The general soultion of the given differential equation 12y'' − 5y' − 3y = 0 is
y = [tex]c_{1}e^{\frac{-1}{3}x } +c_{2}e^{\frac{3}{4} x}[/tex].
According to the given question.
We have a differential equation
[tex]12y^{"} -5y^{'} -3y = 0[/tex]
The above equation can be written as
[tex](12D^{2} -5D -3)y = 0[/tex]
The auxillary equation for the above differential equation is
[tex]12m^{2} -5m-3 = 0[/tex]
[tex]\implies 12m^{2} -9m+4m -3 = 0[/tex]
⇒ 3m(4m - 3) +1(4m - 3) = 0
⇒ (3m + 1)(4m -3) = 0
⇒ m = -1/3 or 3/4
Therefore,
[tex]C.f = c_{1}e^{\frac{-1}{3}x } +c_{2}e^{\frac{3}{4} x}[/tex]
Here, P.I = 0
As we know that the general solution of the differential equation is given by
y = PI + CF
Thereofre, the general soultion of the given differential equation 12y'' − 5y' − 3y = 0 is
y = [tex]c_{1}e^{\frac{-1}{3}x } +c_{2}e^{\frac{3}{4} x}[/tex].
Find out more information about general solution of the differential equation here:
https://brainly.com/question/4537000
#SPJ4
Thomas and Matthew are saving up money to buy a video game together. Thomas has saved $30. Matthew has saved $35. How much money have they saved up together in total?
Answer: $65
Step-by-step explanation:
Thomas saved $30
Matthew saved $35
Saved up together in total is asking how much money they got together which addtion.
so we do 30 +35 which is $65
Use the drawing tools to graph the solution to this system of inequalities on the coordinate plane. y > 2x + 4 x + y ≤ 6 I really need help can someone do it a put the prove that they got it right on edmetom the exact graph
The solution to the system of inequalities y > 2x + 4 and x + y ≤ 6 on the coordinate plane is the darker region shown in the graph.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Inequalities is an expression that shows the non equal comparison of two or more numbers and variables.
The solution to the system of inequalities y > 2x + 4 and x + y ≤ 6 on the coordinate plane is the darker region shown in the graph.
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
2t - 9 - 6t + 2 i really need help
Answer:
-4t-11
Step-by-step explanation:
rearrange the numbers
2t-6t-9+2
Add negative 2
2t-6t-11
2-6
-4t-11
Select the correct answer!
Help asap thanks
The area of the shaded region is 3.125π - 6. The correct option is E. 3.125π - 6
Calculating areaFrom the question, we are to determine the area of the shaded region
The area of the shaded region = Area of the semicircle - Area of the triangle
First, we will determine the diameter, d, of the semicircle
d² = 3² + 4² (Pythagorean theorem)
d² = 9 + 16
d² = 25
d = √25
d = 5
∴ Diameter of the semicircle is 5
Thus,
Radius, r = 5/2 = 2.5
Now,
Area of the shaded region = 1/2(π×2.5²) - 1/2(3×4)
Area of the shaded region = 1/2(π×6.25) - 1/2(12)
Area of the shaded region = 3.125π - 6
Hence, the area of the shaded region is 3.125π - 6. The correct option is E. 3.125π - 6
Learn more on Calculating area here: https://brainly.com/question/14989383
#SPJ1
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Solve the equation .
The solution of the equation is x =
.
In the expression written below. the value of equation x is known to be x=10/c.
What is the equation about?From the question, we were given: 3(cx-7)=9
Therefore, we have to simply it to make x the subject of the formula (to look for x)
Hence: 3(cx-7)=9
=(cx-7)=3
=cx=10
x=10/c
Therefore, In the expression written below. the value of equation x is known to be x=10/c.
See full question below
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Solve the following equation for x, and express its value in terms of c. 3(cx-7)=9
Learn more about numerals from
https://brainly.com/question/1827193
#SPJ1
How many numbers from 100 to 999 have exactly one zero digit
Answer:
180.
Step-by-step explanation:
100 contains 2 zero digits.
101 - 109 have 9 numbers, 110 to 200 have 11 numbers
so for 101 to 200 its 20 numbers
Its also 20 for 201 to 300 and for all sets of 100 up to 900.
- that is 7 * 20 = 140 numbers
Finally from 901 to 999 we have 18.
Total = 20 + 140 + 18
= 2 + 20 + 140 + 18
= 180.
There is a balcony that forms part of a circle around a stage, and they need to put up a safety railing. How long of a railing do they need if the radius of the circle is 40 feet, and the arc takes up 45°? Use 3.14 for pi.
A sector is a part of a circle that is formed by two radii, and an arc. So that the length of the safety railing required is 31.4 feet.
A sector is a part of a circle that is formed by two radii, and an arc, thus forming a central angle.
Thus the required length of safety railing can be considered as the arc of the sector.
So that;
length of an arc = (θ / [tex]360^{o}[/tex]) * 2[tex]\pi[/tex]r
where θ is the measure of the central angle of the sector, and r is the radius of the sector.
From the given question, θ = 45°, and r = 40 feet.
So that,
length of the safety railing = (45° / [tex]360^{o}[/tex]) * 2 * 3.14 * 40
= 0.125 * 2* 3.14* 40
length of safety railing = 31.4
Therefore, the length of the safety railing required is 31.4 feet.
For more clarifications on the length of an arc, visit: https://brainly.com/question/2005046
#SPJ1
what is the equivalent expression (3*5)^6=?
Answer:
15^6
Step-by-step explanation:
According to BODMAS
where;
B - Bracket ()
O - Off (*)
D - Division (/)
M - Multiplication (*)
A - Addition (-)
S - Subtraction (+)
Bracket should be solved first
therefore;
(3*5)^6
15^6 = 11390625
Which can be approximately in standard form written as 1.1*10^7
Here are the scores of 18 students on a history test. 55, 57, 58, 61, 62, 66, 68, 68, 71, 75, 75, 78, 82, 83, 85, 86, 88, 89. Notice that the scores are ordered from least to greatest. Make a box-and-whisker plot for the data.
The box-and-whisker plot for the given data is given below:
A box and whisker plot is defined as a graphical method of displaying variation in a set of data.
The results of a history test taken by 18 students: 55, 57, 58, 61, 62, 66, 68, 68, 71, 75, 75, 78, 82, 83, 85, 86, 88, 89.
Take note of how the scores are listed from lowest to highest.
The median for the given data is 73.
The Lower Quartile and the Upper Quartile would be found after that.
These represent the lower and higher halves' medians.
Lower quartile = 61.75
Upper quartile = 83.5
Make a number line. Mark your median, quartiles, and smallest and largest values.
Learn more about box-and-whisker plot here:
https://brainly.com/question/27849170
#SPJ1
Solve the following equation for a. t=G/a+h
Answer:
t = G/(a + h)
t(a + h) = G
a + h = G/t
a = (G/t) - h
t = (G/a) + h
t - h = G/a
a(t - h) = G
a = G/(t - h)
The quotient equals the divisor, then the dividend equals the
(A) √divisor
(B) divisor
(C) divisor²
(D) quotient
Question #1) x4 = 256 solve for x
In the given equation the value of x is 4.
According to the statement
we have given that the a equation and we have to solve that equation for x and find the value of the x.
So, For the value of x in given statement:
The given equation is
x⁴ = 256
we know that the 2 changes into the square root after rearrangement in the equation so, the equation become
(x²)² = 256
Now,
(x²) = √256
Then equation becomes
(x²) = 16
This is because the square root of the 256 is 16.
Now another square changes into square root then
x = √16
And
x = 4
So, In the given equation the value of x is 4.
Learn more about Square root here
https://brainly.com/question/98314
#SPJ1
Carmen has taken out a loan for $800 to buy a car. she plans to pay back the loan at a rate of $40 per month. ramona has borrowed $500 to buy a car, which she plans to pay back at a rate of $20 per month. how long will it take ramona to pay back her loan? a. 25 months b. 20 months c. 15 months d. 10 months please select the best answer from the choices provided a b c d
Answer:a
Step-by-step explanation: 20 x 25=500
Bentley's family took a road trip to the Grand Canyon. Bentley fell asleep 59% of the way through the trip. If the total length of the trip was 300 miles, how many miles had they travelled when Bentley fell asleep?
Answer:177
Step-by-step explanation:so for short, you need to multiply the 300 miles with the 59 precent we have and divide it to 100 this provides us the answer of miles he slept through the road trip
The number of miles they had travelled when Bentley fell asleep is 177 miles.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, Bentley fell asleep 59% of the way through the trip.
The total length of the trip was 300 miles.
The number of miles
= 59% of 300
= 59/100 ×300
= 59×3
= 177 miles
Therefore, the number of miles they had travelled when Bentley fell asleep is 177 miles.
To learn more about the percentage visit:
brainly.com/question/24159063.
#SPJ2
find PQ if possible
Answer: 11 units
Step-by-step explanation:
We can say that [tex]\triangle TSQ\sim\triangle PSR[/tex] by AA Similarity Postulate. This is since [tex]\angle T\cong\angle P[/tex] and both ∠TSQ and ∠RSP are right angles, making them congruent.
Similar triangles have a property that corresponding sides are proportional. Hence, we can say that
[tex]\frac{ST}{PS}=\frac{SQ}{SR}\\\frac{15}{PS}=\frac{9}{12}\\\frac{15}{PS}=\frac{3}{4}\\60=3*PS\\PS=20[/tex]
We also know that PS is the combined length of PQ and QS. Since we know that QS is 9, let's substitute PQ + 9 in and solve.
[tex]PQ+9=20\\PQ=11[/tex]
What is the independent variable in the following function?
The independent variable of f(c) = -3c + 9 is c
What are variables?Variables in an equation are the unknown parameters of the equation that change in values
There are two types of variables
Dependent variableIndependent variableHow to determine the independent variable?The equation of the function is given as
f(c) = -3c + 9
The dependent variable is the output of the function, while the independent variable is the input of the function
For the function, f(c) = -3c + 9
The input variable is c
Hence, the independent variable of f(c) = -3c + 9 is c
Read more about variables at:
https://brainly.com/question/3764906
#SPJ1
What is the interquartile range of the set of data this box-and-whisker plot represents?
Answer:
3
Step-by-step explanation:
The interquartile range is where the 2nd and 5th dots are, on the opposite ends of the square, from 15-18.
Answer:
3
Step-by-step explanation:
The interquartile range (IQR) is the difference between the upper quartile (Q₃) and the lower quartile (Q₁).
In a box plot:
The left edge of the box represents the lower quartile.The right edge of the box represents the upper quartile.From inspection of the given box plot:
lower quartile (Q₁) = 15upper quartile (Q₃) = 18Therefore:
IQR = Q₃ - Q₁
= 18 - 15
= 3
So the interquartile range of the given box plot is 3.
1 y = 3x - 4
2 x + y = 8
use the method of substitution
Answer:
x = 2.4; y = 3.2
Step-by-step explanation:
y = 3x - 4
2x + y = 8
2x + 3x - 4 = 8
5x - 4 = 8
5x = 12
x = 12 / 5
x = 2.4
y = 3(2.4) - 4
y = 7.2 - 4
y = 3.2
The sum of five consecutive positive integers is 2020. Find the largets of these numbers.
Answer:
406
Step-by-step explanation:
let the 5 consecutive positive integers be
n , n + 1 , n + 2 , n + 3 , n + 4 , then
n + n + 1 + n + 2 + n + 3 + n + 4 = 2020
5n + 10 = 2020 ( subtract 10 from both sides )
5n = 2010 ( divide both sides by 5 )
n = 402
then
largest integer = n + 4 = 402 + 4 = 406
Need help. i dont understand this!!!
By the quadratic formula, the solution set of the quadratic equation is formed by two real roots: x₁ = 0 and x₂ = - 12.
How to find the solution of quadratic equation
Herein we have a quadratic equation of the form a · m² + b · m + c = 0, whose solution set can be determined by the quadratic formula:
x = - [b / (2 · a)] ± [1 / (2 · a)] · √(b² - 4 · a · c) (1)
If we know that a = - 1, b = 12 and c = 0, then the solution set of the quadratic equation is:
x = - [12 / [2 · (- 1)]] ± [1 / [2 · (- 1)]] · √[12² - 4 · (- 1) · 0]
x = - 6 ± (1 / 2) · 12
x = - 6 ± 6
Then, by the quadratic formula, the solution set of the quadratic equation is formed by two real roots: x₁ = 0 and x₂ = - 12.
To learn more on quadratic equations: https://brainly.com/question/1863222
#SPJ1
PLEASE HELP WILL GIVE BRAINLIEST
Which variable did you plot on the x-axis, and which variable did you plot on the y-axis? Explain why you assigned the variables in that way.
Write the equation of the line of best fit using the slope-intercept form of the line y = mx + b. Show all your work, including the points used to determine the slope and how the equation was determined.
What does the slope of the line represent within the context of your graph? What does the y-intercept represent?
Test the residuals of two other points to determine how well the line of best fit models the data.
Use the line of best fit to help you to describe the data correlation.
Using the line of best fit that you found in Part Three, Question 2, approximate how tall is a person whose arm span is 66 inches?
According to your line of best fit, what is the arm span of a 74-inch-tall person?
The variable that you would have to plot on the y axis (height) is the dependent variable while the variable that is on the x axis (arm span) is the independent or the explanatory variable.
How to get the slope of the lineThe slope was gotten through the use of the points (37,39) and (19,25)
This gave the slope of 7/9. This tells us that height of the person got to be raised by 7/9 inches when arm span increases by 1 inch.
From the given model, a person that has the arm span of 66 would have the height of
12 + 7/9 * 66
= 63.3 inches
A person who is 74 inches height the arm span of = 62*9/7
= 79. 71 inches.
Read more on line of best fit here:
https://brainly.com/question/17156587
#SPJ1
(4 + 8 ÷ 2) × 5 – 1?
Answer:
Step-by-step explanation:
(4+8/2)*5-1
8*5-1
39 is your answer
The following are the ages of 13 history teachers in a school district. 24, 27, 29, 29, 35, 39, 43, 45, 46, 49, 51, 51, 56 Notice that the ages are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum: Interquartile range:
The five-number summary and the interquartile range for the data set are given as follows:
Minimum: 24.Lower quartile: 29.Median: 43.Upper quartile: 50.Maximum: 56.Interquartile range: 50 - 29 = 21.What are the median and the quartiles of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set.The third quartile is the median of the second half of the data-set.The interquartile range is the difference between the third quartile and the first quartile.In this problem, we have that:
The minimum value is the smallest value, of 24.The maximum value is the smallest value, of 56.Since the data-set has odd cardinality, the median is the middle element, that is, the 7th element, as (13 + 1)/2 = 7, hence the median is of 43.The first quartile is the median of the six elements of the first half, that is, the mean of the third and fourth elements, mean of 29 and 29, hence 29.The third quartile is the median of the six elements of the second half, that is, the mean of the third and fourth elements of the second half, mean of 49 and 51, hence 50.The interquartile range is of 50 - 29 = 21.More can be learned about five number summaries at https://brainly.com/question/17110151
#SPJ1
greatest common factor of 24,36, and 96
Answer:
12
Step-by-step explanation:
[tex]24=2^{3} \times 3 \\ \\ 36=2^{2} \times 3^{2} \\ \\ 96=2^{5} \times 3[/tex]
Hey there!
What is GCF (Greatest Common Factor)?
Basically, the GCF is the biggest number in a data set that all of your numbers share.
What are the factors of the numbers?
24:1, 2, 3, 4, 6, 8, 12, and 24
36: 1, 2, 3, 4, 6, 9, 12, 18, and 36
96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96
What are the like terms that the numbers share?
1, 2, 3, 4, 6, 8, and 12
What is the biggest number out of the like terms?
12
What is your number?
12
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
What type of number is -560{,}114−560,114minus, 560, comma, 114? Choose all answers that apply: Choose all answers that apply:
The type of numbers which -560 and 114 are include the following:
B. Integer.
C. Rational.
What is a numerical data?A numerical data is also referred to as a quantitative data and it can be defined as a data set that is primarily expressed in numbers only. This ultimately implies that, a numerical data refers to a data set consisting of numbers rather than words.
The types of numbers.In Mathematics, there are six (6) common types of numbers and these include the following:
Natural (counting) numbers: these are 1, 2, 3, 4, 5, 6, .....114, ....560.Whole numbers: these comprises all natural numbers and 0.Integers: these are whole numbers that may either be positive, negative, or zero such as ....-560, ...... -114, ..... -4, -3, -2, -1, 0, 1, 2, 3, 4, .....114, ....560.Rational numbers: these comprises fractions, integers, and terminating (repeating) decimals such as ....-560, ...... -114, ..... -4, -3, -2, -1, -1/2, 0, 1, 1/2, 2, 3, 4, .....114, ....560.Irrational numbers: these comprises non-terminating or non-repeating decimals.Real numbers: these comprises both rational numbers and irrational numbers.In this context, we can infer and logically deduce that -560 and 114 are both an integer and a rational number.
Read more on rational number here: https://brainly.com/question/12088221
#SPJ1
Complete Question:
What type of number is -560, 114? Choose all answers that apply:
A. Whole number
B. Integer
C. Rational
D. Irrational
Help please, also provide work
Answer:
9) 128
10) 78
11) 31
12) 148
Step-by-step explanation:
9) we know that the segment across from the angle 48° is double the angle.
48 · 2 = 96
The segments around the circle should all add up to 360 so we add the two segments we know to find the unknown segment.
136 + 96 = 232
360 - 232 = 128
The answer for 9 is 128.
10)
61 + 80 = 141
180 - 141 = 39
39 * 2 = 78
The answer for question 10 is 78.
11)
236 + 62 = 298
360 - 298 = 62
62 ÷ 2 = 31
The answer for question 11 is 31.
12)
50 · 2 = 100
100 + 112 = 212
360 - 212 = 148
The answer for question 12 is 148.
hey can you help me answer this i am stuck
If the function is f(x)=1/(6x+6) then the value of x cannot be equal to -1.
Given a function of x f(x)=1/(6x+6).
We are told to find out the value of the variable x for which the function does not lie.
Function is like a relationship between two or more variables expressed in equal to form. The values entered in a function is known as domain and the values which we get after entering of values are known as range.
f(x)=1/(6x+6)
It is in form of fraction. Fraction is a combination of numbers in which the above number is numerator and below number is denominator.
In this (6x+6) cannot be equal to 0 because if (6x+6) equal to 0 then the value of function becomes infinity.
So,
6x+6=0
6x=-6
x=-1
Hence if the function is f(x)=1/(6x+6) then the value of x cannot be equal to -1.
Learn more about function at https://brainly.com/question/10439235
#SPJ1
Six 6-sided dice are rolled. What is the probability that exactly two of the dice show a 1 and exactly two of the dice show a 2? Express your answer as a common fraction.
Using it's concept, the probability that exactly two of the dice show a 1 and exactly two of the dice show a 2 is: 10/243.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
One of the six numbers is of 1, and also one out of six is 2. The other two trials can be any of the other 4 numbers, hence the probability for the six rolls has the following format:
p = (1/6)² x (1/6)² x (4/6)²
This considers just one order, while there are six rolls, hence there are 6! possible orders, hence the probability is:
p = 6! x (1/6)² x (1/6)² x (4/6)² = 120 x 16/46656 = 10/243.
More can be learned about probabilities at https://brainly.com/question/14398287
#SPJ1
y=2x + 9
3x + 2y = 4
Answer:
The answer is: (x,y) = (-2,5)
What are the values of the three trigonometric ratios for angle l, in simplest form? sin(l) = 4/5 cos(l) = 3/5 tan(l) = 4/3
The values of the three trigonometric ratios for angle L, in simplest form, are:
[tex]sin(L)=\frac{4}{5}[/tex][tex]cos(L)=\frac{3}{5}[/tex][tex]tan(L)=\frac{4}{3}[/tex]To find the values of the three trigonometric ratios for angle L, in the simplest form:Given -
The triangle LMN is given in the question.
The measurement of side LM is 15 unitsThe measurement of side LN is 25 unitsThe measurement of side MN is 20 unitsAs the trigonometric properties of a triangle state that the value of sin, cos, and tan for the respective angle can be written as:
sin(L) = perpendicular / hypotenusecos(L) = base / hypotenusetan(L) = perpendicular / baseUsing the above trigonometric properties, the value of sin(L):
[tex]sin(L) =\frac{20}{25} =\frac{4}{5}[/tex]Similarly, the value of cos(L):
[tex]cos(L)=\frac{15}{25} =\frac{3}{5}[/tex]And, the value of tan(L) is:
[tex]tan(L)=\frac{20}{15} =\frac{4}{3}[/tex]Therefore, the values of the three trigonometric ratios for angle L, in simplest form, are:
[tex]sin(L)=\frac{4}{5}[/tex][tex]cos(L)=\frac{3}{5}[/tex][tex]tan(L)=\frac{4}{3}[/tex]Know more about trigonometric ratios here:
https://brainly.com/question/1201366
#SPJ4
The question you are looking for is given below:
What are the values of the three trigonometric ratios for angle L, in simplest form?