Answers
Part 1
[tex]x = g(y), \ c \le y \le d\\\\\\x = 3+4y^2, \ 1 \le y \le 2\\\\\\\frac{dx}{dy} = 8y, \ 1 \le y \le 2\\\\\\\displaystyle A = 2\pi \int_{c}^{d}y\sqrt{1+[g'(y)]^2}dy\\\\\\\displaystyle A = 2\pi \int_{c}^{d}y\sqrt{1+\left[\frac{dx}{dy}\right]^2}dy\\\\\\\displaystyle A = 2\pi \int_{1}^{2}y\sqrt{1+(8y)^2}dy\\\\\\\displaystyle A = 2\pi \int_{1}^{2}y\sqrt{1+64y^2}dy\\\\\\\displaystyle A = 2\pi \int_{1}^{2}\sqrt{1+64y^2}*ydy\\\\\\\displaystyle A = 2\pi \int_{65}^{257}\sqrt{u}*\frac{du}{128}\\\\\\[/tex]
In the last two steps I let u = 1+64y^2, so du/dy = 128y which leads to ydy = du/128.
Note the change in the limits of integration. If y = 1, then u = 1+64y^2 = 65. If y = 2, then 1+64y^2 = 257
----------------------------
Part 2
[tex]\displaystyle A = 2\pi \int_{65}^{257}\sqrt{u}*\frac{du}{128}\\\\\\\displaystyle A = 2\pi*\frac{1}{128}\int_{65}^{257}u^{1/2}*du\\\\\\\displaystyle A = \frac{\pi}{64}\int_{65}^{257}u^{1/2}*du\\\\\\\displaystyle A = \frac{\pi}{64}\left(\frac{2}{3}u^{3/2}+C\right)\Bigg]_{65}^{257}\\\\\\\displaystyle A = \frac{\pi}{64}\left(\left(\frac{2}{3}(257)^{3/2}+C\right)-\left(\frac{2}{3}(65)^{3/2}+C\right)\right)\\\\\\\displaystyle A = \frac{\pi}{64}*\frac{2}{3}\left((257)^{3/2}-(65)^{3/2}\right)\\\\\\[/tex]
----------------------------
Part 3
[tex]\displaystyle A = \frac{\pi}{96}\left(\sqrt{257^3}-\sqrt{65^3}\right)\\\\\\\displaystyle A = \frac{\pi}{96}\left(\sqrt{257^2*257}-\sqrt{65^2*65}\right)\\\\\\\displaystyle A = \frac{\pi}{96}\left(\sqrt{257^2}*\sqrt{257}-\sqrt{65^2}*\sqrt{65}\right)\\\\\\\displaystyle A = \frac{\pi}{96}\left(257\sqrt{257}-65\sqrt{65}\right)\\\\\\[/tex]
[tex]\displaystyle A = \frac{\pi}{96}*257\sqrt{257}-\frac{\pi}{96}*65\sqrt{65}\\\\\\\displaystyle A = \frac{257\pi\sqrt{257}}{96}-\frac{65\pi\sqrt{65}}{96}\\\\\\\displaystyle A = \frac{-65\sqrt{65}\pi}{96}+\frac{257\sqrt{257}\pi}{96}\\\\\\[/tex]
Related Questions
What is 1 2/3 - 2 1/3
Answers
Answer:
- 2/3
Step-by-step explanation:
A line passes through the points (1,-6) and (4,3)
What is the y-intercept of this line
Answers
Answer:
The Y-Intercept is -9
Step-by-step explanation:
Distance between x's (Δx) 3
Distance between y's (Δy) 9
Complete the following sentence.
When a system of measurement is based on units of ten, it is called a________ system.
Answers
Answer:
it is called a decimal system
Step-by-step explanation:
.
Answer:
Decimal system
Laura deposits $2,000 in an account that has an annual interest rate of 1.96%,
compounded monthly. How much interest will she earn at the end of 1 month?
Round to the nearest cent. *
Answers
Answer:
$3.23
Step-by-step explanation:
Given that,
Principal, P = $2,000
Rate of interest, r = 1.96%
Tie, n = 1 month = (1/12) years
The formula of compound interest is given by :
[tex]CI=P[(1+\dfrac{R}{100})^n-1]\\\\CI=2000\times [(1+\dfrac{1.96}{100})^{1/12}-1]\\\\CI=3.23[/tex]
So, the interest will she earn at the end of 1 month is $3.23
The amount she earns at the end of 1 month is 200,326cents
The formula for calculating the compound amount is given as:
A = P(1 + r/n)^ntr is the raten is the compounding timet is the timeA = 2000(1 + 0.0196/12)^(12*1/12)
A = 2000 (1+0.00163)^1
A = 2000(1.00163)
A = $2,003.26
Hence the amount she earns at the end of 1 month is 200,326cents
Learn more on compound interest here: https://brainly.com/question/24924853
Find the y intercept of the line 4y=-6x+8
Answers
Answer:
8
Step-by-step explanation:
The Y intercept is 8.
Slope -3/2
Intercept (0,2)
write the equation to solve for x 3x + 21 6x - 60 please help i was given 3x+21=6x-60 thats wrong can someone please help richard u are amazing wish i could message u u can me
Answers
Answer:
3x + 21 = 6x - 60
Step-by-step explanation:
parallel angles are equal
3x + 21 = 6x - 60
combine similar terms:
3x - 6x = -60 - 21
-3x = -81
x = 81/3
x = 27
now, plugin the value of x=27 back into the equation to get the angle:
= 3x + 21
= 3(27) + 21
= 102
= 6x - 60
= 6(27) - 60
= 102
as you noticed, both values are equal 102 = 102 because its a parallel angles
so the equation is 3x + 21 = 6x - 60
================================
i am pretty sure its correct.
How to find a rational function given 2 vertical asymptotes and an X intercept?
It’s question 20 by the way
Answers
Answer:
[tex]\frac{x-4}{(x+3)(x-5)}[/tex]
Step-by-step explanation:
Since the rational function has vertical asymptotes at -3, and 5, the denominator must equal 0 when x is -3 or 5. Therefore, the denominator must be:
(x+3)(x-5)
Now, to make the x-intercept at (4, 0), the numerator must be equal to 0 when x is 4. Therefore, the numerator must be:
x-4
Therefore, that rational function is:
[tex]\frac{x-4}{(x+3)(x-5_}[/tex]
Solve for x: 3x − 24 = 81
Answers
Answer:
34
Step-by-step explanation:
3x -24 =81
+24 +24
3x 102
/3 /3
x = 34
Answer:
Your answer would be 105/3 or one hundred five over three.
Step-by-step explanation:
I took the test and got it correct. :)
What are the solutions of this quadratic equation?
x2 − 10x = -34
Answers
x^2 - 10x = -34
x^2 - 10x + 34 = 0
We cannot easily factor anything, so we resort to the quadratic equation. The work is attached as an image.
The roots of the equation are imaginary numbers, 5+6i, 5-6i.
What is a Quadratic Equation?A quadratic equation is what can be written in the form of ax²+bx+c=0
The quadratic equation is
x² -10x = -34
x² -10x +34 = 0
The roots formula for a quadratic equation is given by
[tex]x = \dfrac{ -b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
Here a = 1
b = -10
c = 34
The roots of the equation are
[tex]x = \dfrac{ 10 \pm \sqrt{(-10)^2 -4*34}}{2}[/tex]
[tex]\rm x = \dfrac{ 10 \pm \sqrt{-36}}{2}\\\\\\x = 5 \pm 6i[/tex]
To know more about Quadratic Equation
https://brainly.com/question/2263981
#SPJ5
The total length of three boards is 7/8 of a yard. The length of two of the boards are 1/4 of a yard and 3/16 of a yard. What is the length of the third board.
Answers
Answer:
7/16 of a yard
Step-by-step explanation:
Let's put the boards to the same denominator so it's easier.
Let's go with a denominator of 16
1/4= 4/16
7/8= 14/16
3/16 stays the same.
So, 4/16+3/16+x=14/16
7/16+x=14/16
x=7/16 of a yard, the length of the 3rd board.
The visa card is giving 5% cash back on all grocery and restaurant purchases, and 1% for all other purchases. You charge $2,000 a month and 1/4 is for grocery and restaurants. Use this information to find your monthly cash back amount.
Answers
500 + 5% = 25
1500 + 1%= 15
Total cash back = 40$
Step-by-step explanation:
Total cashback from grocery and restaurant purchases = 500 * 0.05 = 25$
Total cashback from other purchases
= 1500 * 0.01
= 15$
Total cashback = $ 40
Given the set of numbers: {3, 8, 2, 2, 5} Find the mean. Enter your answer as a whole number with zero decimal places.
Answers
Answer:
4
Step-by-step explanation:
The mean is defined as adding all the numbers up and dividing by how many numbers there are, so:
3+8+2+2+5 = 20, 20/5 = 4
Answer:
4
Step-by-step explanation:
mean is the average so you add up all the numbers and divide by the number of addicts.
3 + 8 + 2 + 2 + 5 = 20
20/ 5 = 4
how do you find max value in a quadratic function?
Answers
Answer:
Using the equation y = ax2 + bx + c.
Step-by-step explanation:
plzplz help me plz i promise i will mark brainliest i need help
Answers
Answer: A discrete
Step-by-step explanation:
Need help with these find x and y of this figure
Answers
9. A company is looking to hire a painter. One painter states that their fee can be determined by
using the expression 50x + 100 where x is the number of hours it takes to paint. A second painter
states that their fees can be determined by using the expression 40x + 125. The company wants
to know when the fee would be the same for each painter. What number of hours makes the
equation 50x + 100 = 40x + 150 true?
Answers
State the rang of relation ?
PLSS HELP:(
Answers
Answer:
Range is the Y values
{1,-5, 7, 0}
What are some ways we can tell that 7x + 2 is not equivalent to 9x?
Answers
Answer:
To determine if two fractions are equivalent, cross multiply. To cross multiply, you multiple the numerator of the first fraction by the denominator of the second. Then you multiply the denominator of the first fraction by the numerator of the second. If the two numbers are equal, the fractions are equivalent
Step-by-step explanation:
I NEED A SERIOUS ANSWER. THANK YOU!!
Answers
I really hope this helped you. If it did, could u plz mark me as brainliest?
the square below represents one whole. express the shaded area as a fraction, a decimal,and a percent of the whole
Answers
Answer:
You got to show the square… LOL
Step-by-step explanation:
80 POINTS, I WILL MARK BRAINLYEST, LEGIT JUST 4 QUESTIONS. PLEASE ANSWER WITH WORK OR NO POINTS FOR YOU!!!!
Television sizes are determined by the length of their diagonal measure. Michael just bought a new television. The height of the television is 37 inches and the length is 71 inches.
Using the Pythagorean Theorem, what is the size of Michael’s new television? Round your answer to the nearest whole inch (whole number).
Part A: What parts of the right triangle have you been given? Are you looking for a leg or the hypotenuse?
Part B: Set-up your equation by substituting the correct numbers into the Pythagorean Theorem formula.
Part C: Solve for the missing length rounded to the nearest whole number. Remember to show ALL work for each step.
Part D: What is the size of the television rounded to the nearest whole inch (whole number)? REMEMBER: We’re looking for the length of the diagonal, as that is the measurement used to determine TV Sizes.
Answers
Answer:
see below
Step-by-step explanation:
given: size of television is height = 37 in, length = 71 in.
A. using Pythagorean theorem:
parts given are legs which is the sides
looking for the hypotenuse.
B. formula:
a² + b² = c² or H² + L² = D²
where H = height = 37
L = length = 71
D = diagonal (which is req'd)
C. D² = 37² + 71²
D = [tex]\sqrt{1369+ 5041}[/tex]
D = [tex]\sqrt{6410}[/tex]
D = 80 in (missing length)
D. size of television:
37 x 71 in
Diagonal is 80 in
hope it helps and good luck!
ANSWER ASAP ILL GIVE A LOT OF POINTS
Answers
Answer:
addition or subtraction (1.)
Step-by-step explanation:
Answer:
Divide both sides by a constant to simplify the equation. Thus the second option.
Step-by-step explanation:
Solve for x:
9 - 10 x = -1
Hint: | Isolate terms with x to the left hand side.
Subtract 9 from both sides:
(9 - 9) - 10 x = -9 - 1
Hint: | Look for the difference of two identical terms.
9 - 9 = 0:
-10 x = -9 - 1
Hint: | Evaluate -9 - 1.
-9 - 1 = -10:
-10 x = -10
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of -10 x = -10 by -10:
(-10 x)/(-10) = (-10)/(-10)
Hint: | Any nonzero number divided by itself is one.
(-10)/(-10) = 1:
x = (-10)/(-10)
Hint: | Any nonzero number divided by itself is one.
(-10)/(-10) = 1:
Answer: x = 1
Juan's grandmother left him 40 shares of Stock A and 150 shares of Stock B. How
much will he get if stock A sells for $225 a share and stock B sells for $27.25 a share?
Answers
Answer:
$13,087.50
Step-by-step explanation:
The sale of the 40 shares of stock A at $225 per share will get Juan ...
40 · $225 = $9000
The sale of the 150 shares of stock B at $27.25 per share will get Juan ...
150 · $27.25 = $4087.50
So, the total Juan will receive from the sale of the stocks will be ...
$9000.00 +4087.50 = $13,087.50
Which pair of ratios is equivalent?
O A. 4:6 and 12:18
O B. 2:3 and 4:8
O C. 3:5 and 6:15
O D. 7:10 and 8:12
Answers
Answer:
A
Step-by-step explanation:
Both ratios simplify down to 2:3
Answer: 4:6 and 12:18
Step-by-step explanation:
Just took the test
HELP PLEASE , ASAP ; 100 POINTS
Answers
Answer:
icoles
Step-by-step explanation:
Answer:
It's 31x
Step-by-step explanation:
Add the numbers up.
Which choice represents 673.983 rounded to nearest hundredth
Answers
Answer: 673.98
Step-by-step explanation: The 8 is the hundredth place, and anything less than five you don't round up
If North high school has 5000 students and south high school has 1 tenth as many how many students dose south high have?
Answers
Please help 100 points and will give Brainliest
Answers
This is a higher grade than mine i dont know sorry :(
Answer:
I think I know what the answers are but I can't be sure.
Step-by-step explanation:
someone please answer!
Answers
Answer:
m=1/2
Step-by-step explanation:
y1= 1
y2=6
x1= -10
x2-0
m= slope
m= y2-y1/x2-x1
m=6-1/0 - - 10
m= 6-1/0+10
m=5/10
m=1/2
Write the b expanded form of 0.031 with fractions
Answers
Answer:
31/1000
Step-by-step explanation:
Equivalent fraction would be 31/1000
Approximate value would be 4/129 or 3/97