Answer: 08:00
Step-by-step explanation:
If you want breakfast to be ready at 08:15 and the cooking time is 15 minutes, you need to start cooking at:
08:15 - 00:15 = 08:00
So you need to start cooking at 08:00 in order to have breakfast ready by 08:15.
The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 35 minutes of calls is $16.83 and the monthly cost for 52 minutes is $18.87. What is the monthly cost for 39 minutes of calls?
Answer: We can use the two given points to find the equation of the line and then plug in 39 for the calling time to find the corresponding monthly cost.
Let x be the calling time (in minutes) and y be the monthly cost (in dollars). Then we have the following two points:
(x1, y1) = (35, 16.83)
(x2, y2) = (52, 18.87)
The slope of the line passing through these two points is:
m = (y2 - y1) / (x2 - x1) = (18.87 - 16.83) / (52 - 35) = 0.27
Using point-slope form with the first point, we get:
y - y1 = m(x - x1)
y - 16.83 = 0.27(x - 35)
Simplifying, we get:
y = 0.27x + 7.74
Therefore, the monthly cost for 39 minutes of calls is:
y = 0.27(39) + 7.74 = $18.21
Step-by-step explanation:
The circle graph below shows the number of animals in Mushu's farm. Sheep Donkeys Camels Goats Cows If there were 24 goats, how many cows are there in the farm?
By assuming that the farmer has goat and cows in the ratio 3:4, the number of cows in the farm will be 32 cows.
If there were 24 goats, how many cows are there in the farm?To find out how many cows are in the farm, we need to know the total number of animals in the farm. Assuming the ratio of goats to cows is 3:4, we can write this as: [tex]3x : 4x[/tex]
Where 3x represents the number of goats, and 4x represents the number of cows. If we know that there are 24 goats, we can set up an equation to solve for x:
3x = 24
Dividing both sides by 3, we get:
x = 8
Now that we know the value of x, we can find the number of cows:
= 4x
= 4(8)
= 32
Therefore, there are 32 cows in the farm.
Read more about ratio
brainly.com/question/12024093
#SPJ1
Help me I don’t understand
Answer: C, 125
Step-by-step explanation: That is the slope of the line, which remains constant. The slope represents the distance over the time, and distance divided by time equals the speed. This means that the speed remains constant throughout.
What is the equivalent to this
None of the given options A, B, C, or D is correct as they all provide different answers.
what is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
The question asks for the equivalent of 6 × 2. This means that we need to find a number that is equal to the result of multiplying 6 and 2 together.
When we multiply 6 and 2, we get:
6 × 2 = 12
So, the equivalent of 6 × 2 is 12.
However, none of the answer options provided matches this answer.
Option A suggests that the equivalent of 6 × 2 is 2 × 1, which is equal to 2, not 12.
Option B suggests that the equivalent of 6 × 2 is 3 × 2, which is equal to 6, not 12.
Option C suggests that the equivalent of 6 × 2 is 9 × 3, which is equal to 27, not 12.
Option D suggests that the equivalent of 6 × 2 is 18 × 1/2, which is equal to 9, not 12.
Therefore, none of the options provided is correct.
To learn more about algebra from the given link:
https://brainly.com/question/24875240
#SPJ1
Camille opened a savings account and deposited $8,063.00 as principal. The account earns 14.69% interest, compounded quarterly. What is the balance after 10 years?
Use the formula A=P1+
r
n
nt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cent.
Save answer
Answer:$26,141.13.
Step-by-step explanation:
Using the formula A = P * (1 + r/n)^(n*t), where A is the balance, P is the principal, r is the interest rate, n is the number of times per year that the interest is compounded, and t is the time in years, we can calculate the balance in the savings account after 10 years:
A = 8,063.00 * (1 + 0.1469/4)^(4*10)
A ≈ 26,141.13
Therefore, the balance in the savings account after 10 years, rounded to the nearest cent, is $26,141.13.
What is the mean of the values in the stem-and-leaf plot?
Enter your answer in the box.
Answer:
mean = 24
Step-by-step explanation:
the mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
the sum of the data set is
sum = 12 + 13 + 15 + 28 + 28 + 30 + 42 = 168
there is a count of 7 in the data set , then
mean = [tex]\frac{168}{7}[/tex] = 24
PLEASE HELP
Find the Area
2cm
___cm^2
Answer:
3.14 cm^2
Step-by-step explanation:
1. Find radius:
If diameter is 2, divide it by 2 to get radius = 1
2. Find formula:
A=πr^2
3. Plug in:
A = π(1)^2
4. Solve (multiply):
A = π(1)^2:
3.14159265359
Or
3.14 cm^2
Answer:
3.14 cm^2
Step-by-step explanation:
A=[tex]\pi[/tex]r^2
r=2
2/2=1
A=[tex]\pi[/tex](1)^2
=[tex]\pi[/tex]1
≈3.14x1
≈3.14cm^2
Find the surface area. Round to the nearest hundredth
Answer:
122.30 cm²
Step-by-step explanation:
Divide the polyhedron into shapes:
+) 2 triangles with the same area.
The area of the triangle is
(4.3×11)÷2 = 23.65 cm².
And with two triangles of the same area we take the sum of both areas
23.65 + 23.65 = 47.3 cm²
+) 3 rectangles with different areas.
(3×6) + (3×8) + (3×11) = 75 cm²
So the surface area is the sum of areas of the triangles and rectangles
47.3 + 75 = 122.3 = 122.30 cm²
solve the system of equations below by graphing both equations. what is the solution? y=x+5 y=-2x-1
Answer:
To solve a system of equations by graphing, you need to graph each equation on the same coordinate system and find the point where the two lines intersect. If the equations are in slope-intercept form, you can identify the slope and y-intercept and graph them. If one of the equations is in slope-intercept form, you can rewrite the other one in that form and graph them. If both equations are in other forms, you can find the x- and y-intercepts and graph them.
In this case, we have two equations:
y = x + 5
y = -2x - 1
To graph these equations, we can start by finding their intercepts:
y = x + 5
0 = x + 5
x = -5
So the intercept for y = x + 5 is (-5, 0). Similarly,
y = -2x - 1
0 = -2x - 1
x = -1/2
So the intercept for y = -2x - 1 is (-1/2, 0). Now we can plot these points on a coordinate plane and draw a line through each point. The point where these two lines intersect is our solution.
Therefore, the solution to this system of equations is (-3, 2).
Step-by-step explanation:
HELPP I NEED HELP WITH MATHH
In a country club of 141 people, 61 play football, 65 play base ball and 72 play hockey hockey.
22. play all the games while 11 play none of the games. An equal number play only two games (How many play only two games (i) How many play only football?
The number of people who play only football is |A' ∩ B' ∩ C'| = 25. So, 25 people play only football.
Describe Statistics?Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of various methods and techniques to draw conclusions from data and make informed decisions.
The main goal of statistics is to provide a systematic approach to understanding and interpreting data, which can be used in a wide variety of fields, including business, social sciences, engineering, medicine, and many others. Statistics is used to study and analyze various types of data, including numerical, categorical, and ordinal data, as well as time series and spatial data.
Let A, B, and C be the sets of people who play football, baseball, and hockey, respectively. We know that:
|A| = 61, |B| = 65, |C| = 72
We also know that:
|A ∩ B ∩ C| = 22, |A ∪ B ∪ C| = 141, |A' ∩ B' ∩ C'| = 11
where A', B', and C' denote the complements of A, B, and C, respectively.
We can use the principle of inclusion-exclusion to find the number of people who play only two games. This principle states that:
|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|
Using the given values, we can substitute and simplify to get:
141 = 61 + 65 + 72 - |A ∩ B| - |A ∩ C| - |B ∩ C| + 22
|A ∩ B| + |A ∩ C| + |B ∩ C| = 75
We also know that an equal number of people play only two games, so let x be that number. Then:
|A ∩ B| = |A ∩ C| = |B ∩ C| = x
Substituting into the previous equation, we get:
3x = 75
x = 25
Therefore, 25 people play only two games. To find the number of people who play only football, we need to subtract the number of people who play baseball and hockey from the number of people who play only two games:
|A' ∩ B ∩ C| = x = 25
|A' ∩ B ∩ C'| = 11
|A' ∩ C ∩ B'| = x = 25
|A ∩ B' ∩ C'| = x = 25
|A' ∩ B| = 65 - (25 + 11) = 29
|A' ∩ C| = 72 - (25 + 11) = 36
|A' ∩ B' ∩ C| = 61 - (25 + 11) = 25
|A ∩ B' ∩ C| = 141 - (29 + 25 + 36 + 11) = 40
Therefore, the number of people who play only football is:
|A' ∩ B' ∩ C'| = 25
So, 25 people play only football.
To know more about equation visit:
https://brainly.com/question/14165926
#SPJ1
Complete the truth table for (A ⋁ B) ⋀ ~(A ⋀ B).
The truth table for (A ⋁ B) ⋀ ~(A ⋀ B) is:
A B (A ⋁ B) ⋀ ~(A ⋀ B)
0 0 0
0 1 0
1 0 0
1 1 0
The truth table is what?A truth table is a table that displays all possible combinations of truth values (true or false) for one or more propositions or logical expressions, as well as the truth value of the resulting compound proposition or expression that is created by combining them using logical operators like AND, OR, NOT, IMPLIES, etc.
The columns of a truth table reflect the propositions or expressions themselves as well as the compound expressions created by applying logical operators to them. The rows of a truth table correspond to the various possible combinations of truth values for the propositions or expressions.
To complete the truth table for (A ⋁ B) ⋀ ~(A ⋀ B), we need to consider all possible combinations of truth values for A and B.
A B A ⋁ B A ⋀ B ~(A ⋀ B) (A ⋁ B) ⋀ ~(A ⋀ B)
0 0 0 0 1 0
0 1 1 0 1 0
1 0 1 0 1 0
1 1 1 1 0 0
So, the only case where the expression is true is when both A and B are true, and for all other cases it is false.
To know more about truth tables, visit:
https://brainly.com/question/31482105
#SPJ1
Triangle PQR is drawn with coordinates P(0, 2), Q(0, 5), R(1, 4). Determine the translation direction and number of units if R′(−7, 4).
8 units down
8 units up
8 units to the right
8 units to the left
It follows that the translation direction is 8 units to the left and 0 units up or down.
Describe translation?A translation is a geometric change in Euclidean geometry where each point in a figure, shape, or space is moved uniformly in one direction. A translation can either be thought of as moving the origin of the coordinate system or as adding a constant vector to each point
The new vertices of a triangle with vertex locations of (0,0), (1,0), and (0,1), for instance, would be (2,3, (3,3), and (2,4) if the triangle were translated 2 units to the right and 3 units up.
We can use the following procedures to get the translation direction and number of units for R′(7, 4):
1. Determine the difference between R and R′'s x-coordinates: −7 − 1 = 8
2. Determine the difference between R and R′'s y coordinates: 4 − 4 = 0
It follows that the translation direction is 8 units to the left and 0 units up or down.
To know more about translation visit:
brainly.com/question/12463306
#SPJ1
The first four terms of a sequence are given.
7, 11, 15, 19, ...
What is the 40th term of the sequence?
Answer:
To find the 40th term of the sequence, we first need to identify the pattern that generates the terms. We can see that each term is obtained by adding 4 to the previous term. So the sequence is an arithmetic sequence with a common difference of 4.
Using this information, we can find the formula for the nth term of the sequence using the formula for the nth term of an arithmetic sequence:
an = a1 + (n - 1)d
Where an is the nth term of the sequence, a1 is the first term, n is the term number, and d is a common difference.
In this case, we have a1 = 7 and d = 4. Substituting these values into the formula, we get:
an = 7 + (n - 1)4
Simplifying this expression, we get:
an = 4n + 3
Now we can use this formula to find the 40th term of the sequence:
a40 = 4(40) + 3
a40 = 160 + 3
a40 = 163
Therefore, the 40th term of the sequence is 163.
A stainless-steel patio heater is shaped like a square pyramid. The length of one side of the base is 10 feet. The slant height is 12 feet. What is the height of the heater? Round to the nearest tenth of a foot.
The height of the heater is approximately 6.6 feet.
What is Pythagoras theorem?According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides.
We can use the Pythagorean theorem to find the height of the pyramid. Let's call the height "h". Then, the slant height is the hypotenuse of a right triangle with base and height both equal to 10 feet, so we have:
h² + 10² = 12²
Simplifying and solving for h, we get:
h² + 100 = 144
h² = 44
h ≈ 6.6 feet
Therefore, the height of the heater is approximately 6.6 feet.
Learn more about Pythagoras theorem on:
https://brainly.com/question/231802
#SPJ1
Help me pleas whith this
A company uses a machine to fill plastic bottles with cola. The volume in a bottle follows an approximately normal distribution with mean μ = 298 milliliters and standard deviation σ = 3 milliliters. Let x-bar be the sample mean volume in an SRS of 16 bottles. The probability that x-bar estimates μ to within ±1 milliliter is 0.8176.
(a) If you randomly selected one bottle instead of 16, would it be more likely, less likely, or equally likely to contain a volume of cola within ±1 milliliter of μ ? Explain your reasoning without doing any calculations.
(b) Calculate the probability of the event described in part (a) to confirm your answer.
Round your answer to 4 decimal places.
Leave your answer in decimal form.
Answer: (a) If you randomly selected one bottle instead of 16, it would be LESS likely to contain a volume of cola within ±1 milliliter of μ.
The reason is that as the sample size increases, the sample mean (x-bar) tends to be a more accurate estimator of the population mean (μ) due to the central limit theorem. With a larger sample size, the sample mean is less likely to deviate significantly from the population mean. In this case, with a sample size of 16 bottles, the probability that x-bar estimates μ to within ±1 milliliter is 0.8176, which means that the sample mean is likely to be within ±1 milliliter of the population mean in about 81.76% of the cases.
On the other hand, if you randomly selected just one bottle instead of 16, the variability of the individual bottle's volume would have a larger impact on the estimate of the population mean. Therefore, it would be less likely for the volume of one individual bottle to fall within ±1 milliliter of μ compared to the sample mean of 16 bottles.
(b) To calculate the probability of the event described in part (a), we can use the z-score formula and the standard normal distribution table.
The given probability that x-bar estimates μ to within ±1 milliliter is 0.8176, which corresponds to a z-score of approximately 0.89 (based on the standard normal distribution table). Since we want to find the probability of the sample mean falling within ±1 milliliter of μ, we need to find the probability of the z-score being between -0.89 and 0.89 (i.e., within ±1 standard deviation from the mean).
Using the z-score formula: z = (x-bar - μ) / (σ / sqrt(n))
where μ = 298, σ = 3, n = 16 (sample size), and z = 0.89 (from the standard normal distribution table),
We can rearrange the formula to solve for x-bar:
0.89 = (x-bar - 298) / (3 / sqrt(16))
Simplifying:
0.89 = (x-bar - 298) / 0.75
Cross-multiplying:
x-bar - 298 = 0.89 * 0.75
x-bar - 298 = 0.6675
Adding 298 to both sides:
x-bar = 298 + 0.6675
x-bar ≈ 298.67
So, the probability of x-bar estimating μ to within ±1 milliliter is approximately 0.8176, which confirms our answer in part (a).
I hope it helped!
Step-by-step explanation:
… Approximate the area of the shaded region.
The approximated area of the shaded region is 92.54 square units
Approximating the area of the shaded region.From the question, we have the following parameters that can be used in our computation:
Two isosceles right trianglesCircleThe area of the shaded region in the figure is calculated as
Shaded region = Circle - Isosceles right triangle 1 - Isosceles right triangles 2
Using the given dimensions, we have
Shaded region = 3.14 * 6^2 - 1/2 * 5^2 - 1/2 * 4^2
Evaluate
Shaded region = 92.54
Hence, the shaded region is 92.54 square units
Read more about area at
https://brainly.com/question/24487155
#SPJ1
Lim x1 (x^2+1/x+1 +x^2+3) what is the value
The limit of the expression as x approaches 1 is 5.
Explain limit
A limit is a value that a function or sequence approaches as the input or index approaches a specific value or infinity. It is used to describe the behaviour of a function or sequence as it approaches a certain point or as the input values become infinitely large or small. The limit is an essential concept in calculus and is used to solve problems involving derivatives, integrals, and infinite series.
According to the given information
Here we use algebraic manipulation and direct substitution to find the limit:
lim x→1 [(x² + 1)/(x + 1) + x² + 3]
= lim x→1 [(x² + 1)/(x + 1)] + lim x→1 (x² + 3) (by the limit laws of algebra)
= [(1² + 1)/(1 + 1)] + (1² + 3) (by direct substitution)
= (2/2) + 4
= 1 + 4
= 5
Therefore, the limit of the expression as x approaches 1 is 5.
To know more about limit visit
brainly.com/question/12211820
#SPJ1
See the photo below
This problem involves integration and algebraic manipulation, and belongs to the subject of calculus. The solutions are:
[tex]A) $\int_{0}^{2} (f(x) + g(x)) dx = -3$[/tex]
[tex]B) $\int_{0}^{3} (f(x) - g(x)) dx = -4$[/tex]
[tex]C) $\int_{2}^{3} (3f(x) + g(x)) dx = -32$[/tex]
This is a problem that asks us to find the values of some definite integrals using given values of other definite integrals. We are given three definite integrals, and we are asked to compute three other integrals involving the same functions, using the given values.
The problem involves some algebraic manipulation and the use of the linearity of the integral.
It also involves finding the constant "a" that makes a definite integral equal to zero. The integral involves two functions, "f(x)" and "g(x)," whose definite integrals over certain intervals are also given.
See the attached for the full solution.
Learn more about integration at:
https://brainly.com/question/18125359
#SPJ1
8. The population P (t) of a bacteria culture is given by P (t) = -1500t² + 60,000t + 10,000, where is the time in hours after the culture is started. Determine the time(s) at which the population will be greater than 460,000 organisms.
The time(s) at which the population will be greater than 460,000 organisms is between 10 and 30 hours after the culture is started.
What is inequality?An inequality is a comparison between two numbers or expressions that are not equal to one another. Symbols like, >,,, or are used to denote it, indicating which value is more or smaller than the other or just different.
To find the time(s) at which the population will be greater than 460,000 organisms, we need to solve the inequality:
P(t) > 460,000
Substituting the given equation for P(t), we get:
-1500t² + 60,000t + 10,000 > 460,000
Simplifying this inequality, we get:
-1500t² + 60,000t - 450,000 > 0
Dividing both sides by -1500 and flipping the inequality sign, we get:
t² - 40t + 300 < 0
We can solve this inequality by factoring the quadratic equation:
(t - 10)(t - 30) < 0
The roots of this equation are t = 10 and t = 30. Plotting these values on a number line, we can see that the solution to the inequality is:
10 < t < 30
Therefore, the time(s) at which the population will be greater than 460,000 organisms is between 10 and 30 hours after the culture is started.
Learn more about inequality on:
https://brainly.com/question/17448505
#SPJ1
Use the graph to answer the question.
graph of polygon ABCD with vertices at 1 comma 5, 3 comma 1, 7 comma 1, 5 comma 5 and a second polygon A prime B prime C prime D prime with vertices at 8 comma 5, 10 comma 1, 14 comma 1, 12 comma 5
Determine the translation used to create the image.
7 units to the right
7 units to the left
3 units to the right
3 units to the left
The translation used to create the image A'B'C'D', from the pre-image, ABCD is; 7 units to the right
What is a translation transformation?A translation transformation is one in which the location of the points on the pre-image is changes but the size, and orientation of the pre-image is preserved.
The coordinates of the vertices of the polygon ABCD are; (1, 5), (3, 1), (7, 1), (5, 5)
The coordinates of the vertices of the polygon A'B'C'D' are; (8, 5), (10, 1), (14, 1), (12, 5)
Whereby the vertices of the image and the preimage are;
A(1, 5), B(3, 1), C(7, 1), D(5, 5), and A'(8, 5), B'(10, 1), C'(14, 1), D'(12, 5), the difference in the x and y-values indicates;
A' - A = (8 - 1, 5 - 5) = (7, 0)
B' - B = (10 - 3, 1 - 1) = (7, 0)
C' - C = (14 - 7, 1 - 1) = (7, 0)
D' - D = (12 - 5, 5 - 5) = (7, 0)
Therefore, the transformation used to create the image A'B'C'D' from the pre-image, ABCD is a translation; 7 units to the right
Learn more on translation transformation here: https://brainly.com/question/25982490
#SPJ1
Find the amount accumulated after
investing a principle P for t years and an
interest rate compounded twice a year.
P = $100 r = 3% t = 5
k=2
Hint: A = P(1 + E) kt
A = $[?]
Answer:
A= $116.05
Step-by-step explanation:
A=P(1+E)kt
A=100(1+0.03/2)^10
A= $116.05
Which geometric term describes ∠ T A G ?
Answer:
angle
Step-by-step explanation:
since there is a < sign, that makes it an angle. I'm not sure if that is the whole problem, or if It is missing a picture. Hope this helps!
Answer: i know it is acute
Will mark brainliest if answer is correct
The x^6y^7 term in the expansion will be 36x^2y^7.
The x^7y^2 term in the expansion will be 36x^7y^2.
How to solveIn the given problem, we have the binomial expansion of (x - y)^n, which includes the term 126x^5y^4.
We will use the binomial coefficient formula to find the coefficients of the desired terms.
The general term of the binomial expansion is given by:
T(k) = C(n, k) * x^(n-k) * y^k
where C(n, k) is the binomial coefficient and can be calculated as:
C(n, k) = n! / (k!(n-k)!)
From the given term, 126x^5y^4, we have:
126 = C(n, 4)
x^5 = x^(n-4)
y^4 = y^4
Now we can find the value of n:
126 = n! / (4!(n-4)!)
Let's solve for n:
126 * 4! = n! / (n-4)!
504 = n! / (n-4)!
Now, we will find the coefficients of the terms x^6y^7 and x^7y^2.
The x^6y^7 term in the expansion will be:
T(k) = C(n, 7) * x^(n-7) * y^7
Since x^5 = x^(n-4), we have n - 4 = 5, so n = 9.
Substituting the value of n:
T(k) = C(9, 7) * x^2 * y^7
Using the binomial coefficient formula:
C(9, 7) = 9! / (7!2!) = 36
So, the x^6y^7 term in the expansion will be 36x^2y^7.
The x^7y^2 term in the expansion will be:
T(k) = C(n, 2) * x^(n-2) * y^2
We already found that n = 9, so substituting the value of n:
T(k) = C(9, 2) * x^7 * y^2
Using the binomial coefficient formula:
C(9, 2) = 9! / (2!7!) = 36
So, the x^7y^2 term in the expansion will be 36x^7y^2.
Read more about binomial expansion here:
https://brainly.com/question/13602562
#SPJ1
solve the equation
a) y''-2y'-3y= e^4x
b) y''+y'-2y=3x*e^x
c) y"-9y'+20y=(x^2)*(e^4x)
Answer:
a) To solve the differential equation y''-2y'-3y= e^4x, we first find the characteristic equation:
r^2 - 2r - 3 = 0
Factoring, we get:
(r - 3)(r + 1) = 0
So the roots are r = 3 and r = -1.
The general solution to the homogeneous equation y'' - 2y' - 3y = 0 is:
y_h = c1e^3x + c2e^(-x)
To find the particular solution, we use the method of undetermined coefficients. Since e^4x is a solution to the homogeneous equation, we try a particular solution of the form:
y_p = Ae^4x
Taking the first and second derivatives of y_p, we get:
y_p' = 4Ae^4x
y_p'' = 16Ae^4x
Substituting these into the original differential equation, we get:
16Ae^4x - 8Ae^4x - 3Ae^4x = e^4x
Simplifying, we get:
5Ae^4x = e^4x
So:
A = 1/5
Therefore, the particular solution is:
y_p = (1/5)*e^4x
The general solution to the non-homogeneous equation is:
y = y_h + y_p
y = c1e^3x + c2e^(-x) + (1/5)*e^4x
b) To solve the differential equation y'' + y' - 2y = 3xe^x, we first find the characteristic equation:
r^2 + r - 2 = 0
Factoring, we get:
(r + 2)(r - 1) = 0
So the roots are r = -2 and r = 1.
The general solution to the homogeneous equation y'' + y' - 2y = 0 is:
y_h = c1e^(-2x) + c2e^x
To find the particular solution, we use the method of undetermined coefficients. Since 3xe^x is a solution to the homogeneous equation, we try a particular solution of the form:
y_p = (Ax + B)e^x
Taking the first and second derivatives of y_p, we get:
y_p' = Ae^x + (Ax + B)e^x
y_p'' = 2Ae^x + (Ax + B)e^x
Substituting these into the original differential equation, we get:
2Ae^x + (Ax + B)e^x + Ae^x + (Ax + B)e^x - 2(Ax + B)e^x = 3xe^x
Simplifying, we get:
3Ae^x = 3xe^x
So:
A = 1
Therefore, the particular solution is:
y_p = (x + B)e^x
Taking the derivative of y_p, we get:
y_p' = (x + 2 + B)e^x
Substituting back into the original differential equation, we get:
(x + 2 + B)e^x + (x + B)e^x - 2(x + B)e^x = 3xe^x
Simplifying, we get:
-xe^x - Be^x = 0
So:
B = -x
Therefore, the particular solution is:
y_p = xe^x
The general solution to the non-homogeneous equation is:
y = y_h + y_p
y = c1e^(-2x) + c2e^x + xe^x
c) To solve the differential equation y" - 9y' + 20y = x^2*e^4x, we first find the characteristic equation:
r^2 - 9r + 20 = 0
Factoring, we get:
(r - 5)(r - 4) = 0
So the roots are r = 5 and r = 4.
The general solution to the homogeneous equation y" - 9y' + 20y = 0 is:
y_h = c1e^4x + c2e^5x
To find the particular solution, we use the method of undetermined coefficients. Since x^2*e^4x is a solution to the homogeneous equation, we try a particular solution of the form:
y_p = (Ax^2 + Bx + C)e^4x
Taking the first and second derivatives of y_p, we get:
y_p' = (2Ax + B)e^4x + 4Axe^4x
y_p'' = 2Ae^4x +
solve for the unknown to find the unit rate
1/5 ?
----- = -----
1/20 1
Answer: 4
Step-by-step explanation:
To find the unit rate, we can cross-multiply the fractions.
Multiplying the numerator of the first fraction by the denominator of the second fraction, we get 1/5.
Multiplying the numerator of the second fraction by the denominator of the first fraction, we get 1/20.
Now we have the equation 1/5 = 1/20.
To solve for the unknown, we can cross-multiply again, which gives us 20 * 1/5 = 4.
Therefore, the unit rate is 4.
Given the expression 3x+2 evaluate the expression for the given values of x when x=(-2)
Answer:
...............................
Jasmine asked her classmates to name all the types of trees they found while on a field trip at a local park.
1/7 reported finding a birch tree.
7/9 reported finding a pine tree.
1/4 reported finding a maple tree.
11/23 reported finding an oak tree.
Based on the results, which statements are true? (Pick all that apply)
A. Most students found a pine tree.
B. More students found a maple tree than a pine tree.
C. More students found a birch tree than an oak tree.
D. More students found a pine tree than a birch tree.
E. More students found a maple tree than an oak tree.
The statements that are correct concerning the outcome of events between Jasmine and her classmates include the following:
Most students found a pine tree.
More students found a pine tree than a birch tree. That is option A and D respectively.
How to calculate the number of students per tree?The quantity of students that found birch tree = 1/7 = 0.14
The quantity of students that found pine tree = 7/9 = 0.8
The quantity of students that found maple tree = 1/4 = 0.25
The quantity of students that found oak tree = 11/23 = 0.48
Therefore, the statement that are correct about the outcome of the event between Jasmine and her classmates is as follows:
Most students found a pine tree.
More students found a pine tree than a birch tree.
Learn more about addition here:
https://brainly.com/question/29793687
#SPJ1
how am i supposed to prove that theyre collinear
Answer:
They are collinear if they are on the same line