Answers
Answer:
C
Step-by-step explanation:
We want to integrate:
[tex]\displaystyle \int\frac{4x^4+3}{4x^5+15x+2}\,dx[/tex]
Notice that the expression in the denominator is quite similar to the expression in the numerator. So, we can try performing u-substitution. Let u be the function in the denominator. So:
[tex]u=4x^5+15x+2[/tex]
By differentiating both sides with respect to x:
[tex]\displaystyle \frac{du}{dx}=20x^4+15[/tex]
We can "multiply" both sides by dx:
[tex]du=20x^4+15\,dx[/tex]
And divide both sides by 5:
[tex]\displaystyle \frac{1}{5}\, du=4x^4+3\,dx[/tex]
Rewriting our original integral yields:
[tex]\displaystyle \int \frac{1}{4x^5+15x+2}(4x^4+3\, dx)[/tex]
Substitute:
[tex]\displaystyle =\int \frac{1}{u}\Big(\frac{1}{5} \, du\Big)[/tex]
Simplify:
[tex]\displaystyle =\frac{1}{5}\int \frac{1}{u}\, du[/tex]
This is a common integral:
[tex]\displaystyle =\frac{1}{5}\ln|u|[/tex]
Back-substitute. Of course, we need the constant of integration:
[tex]\displaystyle =\frac{1}{5}\ln|4x^5+15x+2|+C[/tex]
Our answer is C.
Related Questions
Asha is tiling the lobby of the school with one-foot square tiles. She has 6 bags
of tiles with 50 tiles in each. The lobby is a 30-foot by 8-foot rectangle. How
many tiles will Asha have left over after she tiles the lobby?
Answers
Answer:
60 tiles left over
Step-by-step explanation:
the lobby needs 30 x 8 = 240 tiles.
she has 6 x 50 = 300 tiles
300 - 240 = 60 left over
if Patty has 56 apples and And has 87 pears how many grapes do they have in total including Ava's 890 blueberries?
Answers
Answer:
Patty has 10 onions, And has 500 watermelons and Ava has a banana
dilation of 1.5 about the origin
Answers
Answer:
Step-by-step explanation:
use the rule they tell you of 1.5
so (x,y) ⇔1.5(x,y)
w = (2,0)
x = ( 0,2)
y = (-2, 1)
z = (0, -2)
1.5(x,y)
W' = (3,0)
X'= (0, 3)
Y' = ( -3, 1.5)
Z' = (0, -3)
nice :)
If John gets paid $45.00 an hour and works 10 hours, how much does he earn?
Answers
SOMEONE HELP ME PLEASE!!!!?
Answers
Answer:
139
Step-by-step explanation:
supplementary angles add up to equal 180
so to find the measure of angle ABC we subtract the given angle from 180
180-41=139
so we can conclude that angle ABC= 139
Step-by-step explanation:
< ABC and < CBD are supplementary angles.
< CBD = 41°
< ABC + < CBD = 180° ( Being supplementary angles)
< ABC + 41° = 180°
< ABC = 180° - 41°
< ABC = 139°
Hope it will help :)❤
Identify the correct form of the following geometric sequence.
5 , 35 , 245 , 1,715 , ...
Answers
The correct form of the geometric sequence is:[tex]5, 35, 245, 1,715, ... = 5, 5 * 7, 5 * 7^2, 5 * 7^3, ...[/tex]
how to Identify the correct form of the geometric sequence.To identify the correct form of the geometric sequence 5, 35, 245, 1,715, ..., we can look for a common ratio between consecutive terms.
To find the common ratio, we divide any term by its preceding term. Let's take the second and first terms:
35 / 5 = 7
Now, let's check the third and second terms:
245 / 35 = 7
Similarly, for the fourth and third terms:
1,715 / 245 = 7
Since we obtained the same result (7) for all ratios, we can conclude that the common ratio of this geometric sequence is 7.
Now, let's express the general form of the sequence using the first term (a) and the common ratio (r):
a, ar, [tex]ar^2,[/tex] [tex]ar^3,[/tex] ...
Substituting the given values:
a = 5 (the first term)
r = 7 (the common ratio)
The correct form of the geometric sequence is:
[tex]5, 5 * 7, 5 * 7^2, 5 * 7^3[/tex], ...
Simplifying the terms, we get:
5, 35, 245, 1,715, ...
Therefore, the correct form of the geometric sequence is:
5, 35, 245, 1,715, ... = 5, 5 * 7, 5 * 7^2, 5 * 7^3, ...
Learn more about geometric sequence at https://brainly.com/question/1509142
#SPJ1
Quadrilateral A'B'C'D' Is the image of quadrilateral ABCD under a dilation.
What is the scale factor of the dilation?
Answers
Answer:
Scale factor = [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Formula for the dilation to be used,
Scale factor = [tex]\frac{\text{Dimension of the image}}{\text{Dimension of the original}}[/tex]
= [tex]\frac{A'B'}{AB}[/tex]
= [tex]\frac{1}{4}[/tex]
Therefore, scale factor by which quadrilateral ABCD has been dilated to form image quadrilateral A'B'C'D' is [tex]\frac{1}{4}[/tex].
Help..................
Answers
180=2m-3+m+4+3m+5
Combine like terms
180 = 6m+6
Subtract 6 from 180
174=6m
Divide by 6
m=29
Brainliest if that helped, please :)
(m+4) + (3m+5) + (2m-3) = 180°
m + 4 + 3m + 5 + 2m - 3 = 180°
6m + 6 = 180°
6m = 180° - 6
6m = 174
m = 29°
8. Determine the area of a sector
with a central angle of 42° in a
circle with radius 3 inches.
NEED IT ASAP
Answers
Answer:
[tex]\boxed {\boxed {\sf A \approx 3.3 \ in^2}}[/tex]
Step-by-step explanation:
Since we are given the central angle in degrees, we should use the following formula for sector area.
[tex]A= \frac {\theta}{360}* \pi r^2[/tex]
The angle is 42 degrees and the radius is 3 inches. Therefore,
[tex]\theta= 42 \\r=3 \ in[/tex]
[tex]A=\frac {42}{360} * \pi (3 \ in)^2[/tex]
Solve the exponent.
(3 in)²= 3 in*3in = 9 in²[tex]A=\frac {42}{360} * \pi (9 \ in^2)[/tex]
Multiply all three numbers together.
[tex]A= 0.116666666667* 3.14159265359 * 9 \ in^2[/tex]
[tex]A=3.29867228627 \ in^2[/tex]
Let's round to the tenth place. The 9 in the hundredth place tells us to round the 2 up to a 3.
[tex]A \approx 3.3 \ in^2[/tex]
The area of the sector is approximately 3.3 square inches.
What number divided by 4 equals 6?
Type the correct answer, then press Enter.
Answers
Answer:
24
Step-by-step explanation:
Let x be the number.
[tex]x/4=6[/tex]
Multiply both sides by 4 to isolate x
[tex](x/4)4=6*4\\x=24[/tex]
I hope this helps!
Need someone to help me with my maths tutorial ASP!!
Answers
Answer:
hi! how can i help? <3
Step-by-step explanation:
okay i can stand in for you
3 |a| +5 |b| if a = −2; b = −1
WILL AWARD BRAINLIEST
Answers
Answer:
-11
Step-by-step explanation:
[tex]3( - 2) + 5( - 1)[/tex]
[tex] - 6 + ( - 5)[/tex]
[tex] - 11[/tex]
Select all the expressions that have the same value
Answers
so what was the question again?
Answer:
Step-by-step explanation:
Suppose that a company claims that its batteries last 240 hours on average.
It took many large samples, and each time the mean number of hours was
outside the 95% confidence interval. Based on this information alone, which
of the following is probably not the mean number of hours that the company's
batteries last?
A. 235
B. 240
C. 230
D. 225
help asap
Answers
Answer:
The answer is option B. 240
Calculate the SQRT485 Express answer to nearest hundredth.
Answers
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer: 22.02
Explanation:
I hope this helped!
<!> Brainliest is appreciated! <!>
- Zack Slocum
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Could someone help me with with 6-10??
Answers
Answer:
You need a protractor
Step-by-step explanation:
to measure the angles
A number greater than or equal to 41.
Answers
Answer:
42
Step-by-step explanation:
¯\_(ツ)_/¯
8 x 4 using distributive property with addition
Answers
Answer:
The answer is 32
That's easy
The difference of two numbers is 14.Twice the smaller is 6 more than the larger.Find the numbers.
Answers
What is the probability that a randomly selected graduate has a job if he or she is attending college? Give your answer as
a decimal precise to two decimal places.
P=
What is the probability that a randomly selected graduate attends college if he or she has a job? Give your answer as a
decimal precise to two decimal places.
P-
Answers
Complete question :
Suppose that of the 300 seniors who graduated from Schwarzchild High School last spring, some have jobs, some are attending college, and some are doing both. The following Venn diagram shows the number of graduates in each category. What is the probability that a randomly selected graduate has a job if he or she is attending college? Give your answer as a decimal precise to two decimal places.
What is the probability that a randomly selected graduate attends college if he or she has a job? Give your answer as a decimal precise to two decimal places.
Answer:
0.56 ; 0.60
Step-by-step explanation:
From The attached Venn diagram :
C = attend college ; J = has a job
P(C) = (35+45)/300 = 80/300 = 8/30
P(J) = (30+45)/300 = 75/300 = 0.25
P(C n J) = 45 /300 = 0.15
1.)
P(J | C) = P(C n J) / P(C)
P(J | C) = 0.15 / (8/30)
P(J | C) = 0.5625 = 0.56
2.)
P(C | J) = P(C n J) / P(J)
P(C | J) = 0.15 / (0.25)
P(C | J) = 0.6 = 0.60
a pet shop sells a 6 can multipack of dog food for £3.18 and a 15 can multipack for £7.80. which multipack is the best value for money
Answers
Answer:
the 15 multi pack
Step-by-step explanation:
Simplify:
Camilla goes to the super market and buys two apples. each apple is $1.75. Camilla has $5.00 left. write an expression to represents this problem. Don't forget to use a variable!
Answers
Answer:
[tex] \huge \boxed{ \boxed{t - 3.5 = 5}}[/tex]
Step-by-step explanation:
to understand thisyou need to know about:equationlet's solve:a apple costs 1.75
2 apple costs 1.75×2=3.5
let her total money be t
according to the question
t-3.5=5How do you find the x-intercept of a parabola?
Answers
What is the lateral surface area of this net
Help!!!
Answers
9514 1404 393
Answer:
720 square feet
Step-by-step explanation:
The lateral area is the area of the central rectangle of the net. It is 12+12+12 = 36 feet long and 20 ft wide.
The lateral area is (36 ft)(20 ft) = 720 ft².
what is the volume of the cylinder?
A:703.2ft3
B:50.2ft3
C:602.9ft3
D: 653.1ft3
Answers
Ms. Annand baked an apple pie. The boys in the house ate ⅛ of it and the girls ate 3/5. What fraction of the pie did the boys and girls eat altogether? Please answer
Answers
Answer:
29/40
Step-by-step explanation:
1/8 + 3/5 =
We need a common denominator.
8 = 2^3
5 = 5
8 and 5 have no common factors, so the LCD is their product.
LCD = 5 * 8 = 40
1/8 + 3/5 =
= 5/40 + 24/40
= 29/40
The remaining questions refer to the following situation: Suppose a certain farmer wants to find out if the average length of the green beans in her field is 4 inches. She collects a random sample of 100 beans and get a sample mean of 3.75 inches. (Suppose she knows that the population standard deviation of bean length is 0.5.) What is the population in this situation
Answers
Answer:
The population in this situation is all green beans in her field.
Step-by-step explanation:
Informally, if you take a sample of an object, the population in all of these objects.
In this question:
Sample of 100 green beans in her field. This means that the population in this situation is all green beans in her field.
lol plss we did this literally a week ago and I forgot how to do it
Answers
Answer:
okay so i believe its area (if its not ill comment the right answer) so you just do the height (12) times the length (12) giving you 144
Step-by-step explanation:
The inequality x < 15 can be used to represent how tall a tree is, where x is it’s height in feet. Which of these statements best describes how tall the tree is
Answers
Answer:
The tree is less than 15 feet
Step-by-step explanation:
Given
[tex]x < 15[/tex]
Required
Interpret
The above inequality implies that the value of x is less than 15.
Since x represents the height of the tree in feet.
We can say that:
The tree is less than 15 feet
An ecologist is examining whether the number of fish caught in a large river basin has changed since a fire burned some of the surrounding forested area and vegetation along the river. Data in the form of fishing reports was available for a five-year period before the fire. From a random sample of 195 fishing reports before the fire, the mean catch was 6.3 fish with a standard deviation of 1.6. In a random sample of 143 reports three years after the fire, the mean catch was 7.1 fish with a standard deviation of 2.1.
Required:
What represents the standard error of the difference in the mean number of fish caught before and after the fire?
Answers
Answer:
The standard error of the difference in the mean number of fish caught before and after the fire is 0.2153.
Step-by-step explanation:
Subtraction of normal variables:
When we subtract two normal variables, the standard deviation is the square root of the sum of variances of each variable.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Sample of 195 fishing reports before the fire, the mean catch was 6.3 fish with a standard deviation of 1.6.
The standard error for this sample is:
[tex]s_b = \frac{1.6}{\sqrt{195}} = 0.1246[/tex]
Sample of 143 reports three years after the fire, the mean catch was 7.1 fish with a standard deviation of 2.1.
The standard deviation for this sample is:
[tex]s_a = \frac{2.1}{\sqrt{143}} = 0.1756[/tex]
What represents the standard error of the difference in the mean number of fish caught before and after the fire?
[tex]s = \sqrt{s_a^2 + s_b^2} = \sqrt{0.1756^2 + 0.1246^2} = 0.2153[/tex]
The standard error of the difference in the mean number of fish caught before and after the fire is 0.2153.
Answer:
sqrt [ (1.6^2)/195 + (2.1^2)/143 ]