} \frac{dy}{dx} = \frac{x}{2 + x^2}[/tex][Multiplication Property of Equality] Rewrite Derivative Notation: [tex]\displaystyle \frac{1}{y} dy = \frac{x}{2 + x^2} dx[/tex]Step 3: Find General Solution Pt. 1
Integration
[Equality Property] Integrate both sides: [tex]\displaystyle \int {\frac{1}{y}} \, dy = \int {\frac{x}{2 + x^2}} \, dx[/tex][1st Integral] Integrate [Logarithmic Integration]: [tex]\displaystyle ln|y| = \int {\frac{x}{2 + x^2}} \, dx[/tex]Step 4: Identify Variables
Identify variables for u-substitution for 2nd integral.
u = 2 + x²
du = 2xdx
Step 5: Find General Solution Pt. 2
[2nd Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle ln|y| = \frac{1}{2}\int {\frac{2x}{2 + x^2}} \, dx[/tex][2nd Integral] U-Substitution: [tex]\displaystyle ln|y| = \frac{1}{2}\int {\frac{1}{u}} \, du[/tex][2nd Integral] Integrate [Logarithmic Integration]: [tex]\displaystyle ln|y| = \frac{1}{2} ln|u| + C[/tex][Equality Property] e both sides: [tex]\displaystyle e^{ln|y|} = e^{\frac{1}{2} ln|u| + C}[/tex]Simplify: [tex]\displaystyle |y| = e^{\frac{1}{2} ln|u| + C}[/tex]Rewrite [Exponential Rule - Multiplying]: [tex]\displaystyle |y| = e^{\frac{1}{2} ln|u|} \cdot e^C[/tex]Simplify: [tex]\displaystyle |y| = Ce^{\frac{1}{2} ln|u|}[/tex]Back-Substitute: [tex]\displaystyle |y| = Ce^{\frac{1}{2} ln|2 + x^2|}[/tex]Our general solution is [tex]\displaystyle |y| = Ce^{\frac{1}{2} ln|2 + x^2|}[/tex].
Step 6: Find Particular Solution
Substitute in point: [tex]\displaystyle |2| = Ce^{\frac{1}{2} ln|2 + 0^2|}[/tex]Evaluate |Absolute Value|: [tex]\displaystyle 2 = Ce^{\frac{1}{2} ln|2 + 0^2|}[/tex]|Absolute Value| Evaluate exponents: [tex]\displaystyle 2 = Ce^{\frac{1}{2} ln|2 + 0|}[/tex]|Absolute Value| Add: [tex]\displaystyle 2 = Ce^{\frac{1}{2} ln|2|}[/tex]|Absolute Value| Evaluate: [tex]\displaystyle 2 = Ce^{\frac{1}{2} ln(2)}[/tex][Division Property of Equality] Isolate C: [tex]\displaystyle \sqrt{2} = C[/tex]Rewrite: [tex]\displaystyle C = \sqrt{2}[/tex]Substitute in C [General Solution]: [tex]\displaystyle y = \sqrt{2}e^{\frac{1}{2} ln|2 + x^2|}[/tex]∴ Our particular solution is [tex]\displaystyle y = \sqrt{2}e^{\frac{1}{2} ln|2 + x^2|}[/tex].
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Differential Equations
Book: College Calculus 10e
Related Questions
WILL GIVE U BRAINLIEST
ABCD is a rectangle. AB = x + 7, BC = 2x + 19. What is the CD?
A. 2x + 133
B. X + 7
C. 5x + 38
D. 2x + 14
Answers
Answer:
A rectangle has its Opposite sides Equal.
Draw one so you'd grab it better.
AB=CD
BC= AD
Since CD=AB and We're given AB=x+7...
CD = x + 7
OPTION B IS LEGIT!!
What is the range of y= sec-'(x)? PreCal, send help please!!
Answers
Given:
The function is:
[tex]y=\sec^{-1}(x)[/tex]
To find:
The range of the given function.
Solution:
We have,
[tex]y=\sec^{-1}(x)[/tex]
The range of secant inverse function is:
[tex]Range=\{y|0\leq y\leq \pi , y\neq \dfrac{\pi}{2}\}[/tex]
The range of the given function in interval notation is:
[tex]Range=\left[0,\dfrac{\pi}{2}\right)\text{ and }\left( \dfrac{\pi}{2}, \pi\right ][/tex]
Therefore, the correct option is C.
will give brainliest
Answers
Answer:
respuesta 0.2
Step-by-step explanation:
espero que te sirvan ( ꈍᴗꈍ)
fx= ab*2÷t*2, make t the subhect of the formulae
[tex]fx = ab { }^{2} \div t {?}^{2} [/tex]
Answers
Answer:
t = √ab²/fx
Step-by-step explanation:
fx= ab*2÷t*2, make t the subject of the formulae
Given the function
fx = ab²/t²
We are to make t the subject of the formula
fxt² = ab²
t² = ab²/fx
Take the square root of both sides
√t² = √ab²/fx
t = √ab²/fx
Hence the required value of t is √ab²/fx
16 meters of rope, i want to cut pieces of rope 0.2meters long. how many pieces can cut?
Answers
Answer:
80
Step-by-step explanation:
because 16 decided by 0.2 is 80
hope this helps!!!!
Express 5 cm in metre and kilometre.in decimals........................
Answers
Answer:
0.05 metre
5×10^5 kilometer
1.9685
Fat Kat's offers a special on large two topping pizzas. In how many different ways can you order a two topping pizza if you can choose from 18 toppings? NO LINKS!!!
Answers
=======================================================
Explanation:
There are 18 ways to pick the first topping and 18-1 = 17 ways to pick the next topping. Picking the same topping again doesn't make much sense (though I suppose it could mean that you just want more of that topping than usual?), so that's why we have the 18 drop to 17 when making that second selection.
If the order of toppings mattered, then we'd have 18*17 = 306 permutations. However, the order of toppings doesn't matter. All that matters is the group rather than the individual toppings. When counting out the 306 permutations, we've overcounted by a factor of 2. In other words, we've double counted.
So we must divide by 2 to fix this double count. That leads to 306/2 = 153 combinations
------------------------
The alternative method involves using the nCr combination formula
Use n = 18 and r = 2 in this formula
[tex]_n C _r = \frac{n!}{r!*(n-r)!}[/tex]
the exclamation marks indicate factorial.
PLEASE HELP ASAP
PICTURE PROVIDED
Answers
Answer:
(x+1)(x+3)(x+5)
Step-by-step explanation:
Randy wants to save $21 to buy a basketball he saved $7 each week which array represents the number of weeks randy needs to save $21
Answers
Answer:
he will have to save $7 for 3 weeks to get $21
Step-by-step explanation:
What is the Area of the parallelogram?
Answers
Answer:
117 sq in
Step-by-step explanation:
Please I need it now
A rational number is terminating decimal, if its denominator has
no prime factor other than:
A. 2 and 3 B. 3 and 5 C. 2 and 5 D. 2 and 7
Answers
Answer:
it's C. 2 and 5...
Step-by-step explanation:
If the denominator of rational number contains no prime factors other then 2 or 5 or both, then this rational number can be expressed as terminating decimal. So the correct answer is option is C
Find one value of x that is a solution to the equation:
(x2 – 6)2 = -3x2 + 18
Answers
Suppose the length of each side of a square is increased by 5 feet. If the perimeter of the square is now 56 feet, what were the original side lengths of the square? A. 9 ft B. 11 ft C. 14 ft D. 36 ft
Answers
Answer:
D. 36 ft
Step-by-step explanation:
5 feet added to each of 4 sides is 20 feet
56 - 20 = 36
Please help me I am super confused I would really appreciate it ♥️♥️
Answers
Jill bought 3 boxes of ice pops. Each box contains 4 orange ice pops and some cherry ice pops. The number of cherry ice pops in each box was the same. Jill bought 36 ice pops in all. What are the 2 steps of this equation and how many cherry ice pops are in each box?
Answers
Answer: 9 cherry ice pops
Step-by-step explanation:
if you bought 3 boxes and there is four orange one in each pack the that is
12 and 36 divided by 4 is 9 so there is 9 cherry ice pops
If h(x) = 6 – X, what is the value of (hon (10)? O 4 -2 10 If p(x) = 2x2 - 4x and q(x) = x - 3, what is (pºq)(x)? O 2x2 - 4x + 12 O 2x2 – 16x + 18 O 2x2 – 16x + 30 O 2x2 – 16x + 15
Answers
2(x2-6x+9)-4(x-3) .... Report. 10/05/20 ... Since p(x) = 2x2 - 4x, we get: 4 - 4(x-3) = 4 - 4x + 12 = -8 - 4x (assuming 2x2 ... 4x. Note ** if in the original equation "2x2" means "2 times x to the power of 2" ... No packages or subscriptions, pay only for the time you need.2 answers Top answer:
p(x) = 2x2 – 4x and q(x) = x – 3, (p•q)(x).
The value of h(10) if h(x) = 6 – X and (pºq)(x) are -4 and 2x² - 16x + 18 respectively
How to solve equationh(x) = 6 – x
h(10) = 6 - 10
= -4
If
p(x) = 2x² - 4x
q(x) = x - 3
(pºq)(x)
= (2x² - 4x) (x - 3) × 4
= 2x² - 16x + 18
Learn more about equation:
https://brainly.com/question/2972832
if the simple interest on $1000 for 10 years is $400, then what is the interest rate?
Answers
doctors use gallium in scanning some patients for diseases the table shows the amount of gallium in mg remaining in a patients system after t hours which exponential function best represents the data.
Answers
Step-by-step explanation:
no sn as. kojsshsusishheidhsusjjsbsbshsbsjs7ehsjsnkosvsjsishshshsjdjjddyfygyvrcudjdhdudhsjsudhdjs
escreva na forma ax2+bx+c=0 as seguintes equações do 2° grau
Answers
work out the area of this circle. take pi to be 3.142 and give your answer to be 2 decimal places. 11,2 cm
Answers
Answer:
11.2 i think so but you will write 11.2
Suppose N in L(V) is nilpotent. Prove that the minimal polynomial fo N is z^m+1, where m is the length of the longest consecutive strong of 1st that appears on teh line directly aoce the diagonal in teh matrix of N with respect to any jordan basis for N.
Answers
Answer: your question is poorly written attached below is the complete and well written question
answer : The minimal polynomial has degree m + 1 hence Z^m+1
Step-by-step explanation:
Given that
N ∈ L(V) is nilpotent
attached below is the required prove
Anna bought 3 types of fruit for a fruit salad. She paid three times as much for blueberries as for pears and $2.50 less for strawberries than for blueberries.
If The total cost was $13.25 how much did Anna spend on each type of fruit
Answers
Answer:
Anna spent $ 2.25 on pears, $ 6.75 on blueberries, and $ 4.25 on strawberries.
Step-by-step explanation:
Given that Anna bought 3 types of fruit for a fruit salad, and she paid three times as much for blueberries as for pears and $ 2.50 less for strawberries than for blueberries, if the total cost was $ 13.25, to determine how much did Anna spend on each type of fruit, the following calculation must be performed:
Pears: X
Blueberries: 3X
Strawberries: 3X - 2.5
X + 3X + 3X - 2.5 = 13.25
7X = 13.25 + 2.5
X = 15.75 / 7
X = 2.25
Pears: 2.25
Blueberries: 3 x 2.25 = 6.75
Strawberries: 3 x 2.25 - 2.50 = 6.75 - 2.50 = 4.25
2.25 + 6.75 + 4.25 = 13.25
Therefore, Anna spent $ 2.25 on pears, $ 6.75 on blueberries, and $ 4.25 on strawberries.
PLS HELP ASAP!! need the answer
Answers
Answer:
60 degrees
Step-by-step explanation:
There are 4 red marbles and 8 blue marbles in a bag. Mark draws a blue marble out of the bag and does not replace. then jake draws another blue marble out of the bag.
Now what are the probabilities of drawing another blue marble?
NEED ANSWER ASAP PLS!!!
Answers
Answer:
Probability will be 4 by 6
HELP QUICK!!!!!!!! GIVING BRAINLIEST!!
Answers
3x. =180-90
3x. =90
x. =30
What are the coordinates of the solution of these two linear equations
Answers
Hi there! The solutions of two linear equations can be broken into 3 types:
Infinitely Many SolutionsOne Solution No SolutionThis is from the system of equations where you solve for the y-value and x-value by substitution method or elimination method.
From the question above, the question asks you to find the coordinate of the solution of the equations. But how do we know the coordinate point of the solution if we aren't given any equations? They don't give equatione but they give a graph instead.
Now I would like you to take a look at the graph. You notice that both graphs have one intersect point, right? That point is our solution!
Hence, we can say that an intersection point of two graphs is the solution of both equations.
The graphs intersect each others at (2,1). Thus the answer to this question is (2,1)
Questions can be asked through comment.
Furthermore, an intersection point of two graph is the solution to the equation of the graphs.
Hope this helps, and Happy Learning! :)
What is the volume of a sphere with a surface area of 25pi / (d ^ 2)
Answers
Answer:
B. [tex] \frac{125}{6}* \pi [/tex] yd³
Step-by-step explanation:
Given:
Surface area of a sphere = 25π yd²
Required:
Volume
Solution:
Let's find the radius (r) first.
S.A of sphere = 4πr²
Substitute
25π = 4πr²
Divide both sides by 4π
25π/4π = r²
25/4 = r²
Take the square root of both sides
√25/√4 = r
5/2 = r
r = 5/2 yd
Find the Volume of the sphere
V = ⁴/3*πr³
V = ⁴/3*π*(⁵/2)³
V = ⁴/3*π*125/8
V = ⅓*π*125/2
V = [tex] \frac{1*125}{3*2}* \pi [/tex]
V = [tex] \frac{125}{6}* \pi [/tex] yd³
(1 point) Some shrubs have the useful ability to resprout from their roots after their tops are destroyed. Fire is a particular threat to shrubs in dry climates, as it can injure the roots as well as destroy the aboveground material. One study of resprouting took place in a dry area of Mexico. The investigation clipped the tops of samples of several species of shrubs. In some cases, they also applied a propane torch to the stumps to simulate a fire. Of 16 specimens of a particular species, 7 resprout after fire. Estimate with 99% confidence the proportion of all shrubs of this species that will resprout after fire.
Answers
Answer:
The answer is "[tex]0.45 \pm 0.18204[/tex]"
Step-by-step explanation:
For the +4 sample proportion[tex]= \frac{(7+2)}{(16+4)} = \frac{9}{20} = 0.45[/tex]
Sample percentage measurements estimated stdev
[tex]= \sqrt{\frac{[(0.45)(1-0.45)]}{[(16+4)]}}\\\\ = \sqrt{\frac{[(0.45)(0.55)]}{[(20)]}}\\\\ = \sqrt{\frac{0.2475}{20}}\\\\= \sqrt{0.012375}\\\\=0.111[/tex]
Calculating the critical z for a=0.1, two-tailed = 1.64
Calculating the confidence interval:
[tex]= 0.45 \pm 0.111 \times 1.64 \\\\= 0.45 \pm 0.18204[/tex]
The area of a rectangle is given by 3x3+14x2−23x+6. The width of the rectangle is given by x + 6. Find an expression for the length of the rectangle.
Answers
Answer:
is that 3x or mutiply sign
Answer:
3x^2-4x+1
Step-by-step explanation:
I need the answer n 30 minutes, please!
For which values of the parameter p equation
x ^ 2-px + 3 = 0
has a root in the range [0; 1], and another that does not belong to this range?
Answers
Answer:
p = 4
Step-by-step explanation:
Given the expression x ^ 2-px + 3 = 0
If x = 0 is a solution
Substitute into the expression
0² - 0p + 3 = 0
-0p = -3
p = 3/0
p cannot be determined for this root
If x = 1
1² - 1p + 3 =0
1 - p + 3 = 0
-p+4 = 0
-p = -4
p = 4
Hence the va;ue of p is 4