The given equation is a second order differential equation
What is a differential equation?In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives.
Isaac Newton listed three kinds of differential equations given -
[tex]${\displaystyle {\begin{aligned}{\frac {dy}{dx}}&=f(x)\\[4pt]{\frac {dy}{dx}}&=f(x,y)\\[4pt]x_{1}{\frac {\partial y}{\partial x_{1}}}&+x_{2}{\frac {\partial y}{\partial x_{2}}}=y\end{aligned}}}[/tex]
Given is a differential equation as follows -
d²a/db² + a = 4b + 10sin(b)
The given equation is -
d²a/db² + a = 4b + 10sin(b)
Let y = a and x = b, then we can write -
d²y/dx² + y = 4x + 10sin(x)
A second order differential equation is one that expresses the second derivative of the dependent variable as a function of the variable and its first derivative. It is of the form -
d²y/dx² + P(x) dy/dx + Q(x) y = f(x)
For the equation given -
d²y/dx² + y = 4x + 10sin(x)
On comparing, we get -
P(x) = 0
Q(x) = 1
f(x) = {4x + 10sin(x)}
Therefore, the given equation is a second order differential equation.
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what is an equation of the line that is parallel to y = - 5 x + 6 and passes through the point (-4,-1)
The equation of the line that is parallel to the line y = - 5x + c and passes through (-4, -1) will be y = - 5x - 21.
What is the equation of a parallel line?Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as ax + by + d = 0.
The equation of the line is given below.
y = - 5x + 6
The equation of the line that is parallel to the line y = - 5x + 6 is written as,
y = - 5x + c
The equation passes through (-4, -1), then we have
- 1 = - 5 (-4) + c
- 1 = 20 + c
- 21 = c
The equation of the line that is parallel to the line y = - 5x + c and passes through (-4, -1) will be y = - 5x - 21.
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Find the coordinates of the circumcenter of the triangle with the given vertices.
L(3,−6), M(5,−3), N(8,−6)
P(1.6,-2.9) are the coordinates of circumcentre of the triangle
How to find the coordinates of the circumcenter of a triangle?The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of that particular triangle intersect.
Let L(3,−6), M(5,−3), N(8,−6) be the vertices of the given △LMN.
Let P(x,y) be the circumcentre of △LMN. Then,
PL = PM = PN
Also, PL² = PM² = PN²
PL² = PM²
(x-3)² + (y-(-6))² = (x-5)² + (y-(-3))²
(x-3)² + (y+6)² = (x-5)² + (y+3)²
x²-6x+9 + y²+12y+36 = x²-10x+25 + y²+6y+9
4x + 6y = -11 ---- (1)
Also, PM² = PN²
(x-5)² + (y-(-3))² = (x-8)² + (y-(-6))²
(x-5)² + (y+3)² = (x-8)² + (y+6)²
x²-10x+25 + y²+6y+9 = x²-16x+64 + y²+12y+36
6x - 6y = 27 ---- (2)
Solve (1) and (2) simultaneously by elimination:
6 × (4x + 6x = -11)
4 × (6x - 6y = 27)
24x + 36y = -66
24x - 24y = 108
subtract:
60y = -174
y = -174/60
y = -2.9
Put y = -2.9 into (1):
4x + 6x = -11
4x + 6(-2.9) = -11
4x - 17.4 = -11
4x = 6.4
x = 1.6
Thus, the coordinates of the circumcentre of △LMN are P(1.6, -2.9)
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What is the domain of this function?
F(x)=3 square root x-2
x-2>0= x>2
The domain of the function F(x) = 3 [tex]\sqrt{x-2}[/tex] is {x : x ≥ 2 and x is a real number}.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given function is,
F(x) = 3 [tex]\sqrt{x-2}[/tex]
Domain of this function is all the values of x for which the function is defined.
The expression [tex]\sqrt{x-2}[/tex] is defined only when the value of x - 2 is positive.
x - 2 > 0 ⇒ x > 2
So the function will be defined for all x > 2.
Hence the domain of the function is the set of all x such that x > 2.
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how to work XYZ company's cost function for the next four months is c=500,000+5Q .. If, because of strike, the most the company can produce is br. 100,000 units, should it shutdown? Why or why not?
Answer:
(A) So since BE means cost = revenue, you just need to solve
6Q = 500,000 + 5Q
(B) they told you at the top what the 4-month cost is. That is still true, even if Q=0
(C) find revenue for 100,000. If less than cost, shut down.
The area of the floor of a cubical room is 49square meter. Find the area of 4 walls of room.
Answer:
If the walls are the standard 8 feet tall and the room is square, then:
the wall length and width is both 7 feet.
The area of the walls would be 4x7x8 = 224 ft² (also providing there are no doors or windows)
What's the equation and solution?
Observing the given figure , It is a balanced balance which signifies both side should be equal, The answer is 2=-8-x and x=-10.
What do you mean by equations?An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A collection of one or more linear equations containing the same variables is known as a system of linear equations in mathematics. A set of two or more linear equations with two or more variables each constitutes a system of linear equations, all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy all of the system's equations is necessary to identify the one and only solution to a system of linear equations.
What are the methods to solve system of equations?There are three ways to solve systems of linear equations :
GraphingSubstitution methodElimination method2=-8-x is the required balanced equation.
-x = 2 + 8
x= -10
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I’ll mark brainlist
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No explanation needed but if you want brainlist then u need to do explain
Answer:
B. 6/9 - 4/9
Step-by-step explanation:
Make sure each fraction has a common dominator
2/3 *3/3 = 6/9
4/9 = 4/9
6/9 - 4/9 = 2/9
Answer:
6/9 - 4/9, B
Step-by-step explanation:
6) What is the value of digit 7 in 0.057 *.///what is the answer _____________________
7/10
0.07
7/1000
Answer: 7/1000 (choice C)
This is because the 7 is in the thousandths decimal place. We put the 7 over 1000 to form the fraction 7/1000.
Question 5 of 10
Mackenzie took out a payday loan for $1100 that charged a $95 fee. If the
loan matures in 2 weeks, what is the approximate effective interest rate of the
loan?
OA. 862%
OB. 86%
OC. 76%
OD. 762%
Help me out smartie pants hahahahaahahaha
Answer:
5/8
I had it
Answer: 40
Step-by-step explanation:
HI!
1) first you would get any algebra calculator
2) punch in the numbers
3) get the answer
-YOUR WELCOME
A steel pipe 50 cm long has an outside diameter of 2 cm and an inside diameter of 1.8 cm. If the density of the steel is 7.8 grams per cm3, what is
the mass of the pipe to the nearest gram?
Answer:
the volume is 50x1.8x2
v=180cm³
therefore, density is mass/volume
Step-by-step explanation:
mass =density x volume
mass= 7.8 x 180cm³
mass= 1,404grams
The mass of the pipe to the nearest gram mass= 1,404grams.
We have given that,
A steel pipe 50 cm long has an outside diameter of 2 cm and an inside diameter of 1.8 cm. If the density of the steel is 7.8 grams per cm^3
The volume is 50x1.8x2
v=180cm^3
Therefore, density is mass/volume
What is the formula for mass?
mass =density x volume
mass= 7.8 x 180cm^3
mass= 1,404grams
Therefore, The mass of the pipe to the nearest gram mass= 1,404grams.
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Question
The Gross Domestic Product (GDP) for the United States in the first quarter of 2014 was approximately $1.71 x 1013. If you
wrote this number in standard notation, it would be the number 171 followed by how many zeros?
Answer:
11
Step-by-step explanation:
If you were to write the Gross Domestic Product in standard notation, 171 would be followed by 11 zeros.
What is standard notation?
Standard notation is used in expressing large numbers in smaller numbers. In order to write a number in standard notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10 raised to the number of zeros.
For example:
The number : 2 x 10² is equivalent to 300
The number 3 x 10³ is equivalent to 300
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Suppose there is a bag of 20 marbles. Of these marbles, 12 are green, 5 are blue, 2
are red, and 1 is black. What is the probability of drawing three marbles and having all
three be blue, without replacement?
Answer:
3/20 or (i think %15)
Step-by-step explanation
This is mostly a guess since I haven't done probability in a while. Good luck though.
explain step by step please thank you!
Paco drives an average of 55 miles per hour. Their destination is 274 miles away. wants to arrive at 4:00 p.m. and allow an extra hour for stops. What time should he go out?
Use technology to convert the polar coordinates (5,6.1) to rectangular coordinates. (0.98, – 0.18) (0.98, 0.18) (4.92, – 0.91) (4.92, 0.91)
Answer: (4.92, -0,91)
Step-by-step explanation:
This should be C on edge 2021
Answer:
C: (4.92, –0.91)
Step-by-step explanation:
Took the quiz
Photo attached. Someone please help
Thanks
By using the graph, a solution the given system of equations include the following:
x = 0, y = 3
x = 3, y = 6
What are quadratic functions?In Mathematics, the graph of every quadratic functions (equations) is either an upward or downward parabola, which is typically a u-shaped curve. This ultimately implies that, the graph of a quadratic function (equation) would always form a parabolic curve.
In this scenario, we would use an online graphing calculator to plot the graph of the given system of equations and then determine the point of intersection.
y = x + 3
y = x² - 2x + 3
By critically observing the graph of the given system of equations, the solutions are as follows;
x = 0, y = 3.
x = 3, y = 6.
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Need help please?!?!?! Extra points!!!
Answer:
4.19
Step-by-step explanation:
just use the formula 2pir^2
SAVINGS Natalie has $250 in her savings account, into which she deposits $10 of her allowance each week. The balance of her savings account can be modeled by the function f(w)=250+10w, where w represents the number of weeks. Which function g(w) represents the balance of Natalie’s savings account if she withdraws $40 to purchase a new pair of shoes? Describe the translation of f(w) that results in g(w).
Answer:
Answer:Step-by-step explanation:GivenRequiredDetermine g(w)First, we'll write an expression for g(w)From the question, we understand that she withdrew $40 from her account balance in w weeks.This implies that:Where f(w) is the account balance in w weeks and $40 is the withdrawn amountSubstitute 250 + 10w for f(w)Collect Like TermsRecall that:This means that function f(w) when shifter by 40 units downward, gives g(w)
Step-by-step explanation:
2. An empty box has a weight of 350g. When 15 cans of juice are put into it the total weight is
4850g. What is the weight of one can of juice?
Answer: 300
Step-by-step explanation:
15x+350=4850
15x=4500
x=300
y is equal to 5 less than the product of x and -2. If the output is -27, what is the input?
Answer: 27 over 2,5
Step-by-step explanation:
Toni runs around her school's baseball diamond. Each side is 27 m long. Note: A baseball diamond is square. How far does Toni run? m
Answer:
If we assume she runs around it once and since they tell us its a square: 27x4=108
Step-by-step explanation:
according to a recent article about individuals who have credit cards, the mean number of cards per person with credit cards is 4. To test this results a random survey of 60 individuals who have credit cards were conducted. The survey only includes the number of credit cards per participant
Answer:
The variable of interest is NUMBER OF CREDIT CARDS. it is a QUANTITATIVE variable.
u=4
u<4
use a t1-84 go to stat, edit, input the table set into L1, back to stat, tests, t-test, data, u=4, list:L1, u<, calculate, enter that will give you a t0=-.62
p-value is in the range P-value>0.10
The P-value is GREATER than level of significance. DO NOT REJECT the null hypothesis. there IS NOT sufficient evidence to claim that the mean number of credit cards is LESS THAN 4.
Step-by-step explanation:
a. The first question in the study asked for the variable of interest. The variable is number of credit per participants. This variable is quantitative.
What is the hypothesis?The null hypothesis has H0: u = 4
Alternative hypothesis = H1: u < 4
To solve the for the p value and the test statistic, more data would be needed for this question.
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A jar containing only nickels and dimes contains a total of 60 coins, The value of all the coins in the jar is $4.45. Write a system of equations to find the number of nickels and dimes in the jar. Use x for the number of nickels and y for the number of dimes.
y 10- 9 8 6 5 4 2 1 2 3 4 5 6 7 8 9 10 What is the equation of the blue line? X
Therefore , the solution of this is the required system of equation is,
y=-x+6 and y=x+10.
Explain the equation.A mathematical equation is a formula that links two statements by indicating their equivalence with the equal sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the components 3x + 5 and 14 in the equation 3x + 5 = 14 are separated by an equal sign. The relationship between two sentences on either side of a letter is expressed mathematically. There is frequently only one variable, which doubles as the symbol. say that 2x - 4 Equals 2.
Here,
(0,6) and the blue line pass through them (-2,8). You may figure out the equation for the blue line as,
=> y-6/x-0 = 8-6 /-2-0
=>y-6/x = 2/-2
=> y-6=-1(x)
y=-x+6
(-2, 8) and the red line pass through them (-3,7). The red line's equation can be calculated as,
y-8/x- (-2) = 8-7 /-2-(-3)
y-8 /x+2 = 1
y-8=x+2
y = x + 10
Thus, the required system of equations is,
y=-x+6 and y=x+10.
Therefore , the solution of this is the required system of equations is,
y=-x+6 and y=x+10.
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Four student government officers want to go to the state convention. It will cost them $100 for registration, $375 for transportation and food, and $41 per person for the hotel. There is $425 budgeted for the convention in the student government savings account. They can earn the rest of the money they need by having a car wash. If they charge $5 per car, how many cars must they wash in order to have enough money to pay for the trip?
cars___?
Answer:
$100 + $375 + $41(4) = $516
$516 - $425 = $91
$91 / $5 = 18.2 cars
Therefore, the four student government officers must wash 18 cars in order to have enough money to pay for the trip.
21.
How many sets of 0.3 are there in the number 360?
There are 1200 sets of 0.3 in the number 360
What is the BODMAS rule?According to the BODMAS rule, the brackets have to be solved first followed by powers or roots (i.e. of), then Division, Multiplication, Addition, and at the end Subtraction. Solving any expression is considered correct only if the BODMAS rule or the PEMDAS rule is followed to solve it.
Given here, 360 is to divided by 0.3 thus,
360/0.3 = 3600/3
= 1200
Hence, There are 1200 sets of 0.3 in the number 360
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The derivative of the function f is given by f′(x)=x^2−2−3xcosx. On which of the following intervals in [−4,3] is f decreasing?
The function f'(x) = x² - 2 - 3xcosx is decreasing on (- 4, - 3) and (- 1, 1).
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, A function f'(x) = x² - 2 - 3xcosx.
We know a function f(x) is decreasing if f'(x) is < 0.
Therefore,
x² - 2 - 3xcosx < 0.
x² - 3xcosx < 2.
x(x - 3cosx) < 2.
Now, 3cosx can be [- 3, 3].
x(x - 3) < 2 and x(x + 3) < 2.
x < 2 Or x - 3 < 2 and x < 2 or x + 3 < 2.
x < 2 Or x < 5 and x < 2 or x < - 1.
But x should be in [- 4, 1], Therefore it is decreasing at (- 4, - 3) and (- 1, 1).
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George has two dogs.
One weighs 56.5 pounds
and the other weighs 47.75
pounds.
What is the total weight, in pounds, of the two dogs?
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the answer to this equation is 104.25
What is the surface area of the cylinder with height 2 ft and radius 4 ft? Round your answer to the nearest thousandth.
Answer:
Lateral surface area:
A = 2πrh = 2*3.14*4*2 = 50.24 ft²Total surface area:
S = 2πrh + 2πr² = 50.24 + 2*3.14*4² = 150.72 ft²Answer:
Surface Area = 150.796 ft² (nearest thousandth)
Step-by-step explanation:
Surface area of a cylinder
[tex]\sf SA=2 \pi r^2+2 \pi rh[/tex]
where:
r is the radiush is the heightGiven:
radius (r) = 4 ftheight (h) = 2 ftSubstitute the given values into the formula and solve for SA:
[tex]\begin{aligned}\sf SA & = \sf 2 \pi r^2 + 2 \pi rh\\\implies \sf SA & = \sf 2 \pi (4)^2 + 2 p\i (4)(2)\\& = \sf 2 \pi (16) + 2 \pi (8)\\& = \sf 32 \pi + 16 \pi \\& = \sf 48 \pi \\& = \sf 150.7964474... \\& = \sf 150.796 \:ft^2\: (nearest\:thousandth)\end{aligned}[/tex]
Therefore, the surface area of the cylinder with height 2 ft and radius 4ft is 150.796 ft² (nearest thousandth).
At a bakery, 55 chocolate chip cookies were burned. if that was 15% of the day's production, how many total cookie did they make that day?
The total number of cookies that was made that day given that 55 which is 15% was burnt is 360.
How to solve for the number of cookies madeWe know that the number of burned cookies is 55, and that this represents 15% of the total production for the day.
We can use this information to set up a proportion to find the total number of cookies made that day.
Burned cookies / Total cookies = 15% / 100%
55 / X = 15/100
To find the total number of cookies made, we can cross-multiply and divide:
X = (55 * 100) / 15
X = 365
So, the bakery made a total of 365 cookies that day.
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