Answer:
\(\textsf{A.} \quad e^{-y}=\cos x+2\)
Explanation:
Given differential equation and initial condition:
\(\begin{cases}y'=e^y \sin x\\y(-\pi)=0\end{cases}\)
Rearrange the differential equation so that all the terms containing y are on the left-hand side, and all the terms containing x are on the right-hand side:
\(y'=e^y \sin x\)
\(\dfrac{dy}{dx}=e^y \sin x\)
\(\dfrac{1}{e^y}\; dy=\sin x\; dx\)
\(e^{-y}\; dy=\sin x\; dx\)
Integrate both sides of the equation:
\(\begin{aligned}\displaystyle \int e^{-y}\; dy&=\int \sin x\; dx\\\\-e^{-y}&=-\cos x+C\end{aligned}\)
Substitute the given condition y(-π) = 0 into the equation and solve for C:
\(\begin{aligned}-e^{-0}&=-\cos (-\pi)+C\\\\-1&=1+C\\\\C&=-2\end{aligned}\)
Substitute the found value of C into the equation:
\(-e^{-y}=-\cos x-2\)
Multiply both sides by -1:
\(\boxed{e^{-y}=\cos x+2}\)
\(\hrulefill\)
Integration rules used:
\(\boxed{\begin{minipage}{5.1 cm}\underline{Integrating $e^{ax}$}\\\\$\displaystyle \int e^{ax}\:\text{d}x=\dfrac{1}{ax}e^{ax}+\text{C}$\\\end{minipage}}\)
\(\boxed{\begin{minipage}{5.1 cm}\underline{Integrating $\sin x$}\\\\$\displaystyle \int \sin x\:\text{d}x=-\cos x+\text{C}$\\\end{minipage}}\)
Given points V(10;2) and N (-7;9).
Determine the coordinates of vectors VN and NV
VN =( ; )
NV = ( ; )
what does it mean if the slope of a line is undefined
Answer:
Vertical line (straight up and down)
Step-by-step explanation:
The slope of a line can be positive, negative, zero, or undefined. A horizontal line has slope zero since it does not rise vertically (i.e. y1 − y2 = 0), while a vertical line has undefined slope since it does not run horizontally (i.e. x1 − x2 = 0).
Answer:
Step-by-step explanation:
the slope of any line is rise/run. What this means is that you have the change in y value divided by the change in x. If you have two points whos x value stays the same, or does not change, you have the change in y divided by 0. Dividing any number by 0 gives you the answer “undefined”.
Here is a probability densityfunction:f(x) = 2/9x , 0≤x≤ 3Generate a random number fromthis density using us = 0.127. Show yourwork!
A random number generated from this density using the given us value of 0.127 is approximately 1.068.
To generate a random number from this density using the given us value, we first need to calculate the cumulative distribution function (CDF):
F(x) = ∫(0 to x) f(t) dt
= ∫(0 to x) (2/9)t dt
= (1/9) x^2
Next, we set the CDF equal to the given us value and solve for x:
us = F(x) = (1/9) x^2
0.127 = (1/9) x^2
x^2 = 1.139
x = sqrt(1.139) ≈ 1.068
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50 POINTS!! Please help tysm :) image is attached (sorry about the quality); find the value of x. the answer key says x=10, but I'm not sure how to get there.
please don't put an unrelated answer or just repeat the answer for the points :) I would like a step by step explanation
Answer:
\( \: x = 10\)
Step-by-step explanation:
prefer the attachment
according to the question
\( \displaystyle \: \frac{6}{17.5-x} = \frac{8 + 6}{17.5} \)
simplify addition:
\( \displaystyle \: \frac{6}{17.5-x} = \frac{14}{17.5 } \)
simplify fraction;
\( \displaystyle \: \frac{6}{17.5 - x} = 0.8\)
cross multiplication:
\(\displaystyle 6 = 14 - 0.8x\)
cancel 14 from both sides:
\( \displaystyle - 8= - 0.8x\)
divide both sides by -0.8:
\( \therefore \: x = 10\)
suppose you roll two number cubes and multiply the numbers. what is the probability of getting a multiple of 3 and 4
For given experiment, the probability of getting a multiple of 3 and 4 is 1/7
In this question we have been given an expreiment of rolling two number cubes and multiply the numbers.
We need to find the probability of getting a multiple of 3 and 4
If two number cubes are rolled and multiply the numbers, the maximum output of multiplication would be 36
So, the sample space:
n(S) = 21
The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36
And the multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36
The number of outcomes for getting a multiple of 3 and 4 are:
12, 24, 36
n(A) = 3
so, the required probability would be,
p(A) = n(A)/n(S)
p(A) = 3/21
p(A) = 1/7
Therefore, the probability of getting a multiple of 3 and 4 = 1/7
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What is the lateral area of the prism? 73.5 feet 73.5 square feet 84 feet 84 square feet
Answer:The lateral surface area of the triangular prism will be 84 square feet.correct option is D.
What is the surface area of the triangular prism?Let the sides of the triangle be a, b, c, and a height of H. Then the surface area of the prism is given as SA = H(a + b + c)A triangular prism has bases with three congruent sides, each measuring 4 feet. The height of each triangle is approximately 3.5 feet.The distance between the triangular bases is 7 feet.Then the lateral surface area will beSA = 7 (4 + 4 + 4)SA = 7 x 12SA = 84 square feet. the correct option is D
Step-by-step explanation:
Given: ∆MNP, PM = 8 m∠P = 90°, m∠N = 58° Find: Perimeter of ∆MNP
(Not 22.4 or 22.43)
Please answer ASAP, brainly awarded.
Answer:
Step-by-step explanation:
Triangle MNP is a right triangle with the following values:
m∠P = 90°m∠N = 58°PM = 8Interior angles of a triangle sum to 180°. Therefore:
m∠M + m∠N + m∠P = 180°
m∠M + 58° + 90° = 180°
m∠M + 148° = 180°
m∠M = 32°
To find the measures of sides MN and NP, use the Law of Sines:
\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)
Substitute the values into the formula:
\(\dfrac{MN}{\sin P}=\dfrac{NP}{\sin M}=\dfrac{PM}{\sin N}\)
\(\dfrac{MN}{\sin 90^{\circ}}=\dfrac{NP}{\sin 32^{\circ}}=\dfrac{8}{\sin 58^{\circ}}\)
Therefore:
\(MN=\dfrac{8\sin 90^{\circ}}{\sin 58^{\circ}}=9.43342722...\)
\(NP=\dfrac{8\sin 32^{\circ}}{\sin 58^{\circ}}=4.99895481...\)
To find the perimeter of triangle MNP, sum the lengths of the sides.
\(\begin{aligned}\textsf{Perimeter}&=MN+NP+PM\\&=9.43342722...+4.99895481...+8\\&=22.4323820...\\&=22.43\; \sf units\; (2\;d.p.)\end{aligned}\)
How to write an equation in point -slope form for each line
Plz help i will give
Answer:
The equation to be used is 4/8 × 8/12=1/3
Convert 3.9m^2 into cm^2
I will leave good review!
Answer:
Step-by-step explanation:
To convert square meters to square centimeters, we need to multiply by the conversion factor (100 cm / 1 m)^2.
So,
3.9 m² = 3.9 × (100 cm / 1 m)²
3.9 m² = 3.9 × 10,000 cm²
3.9 m² = 39,000 cm²
Therefore, 3.9 square meters is equal to 39,000 square centimeters.
ANSWER FAST FOR BRAINLIEST!!!
The graph shows f(x). The absolute value function g(x) is described in the table. The graph shows a v-shaped graph, labeled f of x, with a vertex at 0 comma 2, a point at negative 1 comma 3, and a point at 1 comma 3. x g(x) −1 5 0 4 1 3 2 2 3 3 If g(x) = f(x + k), what is the value of k? k = −2 k is equal to negative one half k is equal to one half k = 2
Where the above graph and conditions are given, the value of k that satisfies g(x) = f(x+k) is k = -2.
What is the explanation for the above response?We can determine the value of k by using the given relationship between g(x) and f(x+k).
If g(x) = f(x + k), then we can substitute the given values of x in g(x) to get:
g(-1) = f(-1 + k) --> 5 = f(-1 + k)
g(0) = f(0 + k) --> 4 = f(k)
g(1) = f(1 + k) --> 3 = f(1 + k)
g(2) = f(2 + k) --> 2 = f(2 + k)
g(3) = f(3 + k) --> 3 = f(3 + k)
We know that f(x) is a v-shaped graph with a vertex at (0,2) and points at (-1,3) and (1,3). Therefore, we can conclude that f(k) = 4, which means that k is the x-coordinate of the vertex of f(x) shifted to the left or right.
Since the vertex of f(x) is at (0,2), and the x-coordinate of the vertex of f(x+k) is at k, we have:
k = 0 --> vertex of f(x+k) is at (0,2)
k = -1 --> vertex of f(x+k) is at (-1,2)
k = 1 --> vertex of f(x+k) is at (1,2)
k = 2 --> vertex of f(x+k) is at (2,2)
Therefore, the value of k that satisfies g(x) = f(x+k) is k = -2.
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Regarding the two variables under consideration in a regression analysis, a. what is the dependent variable called? b. what is the independent variable called?
In a regression analysis regarding the two variables, the dependent variable is called the response or outcome variable, meanwhile the independent variable is called the predictor, explanatory, or input variable.
The goal of the analysis is to build a statistical model that can predict or explain the behavior of the dependent variable based on the independent variable(s). In a regression analysis, the two variables under consideration are:
In conclusion, the goal of the analysis is to find the best-fitting line or curve that describes the relationship between the variables. Once we have this model, we can use it to make predictions about the dependent variable based on the values of the independent variable(s).
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c) Suppose that you take a random sample of 5,000 people from the U.S. population.Make a table that shows the expected number of people in your sample who come fromeach of the four age groups
In order to determine the number of people in the sample for each age group, here are the steps:
1. Determine what proportion in the entire population the population of each group. To get the proportion, simply divide the population of each respective group by the entire population.
2. To get the number of samples for each group, multiply the proportion by 5,000 and round the answer to the nearest whole number.
Now, let's apply the steps above in each group.
Let's start with ages under 18.
\(\begin{gathered} Proportion:74,181,467\div308,745,538=0.240267333 \\ Number\text{ }of\text{ }Samples:0.240267333\times5,000=1,201.33\approx1,201 \end{gathered}\)Hence, we are expected to have 1,201 people aged under 18 in the sample.
For those aged 18 - 44,
\(\begin{gathered} Proport\imaginaryI on:112,806,642\div308,745,538=0.3653709224 \\ Number\text{ }of\text{ }Samples:0.3653709224\times5,000=1,826.85\approx1,827 \end{gathered}\)Hence, we are expected to have 1,827 people aged 18-44 in the sample.
For those aged 45 - 64,
\(\begin{gathered} Proportion:81,489,445\div308,745,538=0.2639372395 \\ Number\text{ }of\text{ }Samples:0.2639372395\times5,000=1,319.68\approx1,320 \end{gathered}\)The expected number of samples for people aged 45-64 is 1,320.
Lastly, for aged 65 and over,
\(\begin{gathered} Proportion:40,267,984\div308,745,538=0.1304245051 \\ Number\text{ }of\text{ }Samples:0.1304245051\times5,000=652.12\approx652 \end{gathered}\)The expected number of samples for people aged 65 and over is 652.
To summarize, we have:
Age under 18 ⇒ 1,201 samples
18 - 44 ⇒ 1,827 samples
45 - 64 ⇒ 1,320 samples
65 and over ⇒ 652 samples
.
What is the volume of a pencil
Katrina sketches the graphs of four functions on a coordinate plane. Which of the following functions is linear?
The function that is linear is the function that is a straight line
How to determine the function that is linearA linear function can be identified on a graph by its shape.
A linear function will always have a straight line. So, if the graph of several functions, then the linear function would be a straight line.
To confirm that it is a linear function, you can check if it has the form y = mx + b, where m and b are constants.
In this form, m represents the slope of the line, which is a measure of how steep the line is. and b is the y-intercept
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What is the area of a circle with a diameter of 5 m? Use 3. 14 for pi. Round to the nearest tenth.
Answer:
19.625
Step-by-step explanation:
2.5x2.5x3.15
Subtract − 3 x 2 + 4 x + 10 −3x 2 +4x+10 from 2 x 2 − 2 x 2x 2 −2x.
Answer:
10+12x
Step-by-step explanation:
1. simplify both sides using PEMDAS.
(2 x 2) − ((2 x 2x) 2) −2x
4-8x-2x
4-10x
− (3 x 2) + 4x + 10 −(3x 2) +4x+10
-6+4x-6x+4x+20
2x+14
2. (2x+14)-(4-10x)= 10+12x
sorry if its rong it was kinda confusing finfing if it was an x or multiplecation.
how to solve a question about if one person can do in 5 hours, and another person does in 10 hours, how long will it take for them working togehter
It will take approximately 3.33 hours for both persons working together to complete the job.
What is distance?
Distance is the measure of how far apart two objects or locations are from each other. It is usually measured in units such as meters, kilometers, miles, or feet.
To solve this problem, we can use the following formula:
1 / T = 1 / t1 + 1 / t2
Where T is the time it takes for both persons working together to complete the job, t1 is the time it takes for the first person to complete the job alone, and t2 is the time it takes for the second person to complete the job alone.
Plugging in the given values, we get:
1 / T = 1 / 5 + 1 / 10
Simplifying the right side, we get:
1 / T = 3 / 10
Multiplying both sides by 10T, we get:
10 = 3T
Dividing both sides by 3, we get:
T = 10 / 3 = 3.33 hours
Therefore, it will take approximately 3.33 hours for both persons working together to complete the job.
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need 8, and 9 which definitions go with the
description
In a salt where \( r^{+}=165 \) and \( r^{-}=297, r^{+} \)will occupy what kind of hole? tetrahedral octahedral cubic Any of the above 1 point Match each term with the best definition or description
The salt will acquire octahedral hole. Thus option B is correct .
Given,
\(r^{+} = 165\\ r^{-} = 297\)
Now,
Find the coordination number ,
Radius ratio = \(r^{+} / r^{-}\)
Substitute the values of radius of salt to get the coordination number .
Radius ratio = 165/297
Radius ratio = 0.556 .
If the radius ratio is between 0.414 and 0.732
Range of radius ratio : 0.414 < r < 0.732
Then coordination number is 6 . If the coordination number is 6 then it will acquire octahedral void .
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Determine the domain of (f/g)(x) when f(x)=1/x and g(x)= sqrt x+8
(answer choices in photo)
Answer:
(−8,0)∪(0,∞)
Step-by-step explanation:
This is composition, which I'm going to assume you've covered (sorry if I use any weird terms because of that).
So, anyway, (f/g)(x) is basically \(\frac{f(x)}{g(x)}\).
In this case, the answer would be \(\frac{\frac{1}{x} }{\sqrt{x+8} }\)
I'm going to assume we're using the real number system.
In that case, x can't be less than 0 (can't even be equal to because divide by zero error
So, \(\sqrt{x+8} > 0\)
Solve for x by squaring.
\(\sqrt{x+8} > 0\)
\(x > -8\)
However, in the numerator, there is 1/x. A number divided by 0 is undefined. So, x has to be greater than -8, and it can't be 0.
So, with that, the interval notation is like this.
(−8,0)∪(0,∞)
What is the area of the circle shown? Use 3.14 for pi.
Help me please I need to pass this test
(PLEASE AND ASAP I WILL GIVE 100 PIONTS) What is the horizontal distance between (–14, –20) to (7, –20)?
7 units
21 units
–7 units
–21 units
Answer:
The two points have the same y-coordinate of -20, so they lie on the same horizontal line.
Step-by-step explanation:
To find the horizontal distance between them, we can simply subtract their x-coordinates:
distance = 7 - (-14) = 7 + 14 = 21
Therefore, the horizontal distance between (–14, –20) and (7, –20) is 21 units.
Answer:
Step-by-step explanation:
21 units
Help!!!!!
I need help!!
Answer:
28.
Step-by-step explanation:
First you woukd have to multiply 3 ×2 to get 6 then 12×14 to get 168. Then you would divide 168÷6 to get 28.
Which number sentence is not true?
OA) |-20| < 20
OB) |9| = 9
OC) |-20| > |9|
OD) |9|< 20
Answer:
Option A is correct option
Step-by-step explanation:
We need to find which number sentence is not true.
We will check each option.
Option A
|-20| < 20
We know that |-a|=a
20 < 20 (false)
So, this number sentence is not true.
Option B
|9| = 9
We know that |a|=a
9=9 (true)
So, this number sentence is true.
Option C
|-20|>|9|
We know that |-a|=a
20>9 (true)
So, this number sentence is true.
Option D
|9| < 20
We know that |a|=a
9<20
So, this number sentence is true.
So, Option A is correct option
Michelle read 33 pages of her book on the weekend and read 19 pages per day jillian read 45 pages of her book on the weekend and then read 23 per day write an inequality to represent the number of days that Michelle must read in order to read more pages than jill
The inequality, and we can't find a number of days that Michelle must read in order to read more pages than Jill.
What is inequality?
An inequality is a mathematical statement that compares two values, expressing that they are not equal.
Let "x" be the number of days that Michelle must read in order to read more pages than Jill.
The total number of pages Michelle reads can be represented as:
33 + 19x
The total number of pages Jill reads can be represented as:
45 + 23x
To write an inequality to represent the number of days that Michelle must read in order to read more pages than Jill, we need to compare the two expressions:
33 + 19x > 45 + 23x
Simplifying the inequality, we get:
-12 > 4x
Dividing both sides by 4 (and flipping the inequality because we're dividing by a negative number), we get:
x < -3
However, this solution doesn't make sense in the context of the problem because we can't have negative days of reading.
Hence, there is no solution to the inequality, and we can't find a number of days that Michelle must read in order to read more pages than Jill.
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2x - 80
4x+20
Solve for x
Answer:
2x - 80 = 78x
4x+20=24x
William just accepted a job at a new company where he will make an annual salary of
$60000. William was told that for each year he stays with the company, he will be
given a salary raise of $5000. How much would William make as a salary after 5
years working for the company? What would be his salary after t yehrs?
Salary after 5 years:
Salary after t years:
Answer:
Step-by-step explanation:
He gets a new job and it pays him $60k each year.
Amount per year: 60,000
He gets a raise of $5k
Amount per year: 65,000
After 5 years of working there you times 5 by your amount you get per year.
5 x 65,000 = 325,000
Therefore you get...
$325k every five years
To know how much it is in ten years multiply 325k by 2
325,000 x 2 = 650,000
Salary after 5 years: 325,000
Salary after 10 years: 650,000
<3 Enjoy,
Dea
Which angle is supplementary to the
Please helppp
Answer:
\(\angle FCB\)
Step-by-step explanation:
Supplementary angles are angles that sum to \(180^{\circ}\). In this case, \(\angle FCB\) is supplementary to \(\angle DCF\) since they add up to the angle of a straight line which is \(180^{\circ}\).
Hope this helps :)
3. Lin is reading a 47-page book. She read the first 20 pages in 35 minutes.
a. If she continues to read at the same rate, will she be able to complete this book
in under 1 hour?
nope......cos she spent 35 mins on 20 pages. ...meaning for another 20 pages 35minns will be gone too and for the remaining 17 pages she will not use les than 28mins
Will mark brainliest for whoever answers correctly
Answer:
The answer is 2
Step-by-step explanation:
x+y = (1+i) + (1-i)
open the bracket...
1+i + 1-i
collect like terms
=1+1+i-i
= 2-0
=2