Answers
Answer:
[tex]\dfrac{d^2y}{dx^2} = 5e^{3x} \sin (2x)+12e^{3x} \cos (2x)[/tex]
Step-by-step explanation:
[tex]\large \boxed{\begin{minipage}{5 cm}\textsf{\underline{Product Rule}}\\\\$ \textsf{When } \:y=uv\\\\\dfrac{dy}{dx}=u\dfrac{dv}{dx}+v \dfrac{du}{dx}$\\\end{minipage}}[/tex]
Given:
[tex]y=e^{3x} \sin(2x)[/tex]
First Derivative
[tex]\textsf{let } u=e^{3x} \implies \dfrac{du}{dx}=3e^{3x}[/tex]
[tex]\textsf{let } v= \sin(2x) \implies \dfrac{dv}{dx}=2 \cos (2x)[/tex]
Using the Product Rule:
[tex]\begin{aligned}\dfrac{dy}{dx} & =e^{3x}\cdot 2 \cos (2x) + \sin (2x) \cdot 3e^{3x}\\& = 2e^{3x} \cos (2x) + 3e^{3x} \sin (2x)\\& = e^{3x}(2 \cos (2x) + 3 \sin (2x))\end{aligned}[/tex]
Second Derivative
[tex]\textsf{let } u=e^{3x} \implies \dfrac{du}{dx}=3e^{3x}[/tex]
[tex]\textsf{let } v= 2 \cos (2x)+3 \sin (2x) \implies \dfrac{dv}{dx}=-4 \sin (2x) +6 \cos (2x)[/tex]
Using the Product Rule:
[tex]\begin{aligned}\dfrac{d^2y}{dx^2} & =e^{3x}(-4 \sin (2x) +6 \cos (2x)) +3e^{3x} (2 \cos (2x)+3 \sin (2x))\\& = e^{3x}[-4 \sin (2x) +6 \cos (2x)+6 \cos (2x)+9 \sin (2x)]\\& = e^{3x}[5 \sin (2x) +12 \cos (2x)]\\& = 5e^{3x} \sin (2x)+12e^{3x} \cos (2x)\end{aligned}[/tex]
Answer:
[tex] \tt{ \frac{ {d}^{2} y}{d {x}^{2} } = 5 {e}^{3x} \sin(2x) + 12 {e}^{3x} \cos(2x)}[/tex]
Step-by-step explanation:
⠀
⠀
⠀⠀⠀⠀▩ Question[tex]y = {e}^{3x} \sin(2x) \\ { \sf{To \: find}} \: \frac{ {d}^{2}y }{d {x}^{2} } [/tex]
⠀
⠀
⠀⠀⠀⠀■ Solution⠀
First finding dy/dx⠀
[tex] \sf using \: \frac{d}{dx} uv = u \frac{d}{dx} v + v \frac{d}{dx} u \: formula[/tex]
⠀
⠀
Taking derivative of sin2x and e^3x⠀
[tex] \bold{ \frac{dy}{dx} = {e}^{3x} \frac{d}{dx} \sin(2x) + \sin(2x) \frac{d}{dx} {e}^{3x} } \\ \\ \bold{ \frac{dy}{dx} = {e}^{3x} \cos(2x) \frac{d}{dx} 2x + \sin(2x) {e}^{3x} \frac{d}{dx} 3x}[/tex]
⠀
⠀
Multiplying⠀
[tex] \bold{ \frac{dy}{dx} = {e}^{3x} \times 2 \cos(2x) + \sin(3x) \times 3 {e}^{3x} }[/tex]
⠀
⠀
Value of dy/dx⠀
[tex] \bold{ \frac{dy}{dx} = 2 {e}^{3x} \cos(2x) + 3 {e}^{3x} \sin(2x) }[/tex]
⠀
⠀
Now taking derivative again using same formula as mention in first part, so that to find d²y/dx².⠀
⠀
⠀⠀● First solving 2e^3x cos(2x)
⠀
[tex] \bold{ 2( {e}^{3x} \frac{d}{dx} \cos(2x) + \cos(2x) \frac{d}{dx} {e}^{3x}) }[/tex]
⠀
⠀
Taking derivative of cos2x and e^3x⠀
[tex] \bold{2( {e}^{3x} - \sin(2x) \frac{d}{dx} 2x + \cos(2x) {e}^{3x} \frac{d}{dx} 3x)} \\ \\ \bold{ - 4 {e}^{3x} \sin(2x) + 6 {e}^{3x} \cos(2x) }[/tex]
⠀
⠀
⠀⠀● Now solving 3e^3x sin(2x)
⠀
[tex] \bold{ 3( {e}^{3x} \frac{d}{dx} \sin(2x) + \sin(2x) \frac{d}{dx} {e}^{3x} )}[/tex]
⠀
⠀
Now taking derivative of sin 2x and e^3x⠀
[tex] \bold{ 3( {e}^{3x} \cos(2x) \frac{d}{dx} 2x + \sin(2x) {e}^{3x} \frac{d}{dx} 3x)} \\ \\ \bold{ 6 {e}^{3x} \cos(2x) + 9 {e}^{3x} \sin(2x) }[/tex]
⠀
⠀
Adding both solution⠀
[tex] \bold{ \frac{ {d}^{2}y }{d {x}^{2} } = - 4 {e}^{3x} \sin(2x) + 6 {e}^{3x} \cos(2x) + 6 {e}^{3x} \cos(2x) + 9 {e}^{3x} \sin(2x) } \\ \\ \bold{ \frac{ {d}^{2} y}{d {x}^{2} } = 5 {e}^{3x} \sin(2x) + 12 {e}^{3x} \cos(2x) }[/tex]
Related Questions
2 times a number is 62 less than 284 , find the number
Answers
Answer:
The number is 111
Step-by-step explanation:
284-62= 222
2x111=284
Answer:
x = 111.
Step-by-step explanation:
Based on the given conditions, formulate: 2 * x = 284 - 62 Calculate the sum or difference:2 x = 222
A circle has radius 9.5 cm. Find the length of the arc intercepted by a central angle with measure 120°
Answers
Answer:
Step-by-step explanation:
Discussion
If the radius goes through 1 rotation. The "angle" gone through is 360 degrees. So the method is to figure out circumference of the circle, multiply this by a fraction involving 120, and you are done.
Formula
Arc Length = (120/360) * 2 * pi * r Substitute values into this equation.
Givens
Central angle = 120
r = 9.5
Solution
Arc Length = (120/360) * 2 * 3.14 * 9.5
Arc Length = (0.333) * 2 * 3.14 * 9.5
Arc Length = 19.87 cm
Billy purchased $100$ shirts at a cost of $\$15$ each and planned to resell them. The first week he sold some of them for $\$25$ each. The second week he sold the rest for $\$20$ each. If his total profit was $\$600$, how many shirts did he sell the first week?
Answers
Answer:
Let the number of shirts he sold the first week = x and the number sold the second week = 100 - x
So we have
[Sales] - [Cost] = Profit
[25x + 20(100 - x)] - [15 * 100] = 600 simplify
25x + 2000 - 20x - 1500 = 600
5x + 500 = 600 subtract 500 from both sides
5x = 100 divide both sides by 5
x = 20 = the number of shirts sold the first week
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
Let x = number of shirts sold in Week 1
Let y = number of shirts sold in Week 2
Profit = Selling price - cost price
If Billy purchased the shirts at a cost of $15 each, then
Week 1: Profit per shirt = $25 - $15 = $10Week 2: Profit per shirt = $20 - $15 = $5Equation 1
Total of 100 shirts purchased:
⇒ x + y = 100
Equation 2
Total profit of $600:
⇒ 10x + 5y = 600
Rewrite Equation 1 to make y the subject:
⇒ y = 100 - x
Substitute this into Equation 2 and solve for x:
⇒ 10x + 5(100 - x) = 600
⇒ 10x + 500 - 5x = 600
⇒ 10x - 5x + 500 = 600
⇒ 5x + 500 = 600
⇒ 5x = 600 - 500
⇒ 5x = 100
⇒ x = 100 ÷ 5
⇒ x = 20
Therefore, Billy sold 20 shirts in his first week.
What is the area of a square if one side is 14 centimeters long?
Answers
Answer:
A=a2=142=196cm²
Answer: 196 cm²
hope this helps :)
Answer:
196cm²
Step-by-step explanation:
All of a square's sides are congruent which means if one side is 14cm then all the other sides have to be 14cm as well.
To find the area you multiply the length and the width (A=l*w)
l=14, w=14
14*14=196cm²
pls help plssssss thank you 20 points
Answers
Answer:
7x - 10 < 11
Step-by-step explanation:
B
H
3.
6x
++
For this rectangle, find x.
15
180
90
6
k
Answers
Answer:
x =15
Step-by-step explanation:
its a rectangle all interior angles must be equal to 90 so 6x=90
divide by 6 to get x on its own and you get 15
Which is the graph of x≤2?
Answers
Answer:
Graph 2
Step-by-step explanation:
We are given the inequality x≤2
First off, with the inequality sign being ≤ rather than <, we know that 2 is also included. This means that x can be equal to 2 or less than 2.
Since 2 is included, we know we are looking for a solid line.
That said, we can eliminate the 1st and 4th graphs because there is a dotted line at 2, meaning that 2 is not included.
Next, based on the inequality sign, we know that values less than 2 satisfy it. So judging by the shaded region on each graph, we see that Graph 2 is the one that satisfies it.
For clarity's sake, one trick you can use is thinking of the inequality sign as an arrow. If it points left, values toward the left should be shaded and vice versa.
Lastly, I'll give you the inequality for each graph.
Graph 1: x<2
Graph 2: x≤2
Graph 3: x≥2
Graph 4: x>2
Hope that helps, let me know if you have any questions!
Your friend wants to sell his car (Toyota SUV). Your friend did some online research on similar cars and has found the following prices: $13,500 , $12,900, $15,300 , $13,700, and $12,000. What do you think would be a reasonable price for your friend to sell the car for? How did you come up with this price?
Answers
He should sell the car at a price of $15,300 because the profit is more at this price than the others.
What is the best selling price?The best selling price is defined as if the profit is more than the amount is known as the best selling price.
Your friend wants to sell his car (Toyota SUV).
Your friend did some online research on similar cars and has found the following prices: $13,500 , $12,900, $15,300 , $13,700, and $12,000.
He should sell the car at a price of $15,300 because the profit is more at this price than the others.
More about the best selling price link is given below.
https://brainly.com/question/7644542
#SPJ1
What is the value of 0.8–0.6? Write your answer as a fraction in lowest terms
Answers
Given expression:
[tex]0.8 - 0.6[/tex]To simplify the expression as a fraction in simplest form, let us multiply both terms by 10. Then, both terms must also be divided by 10.
[tex]\implies \dfrac{[10(0.8) - 10(0.6)]}{10}[/tex]
[tex]\implies \dfrac{[8 - 6]}{10}[/tex]
[tex]\implies \dfrac{[2]}{10} = \dfrac{2}{10}[/tex]
When 2/10 is simplified in lowest terms, we get;
[tex]\implies \dfrac{2}{10} \implies \dfrac{1 \times 2}{5 \times 2} \implies \dfrac{1}{5}[/tex]
Therefore, 0.8 - 0.6 in fraction form is 1/5.
solve for y
y/2 = x
thank you
Answers
Answer:
[tex] \frac{y}{2} = x \\ \\ y = 2x[/tex]
I will give brainliest and 40 points, please help
Answers
3. 1/5, 20%, 0.2
4. 1/2, 50%, 0.5
What is the domain of the function graphed below?
O(-2, ∞) O(-3,4] and [7, ∞). O(-∞,4). O [-2,0] and (7, ∞)
Answers
Using it's concept, it is found that the domain of the function graphed below is given by:
[tex](-2,4][/tex] and [tex][7, \infty)[/tex].
What is the domain of a function?It is the set that contains all possible input values for the function. In a graph, it is given by the values of x.
In this problem, x assumes values greater than -2 and less or equal than 4, and then values of 7 or greater, hence the domain is given by:
[tex](-2,4][/tex] and [tex][7, \infty)[/tex].
More can be learned about the domain of a function at https://brainly.com/question/10891721
#SPJ1
help please !!!!!!!!!!
Answers
Answer:
it is -3
Step-by-step explanation:
go to x=-4 and see what the y value of the line is
Answer:
1
Step-by-step explanation:
Find the equation of the line. Start with the y-intercept, which is -1. Next find the slope by doing rise/run. To get from (0, -1) to (2, 0) you rise 1 and run 2, so the slope is 1/2.
The equation is y= 1/2x -1.
Plugin 4 for x and solve for y.
y = 1/2(4) -1
y = 2 - 1
y = 1
Your hair is growing at 1 inch per month. You got your hair cut to 4 inches in length. Write and equation that gives the length of the hair, y, in terms of the months since your haircut, x
Answers
Answer:
Your hair grows 2 to 4 inches in 4 months, 4 to 6 inches in 9 months, and 6 to 8 inches in a year. Though this is how the usual growth cycle works, it also depends on seasonal changes, hair and scalp health, medications, hormonal changes, and diet among other factors.
Step-by-step explanation:
I need help please I’m confused
Answers
Answer:
the answer is bottom left trust
Answer:
bottom left is the answer
Step-by-step explanation:
John has 9 boxes of apples. Each box holds 10 apples. If 7 of the boxes are full, and 2 of the boxes are half full, how many apples does John have?
A. 29
B. 90
C.80
D. 45
Answers
Answer:
80
Step-by-step explanation:
10x7=70
2x5=10
70+10=80
The question is attached.
Answers
Answer:
B
Step-by-step explanation:
1/8 + 1/8 + 1/8 + 2/8 + 5/8 = 10/8 (The total amount of oj in each jug.)
(10/8)/5 = 2/8 (5 for the amount of jugs.)
2/8 = 1/4
a cube has a volume of 3375 cubic units calculate the length of one side of the cube
Answers
Answer:
volume = length^3
3375= length^3
therefore length = 15 units
You spin the spinner once.
4
1
3
2
What is P (odd)?
Write your answer as a percentage.
Answers
4 total numbers, 2 are odd
probability of getting odd = 2/4 = 0.50 =50%
Answer: 50%
Which equation represents the line that passes through the point (4, -5) and is
perpendicular to the line x + 2y = 5?
А
x - 2y = -14
B
x + 2y = -6
C 2x + y = 3
D
2x - y = 13
Answers
Answer:
D. 2x - y = 13
Step-by-step explanation:
We are given the line x + 2y =5
We want to find the equation that is perpendicular to this line, and that also passes through (4, -5)
Perpendicular lines have slopes that multiply to -1
First, let's find the slope of the line
The line is currently in standard form (ax+by=c), which doesn't show the slope; we can convert this line into slope-intercept form (y=mx+b, where m is the slope and b is the y intercept)
To do that, we will need to solve the equation for y
Here it is:
x + 2y = 5
Subtract x from both sides
2y = -x + 5
Divide both sides by 2
y = -1/2x + 5/2
The slope of the line is -1/2
Now, to find the slope of the line perpendicular to it, use this equation:
-1/2m = -1
Multiply both sides by -2
m = 2
The slope of the line perpendicular to it is 2
Here is the equation of the line so far in slope-intercept form
y = 2x + b
We need to find b
As the equation passes through the point (4, -5), we can use it to help solve for b.
Substitute 4 as x and -5 as y.
-5 = 2(4) + b
Multiply
-5 = 8 + b
Subtract 8 from both sides
-13 = b
This is our line:
y = 2x - 13
Even though this is in slope-intercept form, all of the options in your question are in standard form. Ergo, we must convert the line into standard form.
To do this, we can subtract 2x from both sides, as in standard form, x and y are on the same side
-2x + y = -13
Now multiply both sides by -1
2x - y = 13
This makes the answer D.
find the volume of this figure. round your answer to the nearest hundredth. if necessary
radius=8m
height=12m
#3
Answers
Replace the given values in place of the expression
PLEASE HELP?! IM SO CONFUSED!!
Answers
Answer:
C.
Step-by-step explanation:
-3 7/8 rounds down to -4
4.63 rounds up to 5
-4 x 6 + 5
-24 + 5
-19
her answer (-19.14) also rounds to -19
So yes, it is reasonable and the correct response is C.
URGENT!!
Statement:
All integers are irrational numbers.
True or False?
No whole numbers are irrational numbers.
True or False?
Some rational numbers are not integers.
True or False?
Some integers are not whole numbers.
True or False?
Answers
Answers:
FalseTrueTrueTrue====================================================
Explanations:
Any integer is rational. For instance, the integer 7 can be written as 7/1 which is a ratio or fraction of integers. Or we could say 14/2 or 21/3 if you wanted to get a bit creative. Since any integer is rational, this means it cannot be irrational. A real number is either rational or irrational. It cannot be both. The name "irrational" literally means "not rational". This is why statement 1 is false.The claim "no whole numbers are irrational numbers" is a true statement because any whole number is rational (for very similar reasoning as explained in statement 1 above), which means it's not possible for a whole number to be irrational.A rational number like 2/3 is not an integer. A quick way to check is to note that 2/3 = 0.67 approximately. Whole numbers and integers do not have any decimal portion to them. We have confirmed statement 3 is true.The set of integers is {..., -3, -2, -1, 0, 1, 2, 3, ...} while the whole numbers is the set {0, 1, 2, 3, ...}. The key difference is that integers involve negative values. Whole numbers do not have negative values. Something like -7 is an integer, but it is not part of the set of whole numbers. Statement 4 is true because of this.Can someone actually HELP me
Answers
Answer:
See below
Step-by-step explanation:
This is two parallel lines crossed by a TRANSVERSAL forming angles 1 - 8 , which are ALL transversal angles .
Angle 2 = angle 6 = angle 4 = angle 8 (congruent)
Angle 1 and angle 3 and angle 5 and angle 7 are also all equal
A 'straight angle' is a straight line and has a measure of 180 degrees
look at angle 1 and angle 2 ....they add up to a straight line = 180 degrees or angle 1 and angle 6 angle 1 and angle 4 each add to 180 degrees
Any angle in the underlined list above added to any angle in the bold list from above add to 180 degrees ....
Answer + Step-by-step explanation:
Angles 2 and 6 are transversal and congruent . (True) (Reason : Corresponding angles)
Angles 1 and 7 are transversal and congruent . (True) (Reason : Alternate Exterior Angles)
Angles 4 and 6 are transversal and congruent . (True) (Reason : Alternate Interior Angles)
Angles 5 and 7 are transversal and congruent . (True) (Reason : vertically opposite Angles)
What degree is a straight angle ? (180 degrees)
What would angles 1 and 6 add up to ? (180 degrees)
What would angles 8 and 3 add up to ? (180 degrees)
………………………………………………………………………………………
Angles W and Z add up to ? (180 degrees)
The sum of the 3 angles in a triangle (180 degrees)
Angle Z equals what measure ? (180 - (60+45) = 180 - 105 = 75 degrees)
Angle W equals what (180 - Z = 180 - 75 = 105 degrees)
Round 0.675 to the nearest tenth
Answers
Answer:
0.70
Step-by-step explanation:
it’s 0.70 because the 0.675 is rounded
The 7 is more than 5 so it’s closer to 8 which that you round up the 6 to a 7 and the same thing with 5. So that is how I know it’s 0.70 after rounding it.
Answer:
0.70
Consider the rounding rule for each place.
6 ≈ next tenths
7 ≈ next tenths
5 ≈ next tenths
This is because...
Below 5? Round down.5? Round up.More than 5? Round up.Turn the decimal 0.121212….. into a fraction
Answers
Part A - determine the slope of Line MN.
Part B - determine the length of line MN.
Answers
Reason
see attached picture for detailed math
If you have a mean of eight months and a standard deviation of two months approximately what percentage would between 6 to 8 months be
Answers
Answer:
34.1 %
Step-by-step explanation:
One standard deviation below the mean to the mean covers approx 34.1 %
Find the solution(s) to the system of equations represented in the graph? A circle with a line intersection at (-2,0) and (0,2)
Answers
Answer:
This is your teacher if you do this again, I will contact your parents and you will get in big trouble.
Step-by-step explanation:
what is the negation of x is greater than
39
Answers
Step-by-step explanation:
that means the opposite ...
the opposite of
x > 39
is
x <= 39