In mathematics, a differential equation is an equation involving one or more functions and their derivatives. The derivative of a function defines the rate of change of the function at some point.
According to the given Question:
Differential equation:
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, a function generally represents a physical quantity, a derivative its rate of change, and a differential equation defines the relationship between the two. Such relationships are common. Therefore, differential equations play an important role in many fields such as engineering, physics, economics and biology.
The study of differential equations consists primarily of studying their solutions (the set of functions that satisfy each equation) and the properties of those solutions. Only the simplest differential equations can be solved with explicit formulas. However, many properties of solutions to particular differential equations can be determined without exact computation. In many cases, when a closed formula for the solution is not available, the solution can be approximated numerically using a computer. Although the theory of dynamical systems focuses on qualitative analysis of systems described by differential equations, many numerical methods have been developed to determine solutions with some degree of accuracy.
A first-order linear differential equation is an equation that can be written in the form y0 + p(x)y = q(x). where p and q are continuous functions on the interval I. The second-order linear differential equation has a similar form.
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What is an
equation of the line that passes through the points (4,-4) and
(-6,-4)? PLEASE I HAVE TO AWNSER IN 5 minutes
Step-by-step explanation:
[tex]y = - 4[/tex]
[tex]y = - 4[/tex]
Answer:
y=-4
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-4-(-4))/(-6-4)=(-4+4)/-10=0/-10=0
slope is 0
y-y1=m(x-x1) where m=slope
y-(-4)=0(x-4)
y+4=0
y=0-4=-4
y=-4
Multiply: (2x − 5)(4x2 + 7x − 11)
Answer:
14x²-41x+15
Step-by-step explanation:
Answer:
8x^3-6x^2-57x+55
Tell me if you would like an explanation If you need one :D
What is the area of the real bedroom?
Answer:
area of real bedroom = 32 cm²
hope it helps..
Answer:
Bedroom: 32 cm living room: 81 cm
Step-by-step explanation:
Bedroom: 4 x 8 = 32
Living room : 9 x 9 = 81
( if combining bedroom and living room, it’s 113 cm)(81 + 32 = 113)
Hope this helps
yayyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
Answer:
It b
Step-by-step explanation:
We know this because 1/2 is 0.5 while 2/3 is 0.67. With this we can say that 1/2 is least than 2/3
Hope this Helped
what is nthe anwer
5 - 2x + 50
Step-by-step explanation:
= 55 - 2x is the answer .
plz mark my answer as brainlist if you find it useful.
Answer:
Add 5 and 50
−2x + 55
Step-by-step explanation:
EDGE20 ASSIGNMENT, WILL MARK BRAINLIEST FOR WHOLE ASSIGNMENT Quadratic in Form Polynomials
Assignment
Active
Practice writing as a quadratic.
ASSIGNMENT
Answer:
[tex] \bold{ \red{{y}^{2} + 7y - 8 = 0}}[/tex]
Step-by-step explanation:
[tex] {(3x + 2)}^{2} + 7 {(3x + 2)} - 8 = 0 \\ \\ plug \: (3x + 2 )= y \\ \\ so \: above \: quadratic \: equation \: \\transforms \: to \\ \\ \bold{ \red{{y}^{2} + 7y - 8 = 0}}[/tex]
A movie theater is offering a special summer pass. Passholders pay $8 per movie for the first 5 movies and watch additional movies for free, up to a maximum of 15 movies. The function C gives the total cost, in dollars, for a passholder to watch n movies.
Is function C a piecewise function? Explain your reasoning.
probably it's 8 or 4. and as $8 is the initial fee, that sounds like the starting value. :-)
the line equation you need is the slope intercept form y = mx + b where m = gradient and b = y intercept.
in this case, y = 4x + 8 where x = number of movies seen, and y = total cost in $
for this line m = 4 and b = 8. hence, indeed, the y intercept is 8
Mark as brainlist
Answer:
Step-by-step explanation:
C is a piecewise function because it represents more than one type of deal.
PLEASE HELP ME I NEED TO TIRN THIS IN AND I DONT KNOW HOW TO DO THIS !
Answer:
what grade is this ?
Step-by-step explanation:
(WILL GIVE BRAINLYIST IF ANSWER IS RIGHT!)
Choose all the expressions that is equal to 0.25(4y - 36)
1. Y - 9
2. -18/2 - y
3. 0.25y - 36
4. -1/2(-2y + 18)
Answer:
The answer is 1 and 4
Step-by-step explanation:
.25 x 4y = Y
36 divided by 4 = 9
In a recent survey of 655 working americans ages 25-34, the average weekly amount spent on lunch was $43.29 with standard deviation $2.75. The weekly amounts are approximately bell-shaped
Answer:
99.7%
Step-by-step explanation:
Given that:
sample size (n) = 655
sample mean ([tex]\overline x[/tex]) = 43.29
Standard deviation [tex]\sigma[/tex] = 2.75
Let's assume we are to estimate the percentage between $33.72 and $51.54
Then;
The test statistics at 33.72 is :
[tex]Z = \dfrac{X - \mu}{\sigma}[/tex]
[tex]Z = \dfrac{33.72 -43.29}{2.75}[/tex]
[tex]Z = -3.48[/tex]
Z at 51.54
[tex]Z = \dfrac{X - \mu}{\sigma}[/tex]
[tex]Z = \dfrac{51.54 -43.29}{2.75}[/tex]
[tex]Z = 3.00[/tex]
Using the empirical standard rule, the percentage will be 99.7%
Rodrigo plans to buy packs of baseball cards until he gets the card of his favorite player, but he only has enough money to buy at most three packs. Suppose that each pack has a 10 % 10%10, percent chance of containing the card Rodrigo is hoping for. The table below displays the probability distribution of X XX, the number of packs of cards Rodrigo buys. X = # of packs X=# of packsX, equals, \#, start text, space, o, f, space, p, a, c, k, s, end text 1 11 2 22 3 33 P ( X ) P(X)P, left parenthesis, X, right parenthesis 0.10 0.100, point, 10 0.09 0.090, point, 09 0.81 0.810, point, 81 Calculate the mean of X XX.
Answer: 2.71 packs
Step-by-step explanation:
answer asap!!! PLS HELP.
what is the value of x in the figure??
a. 90
b. 60
c. 120
d. 30
Answer:
Step-by-step explanation:
the x is 30
60=2x
x=30
Answer:
d
Step-by-step explanation:
its d i think
A: 5x²+3xy +2y B: 2y²-xy +4x²
С: 12xy+4x²-3y. then :- 1) А-В-С , 2) 2A+3B+4C 3)3A-4B--2C. pls help me will mark u as brainliest
Answer:
-3x² -2y² -8xy +5y
34x² + 51xy - 8y + 6y²
7x² - 11xy +12y - 8y²
Step-by-step explanation:
Given:
A: 5x²+3xy +2y
B: 2y²-xy +4x²
С: 12xy+4x²-3y
Find:
1) А-В-С
2) 2A+3B+4C
3) 3A-4B--2C
Computation:
1) А-В-С
5x²+3xy +2y - [2y²-xy +4x²] - [12xy+4x²-3y]
5x²+3xy +2y -2y² +xy -4x² -12xy -4x²+3y
-3x² -2y² -8xy +5y
2) 2A+3B+4C
2[5x²+3xy +2y]+3[2y²-xy +4x²]+4[12xy+4x²-3y]
10x² + 6xy + 4y + 6y² - 3xy + 8x² + 48xy + 16x² - 12y
34x² + 51xy - 8y + 6y²
3) 3A-4B-2C
3[5x²+3xy +2y]-4[2y²-xy +4x²]-2[12xy+4x²-3y]
15x² + 9xy + 6y -8y² + 4xy - 16x² - 24xy - 8x² +6y
7x² - 11xy +12y - 8y²
Select the correct answer from each drop-down menu. Simplify the given polynomial and use it to complete the statement. The polynomial simplifies to an expression that is a with a degree of .
Answer:
The answer is below
Step-by-step explanation:
Select the correct answer from each drop-down menu. Simplify the given polynomial and use it to complete the statement.
(-5x² - 2x + 4) + (8x² - x - 1) + (x + 2)(x - 5)
.The polynomial simplifies to an expression that is a____
A.quadratic
B.liner
C.constany
A.trinomial
B.binomial
C.monomial
with a degree of____
A.1
B.2
C.0
Solution:
A polynomial is an expression involving operations of addition, subtraction, multiplication, exponents which consists of variables and their coefficient. A trinomial is a polynomial consisting of three terms, while a binomial consist of two terms and a monomial consist of one term.
The degree of a polynomial is the highest degree of any of the terms of the polynomial. If it has a degree of 0 it is a constant, a degree of 1 it is linear while for a degree of 2 it is quadratic.
(-5x² - 2x + 4) + (8x² - x - 1) + (x + 2)(x - 5)
= (-5x² - 2x + 4) + (8x² - x - 1) + (x² -5x + 2x - 10)
= (-5x² - 2x + 4) + (8x² - x - 1) + (x² - 3x - 10)
= (-5x² + 8x² + x² - 2x - x - 3x + 4 - 1 - 10)
= 4x² - 6x - 7
Therefore:
.The polynomial simplifies to an expression that is a quadratic trinomial of degree 2.
If the cocoa to water ratio for a hot chocolate recipe is 1 tablespoon cocoa to 1⁄4 cup water, how much cocoa do you need if you use 1.5 cups of water?
3x+9=36
Show your steps
Answer:
x=9
Step-by-step explanation:
3x+9=36
subtract 9 from both sides
3x=27
divide by 3 on both sides
x=9
The solution to the equation 3x + 9 = 36 is x = 9.
To solve the equation 3x + 9 = 36, we'll perform the necessary steps to isolate the variable x on one side of the equation.
Given equation:
3x + 9 = 36
First, we'll subtract 9 from both sides to eliminate the +9 term on the left side:
3x + 9 - 9 = 36 - 9
3x = 27
Next, to isolate the variable x, we divide both sides by 3:
(3x)/3 = 27/3
x = 9
Therefore, the solution to the equation 3x + 9 = 36 is x = 9.
In this equation, we start with an expression involving the variable x and a constant term. By performing algebraic operations, we manipulate the equation to have x on one side and the constant value on the other side. This isolates the variable and provides us with a specific value for x that satisfies the equation. In this case, the value of x is determined to be 9, which can be verified by substituting it back into the original equation to see if it holds true.
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A spherical balloon has a diameter of 4 feet. Approximate how many cubic feet of air this balloon holds. Use 3.14 as an approximation for pie, and give a numerical answer.
Answer:
3.764
Step-by-step explanation:
just try matgs is a tough de partoeanswer my question PLEASE
Answer:
130
Step-by-step explanation:
AP Calc BC help!
Can someone explain how to do these problems? I care more about the explanation than the actual answer! My course never taught me how to do these kinds of problems.
Thank you!!
Answer:
Question 1) 72
Question 2) 40
Question 3) Both C and D.
Question 4) Both A and C.
Step-by-step explanation:
Question 1)
We are given that:
[tex]\displaystyle \int_1^5f(x)\, dx=8\text{ and we want to find} \int_1^5xf'(x)\, dx[/tex]
We will use integration by parts, given by:
[tex]\displaystyle \int_a^b u\, dv=uv-\int_a^b v\, du[/tex]
We will let:
[tex]u=x\Rightarrow du=dx\text{ and } dv=f'(x)\, dx \Rightarrow v=f(x)[/tex]
Therefore:
[tex]\displaystyle \int_1^5xf'(x)\, dx=xf(x)\Big|_1^5-\int_1^5f(x)\, dx[/tex]
Substitute:
[tex]\displaystyle \int_1^5xf'(x)\, dx=(5(f(5))-(1(f(1))-(8)[/tex]
Evaluate:
[tex]\displaystyle \int_1^5xf'(x)\, dx=75-(-5)-8=72[/tex]
Question 2)
Similarly, we will let:
[tex]\displaystyle u=x\Rightarrow du=dx\text{ and } dv=f'(x)\, dx \text{ so } v=f(x)[/tex]
Hence:
[tex]\displaystyle \int_0^3 xf'(x)\, dx=xf(x)\Big|_0^3-\int_0^3f(x)\, dx[/tex]
Evaluate:
[tex]\displaystyle \int_0^3 xf'(x)\, dx=(3f(3))-(0(f(0))-(2)[/tex]
Thus:
[tex]\displaystyle \int_0^3 xf'(x)\, dx=3(14)-2=40[/tex]
Question 3)
We are given:
[tex]\displaystyle g(x)=\int_4^xf(x)\, dx[/tex]
By the Fundamental Theorem of Calculus:
[tex]g'(x)=f(x)>0[/tex]
The derivative of g is always positive. So, the values of g are always increasing.
The tables that reflect this are C and D.
And there are, as I understand it, no way to determine their exact values. Both C and D are correct.
Question 4)
Similarly, we are given:
[tex]\displaystyle g(x)=\int_{-2}^xf(x)\, dx[/tex]
By the FTC:
[tex]g'(x)=f(x)<0[/tex]
So, g should be decreasing for all x.
The tables that reflect this are A and C.
So, both A and C are correct.
Find the slope of the line represented by the table of values.
A)
12
5
B)
D)
Answer:
B 4456448444424346464646464664646464
Round 26,127 to the nearest hundred.
5 or more add 1
4 or less stays the same
solve : 105/103 = _____
Answer:
1.02
Step-by-step explanation:
I don't understand how to do this problem 3x + y =9
Answer:
35
Step-by-step explanation:
helpp PLSSS 20 PONITS!!
Answer:
c I think
Step-by-step explanation:
can you help me with this question In Lines 23 and 24 of his poem "Chicago", Sandburg uses which poetic device? A Simile - a comparison of two unlike things using "like" or "as" B. Metaphor - a comparison of two unlike objects C. Repetition
Answer: 20
Step-by-step explanation: I LOVE THIS I HATE THIS I CAN SEE THIS SO I JUST GEUSSED HOPE IT IS RIGHT BYE
A number is multiplied by 6, and the result is 48.6.
Answer:
8.1
Step-by-step explanation:
We denote the number as x.
6 * x = 48.6
We can divide both sides by 6 to get,
x = 8.1
Answer:
8.1
Step-by-step explanation:
Let the unknown number be n. Translating this statement into symbols, we get:
6n = 48.6
Solving for n by dividing both sides by 6, we get n = 8.1
The number is 8.1
can someone help me plz
Answer:
Step-by-step explanation:
(2-4x)+(2-4x)+(-2x+8)=12-10x
2/7 of the person at a concert are children 1/4 and men and the rest women what fraction are women
Answer:
15/28 are women
Step-by-step explanation:
2/7 + 1/4 + x = 100%
2/7+1/4= 15/28
9514 1404 393
Answer:
13/28
Step-by-step explanation:
The fraction that are women is found by subtracting the given fractions from 1.
1 - 2/7 - 1/4 = 28/28 -8/28 -7/28 = (28 -8 -7)/28 = 13/28
The fraction that are women is 13/28.
What are the answers
2x = 10; x=?
-3x = 21;x=?
1/3x=6; x=?
-1/2x = -7;x?
Answer:
1) 5 2)7 3)18 4) 14
Step-by-step explanation:
A 17 -ft ladder leans against a building so that the angle between the ground and the ladder is 79 .
Answer:
3.24 feet
Step-by-step explanation:
A 17 -ft ladder leans against a building so that the angle between the ground and the ladder is 79 . Find the distance between the building and the ladder
We solve the above question using the Trigonometric function of Cosine
cos x = Adjacent/Hypotenuse
Adjacent = x feet
Hypotenuse = 17 ft
The angle = 79°
Hence,
cos 79 = x/17
Cross Multiply
x = cos 79 × 17
x = 3.2437529214.feet
Approximately = 3.24 feet
Therefore, the distance between the ladder and the building = 3.24 feet
1/4t-6=-4
What does t equal?
Answer:
t = 8
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 EqualityStep-by-step explanation:
Step 1: Define
1/4t - 6 = -4
Step 2: Solve for t
[Addition Property of Equality] Add 6 on both sides: 1/4t = 2[Division Property of Equality] Divide 1/4 on both sides: t = 8Answer:
t=8
Step-by-step explanation:
1/4 = 0.25
0.25t - 6 = -4
0.25t = -4 + 6
0.25t = 2
t = 2/0.25
t = 8