Let y = x + 22 and dy = dx, so the integral becomes
[tex]\displaystyle \int_3^9 \frac{\mathrm dx}{(x+21)\sqrt{x+22}} = \int_{25}^{31} \frac{\mathrm dy}{(y-1)\sqrt{y}}[/tex]
Now let z = √y, so that z ² = y. Then 2z dz = dy, and the integral becomes
[tex]\displaystyle \int_3^9 \frac{\mathrm dx}{(x+21)\sqrt{x+22}} = \int_{\sqrt{25}}^{\sqrt{31}} \frac{2z}{(z^2-1)z} \\\\ = \int_5^{\sqrt{31}} \frac{2}{z^2-1}\,\mathrm dz[/tex]
Expand the integrand into partial fractions:
[tex]\dfrac{2}{z^2-1} = \dfrac1{z-1}-\dfrac1{z+1}[/tex]
Then we have
[tex]\displaystyle \int_3^9 \frac{\mathrm dx}{(x+21)\sqrt{x+22}} = \int_5^{\sqrt{31}}\left(\frac1{z-1}-\frac1{z+1}\right)\,\mathrm dz \\\\ = \left(\ln|z-1|-\ln|z+1|\right)\bigg|_5^{\sqrt{31}} \\\\ =\left[\ln\left|\frac{z-1}{z+1}\right|\right]\bigg|_5^{\sqrt{31}} \\\\ =\ln\left(\frac{\sqrt{31}-1}{\sqrt{31}+1}\right) - \ln\left(\frac{4}{6}\right) \\\\ =\ln\left(32-2\sqrt{31}\right) - \ln\left(\frac23\right) \\\\ =\boxed{\ln\left(48-3\sqrt{31}\right)}[/tex]
Given the formula a=b+c, rewrite the formula to solve for c
9514 1404 393
Answer:
c = a - b
Step-by-step explanation:
Subtract b from both sides of the equation.
a = b + c
a - b = b + c - b . . . . . show the subtraction
a - b = c . . . . . . . . . . simplify
c = a - b . . . . . . write with c on the left
Solve the following system of equations for x: y = 4 -x^2
X - y =
2
Answer:
B. x=2, x=-3
Step-by-step explanation:
Hello,
We are given this system of equations:
y=4-x²
x-y=2
And we want to solve it for x.
There are a couple ways to solve systems of equations, but let's use substitution in this problem, which we will set one variable equal to an expression containing the other variable, use that expression to solve for the variable the expression contains in the other equation, then use the value of the solved variable to find the value of the other variable.
But in this case, we just need to find x, which is just one of the variables, so there's no need to find the values of y.
In x-y=2, subtract x from both sides.
-y=-x+2
Multiply both sides by -1.
y=x-2
Substitute y as x-2 in y=4-x².
x-2=4-x²
Add x² to both sides.
x²+x-2=4
Subtract 4 from both sides.
x²+x-6=0
Now factor using FOIL.
1 (coefficient in front of x) is the sum of the numbers used in the binomials, while -6 is their product.
Two numbers that add up to 1 but multiply to get -6 are -2 and 3.
So now factor:
(x-2)(x+3)=0
Split and solve:
x-2=0
x=2
x+3=0
x=-3
The solutions for x are x=2 and x=-3, which means the answer is B.
Hope this helps!
YOU THE REAL OG
IF YOU CAN DO THIS FOR ME
YES IT IS HAIKU
How much would you need to deposit in an account each month in order to have $50,000 in the account in 8 years? Assume the account earns 4% annual interest compounded monthly.
THANK YOU TO ANY OG WHO CAN SOLVE THIS , BRAINLIEST GUARANTEE TO ANYONE WHO REALLY TRIES
9514 1404 393
Answer:
$442.80
Step-by-step explanation:
The formula for the amount of an ordinary annuity is ...
A = P(12/r)((1 +r/12)^(12t) -1)
where payment P is made n times per year and interest is accrued at annual rate r.
Filling in the given values, we want ...
50,000 = P(12/0.04)(1 +0.04/12)^(12·8) -1) = 112.91854P
P = 50,000/112.91854 ≈ 442.80
You would need to deposit $442.80 each month for 8 years.
Which equation is represented by the graph below?
Which of these statements is NOT true regarding a randomized block design experiment?
a.)
This design has an advantage of controlling for variables that might confound the response.
b.)
The elements are randomly allocated to treatment and control groups.
c.)
The sample is divided into participants or subjects and then grouped by a variable of interest.
d.)
Elements are randomly selected from equal-sized blocks of the total population.
The correct answer is D. Elements are randomly selected from equal-sized blocks of the total population is NOT true regarding a randomized block design experiment
From the question we are told that one statement is NOT true regarding a randomized block design experiment.
Where
A) This design has an advantage of controlling for variables that might confound the response is TRUEB)The elements are randomly allocated to treatment and control groups is TRUEC)The sample is divided into participants or subjects and then grouped by a variable of interest is TRUED) Elements are randomly selected from equal-sized blocks of the total population is Not True
In conclusion
The all other Options are true except option D which states that Elements are randomly selected from equal-sized blocks of the total population.
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Convert 9x2 + 4y2 – 54x – 8y – 59 = 0 into standard form.
Answer:
[tex]\frac{(x-3)^2}{4^2} +\frac{(y-1)^2}{6^2} =1[/tex]
Step-by-step explanation:
[tex]9x^{2}+4y^{2} -54x-8y-59=0[/tex]
[tex]9x^{2}-54x+4y^{2} -8y=59[/tex]
Factor 9 and 4 out
[tex]9(x^2-6x)+4(y^2-2y)=59[/tex]
Complete the square, don't forget to add the 2 extra numbers
[tex]9(x-3)^2+4(y-1)^2=59+81+4[/tex]
[tex]9(x-3)^2+4(y-1)^2=144\\[/tex]
Divide everything by 144
[tex]\frac{(x-3)^2}{16} +\frac{(y-1)^2}{36} =1[/tex]
Answer:
Step-by-step explanation:
it's D
Rebecca is comparing prices on toilet paper. Charmin has 18 rolls, each with 200 sheets, for $12.97. Angel Soft has 24 rolls, each with 425 sheets, for $19.98. Which is the better value?
The product that provides the better value per sheet is Angel Soft toilet paper.
Each sheet of Angel Soft costs $0.20 whereas each sheet of Charmin costs $0.36.
Data and Calculations:
Charmin has 18 rolls, each with 200 sheets, for $12.97
Angel Soft has 24 rolls, each with 425 sheets, for $19.98
Product Rolls Sheets Total Sheets Total Cost Cost per Sheet
in a Roll (rolls x sheet) (Total cost/No. Sheets)
Charmin 18 200 3,600 (18 x 200) $12.97 $0.36 ($12.97/3,600)
Angel Soft 24 425 10,200 (24 x 425) $19.98 $0.20 ($19.98/10,200)
Thus, Rebecca should go for Angel Soft toilet paper because it provides a better value per sheet than Charmin toilet paper.
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The sum of ten positive odd numbers is 20. Some numbers may repeat, find the largest number that is used in this sum.
(If possible please show me the step-by-step process, it would really help me)
Answer:
11
Step-by-step explanation:
Get the biggest number by making the others small.
the smallest odd number is 1, so if we get 9 ones, that equals to 9. 11+9 = 20. largest number used is 11.
The greatest odd number is 11 to get the sum of 20.
What is summation?The process of increment of any number of quantities or the process of integrating small parts to make a big part is called summation.
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Get the biggest number by making the others small.
The smallest odd number is 1, so if we get 9 ones, that equals 9.
11+9 = 20.
The largest number used is 11.
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Plz help a beggar I don’t get it
Answer: 3
happy learning
Answer:
B.
Step-by-step explanation:
From the point (-1,0) the next point on the graph is up 3, right 1, making the slope a positive 3.
Find the sum end difference between the numbers 473 and the number obtained by reversing the digits
Answer:
Step-by-step explanation:
The given number is 473
The reverse number is 374
The sum is (473 + 274) = 847
The difference is (473 - 274) = 99
The product of 87(10000)
Answer:
870,000
Step-by-step explanation:
When multiplying the two you add as many 0's to 87 as there are in 10,000
Write the following as an inequality: The sum of x and y is no greater than 2.
the answer is x+y≤2
The sum of x and y is greater than or equal to 2
Answer:
x+y<_2
Step-by-step explanation:
A block of wood has a density of 0.6g/cm^3 and a volume of 1.2cm^3.What is the mass of the block of wood?
Answer:
Below
Step-by-step explanation:
You can use this formula to calculate the mass of an object
Mass = Volume x Density
Plugging everything in....
Mass = ( 1.2cm^3 ) ( 0.6g/cm^2 )
= 0.72 g
Hope this helps!
If f(x) = 3x-1 and g(x)= x+2 find (f-g) (x)
Answer:
2x-3
Step-by-step explanation:
f(x) = 3x-1
g(x)= x+2
(f-g) (x) = 3x-1 - (x+2)
Distribute the minus sign
= 3x-1 -x-2
Combine like terms
= 3x-x -1-2
=2x -3
Find 14.6 + 8.52
I really need help !!!!
Answer:
[tex]14.6 + 8.52 \\ = 23.12[/tex]
helppp ASPPP plzz Select the correct answer.
Answer:
C. [tex]-2x^3+2\sqrt{x}[/tex]
Step-by-step explanation:
[tex]\sqrt{x} -x-(2x^3-\sqrt{x} -x)[/tex]
Change the signs of g(x)
[tex]\sqrt{x} -x-2x^3+\sqrt{x} +x[/tex]
Simplify
[tex]-2x^3+2\sqrt{x}[/tex]
I hope this helps!
pls ❤ and mark brainliest pls!
The midpoint of AB is (1.2). The coordinates of A are (-3, 6) Find the coordinates of B.
Answer: coordinates of B are (5,-2)
Step-by-step explanation:
let B be (x2,y2)
x1 = -3 y1 = 6
x = 1
y = 2
so
x = (x2 + x1)/2
1 = (x2+(-3))/2
or, 2 = x2 - 3
so, x2 = 5
now
y = (y2+y1)/2
or, 2 = (y2 + 6)/2
or, 4 = y2 + 6
so, y2 = -2
PLEASE HELP ASAP, I WILL GIVE BRAINLIEST!
9. What is another name for BD?
10. What is another name for AC?
11. What is another name for ray AÉ?
12. Name all rays with endpoint E.
13. Name two pairs of opposite rays.
14. Name one pair of rays that are not opposite rays.
Answer:
#9. Segment DB
#10 Segment CA
#11. Ray EA
#12. Ray EB, Ray EC, Ray ED, Ray EA
#13 Ray EA & Ray EC
#14. Ray EB and Ray EC
Step-by-step explanation:
For future reference, if you are asked to give another name for a segment, just flip the letters around (same for rays.).
Opposite Rays are rays that share 1 common endpoint, but extend in opposite directions ( together they make a 180 degree angle). Ray EB & EC share an endpoint, but they do not extend in opposite directions.
Hope this helps!
what is sixth root of -2i
Answer: 1.08421508 - 0.290514556 i
Step-by-step explanation:
The 6th root of a number is the number that would have to be multiplied by itself 6 times to get the original number
(-(2×i)) = 1.08421508 - 0.290514556 i
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the area of an equilateral triangle of side 8cm is
pls i need answer ASAP
I'll mark brainliest for anyone who can help me
[tex]\\ \sf\longmapsto Area=\dfrac{\sqrt{3}}{4}a^2[/tex]
[tex]\\ \sf\longmapsto Area=\dfrac{\sqrt{3}}{4}(8)^2[/tex]
[tex]\\ \sf\longmapsto Area=\dfrac{64\sqrt{3}}{4}[/tex]
[tex]\\ \sf\longmapsto Area=16\sqrt{3}[/tex]
[tex]\\ \sf\longmapsto Area=16\times 1.732[/tex]
[tex]\\ \sf\longmapsto Area=27.7cm^2[/tex]
which of the following equations has both 1 and -3 as a solution?
A). x^2-2x-3=0
B). x^2+2x-3=0
C). x^2-4x+3=0
D). x^2+4x+3=0
Please help me to find this answer
Step-by-step explanation:
angle of a triangle is 180, therefore to get the remaining one, subtract the sum of the two knows from 180, also for the second one; angle on a straight line is as well 180, since you have fine the interior one, subtract it from 180 to get the second answer
Answer:
so angles in a triangle add up to 180,
32+50+m<MQP=180
82+m<MQP=180
m<MQP=180-82
=98°
and angles on a straight line add up to 180 therefore
m<MQR=180-m<MQP
=180-98
=82
I hope this helps and if you don't understand feel free to ask
How many prime numbers are there between 1 to 100? a) 17 b) 25 c) 32 d) None of these
Answer:
b)25
Step-by-step explanation:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
this is the question of geometry can you solve this for me ☺️
Answer:
x = 130 degrees
Step-by-step explanation:
let's imagine we move the point x further and further to the right (and move the connected lines with it) until we get a flat line that connects the two parallel lines.
in this case we have x = 180 degrees, and the top and bottom angles are both 90 degrees.
so, we have a total of all angles of 180 + 90 + 90 = 360 degrees.
this total had to stay the same no matter how we move x outward or inward.
so, even in the situation in the picture the sum of all 3 angles must be 360 degrees.
therefore we get
360 = 120 + 110 + x
360 = 230 + x
x = 130 degrees
PLEASE HELP ME !!!!!! WILL GIVE POINTS OUT 60 POINTS
Answer:
18/25
Step-by-step explanation:
Due to the fact that the fractions have the same denominator, we can multiply to numerators, and also the denominators. So we get 3x6/5x5.
Which becomes 18/25
Hope this helps!
Answer:
9/5 which simplifies to 1 4/5
Step-by-step explanation:
How far apart are the 2 cities? See picture.
Show steps
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Answer:
373 miles
Step-by-step explanation:
The difference in latitude is ...
39.1° -33.7° = 5.4° = 0.54°(π/180°) radians = 0.03π radians
The arc length is given by ...
s = rθ, where θ is the angle in radians
The length of the arc along the longitude line is ...
s = (3960 mi)(0.03π) ≈ 373 mi
The distance from Atlanta to Cincinnati is about 373 miles.
the surface area of a prism
Answer:
surface area of a prism is
48 km^2
find the area of right-andled triangled whose sight-angled
making side are 3cm and 4cm
Answer:
3*4=12
Step-by-step explanation:
radius is 21 5/8 incercepted by 5Pi/6? What is arc lenght?
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Answer:
(18 1/48)π ≈ 56.61 units
Step-by-step explanation:
Arc length is the product of radius and intercepted arc in radians:
s = rθ
s = (21 5/8)(5π/6) = (18 1/48)π ≈ 56.61 . . . units
27. Which statement is true about the system x+3y=11 y=r-7 a. (8,-1) is a solution to both equations, so it is a solution to the system b. (8,-1) is a solution to one equation but not the other, so it is a solution to the system C. (8,-1) is a solution to one equation but not the other so it is not the solution to the system d. (8,-1) is not a solution to either equation, so it is not a solution to the system
Answer:b. (8,-1) is a solution to one equation but not the other, so it is a solution to the system
Step-by-step explanation:
27. Which statement is true about the system
x+3y=11
y=r-7
a. (8,-1) is a solution to both equations, so it is a solution to the system
b. (8,-1) is a solution to one equation but not the other, so it is a solution to the system
C. (8,-1) is a solution to one equation but not the other so it is not the solution to the system
d. (8,-1) is not a solution to either equation, so it is not a solution to the system
