at any time, even if you haven't studied differential equations. can you think of a mathematical function that when you take the derivative of it twice, the solution is the negative of that function?
Answers
Both sine and cosine functions are solutions to this particular differential equation. These functions are commonly encountered in the study of oscillatory systems, such as simple harmonic motion.
Your question asks if there is a mathematical function that, when you take the derivative of it twice, the solution is the negative of that function. In other words, you are looking for a function f(x) such that f''(x) = -f(x).
The function you are looking for is the sine function, denoted by f(x) = sin(x). Here's a step-by-step explanation of how this function meets the criteria:
Start with the function f(x) = sin(x).
Take the first derivative with respect to x: f'(x) = cos(x).
Take the second derivative with respect to x: f''(x) = -sin(x).
As you can see, after taking the derivative twice, you obtain -sin(x), which is the negative of the original function, sin(x).
Another function that meets this criterion is the cosine function, g(x) = cos(x). Here's the step-by-step explanation:
Start with the function g(x) = cos(x).
Take the first derivative with respect to x: g'(x) = -sin(x).
Take the second derivative with respect to x: g''(x) = -cos(x).
After taking the derivative twice, you obtain -cos(x), which is the negative of the original function, cos(x).
Both sine and cosine functions are solutions to this particular differential equation. These functions are commonly encountered in the study of oscillatory systems, such as simple harmonic motion.
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Related Questions
are natural numbers closed under subtraction
Answers
The natural numbers are "closed" under addition and multiplication. ... The subtraction of two natural numbers does NOT necessarily create another natural number (3 - 10 = -7). The division of two natural numbers does NOT necessarily create another natural number (1 ÷ 2 = ½). not closed under subtraction and division.
The baseball team is running laps along the fence around a rectangular field. They know that one lap around the field is 986ft. The width of the field is 248ft. What is the length of the field that they are running around?
Answers
Answer:
This is perimeter so we take the 248 and multiply it by 2 to get 496. than subtract 496 from 986. 986-496=490 so divide that number by 2 to get 245. 245 is the length of the feild
let me know if i am wRoNg!
Step-by-step explanation:
What is the approximate value of x in the diagram below
Answers
We use Tan in this case:
Tan=(opposite/adjacent)
Tan(36)=23/x
x=23/Tan(36)
x=31.64 length
Hope it helps!
Answer:
x ≈ 31.64
Step-by-step explanation:
Trigonometric ratios
\(\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}\)
where:
\(\theta\) is the angleO is the side opposite the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)Given:
sin 36° ≈ 0.588cos 36° ≈ 0.809tan 36° ≈ 0.727The given trigonometric ratios all use the angle of 36°.
From inspection of the given diagram:
x is the side adjacent to the angle of 36°23 is the side opposite to the angle of 36°Therefore, we should use the tan trig ratio.
\(\implies \sf \tan(36^{\circ})=\dfrac{23}{x}\)
\(\implies \sf x=\dfrac{23}{\tan(36^{\circ})}\)
Substituting the given value for tan 36°:
\(\implies \sf x \approx \dfrac{23}{0.727}\)
\(\implies \sf x\approx31.64\)
Describe in words the surface whose equation is given.
rho^2 - 3rho +2= 0
Answers
The equation of the surface in words is described as follows: The given equation `ρ^2 - 3ρ + 2 = 0` is a quadratic equation in `ρ`, the radial distance from the origin.
It's a sphere with radius `ρ = 1` and the center at `ρ = 2` in the Cartesian coordinate system. When the equation is rearranged to standard form, we get `(ρ - 2) (ρ - 1) = 0`. The equation of the surface in words is described as follows:
The given equation `ρ^2 - 3ρ + 2 = 0` is a quadratic equation in `ρ`, the radial distance from the origin. It's a sphere with radius `ρ = 1` and the center at `ρ = 2` in the Cartesian coordinate system. When the equation is rearranged to standard form, we get `(ρ - 2) (ρ - 1) = 0`.Therefore, the surface represented by the given equation is a sphere with radius `ρ = 1` and the center at `ρ = 2` in the Cartesian coordinate system.
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ASAP HELP
Find the variance and standard deviation of the data set below:
0 0.107
1 0.352
2 0.400
3 0.141
Answers
If the standard deviation of a set of data is 6, then the value of variance is 36
The formula for determining variance is variance = √Standard deviation
Variance of a set of data is equal to square of the standard deviation.
If the standard deviation of a set of data is 6 then we get variance by putting the value of standard deviation in the formula
variance = √Standard deviation
Take square root on both sides
Standard deviation² = 6²
Standard deviation= 36
Hence, standard deviation of a set of data is 6, then the value of variance is 36
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15. (10 points) Determine whether the following improper integrals are convergent or divergent. You need to justify your conclusion. +1+e* dx b) dx dx Ve (a) S2 -1 (b) Dia dos
Answers
The improper integrals in question are (a) \(\int(1+e^x)dx\) and (b) \(\int(1/x)dx\). The first integral is convergent, while the second integral is divergent.
(a) To determine the convergence of the integral ∫(1+e^x)dx, we can find its antiderivative. The antiderivative of 1+e^x is x + e^x + C, where C represents the constant of integration. Since the antiderivative exists, we can conclude that the integral is convergent.
(b) Let's now analyze the integral ∫(1/x)dx. This integral represents the to natural logarithm function, ln|x| + C, as its antiderivative. When calculating the integral between the interval (-∞, ∞), we find a singularity at x = 0. As a result, the integral diverges over these intervals and is not convergent.
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Find the length of the arc.
Answers
Answer:
1st option
Step-by-step explanation:
The length of the arc is calculated as
arc = circumference of circle × fraction of circle
= 2πr × \(\frac{210}{360}\)
= 2π × 13 × \(\frac{21}{36}\)
= 26π × \(\frac{7}{12}\)
= \(\frac{26\pi (7)}{12}\)
= \(\frac{182\pi }{12}\)
= \(\frac{91\pi }{6}\)
how to solve V = 1/3 Ah for h
Answers
Answer:
(3V)/A = h
Step-by-step explanation:
V = 1/3 Ah
Solve the literal equation using inverse operations;
V = 1/3 Ah
*3 *3
3V = Ah
/A /A
(3V)/A = h
Please help! I will give brainliest! :)
Answers
Answer:
25,821
Step-by-step explanation:
To find the town's population in 19 years you just have to do 17,724*\(1.02^{19}\) because each year the population will be 1.02 times the year before. That would be 25,820.5212 which is 25,281 rounded to the nearest whole number.
Hope this helps :)
Can someone please help me i dont understand it.
Answers
Answer:
1. True
2. False
3. True
4. True
Step-by-step explanation:
2/7 = y/28 Find the value of y
Answers
Answer:
\(y=8\)
Step-by-step explanation:
\(\frac{2}{7} =\frac{y}{28}\)
Multiply both sides by 28.
\(\frac{2}{7} * 28=y\)
Express \(\frac{2}{7} *28\) as a single fraction.
\(\frac{2*28}{7} =y\)
Multiply 2 and 28 to get 56.
\(\frac{56}{7}=y\)
Divide 56 by 7 to get 8.
\(8=y\)
Swap sides so that all variable terms are on the left hand side.
\(y=8\)
Hope this helps! Brainliest would be much appreciated! Have a great day! :)
What is true? (Multiple answers can be selected).
17/3 is...
A) A natural number
B) A whole number
C) An Integer
D) A rational number
F) A irrational number
0 is...
A) A natural number
B) A whole number
C) An Integer
D) A rational number
F) A irrational number
3 is...
A) A natural number
B) A whole number
C) An Integer
D) A rational number
F) A irrational number
14 is...
A) A natural number
B) A whole number
C) An Integer
D) A rational number
F) A irrational number
Answers
Answer:
17/3 is...
A) A natural number
B) A whole number
C) An Integer
D) A rational number <------- answer
F) A irrational number
0 is...
A) A natural number
B) A whole number <----- answer
C) An Integer <----- answer
D) A rational number <----- answer
F) A irrational number
3 is...
A) A natural number <----- answer
B) A whole number <----- answer
C) An Integer <----- answer
D) A rational number <----- answer
F) A irrational number
14 is...
A) A natural number <----- answer
B) A whole number <----- answer
C) An Integer <----- answer
D) A rational number <----- answer
F) A irrational number
How do you convert cm into mL?
Answers
Answer:divideing by the whole number
Step-by-step explanation:
The set of ordered pairs shown below is a relation that is a function of x. {(1, 3), (2, 4), (3, 5), (4, 6)} Which ordered pair could be included in the set so that the relation remains a function of x?
A (3, 3)
B(1,6)
C (4,7)
D (0,4)
Answers
Answer:
D (0,4)
Step-by-step explanation:
You want to know an ordered pair that could be added to the given relation such that it remains a function.
FunctionA function cannot have any two ordered pairs that have the same x-value. The given relation has x-values {1, 2, 3, 4}, so none of these can be repeated if the relation is to remain a function.
The only choice with a different x-value is ...
D (0, 4)
__
Additional comment
The set of x-values is the "domain" of the function. It cannot have any repeats. The set of y-values is the "range" of the function. Those values can be repeated.
A function that is "one-to-one" cannot have any repeated range values, either.
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if the sale price is $57, and the percent of discount is 5%, what's the original price? please help
Answers
Answer:$60
Step-by-step explanation:
For melions birthday she wanted to make fruit punch that had 2 1/2 gallons of orange juice, 4 quarts of cranberry juice, and 3 quarts of apple juice. how much did she make in all?
Answers
Answer:
4.25 gallons of juice
Step-by-step explanation:
4 quarts = 1 gallon
3 quarts = 3/4 gallon
2 1/2 + 1 + 3/4 = 3 2/4 + 3/4 = 3 5/4 = 4 1/4
4 1/4 = 4.25
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a line passes through the point (-4, 7) and has a slope of 5/4
Answers
Answer:
y = 5/4x+ 7
Step-by-step explanation:
slope - intercept form : y =mx+b
m = slope
b = y intercept
slope (m): 5/4
y intercept (b) = 7
y = 5/4x+7
1s22s22px22py22pz23s23px23py23pz2
Answers
Given :
Electronic configuration of an electron :
\(1s^2\ 2s^2\ 2p_x^2\ 2p_y^2\ 2p_z^2\ 3s^2 \ 3p_x^2\ 3p_y^2\ 3p_z^2\) .
To Find :
The element having such an electronic configuration .
Solution :
We know , the sum of all the power of s and p in all the orbit gives total number of atoms in elements .
So , atomic number is :
\(Z=2+2+(2+2+2)+2+(2+2+2)\\\\Z=18\)
Since , the atomic number is 18 .
Therefore , the element is Argon .
Hence , this is the required solution .
algebra 2-2
solve \(\sqrt{x}+3=-6\)
√x+3=-6
Answers
The solution of equation is x=-3
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given
The equation;√x+3=-6
Now,
√x=-6-3
√x=-9
x=-3
Therefore the answer of the given equation will be -3
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what is the first 5 cubic numbers
Answers
Answer:
1,8,27,64,125
Step-by-step explanation:
The governor of Utah wants to know how long they have before the entire state is zombified. If there are 3.67 million people living in Utah (3,670,016 to be exact), how many days until the entire state is infected?
options:
19 days
2 years
11 days
52 days
Answers
Answer:
wait.
Step-by-step explanation:
what do u really mean by zombies
Plz help me I need it for a test I don’t have that long
Answers
Answer: 49
Step-by-step explanation:
i worked it out...
A toy cannon ball is launched from a cannon on top of a platform. The equation h(t) = -3t² + 12t + 15gives the height h, in meters, of the ball t seconds after it is launched. (a)Does the ball reach a height of 16 m?(b)How long does it take the ball to hit the ground?
Answers
Answer:
(a)Yes
(b)5 seconds
Explanation:
Given the equation: h(t) = -3t² + 12t + 15
(a)To determine if the ball reaches a height of 16m, we find the maximum height of the cannon ball.
The maximum height occurs at the axis of symmetry.
First, we find the equation of symmetry.
\(\begin{gathered} t=-\frac{b}{2a} \\ =-\frac{12}{2\times-3} \\ =-\frac{12}{-6} \\ t=2 \end{gathered}\)We find h(2).
\(\begin{gathered} h(2)=-3(2)^2+12(2)+15 \\ =-12+24+15 \\ =27\text{ meters} \end{gathered}\)The ball reaches a height of 16 meters since its maximum height is 27 meters.
(b)The ball reaches the ground at the point when h(t)=0.
\(\begin{gathered} -3t^2+12t+15=0 \\ -3t^2+15t-3t+15=0 \\ -3t(t-5)-3(t-5)=0 \\ (t-5)(-3t-3)=0 \\ t-5=0\text{ or }-3t-3=0 \\ t=5\text{ or }-3t=3 \\ t=5\text{ or }t=-1 \end{gathered}\)Since time cannot be negative, the ball hits the ground after 5 seconds.
PLEASE HELP
Answer the following questions:
1.Given () = 5 − 3, find (3) and (7).
2.Given () = 2 + 8, find (4) and (−2).
3.Given () = 1/2x + 12, find (−6) and (16).
Answers
For the given equations the values for f(3) = -4, f(7) = -16, f(4) = 34, f(-2) = -14, f(-6) = 9, f(16) = 20.
What is equation?
In mathematics, an equation is a statement that asserts the equality of two expressions. An equation is made up of two sides, a left-hand side and a right-hand side, separated by an equals sign (=). The expressions on either side of the equals sign can contain variables, constants, coefficients, functions, and operators.
For f(x) = 5 - 3x:
f(3) = 5 - 3(3) = -4
f(7) = 5 - 3(7) = -16
For f(x) = 2 + 8x:
f(4) = 2 + 8(4) = 34
f(-2) = 2 + 8(-2) = -14
For f(x) = (1/2)x + 12:
f(-6) = (1/2)(-6) + 12 = 9
f(16) = (1/2)(16) + 12 = 20
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Find the slope of a line perpendicular to each given line.
1) y = 1/2x - 2
2) y = 2x + 2
Answers
Answer:
It's 1. Have a nice day! :)
Step-by-step explanation:
what information is missing for the interpretation of an anova if you only run an omnibus/overall anova (without any post-hoc tests)? why do we need to run follow up tests when we conduct a one-way anova?
Answers
The statistical method known as analysis of variance (ANOVA) is used to examine how different means differ from one another.
When you only run an omnibus/overall anova without any post-hoc tests, you will be unable to determine which of the groups are statistically different from each other. This is because an omnibus/overall anova simply tells you whether there is a significant difference between any of the groups, but does not tell you which groups are different. Follow up tests are needed to determine which of the groups are statistically different from each other.
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Does the compound event consist of two mutually exclusive events?
Two dice are rolled. The sum of the dice is a 5 or a 11. Yes or No?
Compute the probability of the compound event occurring.
Answers
No, the compound event does not consist of two mutually exclusive events. Two dice are rolled and the sum of the dice can be either a 5 or an 11.
Are the events of getting a sum of 5 and getting a sum of 11 mutually exclusive when rolling two dice?When two dice are rolled, there are a total of 36 possible outcomes. The probability of getting a sum of 5 is 4/36 or 1/9 because there are four ways to get a sum of 5 (1+4, 2+3, 3+2, 4+1). Similarly, the probability of getting a sum of 11 is 2/36 or 1/18 because there are only two ways to get a sum of 11 (5+6, 6+5).
The compound event of getting a sum of 5 or 11 is not mutually exclusive because it is possible to get a sum of 5 and 11 at the same time by rolling two dice that show a 2 and a 3. The probability of the compound event is the sum of the probabilities of the individual events:
1/9 + 1/18 = 3/18 + 1/18 = 4/18 = 2/9
Therefore, the probability of getting a sum of 5 or 11 when rolling two dice is 2/9.
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pls help asap if you can!!!!!
Answers
Answer:
x = 24
Step-by-step explanation:
if a and b are parallel then
62 and 5x - 2 are same- side interior angles and sum to 180° , that is
5x - 2 + 62 = 180
5x + 60 = 180 ( subtract 60 from both sides )
5x = 120 ( divide both sides by 5 )
x = 24
thus for a to be parallel to b , then x = 24
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Solve for the angles below.
find X. :
Find m angle 1 :
Find m angle 2:
Find m angle 3:
Find m angle 4
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Answers
I think your work was right, except you mixed up or lost track of a sign.
7x+5 = 14x-16
subtract 7x and add 16 to both sides:
21 = 7x
divide by 7
3 = x
Now substitute that back into either of angle 1 or angle 2 to find the measure of those. (They'll be the same.)
Then use the fact that angle 1 and angle 2 form a straight line and add up to 180º.
A city has a 5% sales tax. What is the constant of proportionality?
Answers
Answer: 0.05
Step-by-step explanation:
The equation is k = y/x, which is a constant change rate
Take 5 divided by 100 = 0.05
5% = 0.05
So the constant of proportionality is 0.05