Answer:
The integral of the volume is:
[tex]V = 32\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy[/tex]
The result is: [tex]V = 78.97731[/tex]
Step-by-step explanation:
Given
Curve: [tex]x^2 + 4y^2 = 4[/tex]
About line [tex]x = 2[/tex] --- Missing information
Required
Set up an integral for the volume
[tex]x^2 + 4y^2 = 4[/tex]
Make x^2 the subject
[tex]x^2 = 4 - 4y^2[/tex]
Square both sides
[tex]x = \sqrt{(4 - 4y^2)[/tex]
Factor out 4
[tex]x = \sqrt{4(1 - y^2)[/tex]
Split
[tex]x = \sqrt{4} * \sqrt{(1 - y^2)[/tex]
[tex]x = \±2 * \sqrt{(1 - y^2)[/tex]
[tex]x = \±2 \sqrt{(1 - y^2)[/tex]
Split
[tex]x_1 = -2 \sqrt{(1 - y^2)}\ and\ x_2 = 2 \sqrt{(1 - y^2)}[/tex]
Rotate about x = 2 implies that:
[tex]r = 2 - x[/tex]
So:
[tex]r_1 = 2 - (-2 \sqrt{(1 - y^2)})[/tex]
[tex]r_1 = 2 +2 \sqrt{(1 - y^2)}[/tex]
[tex]r_2 = 2 - 2 \sqrt{(1 - y^2)}[/tex]
Using washer method along the y-axis i.e. integral from 0 to 1.
We have:
[tex]V = 2\pi\int\limits^1_0 {(r_1^2 - r_2^2)} \, dy[/tex]
Substitute values for r1 and r2
[tex]V = 2\pi\int\limits^1_0 {(( 2 +2 \sqrt{(1 - y^2)})^2 - ( 2 -2 \sqrt{(1 - y^2)})^2)} \, dy[/tex]
Evaluate the squares
[tex]V = 2\pi\int\limits^1_0 {(4 +8 \sqrt{(1 - y^2)} + 4(1 - y^2)) - (4 -8 \sqrt{(1 - y^2)} + 4(1 - y^2))} \, dy[/tex]
Remove brackets and collect like terms
[tex]V = 2\pi\int\limits^1_0 {4 - 4 + 8\sqrt{(1 - y^2)} +8 \sqrt{(1 - y^2)}+ 4(1 - y^2) - 4(1 - y^2)} \, dy[/tex]
[tex]V = 2\pi\int\limits^1_0 { 16\sqrt{(1 - y^2)} \, dy[/tex]
Rewrite as:
[tex]V = 16* 2\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy[/tex]
[tex]V = 32\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy[/tex]
Using the calculator:
[tex]\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy = \frac{\pi}{4}[/tex]
So:
[tex]V = 32\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy[/tex]
[tex]V = 32\pi * \frac{\pi}{4}[/tex]
[tex]V =\frac{32\pi^2}{4}[/tex]
[tex]V =8\pi^2[/tex]
Take:
[tex]\pi = 3.142[/tex]
[tex]V = 8* 3.142^2[/tex]
[tex]V = 78.97731[/tex] --- approximated
a culture of bacteria has an initial population of 2100 bacteria and doubles every 4hours. using the formula Pt = P0 • 2 t/d, where Pt is the population after t hours, P0 is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 11hours, to the nearest whole number?
Answer:14127
Step-by-step explanation:
Po=2100
T=11
D=4
Pt=po•2 t/d
Pt=2100•2 11/4
Pt=14127.0598=14127
The answer and I will mark Brainalist
Answer: G would be your answer, or c = 8k + 24
Step-by-step explanation:
Answer:
it is G) c=8k + 24
Step-by-step explanation:
brainliest pls
ill mark brainlist plss help
Answer:
25 in²
Step-by-step explanation:
formula for area of a triangle:
1/2(bxh)
1/2(5x10)
1/2(50)
25
Answer:
D. [tex]25^{2}[/tex]
Step-by-step explanation:
Need help I’m on a timer
Answer:
b. 59
Step-by-step explanation:
cosΘ = 42/82
Θ ~= 59.1898
Find the value of x in the picture below.
Answer:
I think that the answer is 2.5 , the second item .
At a Dance Team fundraiser, there is a pie toss going on and Claudia is
tossing pies at her coach.
The path of a pie models a quadratic, and the height is shown in this table.
What is the maximum height of the pie?
Jordan is flying a kite, which gets caught in the top of a tree. The angle of elevation made by the string on the ground is 44 degrees. The distance from the bottom of the string to the base of three is 90 feet. What is the height of the tree
Answer:
87 Feet
Step-by-step explanation:
It's been a while since I used trigonometry, but here is what I got.
We know that 44 degrees in the angle from the string to the base of the ground.
We also know that the length from that angle to the base of the tree is 90 feet.
So using the SOH, CAH, TOA rule we know that to figure out the opposite side (x) length using the adjacent side (90) length we need to use tangent of 44 degrees.
The equation should be tan(44°) = x/90
Tan(44°)=0.96589
Now you multiply that number by 90 to find x.
Hope that helped, let me know if it did or not.
Need this right now! TwT
Answer:
[ -3 +(-5)][-3-(-5)]
( -8)(2)
= 16
Step-by-step explanation:
where there's x put-3 and where there's y put-5
I don't see =0 so I don't believe you will have to equate further
Answer:
-16
Step-by-step explanation:
Hello There!
For this one we also need to plug in the values and solve
(-3+(-5)(-3-(-5)
first lets distribute the -3 to -3 and -(-5)
-3x-3=9
-3x5=-15
9-15=-6
now lets distribute the -5 to the -3 and -(-5)
-5x-3=15
-5x5=-25
-25+15=-10
-10-6=-16
so the answer would be -16
determine the value of X, and the measure of angle E
Answer:
y = 55
x = 6
∠E = 70
Step-by-step explanation:
Hello There!
Segment DE and segment EF are congruent meaning that there opposite angles are congruent
So angle D and angle F are congruent
Because ∠D = 55 ∠F also equals 55
now we can solve for x
Remember all of the angles in a triangle add up to equal 180 so we use this equation to solve for x
180=55+55+11x+4
step 1 combine like terms
55+55+4=114
now we have
180=11x+114
step 2 subtract 114 from each side
180-114=66
now we have
66=11x
step 3 divide each side by 11
66/11=6
11x/11=x
we´re left with
x=6
Now we can plug in 6 to x to find the measure of angle E
6x11=66
66+4=70 so angle E = 70
Number of points scored in each basketball game: 28,16,38,44,21,38,35,48,33,29,37,39,18,38,42,37,32
Answer:
unm okay? is there anything more to the question?
helpp it due in 10 min!!!
the answer for that should be C
Answer:
I think its c
Step-by-step explanation:
4 is the initial cost and 55 is the amount per ticket
The rate of change of the number of students at a high school in Naples is the same from 2005 to 2013 as it is from 2013 to 2021. Is function f constant, linear, quadratic, or exponential?
A. Linear
B. Quadratic
C. Exponential
Answer:
Step-by-step explanation:
Linear
About 40% of athletes at a gym use a professional trainer. The proportion of successes is when p = 0.4. You choose a random sample of 50 athletes at the gym.
Answer: 0.089
Step-by-step explanation:
Math
Shirley's water bottle is half full. She pours it into another bottle that is
one-third full, and it fills that bottle. If the second bottle holds 2 quarts,
how much did the first bottle hold? *
pls be right, im on rush time guys
Answer:
Step-by-step explanation:
She poured ⅔×2 = 4/3 qt into the second bottle.
Her bottle holds 2×4/3 = 8/3 qt
Carl has 50 apps on his phone. Of these apps, 12 are music apps. What percent of Carl’s apps are music apps?
AANNSSWWEER
AASSAAPP
Answer:
12 50 I don't know
Step-by-step explanation:
Sorry, you guys I put the subject in Math its english! But have a nice day! and please help me!
Answer:
disappoint
recall
disgusted
reunited
prepare
Show how to approximate the required work by a Riemann sum. Then express the work as an integral and evaluate it. A spherical water tank, 24 ft in in diameter, sits atop a 60 ft tower. The tank is filled by a hose attached to the bottom of the sphere. If a 1.5 horsepower pump is used to deliver water up to the tank, how long
Answer:
The time it will take is approximately 104,128 seconds
Step-by-step explanation:
The given parameters are;
The diameter of the tank, D = 24 ft.
Therefore, the tank radius, R = D/2 = 24 ft./2 = 12 ft.
The height of the tower on which the tank sits, h = 60 ft.
The hose through which the tank is filled is attached at the bottom of the tank
The radius of a slice of sphere, r = √(R² - y²) = √(12² - y²)
The power of the pump which is used to deliver the water = 1.5 horsepower
The volume of a slice of water in the tank, V = π·r²·Δx = π·(√(12² - y²))²·Δx ft³ = (144 - y²)·π·Δx ft³
The force of the slice, F = V·g·ρ = (144 - x²)·π·Δx ft³ × 62.5 lb/ft³
Let '[tex]y_i[/tex]' represent the height to which each slice is pumped in the tank, we have;
y = R - (√(R² - x²)) = 12 - (√(144 - x²)
[tex]\lim\limits_{n \to \infty}\ \sum\limits_{i=0}^n (144 - x^2) \cdot \pi \times 62.5 \cdot y_i\ \Delta x \ lb[/tex]
The work done is therefore;
[tex]W = 62.5\times\pi \times \int\limits^{12}_{-12} {(144 - x^2) \cdot(12-(\sqrt{144-x^2} ) \ } \, dx = 632044.366475 \ ft. \cdot lb[/tex]
The work done in filling the tank, W = 632,044.366475 ft·lb
The work done in lifting the water to the base of the tank, W₂ = V·ρ·g×h
[tex]\therefore W_2 = 60 \times 62.5\times\pi \times \int\limits^{12}_{-12} {(144 - x^2) \ } \, dx = 632044.366475 \ ft. \cdot lb = 85273382.0257[/tex]
Therefore, W₂ = 85,273,382.0257 ft.lb
The total work done by the pump,
W = 85,273,382.0257 ft.lb + 632,044.366475 ft·lb = 85,905,426.3922 ft.lb
The time it will take the pump to fill the tank, 't', is given as follows;
1
Power, P = Work, W/(Time, t)
∴ t = W/P
P = 1.5 HP = 550 × 1.5 ft·lb/s = 825 ft·lb/s
t = 85,905,426.3922 ft.lb/(825 ft·lb/s) = 104,127.789566 s
The time it will take, t ≈ 104,128 seconds
WILL MARK BRAINLEST AND THANKS Area: 28.67 sq m and the side is 4.7 m The missing side length is equal to:??? m
Answer:
The area of this is 28.67 meters squared
Step-by-step explanation:
You must use division in order to complete the question
I WILL GIVE BRAINERLEST ABD LIKE AND 5 STARS IF YOU ANSWER
How many people n would be seated in
each section if there were 27 total
people in the gym?
Answer:
IT SAYS IT 27 PEOPLE WOULD BE SEATED
Step-by-step explanation:
X2 + 8x + y2 - 2y =64
Write the equation for a line with a slope of 1/3 that passes through the point 6,12
Answer:
y-12=1/3(x-6)
Step-by-step explanation:
Using the slope intercept form:
[tex]y - yo = m(x - xo) [/tex]
We can see from the given point (6,12) that yo = 12 and xo = 6. The slope, m, is 1/3. Plugging in the values gives us this equation in slope-intercept form that can then be converted to any other form.
Find the capacity of the tanks with the following internal dimensions. Express the capacity in cubic meters and liters for each tank.
Step-by-step explanation:
i) Capacity(Volume) = length x breadth x depth
= 3.2 x 2.9 x 1.5
= 13.92 m³
In litres, 13.92 x 1000 = 139,20 litres
ii) Capacity(Volume) = length x breadth x depth
= 2.5 x 1.6 x 1.3
= 5.2 m³
In litres, 5.2 x 1000 = 5200 litres
iii) Capacity(Volume) = length x breadth x depth
= 7.3 x 3.6 x 1.4
= 36.792 m³
In litres, 36.792 x 1000 = 36,792 litres
I need help with this
Answer:
i need help with this so you can ready
"K Co.'s" bonds currently sell for $1,150. They have a 6.75% semi-annual coupon rate and a 15-year maturity and are callable in 6 years at $1,067.50. Assume that no costs other than the call premium would be incurred to call and refund the bonds, and also assume that the yield curve is horizontal, with rates expected to remain at current levels on into the future. Under these conditions, what rate of return should an investor expect to earn if he or she purchases these bonds, the YTC or the YTM? Why?
Ans.......
YTC ...................................
Step-by-step explanation:
If Matrix A is 3 x 4, and Matrix B is 4 x 2, what is the size of matrix BA? If BA is undefined, please state so.
Answer:
Joe Mok
Step-by-step explanation:
Joe MAMA
Can someone help please
Answer:
Angle 2 = 34 degrees
Angle 4 = 34 degrees
Step-by-step explanation:
Angle 7 = Angle 1
180 - 146 = 34 degrees
so Angle 2 and 4 are 34 degrees, since they are congruent.
Hope this helped! Have a nice day! Plz mark as brainliest!!! :D
-XxDeathshotxX
HELP!!!!! WILL GIVE BRANLIEST !!!!!
Answer:
F = (-2,4); E = (-2,0); D = (2,0)
Step-by-step explanation:
F = 4 points from A, so by a scale factor of 2, it would be 2 times father away from A. The same thing applies for all of the other points; just find how much father A is from a point, then dilate that point by multiplying it by the scale factor, and settling the point closer or father from A.
5. What type of quadrilateral is DEFG?
A square
B rhombus
trapezoid
D parallelogram
Answer:
parallelogram
options D
I took the test and got it right.
Help pls will give BRAINLY
Answer:
A. Mean
Step-by-step explanation:
Rita has a sister named Gabriela who is 4 years older than she is. The product of their ages is 21. Write an equation to find their ages.
Step-by-step explanation:
let Rita = R
Let Gabriela = G
so we have
G ×R = 21
G= R + 4
(R+4)(R) = 21
R^2+4R -21=0