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
Given the triangle shown below, find the length of [BC]
Answers
Hyp²=ADJ²+OPP²
28²=17²+X²
784=289+x²
x²=784-289
x²=495
x=22
here is your answer 22
can you help thanks
Answers
2 pounds at max, she is NOT able to buy 2.3 pounds, since 2.3 > 2.18
Someone pls explain what to do and give answer <3 thank you
Answers
Answer:
you just have to add everything together.
Step-by-step explanation:
H=6
E=x+5
F=12
D=9
G=6
The thickness of a flange on an aircraft component is uniformly distributed between 0.95 and 1.05 millimeters. (a) Determine the proportion of flanges that exceeds 1.00 millimeters. Enter your answer in accordance to the item a) of the question statement (b) What thickness is exceeded by 90% of the flanges
Answers
Answer:
a) 0.5 = 50% of flanges exceed 1 millimeter.
b) A thickness of 0.96 millimeters is exceeded by 90% of the flanges
Step-by-step explanation:
A distribution is called uniform if each outcome has the same probability of happening.
The uniform distributon has two bounds, a and b, and the probability of finding a value higher than x is given by:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
The thickness of a flange on an aircraft component is uniformly distributed between 0.95 and 1.05 millimeters.
This means that [tex]a = 0.95, b = 1.05[/tex]
(a) Determine the proportion of flanges that exceeds 1.00 millimeters.
[tex]P(X > 1) = \frac{1.05 - 1}{1.05 - 0.95} = \frac{0.05}{0.1} = 0.5[/tex]
0.5 = 50% of flanges exceed 1 millimeter.
(b) What thickness is exceeded by 90% of the flanges?
This is x for which:
[tex]P(X > x) = 0.9[/tex]
So
[tex]\frac{1.05 - x}{1.05 - 0.95} = 0.9[/tex]
[tex]1.05 - x = 0.9*0.1[/tex]
[tex]x = 1.05 - 0.9*0.1[/tex]
[tex]x = 0.96[/tex]
A thickness of 0.96 millimeters is exceeded by 90% of the flanges
Suppose that 20% of the residents in a certain state support an increase in the property tax. An opinion poll will randomly sample 400 state residents and will then compute the proportion in the sample that support a property tax increase. How likely is the resulting sample proportion to be within .04 of the true proportion (i.e., between .16 and .24)
Answers
Answer:
0.9544 = 95.44% probability of the resulting sample proportion being within .04 of the true proportion
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
20% of the residents in a certain state support an increase in the property tax. Sample of 400.
This means that [tex]p = 0.2, n = 400[/tex]
Mean and standard deviation:
Mean [tex]\mu = p = 0.2[/tex]
Standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.2*0.8}{400}} = 0.02[/tex]
How likely is the resulting sample proportion to be within .04 of the true proportion (i.e., between .16 and .24)?
This is the pvalue of Z when X = 0.24 subtracted by the pvalue of Z when X = 0.16. So
X = 0.24
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.24 - 0.2}{0.02}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
X = 0.16
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.16 - 0.2}{0.02}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
0.9772 - 0.0228 = 0.9544
0.9544 = 95.44% probability of the resulting sample proportion being within .04 of the true proportion
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
Given the word ACCOMPLISHMENT, what is the ratio of consonants to vowels? Give your answer in simplest form.
Answers
Answer:
4:7
Step-by-step explanation:
The word ACCOMPLISHMENT has 4 vowels (A, O, I, and E), which is where I got the four. It also has 7 consonants (C, C, M, P, L, S, H, M, N, T). Hence where the 7 was found.
PLEASE HELP ME OUTTT
Answers
2.) 242-221=21
1.) 242+117+221=580 595-580=15
they don’t have enough for a party yet.
2.) they need to sell at least 15 more.
Please answer ASAP
Will mark BRAINLYEST and 40 points
Answers
Answer:
a. a + 10 is the correct option.
Answer:
D
Step-by-step explanation:
45,678 in unit form
Answers
6 hundreds
7 tens
8 ones
May you please help me figure out every angle?
Answers
Answer:
<D = 82°
<E = 49°
<F = 49°
Step-by-step explanation:
This is an isosceles triangle because two of the sides are the same length which means the 2 bottom angles are the exact same which means we can set them equal to each other to solve for it.
Complete please! All of them
Answers
Answer: #1: 15/12 aka 1 3/12 #2: < #3 11/9 aka 9 2/11
Step-by-step explanation: Hope it helps ya
Should I do any programs in middle school? Will it benefit me in college or is it a waste of time?
Answers
Answer: Honestly, they wouldn't really look at your clubs and attendance for sports for Middle School. They would most likely check for High School and beyond that.
I would just have fun while you can. Or try getting into a good High School with good academics scoring for a good chance to get selected to a dream college. Hope this help!
Edit: If there's programs for college- then try taking them! But I doubt it'll catch the eyes of those who look through college applications for how strict they are.
Answer:
you actually should its way better that you do because joining all the clubs they have in school can help YOU and your record.
the measures of the angles of a triangle are shown in the figure below. solve for x
Answers
Answer:
Brainliest????
Step-by-step explanation:
X=23°
Which transformation should be applied to show similarity?
Answers
Evaluate. 32−[(4+2×3)×2] Enter your answer in the box.
will give brainliest!!!!!
Answers
I don't understand ....the teacher gave us this question with a diagram ... if you get it correctly I will mark you as the brainlist ❤️
Answers
Answer:
I think the answer is a I think
abc~def what sequence of transformation will move ABC onto def
Answers
Answer:
c
Step-by-step explanation:
Answer:
is C guys
Step-by-step explanation:
a quadratic patterns has a second term equal to 1,a third term equal to -6 and fifth term equal to -14 .hence or otherwise calculate the first term of the pattern
Answers
Answer:
first term of the pattern (T₁) : 10
Step-by-step explanation:
T₁ ; 1 ; -6 ; T₄ ; -14
1-T₁ ; -6-1 ; T₄-(-6) ; -14 -T₄ (First Tₙ-Tₙ₋₁)
-8+T₁ = T₄+13 = -2T₄-20 (2nd Tₙ-Tₙ₋₁ is constant)
T₄+13 = -2T₄-20 3T₄ = -33 T₄ = -11
-8+T₁ = T₄+13 -8 + T₁ = -11 + 13 = 2
T₁ = 10
Please help me with my homework
Answers
Answer:
0.8
Step-by-step explanation:
0.4*2=0.8
hope this helps.
You would multiply 0.4 and 2 which gets you 0.8.
A certain polygon has its vertices at the following points.
(2,4), (4,5), (6,4), and (4,3)
What is the best description of this polygon?
OA. pentagon
OB. rectangle
OC. square
OD. rhombus
Worth 30 points plzzzzz help quick I will report if you put anything
Answers
Answer:
D
Step-by-step explanation:
d
Answer:
[tex]\huge\boxed{\sf Rhombus}[/tex]
Step-by-step explanation:
When we plot the given vertices on a graph, We get a shape which has the following characteristics.
=> Opposite angles are equal.
=> The diagonals are perpendicular to each other.
=> Opposite sides are parallel to each other.
=> Sum of adjacent angles in equal to 90 degrees.
But, the shape does not seem to be like pentagon, square and rectangle. Hence, It's a rhombus.
See the attached file!
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807If a square has an area of 25x², write an expression for the length of one side.
:)
Answers
Since all sides of a square are the same, the area of a square is one side squared.
Meaning if a square had a side of 4, the area would be 16 since 4 squared is equal to 16.
The opposite is to square root the area. If you calculate the square root of 16, you get 4.
In this situation, we have to square root "[tex]25x^{2}[/tex]." We can split the area up into "25" and [tex]x^{2}[/tex]. The square root of 25 is 5, and the square root of x squared is just x. Multiply 5 and x together, you get 5x.
Easy as that, you get your answer!
5x
Please find the square root. Round your answer to the nearest tenth.
√81.4 =
Answers
0Answer: 9.0
Step-by-step explanation:
.
What is the slope of the line below?
(1-2)
(
4-2)
A. negative
B. undefined
C. positive
D. Zero
Answers
Answer: D. Zero
Step-by-step explanation:
It’s a flat line. Flat horizontal lines are ALWAYS zero
resulve las siguientes operaciones matematicas en tu cuadernk
Answers
Dijo "Resuelva las siguientes operaciones matemáticas en su cuaderno", pero no indicó su cuaderno en la pregunta. Por favor arregle esto.
A 2p coin has a radius of 1.3 cm
A 1p coin has a diameter of 1.8 cm
Which coin has the greater area?
Answers
Answer:
hello! As I think it is 2p coin but not sure
R=1.3
Formula for area= pi times radius squared
= pi* 1.3 squared
=5.31
1P
D=1.8
Area= radius squared we have a diameter so since the radius is half of a diameter we need to have 1.8 which is 0.9 then we would square 0.9 and times it by pi since its now a radius
=0.9 squared times pi
= 2.544690049 round it to 2dp= 2.54
Hope this helped
HELP ME NOW PLEASE!!!!!
The question says "State the coordinates of Point G after a rotation of 90 degrees clockwise followed by a dilation with scale factor 2." The coordinates are G(4.5, 3).
Answers
Answer:
Hiiiiiiiiiiiii Picture pls?
Step-by-step explanation:
:))
HELP PLZ, 100 points!!!
Answers
hope it helps you ❣️
Answer:
10.25%
Step-by-step explanation:
Let the original number be represented with x.
Increase by 5% = 5% of x = 5/100 x X = 0.05x
So, the next number = x + 0.05x = 1.05x
Increase again by 5% = 5% of 1.05x = 5/100
x1.05x = 0.05 x 1.05x = 0.0525
So, the current number = 1.05x + 0.0525x =1.1025x
[tex] \frac{1.1025x - x}{x} = 0.1025 \times 100 = 10.25\%[/tex]
Help please!!!!!! I don't have a lot of time
Answers
Answer:
Its 5,...................
Answer:
5
Step-by-step explanation:
simplify the exponent
35/8-1
simplify
35/7
simplify
5
452 x 12 _____ = 452
fill in the blank
Answers
Answer:
38 remander 8
Step-by-step explanation: