The solution to the equation are as follows.
y = c₁[tex]e^{\sqrt{-3 -sin²(x)x} }[/tex] + c₂ [tex]e^{\sqrt{-3 -sin²(x)x} }[/tex]
What is differential equation?
In arithmetic, a equation is associate equation that relates one or a lot of unknown functions and their derivatives.
Main body:
Find the first derivative.
dy/dx=r[tex]e^{rx}[/tex]
Find the second derivative.
d²y/dx² =r² [tex]e^{rx}[/tex]
Substitute into the differential equation.
r²[tex]e^{rx}[/tex]+4[tex]e^{rx}[/tex]=cos ²x
Factor [tex]e^{rx}[/tex]out of r²[tex]e^{rx}[/tex].
[tex]e^{rx}[/tex]r²+4[tex]e^{rx}[/tex]=cos²x
Factor [tex]e^{rx}[/tex] out of 4[tex]e^{rx}[/tex].
[tex]e^{rx}[/tex]r²+[tex]e^{rx}[/tex]⋅4=cos²x
Factor out of [tex]e^{rx}[/tex]r²+4[tex]e^{rx}[/tex]
[tex]e^{rx}[/tex](r²+4)=cos²x
Since exponentials can never be zero, divide both sides by
[tex]e^{rx}[/tex]r²+4=cos²x
Use the double-angle identity to transform
cos²x to 1−sin²(x).
r² +4=1−sin²(x)
Subtract 4 from both sides of the equation.
r²=1−sin²(x)−4
Simplify the right side.
r² = -3 -sin²x
r = √-3 -sin²x
By the principle of superposition, the general solution is a linear combination of the two solutions for a second order homogeneous linear differential equation.
y = c₁[tex]e^{\sqrt{-3 -sin²(x)x} }[/tex] + c₂
Hence the differential solution is as follows.
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5. Which of the following shows the complete factoriza
O A. x(x² + 3x)
O B. x²(x² + 3)
O C. x²(x-3)
O D. x²(x + 3)
Answer:
D
Step-by-step explanation:
x³ + 3x² ← factor out x² from each term
= x²(x + 3)
Given f(x) = 2x^2 - 3x -12, find f(7).
Answer:
Step-by-step explanation:
Richard buys 13 pizzas for £54.08. If all the pizzas are the same price,
how much does one pizza cost? Give your answer in pounds (£).
Answer: 4.16 per pizza
Step-by-step explanation: 54.08 divided by 13 is 4.16
2 ounces is how many grams? Hint: 1oz≈28.3g
Answer: 56.70 g
Step-by-step explanation:
IXL Help Please Fast!
Answer:
y = -3/8 x - 4
Step-by-step explanation:
y-(-7) = -3/8 (x-8)
y+7 = -3/8x + 3
y = -3/8 x +3 - 7
y = -3/8 x -4
need answer asap. pls tyy
Answer:
1. [tex]\frac{6}{11}[/tex] × [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{22}[/tex]
2. [tex]4\frac{1}{3}[/tex] × [tex]\frac{9}{14}[/tex] = [tex]\frac{13}{3}[/tex] × [tex]\frac{9}{14}[/tex]
= [tex]\frac{39}{14}[/tex]
= [tex]2\frac{11}{14}[/tex]
3. [tex]3\frac{3}{6}[/tex] × [tex]\frac{2}{3}[/tex] = [tex]\frac{21}{6}[/tex] × [tex]\frac{2}{3}[/tex]
= [tex]\frac{7}{3}[/tex]
= [tex]2\frac{1}{3}[/tex]
4. [tex]\frac{6}{15}[/tex] ÷ [tex]\frac{2}{5}[/tex] = [tex]\frac{6}{15}[/tex] × [tex]\frac{5}{2}[/tex]
= 1
5. [tex]1\frac{4}{5}[/tex] ÷ [tex]\frac{3}{25}[/tex] = [tex]\frac{9}{5}[/tex] × [tex]\frac{25}{3}[/tex]
= [tex]\frac{45}{3}[/tex]
= 15
Adding and Subtracting Functions
The value of addition for the equation (f + g) (-2) is 15 and the value of subtraction for the equation (f + g) (-2) is 39.
A function is a relationship that assigns exactly one output value to each input value. Like numbers and polynomials, functions can be added, subtracted, multiplied, and divided to create new functions. Here are the rules for performing these operations on functions.
Let f(x) and g(x) be two functions:
Addition:
We can add two functions:
(f + g)(x) = f(x) + g (x) ...... (1)
Given that:
f(x) = 5x^2 + 7
g(x) = 3x - 6
Putting the value of f(x) and g(x) in equation (1).
(f + g)(x) = 5x^2 + 7 + 3x - 6
(f + g)(x) = 5x^2 + 3x + 1 .......(2)
We have to evaluate the value of (f + g) (-2). Therefore, put the value of x = -2 in equation (2). We get,
(f + g) (-2) = 5 (-2)^2 + 3 x -2 + 1
(f + g) (-2) = 20 - 6 +1
(f + g) (-2) = 15
Hence, for the addition of the equation (f + g) (-2) the value is equal to 15.
Subtraction:
We can add two functions:
(f - g)(x) = f(x) - g (x) ...... (3)
Given that:
f(x) = 5x^2 + 7
g(x) = 3x - 6
Putting the value of f(x) and g(x) in equation (3).
(f - g)(x) = 5x^2 + 7 - (3x - 6)
(f - g)(x) = 5x^2 + 7 - 3x + 6
(f - g)(x) = 5x^2 - 3x + 13 ....... (4)
We have to evaluate the value of (f - g) (-2). Therefore, put the value of x = -2 in equation (4). We get,
(f - g)(-2) = 5(-2)^2 - 3(-2) + 13
(f - g)(-2) = 5 x 4 + 6 + 13
(f - g)(-2) = 20 + 6 + 13
(f - g)(-2) = 39
Hence, for the subtraction of the equation (f - g) (-2) the value is equal to 39.
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Delaney would like to make a 5 lb but mixture that is 60% peanuts and 40% almonds. she has several kinds of peanuts and several kinds of a mixture that is 20% peanuts and 80% almonds. let p represent the number of punts of peanuts needed to make the mixture, and let m represent the number of pounds of the 80% almond-20% peanut mixture. What is the system that models this situation
a) The ratio system that models this situation which has an equation.
0.20 m + 1 (5 m) = 0.60 x (5)
0.80 m + 0 (5 m) = 0.40 x (5)
b) The system solution is:
m = 2.5 lb
p = 5-m = 2.5 lb
This is a mixing issue.
Mixture A of 20% peanuts + 80% almonds
Let's call the 100% peanut mixture B and the mixture C of 60% peanuts + 40% almonds
Adding mixture A and mixture B together gives mixture C, so we know that the pounds of mixture A and mixture B is 5 lb.
Let m be the amount in pounds of the 20% peanut and 80% almond mixture or mixture A
When 5-m = p is the amount of mixture B in pounds.
The system of equations that models this situation is, therefore:
0.20 m + 1 (5 m) = 0.60 x (5) ...... (1)
0.80 m + 0 (5 m) = 0.40 x (5) ...... (2)
Solving any of the above equations we find the value of m = 2.5 lb
Amount of mixture A in pounds = 2.5 lb
Amount of mixture B in pounds = 5-2.5 = 2.5 lb
The system solution is:
m = 2.5
p = 2.5
So, we can make 5 lbs of mixture C (60% peanuts + 40% almonds) from 2.5 lbs of mixture A (20% peanuts + 80% almonds) and 2.5 lbs of mixture B (100% peanuts).
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If 1=3
2=3
3=5
4=4
5=4
Then, 6=?
The value of 6 is equal to 3.
Given that:
If 1=3, 2=3, 3=5, 4=4, 5=4.
So, we have to find the value of 6.
To calculate the value of 6 we have to think logically.
Looking at this question logically,
1 is written as ONE, so it contains three alphabets.
2 is written TWO, so it contains three alphabets.
3 is written as THREE, so there are 5 alphabets.
4 is written as FOUR, so it contains four alphabets.
5 is written as FIVE, so it contains four alphabets.
6 is written as SIX, so it contains three alphabets.
So, in this way, 6 can be written as 3.
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PT:1
Use the results from a survey of a simple random sample of 1014 adults. Among the 1014 respondents, 84% rated themselves as above average drivers. We want to test the claim that 4/5 of adults rate themselves as above average drivers. Complete parts (a) through (c).
a. Identify the actual number of respondents who rated themselves as above average drivers.
The actual number of respondents who rated themselves as above average drivers is 852 and we can conclude that the proportion respondents who rated themselves as above average drivers is greater than 0.5007.
Given that, 84% of the sample of 1014 adults rated themselves as above average drivers.
What is random sampling?In statistics, a simple random sample is a subset of individuals chosen from a larger set in which a subset of individuals are chosen randomly, all with the same probability. It is a process of selecting a sample in a random way.
Now,
84% of 1014
= 0.84×1014
= 851.76
≈ 852
Thus, the actual number of respondents who rated themselves as above average drivers is 852.
At the null hypothesis, we test if the proportion is 4/5 =0.8, that is
[tex]H_0:p=0.8[/tex]
At the alternative hypothesis, we test if the proportion is greater than 80%, that is:
[tex]H_0:p\ge0.8[/tex]
The test statistic is given by
[tex]z=\frac{\bar{p}-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]
In which:
[tex]$\bar{p}$[/tex] is the sample proportion.
p is the proportion tested.
n is the size of the sample.
In this problem, the parameters are [tex]$\bar{p}$[/tex]=0.84, p=0.8 and n=1014
Thus, the value of the test statistic is
[tex]z=\frac{0.84-0.8}{\sqrt{\frac{0.8(1-0.8)}{1014} } }[/tex]
= 0.04/0.0125
z=3.2
0.4993
So, 1-0.4993=0.5007
Therefore, the actual number of respondents who rated themselves as above average drivers is 852 and we can conclude that the proportion respondents who rated themselves as above average drivers is greater than 0.5007.
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A fish tank is being drained at a constant rate. The graph shows the linear relationship between the volume of water in the fish tank in liters and the time in minutes the tank has been draining.
The rate of change in the volume of water will be -6 L/min in the fish tank. which is the correct answer would be an option (A).
The given graph shows the linear relationship between the volume of water in the fish tank in liters and the time in minutes the tank has been draining.
To determine the rate of change in the volume of water in the fish tank
The rate of change in the volume of water is equal to the slope of the given linear function.
As per the given graph, we take two points (0, 60) and (10,0)
The slope of the linear function = (0 - 60) / (10 - 0)
The slope of the linear function = -60/10
The slope of the linear function = -6
Therefore, the rate of change in the volume of water will be -6 L/min in the fish tank.
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The question seems to be incomplete the correct question has been attached below.
y ≥ 2x+4
y≤ - x² +6
Need to list all points of intersection from system of inequalities
Answer:
Step-by-step explanation:
The intersection consists of the elements that are contained in all of the intervals.
(-2, 2) (-1, 4) (0, 6)
Correct me if im wrong
HELPPPP GUYSSS PLEASE PLEASE PLEASEEEEEEEEEE
Answer:
b
Step-by-step explanation:
A gym scores their clients on a scale of 1-100 and claims that they can help their clients improve on their
exercises. After two months with a gym membership, eleven gym members are assessed to see how much
they have improved on their exercises.
Here are two different data displays of the same data that represent how much the eleven gym members hav
improved.
Answer:
u need a chart image
Step-by-step explanation:
A page in a photo album holds
6 pictures. A photographer fills
9 pages with pictures. How many
pictures were put in the album
Answer: 54, if there are 9 pages with 6 photos each, then you would do 6 x 9 = 54.
Answer:
54 pictures
Step-by-step explanation:
9 pages, 6 pictures in each page, 9*6=54
Solve the equation 2.3y - 4.2 = -18 for y.
Answer:
y=-6
Step-by-step explanation:
2.3y - 4.2 = -18
+4.2 +4.2
---------------------------
2.3y = -13.8
divide by 2.3 on both sides
y = -6
The value of y for the given equation, 2.3y - 4.2 = -18 will be 6.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, the equation is 2.3y - 4.2 = -18.
We have to simplify the equation in order to find the value of y as,
2.3y - 4.2 = -18.
Rearrange the equation as
2.3y= -18+4.2
2.3y= -13.8
y= -13.8/2.3
y= 6
Thus, the value of y for the given equation, 2.3y - 4.2 = -18 will be 6.
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PLEASE HELP
The smallest number with exactly three
different prime factors is 30.
The prime factors of 30 are 2, 3 and 5.
What is the smallest number with exactly
four different prime factors?
210 is the smallest number with exactly four different prime factors.
Prime factors:
In math, the natural number, other than 1, whose only factors are 1 and itself. And the first few prime numbers are actually 2, 3, 5, 7, 11, and so on.
Given,
The smallest number with exactly three different prime factors is 30.
The prime factors of 30 are 2, 3 and 5.
Here we need to find the smallest number with exactly four different prime factors.
While we looking into the given question we have identified that the first three smallest prime factors are,
=> 2, 3 and 5
Now, we have to identify the fourth prime factor,
According to the definition of the prime factors, we have identified that the fourth prime factor is 7.
So, the number is calculated as,
=> 2 x 3 x 5 x 7
=> 210.
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a number divisible by 3, then drawing a 1
The numbers which are divisible by 3 are 6, 6, 6, and 9.
What is the divisibility of 3?
The rule of three states that a number is completely divisible by three if the sum of its digits is divisible by three.
Consider the number 308: To determine whether 308 is divisible by three, add the digits together (i.e. 3+0+8= 11). Check to see if the total is divisible by three.
From the given numbers the numbers which are divisible by 3 are:
6, 6, 6, and 9.
Hence, The numbers which are divisible by 3 are 6, 6, 6, and 9.
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factor the expression below completely
x^-1/2+x^-3/2+x^-5/2
After simplification, the factor of the expression [tex]x^{-1/2}+x^{-3/2}+x^{-5/2}[/tex] is [tex]\frac{x^2+x+1}{x^{5/2}}[/tex].
In the given question,
We have to factor the expression [tex]x^{-1/2}+x^{-3/2}+x^{-5/2}[/tex].
The given expression is [tex]x^{-1/2}+x^{-3/2}+x^{-5/2}[/tex].
The given all term having negative power. So make the term in positive we can write it as
[tex]x^{-1/2}+x^{-3/2}+x^{-5/2}=\frac{1}{x^{1/2}}+\frac{1}{x^{3/2}}+\frac{1}{x^{5/2}}[/tex]
Taking 1/[tex]x^{1/2}[/tex] from the left side
[tex]x^{-1/2}+x^{-3/2}+x^{-5/2}=\frac{1}{x^{1/2}}(1+\frac{1}{x}+\frac{1}{x^2})[/tex]
Now solving the bracket by multiply and divide [tex]x^2[/tex] in each term.
[tex]x^{-1/2}+x^{-3/2}+x^{-5/2}=\frac{1}{x^{1/2}}(1\times\frac{x^2}{x^2}+\frac{1}{x}\times\frac{x^2}{x^2}+\frac{1}{x^2}\times\frac{x^2}{x^2})[/tex]
[tex]x^{-1/2}+x^{-3/2}+x^{-5/2}=\frac{1}{x^{1/2}}(\frac{x^2}{x^2}+\frac{x}{x^2}+\frac{1}{x^2})[/tex]
Simplifying the bracket
[tex]x^{-1/2}+x^{-3/2}+x^{-5/2}=\frac{1}{x^{1/2}}(\frac{x^2+x+1}{x^2})[/tex]
[tex]x^{-1/2}+x^{-3/2}+x^{-5/2}=\frac{x^2+x+1}{x^{5/2}}[/tex]
Hence, the factor of the expression [tex]x^{-1/2}+x^{-3/2}+x^{-5/2}[/tex] is [tex]\frac{x^2+x+1}{x^{5/2}}[/tex].
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Triangle D E F is shown. Angle E D F is a right angle. The length of D E is 8 and the length of hypotenuse E F is 10.
Given right triangle DEF, what is the value of sin(E)?
Answer: sin(E) = 0.6
Step-by-step explanation:
10² = DF² + 8² ( Pythagoras theorem)
100 = DF² + 64
DF² = 36
DF = 6
sin(E) = opposite side/ Hypotenuse
= DF/EF
= 6/10 = 3/5 = 0.6
A roller coaster traveling 20.0 m/s decelerates to 2.0 m/s in 6.0 s as it climbs a hill. Calculate the magnitude of its deceleration.
The roller coaster has a deceleration of 3 meters per second.
How to determine the deceleration experimented by the roller coster
In this problem we need to calculate the magnitude of the deceleration experimented by the roller coster, which is under uniform accelerated motion. This can be easily found by means of the following formula:
a = (v' - v) / t
Where:
v - Initial speed of the roller coster, in meters per second. v' - Final speed of the roller coster, in meters per second.t - Time, in seconds.If we know that v = 20 m / s, v' = 2 m / s and t = 6 s, then the magnitude of the deceleration of the roller coster is:
a = [(2 m / s) - (20 m / s)] / 6 s
a = - 18 m / s / 6 s
a = - 3 m / s²
The magnitude of deceleration is 3 meters per square second.
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An equation perpendicular to y = x + 3 through the point
(4, -1)
Find the negative reciprocal of the original line and use point slope formula y-y1=m(x-x1) to find the perpendicular line.
y= -x+3
A painter leans a ladder against a vertical wall. The top of the ladder is 7 meters above the ground. When the bottom of the ladder is moved 1 meter
farther away from the wall, the top of the ladder is now 5 meters above the ground. What is the length of the ladder?
O There is not enough information to solve this problem.
O the ladder is 7.89 meters long
O the ladder is 8.60 meters long
O the ladder is 13.46 meters long
The length of ladder is 11.5 m.
What is arithmetic?
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Main body:
Let the length of ladder = y
And distance of bottom of ladder from the wall = X
According to the given,
Length of ladder y =
√(7² + x²)
Since, the bottom of the ladder is moved 1 meter farther away from the wall, so
Length of ladder y = √(5² +(x+1)²)
as in both equation y is equated
√(7² + x²) = √(5² +(x+1)²)
square root will get cancel on both sides
(7² + x²) = (5² +(x+1)²)
49 + x² = 25 + x² +1+2x
cancelling x² on both sides
49 = 26 +2x
2x = 23
x =11.5 meters
Hence the length of ladder is 11.5 m
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The linear function m = 200 − 50v represents the amount m (in dollars) of money that you have after buying v video games. a. Interpret the terms and coefficient in the equation. b. Find the domain of the function. Is the domain discrete or continuous? Explain. c. Graph the function using its domain.
a. The function m = 200 - 50v is interpreted as
m = amount left
200 = amount available for buying video games
50 = cost per video game
v = number of video games
b. The domain of the function is 0 < v ≤ 4
the domain is discrete
c. explanation of the graph is below
How to fine the domain of the graphIn the graph, the input values is the number of video games, v while the output value is amount, m(in dollars) left for buying games.
The domain is controlled by the input values. considering the amount set out for games which is 200 we solve for v at zero amount
0 = 200 - 50v
50v = 500
v = 4
The maximum number of video games the amount can buy is 4. For the minimum we can not buy 0 video game but the graph can show amount available before buying the game.
The domain starts from 0, with 0 not inclusive to 4 with 4 included
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Use the Pythagorean theorem to find the unknown side of the right triangle.
√7
√9
A. 2
B.√16
C. 16
D. √2
Answer:
B
Step-by-step explanation:
because im smart :) give me brainliest or else
Number of ounces in a juice box is an example what kind of data?
O Categorical
O No answer text provided.
No answer text provided.
Quantitative
Number of ounces in a juice box is an example of quantitative.
What is Quantity?
A property called quantity or amount can take the form of a plurality or magnitude, which shows both discontinuity and continuity. Comparing quantities can be done by using phrases like "greater," "less," or "equal," as well as by assigning a numerical value that is a multiple of the unit of measurement.
Let the number of ounces in a juice box means, there are number of ounces in a box.
The term "number of" is referred as quantity.
Therefore, the number of ounces in a juice box is an example of quantitative.
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if you horizontally stretch the quadratic parent function, f(x)=x^2, by a factor of 5, what is the equation of the new function?
Answer:
f(x)=5(x^2)
Step-by-step explanation:
Find the product of (3 x 10 9) and (2 x 10 9). Write the final answer in scientific notation.
6 x 10 81
6 x 100 18
6 x 10 18
6 x 10 9
Product of the given expression (3 x 10⁹) and (2 x 10⁹) in the scientific notation is given by 6 x 10¹⁸.
As given in the question,
Given expression is equal to :
(3 x 10⁹) and (2 x 10⁹)
Apply law of indices of multiplication to get the product of the given expression
mᵃ × mᵇ = mᵃ⁺ᵇ
Product of the given expression (3 x 10⁹) and (2 x 10⁹) in the scientific notation is equal to
(3 x 10⁹) and (2 x 10⁹)
= ( 3 × 2 ) × ( 10⁹ × 10⁹ )
= 6 × 10⁹ ⁺ ⁹
= 6 × 10¹⁸
Therefore, product of the given expression (3 x 10⁹) and (2 x 10⁹) in the scientific notation is given by 6 x 10¹⁸.
The complete question is:
Find the product of (3 x 10⁹) and (2 x 10⁹). Write the final answer in scientific notation.
6 x 10⁸¹
6 x 100¹⁸
6 x 10¹⁸
6 x 10⁹
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Mohan and Eve have recently got married and decided to merge their finances.
Mohan has 2 current accounts, the first has a balance of $101.46.
The second has -$21.21.
Eve's current account balance is -$45.91.
Which account has the lowest balance?
Select...
When they merge their accounts, what will their total balance be?
$
Eve has a savings account with $231.56 in it. She wants to buy a new coat at $75.00. She calculates that she will have $156.56
remaining.
Which sum could she use to check she is right? Select...
The total amount after merging their account will be $34.34.The sum of $75 + $156.56 will make $231.56.
What is summation?A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities. Here are always an integer number of terms in a summation. There could be only two terms, but there could be one hundred, a thousand, or a million. There are summations with an infinite set of parameters.
As per the given,
Mohan has 2 current accounts, the first has a balance of $101.46.
The second has -$21.21.
Total amount of Mohan = 101.46 - 21.21 = $80.25
Eve's balance = -$45.91
Combined balance = $80.25 - $45.91 = $80.25
As per the given,
Eve has a savings account with $231.56 in it. She wants to buy a new coat for $75.00. She calculates that she will have $156.56
$231.56 = $156.56 - $75
$231.56 + $75 = $156.56
Hence "The total amount after merging their account will be $34.34.The sum of $75 + $156.56 will make $231.56".
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Two children share 2 1/2 chocolate bars with each child getting the same amount how much does each child get?
Answer:
1 1/4
Step-by-step explanation:
2 divided by 2 is 1.
1/2 or 0.5 divided by 2 is 0.25. this is equal to 1/4.
Answer: 1 [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
First of all, we need to multiply 2 [tex]\frac{1}{2}[/tex] by 1/2.
But to do that, we need to turn 2 [tex]\frac{1}{2}[/tex] into an improper fraction.
First of all, we need to multiply the whole number by the denominator, which is 2 x 2, to get 4.
Now, we need to add the numerator to our product, which is 4 + 1.
This gives us the improper fraction of 5/2.
Now, we need to multiply 5/2 by 1/2.
To do this, we need to multiply across.
5 x 1 = 5
2 x 2 = 4
This gives us 5/4.
Now, we turn it into a mixed number.
5/4 is 1 [tex]\frac{1}{4}[/tex].
This gives us our final answer of 1 [tex]\frac{1}{4}[/tex]
