I think the given integral reads
[tex]\displaystyle \int_{-3}^3 \int_0^{9-x^2} \int_{x^2+y^2}^{9-x^2-y^2} \mathrm dz\,\mathrm dy\,\mathrm dx[/tex]
In cylindrical coordinates, we take
x ² + y ² = r ²
x = r cos(θ)
y = r sin(θ)
and leave z alone. The volume element becomes
dV = dx dy dz = r dr dθ dz
Then the integral in cylindrical coordinates is
[tex]\displaystyle \boxed{\int_0^\pi \int_0^{(\sqrt{35\cos^2(\theta)+1}-\sin(\theta))/(2\cos^2(\theta))} \int_{r^2}^{9-r^2} r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta}[/tex]
To arrive at this integral, first look at the "shadow" of the integration region in the x-y plane. It's the set
{(x, y) : -3 ≤ x ≤ 3 and 0 ≤ y ≤ 9 - x ²}
which is the area between a paraboloid and the x-axis in the upper half of the plane. So right away, you know θ will fall in the first two quadrants, so that 0 ≤ θ ≤ π.
Next, r describes the distance from the origin to the parabola y = 9 - x ². In cylindrical coordinates, this equation changes to
r sin(θ) = 9 - (r cos(θ))²
You can solve this explicitly for r as a function of θ :
r sin(θ) = 9 - r ² cos²(θ)
r ² cos²(θ) + r sin(θ) = 9
r ² + r sin(θ)/cos²(θ) = 9/cos²(θ)
(r + sin(θ)/(2 cos²(θ)))² = 9/cos²(θ) + sin²(θ)/(4 cos⁴(θ))
(r + sin(θ)/(2 cos²(θ)))² = (36 cos²(θ) + sin²(θ))/(4 cos⁴(θ))
(r + sin(θ)/(2 cos²(θ)))² = (35 cos²(θ) + 1)/(4 cos⁴(θ))
r + sin(θ)/(2 cos²(θ)) = √[(35 cos²(θ) + 1)/(4 cos⁴(θ))]
r = √[(35 cos²(θ) + 1)/(4 cos⁴(θ))] - sin(θ)/(2 cos²(θ))
Then r ranges from 0 to this upper limit.
Lastly, the limits for z can be converted immediately since there's no underlying dependence on r or θ.
The expression above is a bit complicated, so I wonder if you are missing some square roots in the given integral... Perhaps you meant
[tex]\displaystyle \int_{-3}^3 \int_0^{\sqrt{9-x^2}} \int_{x^2+y^2}^{9-x^2-y^2} \mathrm dz\,\mathrm dy\,\mathrm dx[/tex]
or
[tex]\displaystyle \int_{-3}^3 \int_0^{\sqrt{9-x^2}} \int_{x^2+y^2}^{\sqrt{9-x^2-y^2}} \mathrm dz\,\mathrm dy\,\mathrm dx[/tex]
For either of these, the "shadow" in the x-y plane is a semicircle of radius 3, so the only difference is that the upper limit on r in either integral would be r = 3. The limits for z would essentially stay the same. So you'd have either
[tex]\displaystyle \int_0^\pi \int_0^3 \int_{r^2}^{9-r^2} r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]
or
[tex]\displaystyle \int_0^\pi \int_0^3 \int_{r^2}^{\sqrt{9-r^2}} r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]
Arthur is saving money to buy a used car in 8 months. The car costs $2,180. Arthur plans to start with an initial deposit and then deposit 25% more than the previous month until he has enough money to buy the car. What is the minimum initial deposit Arthur must make? Round to the nearest whole dollar.
The minimum initial deposit Arthur must make is $ 4.24.
Since Arthur is saving money to buy a used car in 8 months, and the car costs $ 2,180, and Arthur plans to start with an initial deposit and then deposit 25% more than the previous month until he has enough money to buy the car, to determine what is the minimum initial deposit Arthur must make the following calculation should be performed:
X x 1.25 x 1.56 x 1.95 x 2.44 x 3.05 x 3.81 x 4.76 = 2180 514.10X = 2180 X = 2180 / 514.10 X = 4.24
Therefore, the minimum initial deposit Arthur must make is $ 4.24.
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Camry has 612 photos she needs to put
into albums. If each album holds 36
pictures, how many albums will it take
to hold all the photos?
Answer:
36 = 1
612 =?
(612×1)
----------
36
=17
You decide to reduce the amount you spend eating out by $150 a month and invest the total saved at
the end of each year in your retirement account. How much will the account be worth at 5% in 15
years? (Use Table 13.1.) (Do not round intermediate calculations. Round your answer to the
nearest cent.)
The type of savings is the saving of uniform amount with interest applied to the sum of the amount in the account.
The amount the account is worth after 15 years is approximately $38,841.1Reasons:
The amount saved per month = $150
Amount saved per year, A = 12 × $150 = $1,800
The interest rate on the account, i = 5%
The amount, F, in the account after 15 years is given as follows;
The uniform series compound amount factor formula is presented as follows;
[tex]\displaystyle F = \mathbf{\frac{A \cdot \left[ \left(1 + i \right)^n - 1 \right]}{i}}[/tex]
Therefore;
[tex]\displaystyle F = \frac{1,800 \times \left[ \left(1 + 0.05 \right)^{15} - 1 \right]}{0.05} \approx \mathbf{38,841.4}[/tex]
The amount the account is worth after 15 years to the nearest cent is approximately $38,841.4.
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Which of the lines listed below is parallel to the line with the equation y = 3/2x + 5?
use desmos graphing calculator
(f+g)(x)
f(x)= x-3, g(x)= 2x+8
Answer: 13x4+g
Step-by-step explanation:
You plant 9 rows of different bulbs in a garden. For each row, you use the rule, “onion, onion, garlic, flower.” How many garlic and flower bulbs do you plant altogether? How many bulbs do you use in all?
Answer: Who the actual fudge gardens anymore????? like what are you an old lady? ur name edna? ethel? doreen? geez louise u are old.
Step-by-step explanation:
Which side lengths form a right triangle?
Choose all answers that apply
(Choice A)
A
3
,
27
,
6
3,
27
,63, comma, square root of, 27, end square root, comma, 6
(Choice B)
B
8
,
15
,
17
8,15,178, comma, 15, comma, 17
(Choice C)
C
Answer:
4, 7.5, 8.54,7.5,8.5
Step-by-step explanation:
We can use the Pythagorean Theorem to see if the side lengths will form a right triangle.
The equation for the Pythagorean Theorem is
a^2 + b^2 = c^2a
2
+b
2
=c
2
a, squared, plus, b, squared, equals, c, squared
where aaa and bbb are the lengths of the two legs of the triangle, and ccc is the length of the hypotenuse.
[How can I tell which side is the hypotenuse?]
Hint #22 / 5
Let's check each set of numbers:
\begin{aligned} a^2 + b^2 &= c^2 \\\\ 4^2 +\sqrt8^2 &\stackrel{\large?}{=} 24^2 \\\\ 16 + 8&\stackrel{\large?}{=} 576\\\\ 24&\neq 576\\\\ \end{aligned}
a
2
+b
2
4
2
+
8
2
16+8
24
=c
2
=
?
24
2
=
?
576
=576
The side lengths 4, \sqrt8, 244,
8
,244, comma, square root of, 8, end square root, comma, 24 do not form a right triangle.
Hint #33 / 5
\begin{aligned} a^2 + b^2 &= c^2 \\\\ 5^2 + 5^2 &\stackrel{\large?}{=} 5^2 \\\\ 25+ 25&\stackrel{\large?}{=} 25\\\\ 50&\neq 25\\\\ \end{aligned}
a
2
+b
2
5
2
+5
2
25+25
50
=c
2
=
?
5
2
=
?
25
=25
The side lengths 5, 5, 55,5,55, comma, 5, comma, 5 do not form a right triangle.
Hint #44 / 5
\begin{aligned} a^2 + b^2 &= c^2 \\\\ 4^2 + 7.5^2 &\stackrel{\large?}{=} 8.5^2 \\\\ 16+ 56.25&\stackrel{\large?}{=} 72.25\\\\ 72.25&\stackrel{\checkmark}{=} 72.25\\\\ \end{aligned}
a
2
+b
2
4
2
+7.5
2
16+56.25
72.25
=c
2
=
?
8.5
2
=
?
72.25
=
✓
72.25
Answer:
4, 7.5, 8.5
Step-by-step explanation:
I had this question on Khan, and it was right (:
what is the surface area of a polyhedron with measurements 4cm x 4cm x 7cm?
Check the picture below.
so let's add all sides and that'd be the area of the rectangular prism.
[tex]\stackrel{\textit{top and bottom}}{2(4\cdot 7)}+\stackrel{\textit{left and right}}{2(4\cdot 4)}+\stackrel{\textit{front and back}}{2(4\cdot 7)}\implies 56+32+56\implies 144[/tex]
what is the value of y so that the equation is true y^2 = -81
Step-by-step explanation:
to make the equation true the value of y must be.
-1×9²-1×81-81hope it helps.
stay safe healthy and happy.
Answer:
y=-/+9
Step-by-step explanation:
y^2=81
find the square root
y=positive/negative 9
Determine the value of cos 45 X 29
Answer:
20.50609665
around 20.506
Can someone help me I will mark u brilliant
Answer: its 45% for sure
Answer:
i believe 45%
Step-by-step explanation:
hope this helps! :D
have a miraculous day, and brainliest is immensely appreciated!! <3
what is the area of 146km 6.3km and 5.4km
Answer:
Step-by-step explanation:
Ask Siri
Answer:
Step-by-step explanation:
Subtract 38¢ from $5.60. Include the dollar sign and no spaces in your answer.
Answer:
5.22
Step-by-step explanation:
Answer:
its easy, just subtract 50 - 38 = 22 so its $5.60
(your welcome and math makes me notalisgica :) )
Step-by-step explanation:
Simplify: (ab + bc) (ab - bc)
[tex] \: \: \: \: [/tex]
[tex] = {a}^{2} \: {b}^{2} - {b}^{2} \: {c}^{2} [/tex]
Step-by-step explanation:
[tex](ab + bc)(ab - bc)[/tex]
use ( a + b ) ( a + b ) = a² - b² to simply the product[tex](ab {)}^{2} - (bc {)}^{2} [/tex]
to raise a product to a power ,raise each factor to that power[tex] = {a}^{2} {b}^{2} - {b}^{2} {c}^{2} [/tex]
hope it helps
PHOTO ATTACHED PLESE HELPPPP!!!!!!!!!!!!!!
Answer:
[tex]5x^2 + 3x - 2[/tex]
This answer is correct because I simplified using like terms.
Step-by-step explanation:
Subtracting Polynomials
They key to subtract, multiply, add, and divide polynomials is by using like terms. Like terms are values with the same bases. For example :
[tex]ax^2[/tex] and [tex]2ax^2[/tex] are like terms because they have the base [tex]ax[/tex]
Step 1: Move like terms together
First, let's remove all parenthesis:
[tex](3x^2 + 9x-6)-(2x^2-4x^2+6x-4)\\\\= 3x^2+9x-6-2x^2+4x^2-6x+4[/tex]
Now let's move all like terms together:
[tex]3x^2+9x-6-2x^2+4x^2-6x+4= \\3x^2-2x^2+4x^2+9x-6x-6+4[/tex]
Step 2: Simplify
Now we can add and subtract the like terms like we do in any other problem
[tex]3x^2-2x^2+4x^2+9x-6x-6+4 = \\5x^2+3x-2[/tex]
Step 3: Explaining your answer
Just say: "This answer is correct because I simplified using like terms"
-Chetan K
What is the slope of the line (-5,-7) and (4,-1)
Answer:
2/3
Step-by-step explanation:
slope = change in y / change in x = (-7-(-1))/(-5-4) = (-6)/(-9) = 2/3
Explain in your own words the steps to dividing decimals by decimals.
How can one determine the number of x-intercepts of the graph of a quadratic function without graphing the function?
Answer:
The easiest method is to find the x-intercepts of the quadratic function by substituting y=0 in the function and solving it to find the possible values of x. The number of all possible values of x is the number of x-intercepts of the graph.
YOU’RE GETTING A BRAINLIST IF YOU ANSWER THESE:
If you and I meet halfway between the fountain and the restrooms what are the coordinates of our meeting place?
If my cat and your dog meet halfway between the ball field and the swings what are the coordinates of their meeting place?
Now to the nearest yard how far are you and I to our pets after arriving to our meeting place?
Answer:
(0.5,-0.5)(0.5,0.5)2 yardsWhich of the following have a sum of 0? (Pick 2) *
1:The football team gained 10 yards on the first play, gained 10 yards on the second play, and lost 10 yards on the third play. What was the overall change in yardage?
2: While playing the integer game, Sam pulled the following cards: 8, 4, 5, -6, -8, -3. What is the sum of Sam's hand?
3: -15 - 8 + 12 + 11
4: 6 + (-5) - 7 + (-4) + (-4)
Answer:
The answer is number 3.
Step-by-step explanation:
-15 - 8 = -23
12 + 11 = 23
When you subtract -23 from 23 you have a sum of 0
Therefore the answer is 0
PLEASE HELP ILL GIVE A HEART AND 5 STARS
Answer:
I Think it's True (If it's not please don't hate)
y= 3/4x + 3 Find the y and x intercept
[tex]y - intercept = 3[/tex]
[tex]x - intercept = - 4[/tex]
What is the diameter of a circle with the equation x2 + y2 - 8x + 2y - 8 = 0?
5 units
6 units
9 units
10 units
Answer:
Diameter is 10 units
Step-by-step explanation:
Convert standard form to general form by completing the square:
[tex]x^2+y^2-8x+2y-8=0[/tex]
[tex]x^2-8x+y^2+2y-8=0[/tex]
[tex]x^2-8x+y^2+2y=8[/tex]
[tex]x^2-8x+16+y^2+2y+1=8+16+1[/tex]
[tex](x-4)^2+(y+1)^2=25[/tex]
[tex](x-4)^2+(y+1)^2=5^2[/tex]
So, since the radius of the circle is 5 units, then the diameter is twice the radius, which is 10 units.
Answer:
50
Step-by-step explanation:
x2 + y2 - 8x + 2y - 8 = 0
first we find the radius with the equation.
write the equation in standard form.
x2 + y2 - 8x + 2y - 8 = 0
(x-4)^2 + (y+1)^2 = 25
(x-h)² + (y-k)² = r²
this means 25 is the radius and the diameter is two times the radius so,
25 x 2 = 50
Jaime is three years younger than his brother Keegan. In five years, the sum of their ages will be thirty-nine.
How old are they now?
Answer:
Keegan is 16 and Jamie is 13.
Step by Step Explanation:
So if we were to take the number 39 and divide it by 2, we would get 19.5. Since Jaime is 3 years younger, we would subtract 3 from one of the 19's. Then we would add 1.5 to both of the numbers since that 3 we subtracted has to go somewhere in that 39, and we come up with the numbers 21 and 18. Since it is asking how old they are NOW and not in the future, we subtract 5 from both numbers to account for the 5 years, and we end up with the years 16 and 13.
Math:
39÷2 = 19.5
19.5 19.5
-3
___________
16.5 19.5
+1.5 +1.5
___________
18 21
-5 -5
13 16
A rectangular field is four times as long as it is wide if the perimeter of the field is 420 yards what are the fields dimensions
Answer:
168yards by 42yards
Step-by-step explanation:
Perimeter =2(l+b)
Perimeter =420yards
length=4×breadth
l=4b
P=2(l+b)
P=2(4b+b)
P=2(5b)
P=10b
420=10b
b=420/10
b=42yards
l=4b=4×42yards
l=168yards
hence the dimensions are 168yards by 42yards
What is correct answer For this problem
The table shows how the length of a fish changes over time.
Which equation represents the relationship between x, the time in years, and y, the length in centimeters?
Question options:
x = 4.5y
x = 9y
y = 4.5x
y = 9x
Answer:
C. y=4.5x
Step-by-step explanation:
divide y by x
The graph shows the relationship between time
and the number of soda bottles a machine can
make. Use the points (2,48) and (7,168) to find
the number of soda bottles the machine can make
each minute.
Answer:
24
Step-by-step explanation:
The number of soda bottles the machine can make each minute is the unit rate, slope. To find slope using those two points, use the formula:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Identify the points: (2,48) (7,168)
[tex]y_2=168[/tex]
[tex]y_1=48[/tex]
[tex]x_2=7[/tex]
[tex]x_1=2[/tex]
Plug these into the formula then solve:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\frac{168-48}{7-2}[/tex]
[tex]=\frac{120}{5}[/tex]
[tex]=24[/tex]
The slope is 24, and therefore the unit rate. Hence, the machine can make 24 soda bottles each minute.
Simple way
Where you see the point at 48 and 2, it means [tex]\frac{48}{2}[/tex]. So divide
48 ÷ 2 = 24.
9 x 6 and explenation will win a brainliest
Answer:
54
Step-by-step explanation:
9 = 3 x 3
6 = 3 x 2
9 x 6
= 3 x 3 x 3 x 2
= 54
Answer:
54
Step-by-step explanation:
9+9+9+9+9+9 = 54
Hope that helps. Can i have the brainliest :)
Enter the number that belongs in the green box
Answer:
72°
Step-by-step explanation:
The diagonals of a parallelogram intersect at a point that forms the center of symmetry of the parallelogram.
If [tex]a\ \textless \ b[/tex], there are three ordered pairs of positive integers [tex](a,b)[/tex] that satisfy [tex]a^{2}+b^{2}=10(123)^{2}[/tex] If two of these ordered pairs are [tex](39,387)[/tex] and [tex](201,333)[/tex]. What is the third such ordered pair?
The third ordered pair that satisfies the equation of the circle is (123, 369).
The given parameters;
[tex]a^2 + b^2 = 10(123)^2[/tex]First pair of the equation, = (39, 387)Second pair of the equation = (201, 333)The third ordered pair of the equation can be determined by using general equation of a circle;
[tex]a^2 + b^2 = r^2\\\\a^2 + b^2 = (123\sqrt{10} )^2\\\\a^2 + b^2 = (\sqrt{151290} )^2\\\\a^2 + b^2 = 151290\\\\a^2 = 151290- b^2\\\\ a= \sqrt{151290 - b^2}[/tex]
The radius of the circle is calculated as;
[tex]r^2 = 151290\\\\r = \sqrt{151290} \\\\r = 388.96[/tex]
The value of a can be obtained by randomly choosing numbers less than the radius as values of b.
[tex]b < r\\\\b < 388.96[/tex]
[tex]a = \sqrt{151290 \ - \ (387)^2} \\\\a = 39\\\\(39, \ 387)\\\\a = \sqrt{151290 \ - \ (333)^2}\\\\a = 201\\\\(201, \ 333)\\\\a = \sqrt{151290 \ - \ (369)^2}\\\\a = 123\\\\(123, \ 369)[/tex]
Thus, the third ordered pair that satisfies the equation of the circle is (123, 369).
Learn more about equation of circle here: https://brainly.com/question/11711668
