Answers
Answer:
C
Step-by-step explanation:
We want to evaluate the definite integral:
[tex]\displaystyle \int_0^1 (x+2)(3x^2+12x+1)^{1/2}\, dx[/tex]
Again, notice that the radicand is quite similar to the outside factor. So, we can use u-substitution again. We will let:
[tex]\displaystyle u=3x^2+12x+1[/tex]
Then:
[tex]\displaystyle \frac{du}{dx}=6x+12[/tex]
Hence:
[tex]\displaystyle du=6x+12 \, dx[/tex]
And we can divide both sides by 6:
[tex]\displaystyle \frac{1}{6}\, du=x+2\, dx[/tex]
Note that the limits of integration of our original integral (from x = 0 to x = 1) is in the domain of x. Since we changed variables, we should also change the limits of integration to u. So:
[tex]u(0)=3(0)^2+12(0)+1=1[/tex]
And:
[tex]u(1)=3(1)^2+12(1)+1=16[/tex]
Hence, our new limits of integration is from u = 1 to u = 16.
Perform the substitution:
[tex]\displaystyle =\int_{1}^{16} u^{1/2}\Big(\frac{1}{6}\, du\Big)[/tex]
Simplify:
[tex]\displaystyle =\frac{1}{6}\int_1^{16}u^{1/2}\, du[/tex]
Integrate:
[tex]\displaystyle =\frac{1}{6}\Big(\frac{2}{3}u^{3/2}\Big)\Big|_{1}^{16}[/tex]
Simplify:
[tex]=\displaystyle \frac{1}{9}\Big(u^{3/2}\Big|_1^{16}\Big)[/tex]
Evaluate:
[tex]\displaystyle =\frac{1}{9}\Big(16^{3/2}-1^{3/2}\Big)=\frac{1}{9}(64-1)=7[/tex]
The answer is C.
Related Questions
Sue and Bill share a 16 ounce bucket of clay. By the end of the week, Sue has used 5/8 of the bucket, and Bill has used 1/4 of the bucket of clay. How many ounces are left in the bucket?
Answers
Answer:
2
Step-by-step explanation:
16×5/8=10
16×1/4=4
16 - 10 - 4 =2
There is 12 inches in a whole hole how many inches is in a half of a hole?
Answers
Answer:
6 is hoing to be your answer
Answer:
6in
Step-by-step explanation:
Hi hi dude I just don’t want to play anymore I just don’t want to play
Answers
9514 1404 393
Answer:
equation: 8 = v + 5solution: v = 3Step-by-step explanation:
The green line is shown as having a length of 8.
The black line is shown as having two parts that add up to the total length of the black line: v + 5.
The problem statement tells you these are the same length. An equation that says they are equal is ...
8 = v + 5
__
This is solved by subtracting 5 from both sides of the equation.
8 -5 = v +5 -5
Combining like terms gives ...
3 = v
The solution is v = 3.
The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of 4 cm/s. When the length is 15 cm and the width is 12 cm, how fast is the area of the rectangle increasing
Answers
Answer:
The area of the rectangle is increasing at a rate of 168 square centimeters per second.
Step-by-step explanation:
Geometrically speaking, the area of a rectangle ([tex]A[/tex]), in square centimeters, is described by following expression:
[tex]A = w\cdot l[/tex] (1)
Where:
[tex]w[/tex] - Width, in centimeters.
[tex]h[/tex] - Height, in centimeters.
By Differential Calculus, we find an expression for the rate of change of the area of the rectangle ([tex]\dot A[/tex]), in square centimeters per second:
[tex]\dot A = \dot w\cdot l + w\cdot \dot l[/tex] (2)
Where:
[tex]\dot w[/tex] - Rate of change of the width of the rectangle, in centimeters per second.
[tex]\dot l[/tex] - Rate of change of the length of the rectangle, in centimeters per second.
If we know that [tex]w = 12\,cm[/tex], [tex]l = 15\,cm[/tex], [tex]\dot w = 4\,\frac{cm}{s}[/tex] and [tex]\dot l = 9\,\frac{cm}{s}[/tex], then the rate of change of the area of the rectangle is:
[tex]\dot A = \dot w\cdot l + w\cdot \dot l[/tex]
[tex]\dot A = 168\,\frac{cm^{2}}{s}[/tex]
The area of the rectangle is increasing at a rate of 168 square centimeters per second.
I WILL GIVE BRAINLIEST !!!What is the product of 4 and 7?
7
O
o
8 9
14
9
14
7
8
Answers
When someone says the product of x means they are looking to multiply!
Answer:
8? I think I'm not quite sure. lmk
which is the following is true about the graph of linear inequalities?
a.)it is a line
b.)it is a parabola
c.)it os a curve
d.)it is a half-plane
Answers
Answer:
d.) half-plane..
Reason:
A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥. The half-plane that is a solution to the inequality is usually shaded.
Find the measurement of KL (round your answer to the nearest one hundredth. Which theorem did you use?
Answers
Using the Pythagorean theorem:
KL = sqrt( 8^2 + 5^2)
KL = sqrt( 64 + 25)
KL = sqrt(89)
KL = 9.43
The answer is 9.43
PLEASE I NEED HELP CLICK ON THIS IMAGE
Answers
Answer:
D, 261
Step-by-step explanation:
Divide all of the answer choices by 9. The answer is the one with the whole number. 261/9=29 29=whole number so D is the answer.
Hope this helps! If it did, please give brainliest! It would help a lot! :D
Answer:
261
Step-by-step explanation:
If the farmer used 9 boxes and each had the same number, we need to find the number that's divisible by 9.
There's a great fact - a number is divisible by 9 if its sum of digits is divisible by 9.
Let's use that fact on the answers first:
281 -> 2 + 8 + 1 -> 11 -> 1 + 1 -> 2; not divisible by 9
273 -> 2 + 7 + 3 -> 12 -> 1 + 2 -> 3; not divisible by 9
261 -> 2 + 6 + 1 -> 9; divisible by 9
Please note that we could just say that 11 is not divisible by 9, but I wanted to show that we can do it again - nothing stops us and it still works.
To know why this method works, note that a number ABC is equal to:
100 * A + 10 * B + C = 99 * A + 9 * B + (A + B + C) = 9*(11*A + B) + (A + B + C)
And we know that 9*(11*A + B) is divisible by 9 because it's literally 9 times something. So A+B+C is equal to ABC minus something divisible by 9, and that proves what we needed.
Jerome just graduated college and has two job offers. Both jobs offer a starting
salary of $45,000 per year, but they differ in their projected future salaries.
Employer A offers a yearly salary increase of $1250 per year. Employer B offers
an increase of 3% per year.
?
Answers
Answer:
I would say Employer A
Step-by-step explanation:
Employer A because that would give you more money.
The mayoral election results for the town of Jainsville are shown in the table below.
Voters were able to vote for one of three candidates, each represented by one of the three parties shown in the table. Each voter was given a six-digit identification number. What is the probability that if an identification number is randomly chosen, a 50-year-old or younger voter from the winning party will be chosen from the pool of voters? Round your answer to the nearest hundredth of a percent.
Answers
Answer:
ponlo en español para ayudarte
Convert: 2 pounds ounces Submit convert it
Answers
Answer:
Every 2 pounds its 32 ounces
Step-by-step explanation:
Answer:
32 oz (ounces)
Step-by-step explanation:
1 lb = 16 oz
16
x 2
-----
32 oz = 2 lbs
1 Which of the following is an equation of the line containing points (0, -5) and (5, -3)?
Answers
Answer:
y=8/5x-11
Step-by-step explanation:
first you find the gradient of the line:- y(of the first point)minus y(of the second point) divided by x(of the first point)minus x(of the second point)
-5-3=-8
0-5=-5 gradient=8/5
finding equation8=y-3
5=x-5 then cross multiply you will get :-
5(y-3)=8(x-5)
5y-15=8x-40
5y=8x-40+15
5y=8x-25
5y=8x-25
5 5 5
y=8x-5
5
A bag of 4 balls weighs 6 pounds. Each ball weighs the same amount. What is the weight of each ball?
Answers
Answer: 1.5 pounds
PEASE HELP DUE IN 5 MINUTES I WILL MARK YOU BRAINLIST
Find the area of a regular hexagon with side length of 3 ft. Round your answer to the nearest tenth
7.8 ft2
11.7 ft2
23.4 ft2
40.5 ft2
Answers
23.4 ft2
Step-by-step explanation:
jvuctctctcrxrxrxrxrxr
Among all pairs of numbers whose difference is 6, find a pair whose product is as small as possible. What is the minimum produc The pair of numbers whose difference is 6 and whose product is as small as possible is ?
Answers
Answer:
pairs of numbers is 3,-3
Step-by-step explanation:
The computation is shown below:
Let us assume a and b are the pairs of the numbers whose difference is 6
i.e.
a - b = 6
a = 6 + b
So
f = ab
f = (6 + b)b is minimum
Now
d ÷ db (6+ b)b = 0
(6+ b) + b = 0
2b = -6
b = -3
Now
a = 6 + b
= 3
So pairs of numbers is 3,-3
Please help I will give brainliest
Answers
Answer:
i cant see the picture with the question
Step-by-step explanation:
i cant see, sorry
Graham carves a block of wood shaped like a cube with a square pyramid on top. How much paint will Graham need to paint the toy? Enter your answer in the box.
A cube with side length 12 centimeters and a square pyramid on top. The height of one triangular face of the pyramid is 15 centimeters.
Answers
Answer:
1224
Step-by-step explanation:
12 x 12 = 144 then do 144 x 6 = 864
15 x 12 x 1/2 = 90 then 90 x 4 = 360
Add 864 + 360 = 1224
BUT
I am not sure if this is correct. I looked up this equation and I see that it says the answer is 1080 so let me know which one you got right
The set of negative energy is greater than -7
Answers
Answer:
i don't have lesion kau you forever i am sorry
Step-by-step explanation:
your browser to mo Lego house of blues festival
An IQ test is designed so that the mean is 100 and the standard deviation is 24 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 95% confidence that the sample mean is within 8 IQ points of the true mean. Determine the required sample size using the TI-83/84. The required sample size is________
Answers
Answer:
The required sample size is 35.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Determine the required sample size.
The required sample size is n, which is found when [tex]M = 8[/tex]
The standard deviation of 24 means that [tex]\sigma = 24[/tex]. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]8 = 1.96\frac{24}{\sqrt{n}}[/tex]
[tex]8\sqrt{n} = 1.96*24[/tex]
Simplifying both sides by 8
[tex]\sqrt{n} = 1.96*3[/tex]
[tex](\sqrt{n})^2 = (1.96*3)^2[/tex]
[tex]n = 34.6[/tex]
Rounding up:
The required sample size is 35.
Two bags of flour have a total weight of 8 3/4 pounds. What could be their individual weight
Answers
Answer:
4 3/8 lbs.
..................
There are infinitely many possible values for the individual weights of the bags of flour that would add up to a total weight of 8(3/4) pounds.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
The individual weights of the bags of flour must add up to a total weight of 8 3/4 pounds.
We can express 8 3/4 as an improper fraction by multiplying the whole number 8 by the denominator 4 and adding the numerator 3, giving us 35/4.
Therefore, we can set up an equation:
x + y = 8 3/4
where x is the weight of one bag of flour, and y is the weight of the other bag of flour.
We can simplify 8 3/4 to 35/4, so the equation becomes:
x + y = 35/4
We can solve for one variable in terms of the other:
x = 35/4 - y
Now we can substitute this expression for x into the original equation and solve for y:
x + y = 35/4
(35/4 - y) + y = 35/4
35/4 = 35/4
This equation is true for any value of y.
Therefore, there are infinitely many possible values for the individual weights of the bags of flour that would add up to a total weight of 8(3/4) pounds.
For example, one bag could weigh 4 pounds and the other could weigh 4 3/4 pounds, or one bag could weigh 3 pounds and the other could weigh 5 3/4 pounds, and so on.
Thus,
There are infinitely many possible values for the individual weights of the bags of flour that would add up to a total weight of 8(3/4) pounds.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ3
Please if you don’t know it answer (NO LINKS) help me no lying!! This is the clearest I can get!
Answers
Answer:
I can solve 1
Step-by-step explanation:
First you would do 2.9*1.5 then do 1.5*2.9 divided by 2 for the triangle then add them together
A recipe calls for 2 cups flour and 1 1/2 cup milk to make seven servings. Ming has plenty of flour, but only 5 cups of milk. How many servings can he make? Ming can make (answer) servings with 5 cups of milk.
Answers
Answer:
21 or 23 servings.
Step-by-step explanation:
Choose the function whose graph is given below.
A. y = sec X
O B. y = tan x
O C. y = CSC X
O D. y = cotx
Answers
Answer: B. y = tan x
Step-by-step explanation:
The function whose graph is show below will be tan x. Then the correct option is B.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
The secant of angle x is not defined, for some value of x. Then the domain of the sec x will be
Domain = R – (2n + 1) π/2
But the graph of the sec x looks like U. Then it is incorrect.
The tangent of angle x is not defined, for some value of x. Then the domain of the tan x will be
Domain = R – (2n + 1)π/2
Then it is correct.
The co-secant of angle x is not defined, for some value of x. Then the domain of the csc x will be
Domain = R – nπ
Then it is incorrect.
The co-tangent of angle x is not defined, for some value of x. Then the domain of the cot x will be
Domain = R – nπ
Then it is incorrect.
Then the correct option is B.
More about the trigonometry link is given below.
https://brainly.com/question/22698523
#SPJ5
The teacher wants to group 87 students into teams which have the same number of students. There must be more than one team. At least how many teams are there and how many students are there in each team?
Answers
Answer:
3 teams and 29students in each team.
let, the team be x,y,&z
given all the team r equal so, x=y=z
x+y+z=87
3x=87
x=87/3
x=29
we get, x=y=z=29
hope it helps.
HELP WITH MATH!! RLLY COULD USE IT
Answers
Answer:
120 square units
Step-by-step explanation:To find the area you do length times hight or l x h. If you want you can also make the triangle and move it to the other side to create a square if thats helps :) but you always do LxH for area :)
Answer:
120
Step-by-step explanation:
Since it's a parallelogram, it has to be A = BH.
Base in this problem: 10
Height in this problem: 12
10x12=120
An online store sells specialty bags. They charge $8 for shipping and $21 per bag ordered.
Write an expression that can be used to find the cost in dollars for b bags including shipping.
Answers
Answer:
b=21x+8
Step-by-step explanation:
she sell bags 21 dollars for every bag(x) and they only add 8 dollars 1 time
I need these three, I’ll give brainliest
Answers
A. E+17-1=2x. b. R0 + x=12 C. 13= x-1+15+10-1 divided by 10=24
hope this helps!!
and I hope you understand it lol!
ASAP I WILL GIVE 100 POINTS AND BRAINIEST ASAP
Find the length of the model train.
Answers
Answer:
It would be 7.5 inches.
Hope this helped!!
HELP FAST PLEASE
A right triangular prism is constructed so that its height
is equal to the leg length of the base.
What expression represents the volume of the prism, in
cubic units?
1x + x
2x²
o 2x²+x
Answers
Answer:
1/2x*3
Step-by-step explanation:
I looked it up....
Forty people used a popular weight loss program. The mean weight loss was 3.0 lb and the standard deviation was 4.9 lb. Use a 0.01 significance level to test the claim that the mean weight loss is greater than o lb. Use Table A-3 to find the range of values for the P-value.
Answers
Answer:
P-value < 0.005
Step-by-step explanation:
just took it