Answer:
f(g(x))=2x-5
Step-by-step explanation:
f(g(x))=2(x-3)+1
U-substitutions only work for specific kinds of expressions. Below, you are asked to choose a value of n for which u-substitutions will be a useful integration technique. Then, you are to compute the antiderivative with that specific n. (E.g., if n = 5 makes u-subs work, then solve the integral with a 5 in place of n).
(a) [ zºeke*+1 "'de
(b) /co cos(1/2) dr
(c) / r+n dr 22 + 8x - 4
Answer:
Step-by-step explanation:
(a) [tex]\int x^n e^{5x^4+1} \ dx[/tex]
Suppose [tex]5x^4 + 1 = f[/tex]
by differentiation;
[tex]\implies \ 20 x^3 dx = df --- (1)[/tex]
Suppose n = 3
Then, the integral
[tex]I = \int x^ 3 e^{5x^4 + 1} \ dx[/tex]
[tex]= \int e^f \ \dfrac{df}{20}[/tex]
[tex]= \dfrac{1}{20} \int e^f \ dt[/tex]
[tex]= \dfrac{1}{20} e^f + C[/tex]
recall that [tex]f = 5x^4 + 1[/tex]
Then;
[tex]\mathbf{ I = \dfrac{1}{20}e^{5x^4+1}+C}[/tex]
(b) [tex]\int \dfrac{cos (\dfrac{1}{x^3})}{x^n } \ dx[/tex]
suppose; [tex]\dfrac{1}{x^3} = f[/tex]
[tex]x^3 = f[/tex]
[tex]\implies -3x^{-4} \ dx = df[/tex]
[tex]\implies \dfrac{1}{x^4} \ dx =-\dfrac{1}{3} df[/tex]
If n = u, then the integration is:
[tex]I = \int \dfrac{1}{x^4} \ cos (\dfrac{1}{x^4}) \ dx[/tex]
[tex]= \int -\dfrac{1}{3} \ cos \ f \ df[/tex]
[tex]= -\dfrac{1}{3} \int \ cos \ f \ df[/tex]
[tex]= -\dfrac{1}{3} \ sin \ f + C[/tex]
Since; [tex]x^3 = f[/tex]
Then;
[tex]\mathbf {I = -\dfrac{1}{3} \ sin \ \Big( \dfrac{1}{x^3}\Big) + C}[/tex]
(c) [tex]\int \dfrac{x+n}{x^2 + 8x -4} \ dx[/tex]
Suppose [tex]x^2 + 8x - 4 = f[/tex]
Then, by differentiation of both sides
[tex](2x + 8) \ dx = df[/tex]
[tex](x + 4) \ dx = \dfrac{1}{2} \ df[/tex]
Suppose n = 4 in integration, then:
[tex]I = \int \dfrac{(x + 4) }{x^2 +8x -4} \ dx[/tex]
By substitution;
[tex]I = \int \dfrac{1}{2}\dfrac{1}{f} \ df[/tex]
[tex]= \dfrac{1}{2} \ \ { In |f|} + C[/tex]
[tex]\mathbf{= \dfrac{1}{2} \ \ { In |x^2+8x -4|} + C}[/tex]
The suitable substitutions of n are 3,4,4 respectively.
What is integration?The process of finding integrals is called integration.
a)[tex]f(x)=\int\limits {x^3e^{5x^4+1} } \, dx[/tex]
Suppose
[tex]5x^4+1 =t\\20x^3 dx =dt[/tex]
So, we need n=3 for easy integration.
[tex]f(x)=\int\limits {x^3e^{5x^4+1} } \, dx[/tex]
[tex]I = \frac{1}{20} \int\limits {e^{t} } \, dt[/tex]
[tex]I=\frac{e^{t} }{20}[/tex]
[tex]I = e^{5x^{4}+1 }/20 +c[/tex]
b)Similarly for [tex]f(x) = \int\limits\frac{cos(\frac{1}{x^3} )}{x^n} \, dx[/tex]
n=4 is needed for easy integration.
I = [tex]\frac{-1}{3} sin(\frac{1}{x^3} ) +c[/tex]
c)For [tex]f(x) = \int\limits \frac{x+n}{x^{2} +8x-4} \, dx[/tex]
n=4 is needed for easy integration.
[tex]I = \frac{1}{2} log(x^{2} +8x-4)[/tex]
Hence, the suitable substitutions of n are 3,4,4 respectively.
To get more about integration visit:
https://brainly.com/question/2633548
−2y−8+4yminus, 2, y, minus, 8, plus, 4, y
Answer:
a number 12
Step-by-step explanation:
duh bro
Work out the surface area of this cylinder 8.2cm 17.5cm
Answer: 1324.12 sq. cm.
Step-by-step explanation:
A=2πrh+2πr2
A = 2π x 8.2 x 17.5 + 2π x 8.2^2
A = 2π x 143.50 + 2π x 67.24
A= 1324.12
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Stephanie swims 4/5 of a mile in 5/6 of an hour.
Enter the number of miles Stephanie swims in 1 hour.
Hi.. U should do like this
4/5 mile in 50 min
X mile in 60 min
X=5/4 mile
Answer:
5 milesss
:)))
Help me with this thx <3
Pls find this asap I am already late for this pls
Answer:
Step-by-step explanation:
I'm not sure about number 3, but I have the answer for number. The answer is 1:32.
3: 69
3/69
Then we reduce the fraction to the lowest term
3/69 = 1/32
1:32
Just divide 96/3 and you can see that one bus can hold 32 students
All flour from five bags with 3/8 lbs of flour in each was divided into equal parts to make 7 loaves of bread. How can you calculate the amount of flour used for each loaf? select all that apply
was divided into equal parts to make 7 loaves of bread. How can you mount of flour used for each loaf? select all that apply
Step-by-step explanation:
Answer:
B, C, F
Step-by-step explanation:
C = 3/8 divided 7 times 5. 3/8 lbs of flour in each was divided into equal parts to make 7 loaves. 3/8 divide by 7. Since there are 5 bags, times 5.
B = 3/8 times (for the five bags) times 5 divided by 7 samething from C.
F = You know the pattern now. Hint: B is the answer...
write an equivalent expression for the following using distributive property A(9b+13)
apply distributive property AKA (A • 9b)+(A • 13)
9Ab + 13A
I hope this helps :)
Only answer if you're sure its correct!
Answer:
im sure its D.)
Step-by-step explanation:
Heather is a cashier. She can ring up 121 customers in 9 minutes.
At this rate, how many minutes does it take her to ring up 4 customers
Answer:
In four minutes Heather can ring up 52 maybe even 53 customers.
Step-by-step explanation:
To find this answer you would have to find how many customers Heather can rind up in one minute. To do this you can do 121 divided by 9 which equals about 13 so you can use 13. And then you would do 13 times 4 because that's how many minutes the question is asking for, and your answer would be about 52, so your answer is about 52 close to 53, you might not get an exact answer for a problem like this. :)
Write an equation in the first box (use x as your variable). Then, solve (in second box).
Answer: 3.2x = 48
Step-by-step explanation: So that means x = 15.
Hal is going over the credit scores he received from the three major credit bureaus. He Experian score is 711, his
Equifax score is 736, and his TransUnion score is 736. What is the mode of Hal's credit scores? (Round to the nearest
whole point, if applicable.)
736
b 728
723
d There is no mode in this group
a
С.
Please select the best answer from the choices provided
A
B
ОООО
C
D
Mark this and retum
Save and Exit
Next
Submit
Answer:
A
Step-by-step explanation:
It is letter A I got 100!
Answer:
A
Step-by-step explanation:
EDGE 2021
What is the measure of the missing leg of a right triangle if the hypotenuse measures 10 ft and the other leg measures 8 ft?
Answer:
2?
Step-by-step explanation:
Shannon, Oscar, and Ella contribute the same amount to their father’s gift. Their older sister Moriah contributes $12. How much does Oscar contribute if the total for the gift is $36? Write and solve an equation.
Answer:
Amount contributed by Oscar = $8
Step-by-step explanation:
Given that:
Amount spent on gift = $36
Amount contributed by Moriah = $12
Let,
x be the amount contributed by each of them.
Thus,
Gift total = Contribution of all
36 = x+x+x+12
36 = 3x+12
3x+12 = 36
3x=36-12
3x=24
Dividing both sides by 3
[tex]\frac{3x}{3}=\frac{24}{3}\\x=8[/tex]
Hence,
Amount contributed by Oscar = $8
please help me guys lol?
Answer:
Hey
Step-by-step explanation:
Write the fraction in simplest form
[tex] - \frac{29}{18} [/tex]
EXPLANATION[tex] \frac{8}{9} - \frac{5}{2} [/tex]
Find the difference between 8/9 and 5/-2
[tex] \frac{8}{9} - \frac{5}{2} [/tex]
[tex] \frac{8 \times 2}{9 \times 2} - \frac{5 \times 9}{2 \times 9} [/tex]
[tex] \frac{16}{18} - \frac{45}{18} [/tex]
[tex] \frac{16 - 45}{18} [/tex]
[tex] \frac{ - 29}{18} [/tex]
[tex] - \frac{29}{18} [/tex]
how might you ask for 1/10 of a liter of water
Answer:
weird questions but...
May I have 4 cups of water please?
Answer:
deciliter of water
Step-by-step explanation:
a unit of capacity equal to 1/10 of a liter.
express the surface area A of a cube in terms of its volume V
Translate and solve: fifty times n is at most 500.
Answer:
n must be less than or equal to 10
Step-by-step explanation:
The general manager, marketing director, and 3 other employees of Company A are hosting a visit by the vice president and 2 other employees of Company B. The eight people line up in a random order to take a photo. Every way of lining up the people is equally likely.
(a) What is the probability that the general manager is next to the vice president?
(b) What is the probability that the marketing director is in the leftmost position?
(c) Determine whether the two events are independent. Prove your answer by showing that one of the conditions for independence is either true or false.
Solution :
Let the three places be 1, 2, 3, 4, 5, 6, 7, 8
a). Number of the cases when a general manager is the next to a vice president is equal to 7 and the these 2 can be arranged in 21 ways. So the total number of ways = 7 x 2
= 14
[(1,2)(2,1) (2,3)(3,2) (3,4)(4,3) (4,5)(5,4) (5,6)(6,5) (6,7)(7,8) (8,7)(7,6)]
Therefore the required probability is
[tex]$=\frac{14}{8!}$[/tex]
= [tex]$\frac{14}{40320} = 0.000347$[/tex]
b). The probability that the marketing director to be placed in the leftmost position is
[tex]$=\frac{7!}{8!}$[/tex]
[tex]$=\frac{1}{8} = 0.125$[/tex]
c). The two events are not independent because
[tex]$P(A \cap B) \neq P(A) \times P(B)$[/tex]
[tex]$\frac{12}{8!} \neq \frac{14}{8!} \times \frac{1}{8}$[/tex]
where A is the case a and B is the case b.
(a) The possibility of the general manager is next to the vice president is [tex]\frac{1}{4}[/tex].
(b) The possibility of the marketing director is in the leftmost position is [tex]\frac{1}{8}[/tex].
(c) So, the two events are dependent on each other.
Probability:
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it. The probability of all the events in a sample space adds up to 1.
Total people in company A and company B is [tex]=8[/tex]
Overall ways in which these [tex]8[/tex] people can be lined up[tex]=8![/tex]
[tex]=40320[/tex]
(a) The probability that the general manager is next to the vice president is[tex]=P(A)[/tex]
Now, we can combine the general manager and vice president as one, then the total people in both the company will become [tex]7[/tex].
by arranging these [tex]7[/tex] people in one line [tex]=7![/tex]
[tex]=5040[/tex]
Again, combine the general manager and vice president in one line[tex]=2![/tex]
[tex]=2[/tex]
Therefore, [tex]P(A)=\frac{5040\times 2}{40320}[/tex]
[tex]=\frac{10080}{40320}[/tex]
[tex]P(A)=\frac{1}{4}[/tex]
(b) The probability that the marketing director is in the leftmost position is[tex]=P(B)[/tex]
Now, fixing the position of marketing director in the leftmost.
arranging the [tex]7[/tex] other people in [tex]7![/tex] ways [tex]=5040[/tex]
Therefore,[tex]P(B)=\frac{5040}{40320}[/tex]
[tex]=\frac{1}{8}[/tex]
[tex]P(B)=\frac{1}{8}[/tex]
(c) Assuming event B already occurred which means that the position of marketing director is already fixed in the leftmost position.
Now, trying to find out the probability of the general manager next to the vice president is event A. it comes different because we are not allowed to arrange rest [tex]7[/tex] people, we have to fix the position of one person that causes the repetition of probability.
So, the two events are dependent on each other.
Learn more about the topic of Probability: https://brainly.com/question/26959834
Pls help extra points and mark brainlist easy reading
Answer: It's the third one down
Step-by-step explanation:
Where art thou smart people
Answer:
a smart person is not me clearly lol
Step-by-step explanation:
What is the product of (2x – 3)(4x + 1)
Answer: 8x^2 - 10x - 3
Step-by-step explanation:
first, we multiply the parentheses.
2x x 4x + 2x - 3 x 4x - 3
then, we calculate all of that junk.
8x^2 + 2x - 12x - 3
finally, we collect the like terms.
8x^2 - 10x - 3
Answer:
8x^2-10x3
Step-by-step explanation:
8x^(add the 2 upbove the x)-10x-3
Jessica locates her garden using a coordinate grid with yards as the units. The two points
(-5, -2) and (-8, -3) represents the two corners of the garden. Approximately how far
apart are the two corners?
Answer:
These two corners are [tex]\sqrt{13}[/tex] units apart.
Step-by-step explanation:
Distance between two points:
Suppose we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Approximately how far apart are the two corners?
We have to find the distance between the points (-5,-2) and (-8-3). So
[tex]D = \sqrt{(5-(-8))^2+(-2-(-3))^2} = \sqrt{13}[/tex]
These two corners are [tex]\sqrt{13}[/tex] units apart.
A convex polygon has 6 sides what is the sum of its interior angles 1980°.
Step-by-step explanation:
Sum of interior angles in a polygon
= 180°(n - 2), where n is the number of sides.
Hence a convex polygon with 6 sides
=> 180°(6 - 2) = 720°.
I need help plz I will mark brainliest
please help i am really struggling
Answer:
greater than...
equal
Step-by-step explanation:
welcome
Need help on this one, can someone please answer this?
Answer:
quadrant 3
Step-by-step explanation:
CORRECT ANSWER AND I WILL THANK, GIVE 5 STARS, AND GIVE BRAINLIEST!!!!
System Of equations:
Solve by elimination:
7x + 2y = 13
x - 2y = 11
Group of answer choices
(3 . -4)
(3 , 4)
(4 , 3)
(-4 , -3)
[tex](7x + 2y) + (x - 2y) = 13 + 11 \\ 8x = 24 \\ x = \frac{24}{8} \\ x = 3[/tex]
Substitute x = 3 in any given equations.[tex]x - 2y = 11 \\ 3 - 2y = 11 \\ 3 - 11 = 2y \\ - 8 = 2y \\ \frac{ - 8}{2} = y \\ - 4 = y[/tex]
Answer Check
Substitute x = 3 and y = - 4 in both equations.[tex]7x + 2y = 13 \\ 7(3) + 2( - 4) = 13 \\ 21 - 8 = 13 \\ 13 = 13[/tex]
[tex]x - 2y = 11 \\ 3 - 2( - 4) = 11 \\ 3 + 8 = 11 \\ 11 = 11[/tex]
Both equations are true for x = 3 and y = 4.
Answer[tex] \large \boxed {(3, - 4)}[/tex]
Feel free to ask if you have any questions related to the answer or the explanation.
how do you create a graph for linear equation? I need to graph 3x=4
Answer:
Look at the graph below, hope this helped.
Step-by-step explanation:
The dimensions of a cylindrical water tank are shown below.
18 yd
o
58,320 yd
3,240 yd
60 yd
O
19,440 yd
15,270 yd3
Which of the following is the best estimate of the volume of
this water tank?