Answers
Answer:
[tex] I = \frac{1}{8} e^{4x^2} + C [/tex]
Step-by-step explanation:
This can be solved using substitution method. Let us work it out.
[tex] Let \: I = \int xe^{4x^2} dx[/tex]
[tex] \implies \: I = \int e^{4x^2} xdx[/tex]
[tex] Put \:4x^2 = t [/tex]
[tex] \implies 8x dx = dt [/tex]
[tex] \implies x dx = \frac{1}{8}dt [/tex]
[tex] \implies \: I = \int e^{t} \frac{1}{8}dt [/tex]
[tex] \implies \: I = \frac{1}{8} \int e^{t}dt [/tex]
[tex] \implies \: I = \frac{1}{8} e^{t} + C [/tex]
[tex] \implies \: I = \frac{1}{8} e^{4x^2} + C [/tex]
[tex] \implies \: \int xe^{4x^2} dx = \frac{1}{8} e^{4x^2} + C [/tex]
Related Questions
The pie chart below indicates the eye colors of students
in a statistics class
Which of the following could be the percentage of
students with brown eyes?
Eye Colors
O 10%
15%
20%
O 35%
Blue
Brown
Green
Hazel
Gray
Answers
Answer:
15% could be for brown eyes
Company A has three times as many customers as company B. Company C has 10 customers more than company B. Let x represent the number of customers held by company B. What is the expression that represents the total number of customers held by all three companies?
Answers
The expression that represents the total number of customers held by all three companies is 5x + 10
System of equationSystems of equations are made of several equations with unknown variables.
Let the amount of customers company B has be x
If Company C has 10 customers more than company B, then the total customers for company B is x + 10
If Company A has three times as many customers as company B, the total customers for company A is 3x
Total customers = x + 10 + x + 3x
Take the sum
Total customers = 5x + 10
Hence the expression that represents the total number of customers held by all three companies is 5x + 10
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An astronaut on the moon throws a baseball upward. The astronaut is 6 ft 6 in tall, and the initial velocity of the ball is 40 ft per sec. The height s of the ball in feet is
given by the equation s = -2.7t^2 + 40t + 6.5, where t is the number of seconds after the ball was thrown. Complete parts a and b.
a. After how many seconds is the ball 14 ft above the moon's surface?
After ____ seconds the ball will be 14 ft above the moon's surface.
(Round to the nearest hundredth as needed. Use a comma to separate answers as needed.)
Answers
Answer: 0.19s and 14.6s
Step-by-step explanation:
The distance of the ball at any time is given by the function s(t). For now, you can ignore all the details about the height of the man and the intial velocity of the ball. We only care about what time 't' will the ball be 14 feet off the ground. In math terms, they are asking when:
[tex]s(t)=14[/tex]
Where:
[tex]s(t)=-2.7t^2+40t+6.5=14[/tex]
Subtract 14 on both sides:
[tex]s(t)=-2.7t^2+40t-7.5=0[/tex]
Use the quadratic formula to solve for the variable 't'. This will give the possible time values where the ball will be 14 feet off the ground:
[tex]t=-b+\sqrt{b^2-4ac} /2a[/tex]
[tex]t=-b-\sqrt{b^2-4ac} /2a[/tex]
[tex]a=-2.7[/tex]
[tex]b=40[/tex]
[tex]c=-7.5[/tex]
Therefore:
[tex]t=(-40)+\sqrt{40^2-4(-2.7)(-7.5)} /2(-2.7)=0.19s[/tex]
[tex]t=-40-\sqrt{40^2-4(-2.7)(-7.5)} /2(-2.7)=14.6s[/tex]
This is saying the ball almost immediately hits 14 feet given the intial velocity, then it reaches its peak and falls back down to 14 feet again, where it will eventually hit the ground again
Help please i need this fast
Answers
Answer:
Mean=5, 77 Median=6 Mode=6 I hope this will help you
A game app costs a base fee of $5.
You can download additional booster packs for $1.50 per pack.
If you spend a total of $23 on the game, which equation correctly models the situation, where n is the number of booster packs purchased?
Answers
Answer:
Step-by-step explanation:
So you have a constant value of 5 dollars and a variable value of 1.50 dollars. some equation of these numbers equals 23 dollars. That equation is
23=5+(1.50n) where n is the number of booster packs.
Answer:
$23 = $5 + 1.5x
Step-by-step explanation:
We can make a format to find the equation.
Total = base fee + $ per pack
Let x = the number of packs
Therefore, the equation will be like this:
$23 = $5 + 1.5x
I hope this helps and please mark me as brainliest!
What is the value of x?
-5x = 60
Answers
Answer:
x = -12
Step-by-step explanation:
⇒ -5x = 60
Isolate the variable "x" by dividing by -5 on each side.
⇒ -5x/-5 = 60/-5
⇒ x = -12
The solution is x = -12
[tex]\boxed{ \sf \bold{x = -12}}[/tex]
Explanation:
[tex]\dashrightarrow \ \ \sf -5x = 60[/tex]
divide both sides by -5
[tex]\dashrightarrow \ \ \sf \dfrac{-5x}{-5} = \dfrac{60}{-5}[/tex]
simplify
[tex]\dashrightarrow \ \ \sf x = -12[/tex]
Please answer and have a great day :)
Answers
Answer:
180-108=72.
72/3=24.
24x2=48
Spencer deposited $10 in an account earning 5% interest compounded annually.
To the nearest cent, how much will he have in 3 years?
Answers
Answer:
I (interest) = $1.58
Step-by-step explanation:
A = $11.58
A = P + I where
P (principal) = $10.00
I (interest) = $1.58
First, convert R as a percent to r as a decimal
r = R/100
r = 5/100
r = 0.05 rate per year,
Then solve the equation for A
A = P(1 + r/n)^nt
A = 10.00(1 + 0.05/1)^(1)(3)
A = 10.00(1 + 0.05)^(3)
A = $11.58
Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $10.00 at a rate of 5% per year compounded 1 times per year over 3 years is $11.58
IM STUCK CAN SOMEBODY SOLVE EQUATION
Answers
Answer:
1.) 1169
2.) 7
3.) 167 students/year
4.) 1879
5.) 1879+167t
6.) 4050
Step-by-step explanation:
1.) Find the difference between the number of students in 2002 and 2009:
[tex]3382-2213=1169[/tex]
2.) Find the difference in the years:
[tex]2009-2002=7[/tex]
3.) To find the average growth, find the change between 2002 and 2009 and divide by 7.
[tex](3382-2213)/7=y\\1169/7=y\\167=y[/tex]
4.) To find the population of the students in the year 2000, we need to subtract the average growth time and the difference of years from 2213.
[tex]2213-167(2002-2000) = y\\2213-334=1879[/tex]
5.) Taking the equation above, and changing it to match the requirements, we get:
[tex]P = 1879+167t[/tex]
6.) Now find the difference between 2013 and 2000, and substitute for t to get:
[tex]P = 1879+167(2013-2000)\\P = 1879+167*13\\P = 4050[/tex]
Which of the following is in vertex form of quadratic?
Answers
The vertex form of quadratic equation is f(x) = -5(x-1)^2 + 6
Vertex form of a quadratic equation
A quadratic equation is written in its vertex form in order to easily determine the maximum or minimum point on the curve.
The standard vertex form of an equation is given as:
a(x-b)^2 + k
From the given option, we can see that the only eqeuation writen in this form is f(x) = -5(x-1)^2 + 6
Hence the vertex form of quadratic equation is f(x) = -5(x-1)^2 + 6
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Please help me asap I’ll mark brainly
Answers
Answer: 36
Step-by-step explanation:
Answer:
Step-by-step explanation:
first box (far left) should be 1/6
second box should be 24
third box (far right on first equation) should be 10
p = 24
KILP: Algebra 1B [M] (Sequential) / 4:Radical Expressions and Equations
The sales of a certain product after an initial release can be found by the equation
s=12 4t +10, where s represents the total sales in thousands) and t represents
the time in weeks after release.
Make a table of values, graph the function and use the graph to estimate the sales
1. 12 weeks after release.
O about $586
O about $586,000
O about $93
about $93,000
Answers
The correct table of values, graph the function and use the graph to estimate the sales 1 .... 12 weeks after release is,
t s = 12 √4t + 10
1 34
2 43.94
3 51.56
4 58
5 63.66
6 68.78
7 73.49
8 77.88
9 82
10 85.89
11 89.59
12 93.13
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The sales of a certain product after an initial release can be found by the equation,
⇒ s = 12 √4t + 10
where s represents the total sales (in thousands) and t represents the time in weeks after release.
Here, The equation is,
⇒ s = 12 √4t + 10
where, s represents the total sales (in thousands) and t represents the time in weeks after release.
We put t=1,2,3,.....,12 and create a table
t s = 12 √4t + 10
1 34
2 43.94
3 51.56
4 58
5 63.66
6 68.78
7 73.49
8 77.88
9 82
10 85.89
11 89.59
12 93.13
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A contractor on construction job specified a penalty for delay of completion beyond a certain date as: Rs.200 for the first day, Rs.250 for the second day, Rs300 for the third day and so on. The penalty for each succeeding day being Rs50 more than that of preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by 30 days?
Can someone tell me the answer of this??
Answers
Answer:
Rs 27750Step-by-step explanation:
The penalty for each day forms a sequence
200, 250, 300, ...This is an AP with the first term of 200 and common difference of 50
The sum of the first 30 terms is
[tex]S_{30}=30*(a_1+a_{30})/2=15(200+200+29*50) = 27750[/tex]Answer :
Refer to the attachmentAdditional Information :
Arithmetic progression (A.P.) is a sequence in which each term can be found by adding a certain quantity to its preceding termDifference between two consecutive terms is called common differenceProgression means it's a type of sequence in which each term is related to its predecessor and successor.You have a bag of gummy worms with 5 green, 3 blue, 6 red, and 2 orange. Which expression represents the probability that you will reach into the bag and pull a red worm, eat it, and then pull a green worm?
Answers
Answer:
[tex]\frac{1}{8}[/tex] I think
Step-by-step explanation:
you have a bag witha a total of 16 gummy worms right? 6 out of 16 of them are red, 5 out of 16 are green.
so you pull out a red one and eat it. the probabilty of you doing that is [tex]\frac{6}{16}[/tex] . keep it in mind that you ate a gummy worm.after enjoying that gummy worm you decide to take another one, but this time, it's green. you know you just ate one right, but you did not replace it now did you? what that means is out of the 16 gummies you had, you are now left with 15 (because you ate one).now you are left with 15 gummy worms. you take a green one out of the packet. the probabilty of you doing that is [tex]\frac{5}{15}[/tex].now that you've got your probabilities all sorted, now it's time to use some basic probability principles. if you ever come across a probability question with the word and, you need to know automatically that you are multiplying. if you ever come across the word or, you are adding. it's always gonna be like this.
so when you multiply your two probabilities, you get the answer [tex]\frac{1}{8}[/tex]
whenever you're dealing with probability, make sure you're aware of things that are being taken. check whether they're being replaced or not. the way I attempted at working it out is how the other probability questions involving replacements are solved, no matter what it is.
I really hope you found this helpful (that is if all I said is correct) :)
What is the value of the x-coordinate of point A?
Answers
Answer:
(1/2,square root 3/2) is the answer
hey, can I have some help with this? I don't get it so let me know if you have an explentation. Thanks :)
Answers
Answer: 250
Step-by-step explanation:
This problem is attempting to explain the distributive property to you.
The distributive property states that if you have the numbers a, b, and c:
[tex](a*c) + (b*c) = c * (a+b)[/tex]
In your specific case, this would look like this:
[tex](23+37) * 4\frac{1}{6}[/tex]
[tex]60 * \frac{(4*6)+1}{6}[/tex]
[tex]60*\frac{25}{6}[/tex]
To simplify, we factor a 6 out of the equation:
[tex]10*25 = 250[/tex]
If the perimeter of the triangle shown below is 48x + 9, what is the length of the missing side? 4x+2 3x – 9 NEED ANSWER ASAP
Answers
Answer:
41x+16
Step-by-step explanation:
4x+2+3x-9+c=48x+9. You can move all the things you know to the other side.
c= 48x-4x-3x-2+18
c=41x+16
The Jones' old $47,000, 30 year, 12.8% mortgage has a monthly payment of $512.58. Over the 6 years since they took the loan, mortgage rates dropped. They can now apply for a mortgage at 9.05%, which will result in a new monthly payment of $369.36. To refinance, they must pay $1,020 in closing costs and a $480 prepayment penalty. Find the net amount they will save in the first year.
Answers
The net amount that will be saved by the Jones for the first year will be $814.32.
How to calculate the net amount?From the information given, the old mortgage yearly payment will be:
= Monthly payment × Months
= $259.32 × 12
= $3111.84
The new monthly yearly payment will be:
= Monthly payment × Months
= $327.18 × 12
= $3926.16
Therefore, the net amount that will be saved will be:
= $3926.16 - $3111.84
= $814.32
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At a concession stand, three hot dog(s) and two hamburger(s) cost $7.50, two hot dog(s) and three hamburger(s) cost $8.75. Find the cost of one hot dog and the cost of one hamburger
Answers
Step-by-step explanation:
If 3 HD and 2HB cost $7.50
2 HD and 3HB cost $8.75
Let,y be HD
Y be HB
So 3y + 2x = $7.50. Eqn 1
2y + 3x = $8.75. Eqn 2
Solve simultaneously
Make x the subject in Eqn 1
3y + 2x = 7.50
2x = 7.50 - 3y
Devide by the coefficient of x
2x/2 = (7.50 - 3y) / 2
X = (7.50 - 3y) /2 Eqn 3
Put Eqn 3 into 2
2y + 3(7.50 - 3y) / 2 = 8.75
2y (22.5 - 9y) / 2 =8. 75
Multiply by the lcm of the denominators
2y x 2 + ((22.5 - 9) / 2) x 2 = 8.75 x2
4y + 22.5 - 9y = 17.50
Group like terms
22.5 - 17.50 = 9y - 4y
5 = 5y
5/5 = (5y) / 5
1 = y Eqn 4
Therefore 1 HD is $1
Put Eqn 4 into eqn 3
X = (7. 50 - 3y) / 2
X = (7.50 - 3(1)) / 2
X = 4.5 / 2
X = 2.25
Therefore 1 HB is $2.25
A storage compartment is shaped like this hexagonal prism. The prism has a base area of 7.35 cm². What is the volume of the compartment? Enter your answer as a decimal in the box.
Answers
I don’t understand, can anyone help me?
Answers
Answer:
Step-by-step explanation:
If x = 0, f(x) = -15.
If f(x) = 27, x = 3.
what is 1 1/2 multiply 12
Answers
Answer:
66
Step-by-step explanation:
hello :
1 1/2 multiply 12 means : (11×12/2)= (11×6×2)/2 =66
Write an equation of the line with a slope of -3 and y -intercept of 0 .
y=
Answers
Answer:
y=-3x
Step-by-step explanation:
2. A classroom fish tank contains x clchilds. The tank contains 3-times as many glowlight tetras as cichlids.
Enter an equation that represents the total number of glowlight tetras, y, in the fish tank.
Answers
The equation that represents the total number of glowlight tetras, y, in the fish tank is y = 3x.
How to form a equation?
The classroom fish tank contains x cichilds. Therefore,
number of cichilds = x
The tank contains 3-times as many glowlight tetras as cichlids.
where
y = total number of glowlight tetras in the fish tank
Therefore, the equation that represents the total number of glowlight tetras, y, in the fish tank is as follows:
y = 3x
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Find the measure of the missing angle.
Answers
Answer:
You see that 73 degrees and angle 'a' must add up to be = to 180 degrees since both angles form that straaight line on the left. So 180 degrees - 73 = 107 degrees which is measure of angle 'a'
Step-by-step explanation:
Answer:
107°
Step-by-step explanation:
The two angles below form a linear pair.
They are characterized by forming a sum of 180°, which is the standard angle measure of any line.
⇒ a + 73° = 180°
⇒ a = 107°
Please help me I’ll mark brainly
Answers
Answer:
Step-by-step explanation:
In the first equation, -4 x -b should be postive 4b, so +4b, because a negative times a negative equals a postive
Answer: 7
Step-by-step explanation: -4(6 - b) = 4
-24 + 4b = 4
The negative turns into a postive for 4b because two negatives make a postive.
4b (positive) = 28
b = 7
Manuel wants to rent a boat and spend at most 34. The boat costs 8 per hour, and Manuel has a discount coupon for 6 off. What are the possible numbers of hours Manuel could rent the boat?
Answers
5 hours
6 times 5 is 30, and if hes not wanting to go over, then it'd be 5 hours for $30
Oliver earns five dollars for each lawn he mowed.If he he’d six lawns to move but forgot to mow three of them how much money did he actually earn
Answers
$15
Explanation:
For each lawn he mows = $5
He should mow 6 lawns but did only 3 lawns as other 3 he forgot to mow.
earned:
mows lawn-d * $53 * $5$15Puzzle Two
Determine the volume of the following spheres with the given dimensions. To break
the code find the mean of all your answers. Round your answers to the hundredth
place. Use 3.14 for an approximation for pl.
1)
3)
18 in
3 cm
2)
4).
10
42 in
Code:
B
Answers
The volume of a sphere is the amount of space in it
The volumes of the spheres are 24416.64, 113.04 and 310181.76
How to determine the volume of the spheres?The volume of a sphere is calculated using:
V = 4/3 πr^3
When the radius, r = 18, we have:
V = 4/3 * 3.14 * 18^3
V = 24416.64
When the radius, r = 3, we have:
V = 4/3 * 3.14 * 3^3
V = 113.04
When the radius, r = 42, we have:
V = 4/3 * 3.14 * 42^3
V = 310181.76
Hence, the volumes of the spheres are 24416.64, 113.04 and 310181.76
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Please help me with Part C of this question!!!
Answers
Answer:
a. 3/4 inches per minute
b. -1 1/8 inches per minute
c. B is fastest; 1 1/8 is more than 3/4
Step-by-step explanation:
A change is a difference. A rate of change is one difference divided by another, usually the change in y-value divided by the change in x-value.
__
a.The change in elevation is the difference between the elevation at the end of the period (6 inches) and the elevation at the beginning of the period (3 inches). The change in time period is the difference between the end time (8 min) and the beginning time (4 min).
change in elevation per minute = (6 -3 inches)/(8 -4 min)
= (3 inches)/(4 min) = 3/4 inches/minute
__
b.Similarly, ...
change in elevation per minute = (3 -7 1/2 inches)/(18 -14 min)
= (-4 1/2 inches)/(4 min) = -1 1/8 inches/minute
__
c.We know that 3/4 is more than -1 1/8, but when we talk about the "fastest rate of change", we're generally interested in the magnitude--the value without the sign. That means we understand a rate of change of -1 1/8 inches per minute to be "faster" than a rate of change of 3/4 inches per minute.
The rate of change from Part B is fastest. 1 1/8 inches per minute is more than 3/4 inches per minute.