An iterated integral is the outcome of taking integrals toward a function of more than one variable in such a way that part of the variables is treated as constants for each of the integrals.
From the given parameters, we are to write out five iterations for a triple integral;
[tex]\mathbf{\int ^8_0\ \int^{x^2}_{0} \ \int^y_0 \ \ f(x, y, z) \ dz dy dx }[/tex]
where;
the region is bounded by 0 ≤ z ≤ y, 0 ≤ y ≤ x², 0 ≤ x ≤ 8.Thus, since x, y, z are functions of at least one variable, we can have the following iterations:
[tex]\mathbf{\int^{64}_{0} \ \int^{8}_{\sqrt{y}} \ \int^{y}_{0} \ \ f(x,y,z) dz dxdy}[/tex] [tex]\mathbf{\int^{64}_{0} \ \int^{y}_{0} \ \int^{8}_{\sqrt{y}} \ \ f(x,y,z)\ dxdzdy}[/tex] [tex]\mathbf{\int^{64}_{0} \ \int^{64}_{z} \ \int^{8}_{\sqrt{y}} \ \ f(x,y,z)\ dxdydz}[/tex] [tex]\mathbf{\int^{8}_{0} \ \int^{x^2}_{0} \ \int^{x^2}_{z} \ \ f(x,y,z)\ dydzdx}[/tex] [tex]\mathbf{\int^{64}_{0} \ \int^{8}_{\sqrt{z}} \ \int^{x^2}_{z} \ \ f(x,y,z)\ dydxdz}[/tex]Learn more about iterated integrals here:
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Explain the step by step process of finding a function for a hyperbola given the center (1,4), vertices (-7,4) and (9,4), and a point on the hyperbola at (-11, -6). Make sure to include the location of the foci.
NO LINKS!!
Answer:
(x -1)²/64 -(y -4)²/80 = 1foci (-11, 4) and (13, 4)Step-by-step explanation:
The standard form of a hyperbola whose transverse axis is horizontal is ...
(x -h)²/a² -(y -k)²/b² = 1 . . . . center (h, k); transverse axis 2a; conjugate axis 2b
The distance between the two vertices is given as (9 -(-7)) = 16 = 2a, so the value of a is 8 and we have the partial equation ...
(x -1)²/8² -(y -4)²/b² = 1
Filling in the given point value gives us an equation for b².
(-11 -1)²/8² -(-6 -4)²/b² = 1
9/4 -100/b² = 1
5/4 = 100/b²
b² = 80
So, the equation is ...
(x -1)²/64 +(y -4)²/80 = 1
__
The distance between the foci is 2c, where c² = a² +b².
c² = 64 +80 = 144 = 12²
c = 12, so the foci are at ...
(x, y) = (1 ±12, 4) . . . . . . . 12 units either side of the center
The foci are (-11, 4) and (13, 4).
_____
Additional comment
The steps are ...
use the given information to fill in as much of the equation as you can.use any given points or additional information to find the unknown values in the equationdetermine any additional information asked for (foci, asymptotes, ...)The relevant relations are ...
2a = length of transverse axis (distance between vertices)
2b = length of conjugate axis (distance between co-vertices)
±b/a = slope of asymptotes, which are lines through the center
2c = distance between foci, where c² = a² +b²
The equation is (x -h)²/a² -(y -k)²/b² = 1 for a hyperbola that opens horizontally with center (h, k). Swapping variables x and y will give a hyperbola that opens vertically. If the figure opens vertically, the asymptotes will have slope ±a/b.
The distances from a point to the foci have a constant difference of 2a.
What is equivalent to 10/100
Answer:
1/10
Step-by-step explanation:
10/100
Dividing both sides by 10
10 ÷ 10/100 ÷ 10
1/10
Hence,
10/100 is equivalent to 1/10
Answer:
Decimal: 0.1 (One tenth)
Fraction: 1/10
Percentage: 10%
Step-by-step explanation:
For decimal that would be 10% out of 100% which is what 10/100 is as a percentage. The fraction would have the numerator and denominator divided by 10.The decimal would be equivalent when it is turned into a fraction 1/10 which is equivalent to 10/100.
I Hope this Helps
When Abrams born his parent put $2000 in account that you did 1.2% interest compounded semi annually when he turns 16 in Spain to give him the money to buy a car how much will Abrams you receive on his 16th birthday
Answer:
$2421.95
Step-by-step explanation:
To calculate the final value from compound interest, we can use the formula
A = P(1+r/n)^(nt), where A represents the final amount, P is the initial amount, r is the rate, n is the number of times compounded per time period, and t is the amount of time.
Here, P is 2000, 1.2% is the rate (to convert to a decimal, we can divide by 100 to get 0.012), n = 2 because it is compounded semi-annually, and 16 is the number of years, or t. Plugging these in, we get
2000(1+0.012/2)^(2*16) = 2421.95
Your friend says that the equations y - 9 = -5(x + 2) and y = -5x – 19 represent two different lines. Is your friend correct? Explain.
Answer:
Step-by-step explanation:
The second equation is y = -5x - 19
The first equation needs a little work
y - 9 = -5(x + 2) Remove the brackets
y - 9 = -5x - 10 Add 9 to both sides.
y = -5x -10 + 9 Combine
y = - 5x - 1
There are two lines there. They are parallel, but they never cross. The y intercepts are not equal and they don't lie on top of each other.
Would 5/5x2 3/4 be less greater or equal to 2 3/4
Answer:
greater
Step-by-step explanation:
if you add them and do the multiplication it is greater
Answer:
It would be equal
Step-by-step explanation:
You first divide 5/5, which is equal to 1, multiply that by 2 to get 2.
After that, there is a 3/4 sitting around so you add 3/4 to 2.
Then you will see that both are equal.
The perimeter of a square is 252 feet how long is each side
I’m not sure how to set up this problem
Answer:
63 feet
Step-by-step explanation:
perimeter is the sum of all four sides and, since it's a square then all sides are equal
to find how long each side is divide 252 by 4
252÷4 = 63
Answer:
It seems like you want to solve the question, so I'll not include the answer
Square has 4 sides and each sides are identical length so.
And Perimeter is just the total length of the sides of the shape. So...
Mathematically
Perimeter of square = 4s
where s is length of one side of square
Does the table show a proportional relationship between x and y? Explain.
x y
2 4
4 16
7 79
10 100
Answer:
no
Step-by-step explanation:
if the y 79 was changed to 49 then yes(in that case y=x^2) but the x 7 y 79 messes the relationship up.
how important is the 3 candle of advent?
[tex]\large\huge\green{\sf{Answer:-}}[/tex]
The third candle which is pink or rose, represents Gaudette Sunday and the joy that the birth of Christ brought to the world. Traditionally, on Gaudette Sunday one takes a break from Advent fasting to experience the joy of the day.
simplify.
|−6 + (−3)| (−3) + 8 ÷ 2
If the expression inside the absolute value bars which is -6 .Simplifying the expression |−6 + (−3)| (−3) + 8 ÷ 2 is: 9.
What is the expression?Let simplify the given expression step by step:
|-6 + (-3)| = |-9| = 9
First calculate the expression inside the absolute value bars which is -6 + (-3) = -9. Then take the absolute value of -9, which is 9.
(-3) + 8 ÷ 2 = (-3) + 4 = 1
We follow the order of operations (PEMDAS/BODMAS).
First perform the division:
8 ÷ 2 = 4
Add -3 to 4 which gives us 1.
Simplified expression :
9 * 1 = 9
Therefore the expression is 9.
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A researcher at the Centers for Disease Control and Prevention is studying the growth of a certain bacteria. He starts his experiment with 500 bacteria that grow at a rate of 16% per hour. He will check on the bacteria every 8 hours. How many bacteria will he find in 8 hours? Round your answer to the nearest whole number.
The population of the bacteria after 8 hours is 1639 bacteria.
An exponential function is given by:
y = abˣ
where y, x are variables, a is the initial value of y and b is the multiplier.
Let y represent the population of bacteria after x hours.
Given that he starts his experiment with 500 bacteria, hence
a = 500
The bacteria grow at a rate of 16% per hour, hence:
b = 100% + 16% = 1.16
The exponential equation becomes:
y = 500(1.16)ˣ
After 8 hours:
y = 500(1.16)⁸ = 1639
The population of the bacteria after 8 hours is 1639 bacteria.
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Identify the parent function. 5 -5 5 -5 A. Cube root
A doughnut shop sells 30 kinds of doughnuts. In how many ways can you get a bag of 12 doughnuts if you want at least 3 glazed doughnuts and at least 4 raspberry doughnuts
Answer:
86493225
Step-by-step explanation:
Hope it helps
find the 99th term of the arithimic sequence 2, 5/2, 3, 7/2, ...
Answer:
99th term is 51
Step-by-step explanation:
Arithmetic sequence equation
a1= first term = 2
d= common difference = 0.5 or 1/2
2, 5/2 = 5/2 - 2 = 0.5 or 1/2
3 - 5/2 = 1/2
7/2 - 3 = 1/2
an = a1 + (n - 1)d
a99 = 2 + (99-1) 1/2
a99= 2 + 98 (1/2)
a99 = 2 + 49
a99 = 51
Help help help help help help help help
Answer:
y=2
y=4
y=6
y=8
Step-by-step explanation:
please mark brainlist
I need help with this
Answer:
check online for more information
plssssssssssssssssssssss help me i will mark you the brainlyest Graph.
y= –34x–1
Answer:
the x-axis is 0,1
the y -axis is -1, - 35
sorry if im rong
Step-by-step explanation:
Answer:
look at explanation
Step-by-step explanation:
the first thing to do when graphing is to look at your y coordinate, the last number without a variable behind it. this would be (-1).
mark -1 on your graph, which should be one slot to the left of zero.
the slope (the number with the variable behind it) can be read as rise/run. turn -34 into a fraction by simply putting it over 1. this will give you -34/1.
your rise in this case would be -34, which means from -1, go down 34 slots and put a nother dot. your run(denominator in fraction) is where you move horizontally. since the run is 1, move over 1 spot from where your last dot is and that is your final plot. connect the first dot you made tot he third dot you made and you have officially graphed it.
what is the answer of solve the following equations and verify your answer
Answer:
Solution !![tex] \implies{\sf{ \dfrac{p + 7}{p - 6} = \dfrac{1}{3}}}[/tex]
By cross multiplication :
[tex] \implies{\sf{ {3(p + 7)} = 1{(p - 6)} }}[/tex]
[tex]\implies{\sf{3p + 27 = p - 6 }}[/tex]
[tex]\implies{\sf{3p - p = - 6 - 21}}[/tex]
[tex]\implies{\sf{2p = - 27}}[/tex]
[tex]\implies{\sf{\underline{\underline{\red{p = \dfrac{ - 27}{2}}}}}}[/tex]
Hence, the value of p is -27/2
[tex]\begin{gathered}\end{gathered}[/tex]
Verification !![tex] \implies{\sf{ \dfrac{p + 7}{p - 6} = \dfrac{1}{3}}}[/tex]
Substituting the value of (p = -27/2)
[tex] \implies{\sf{ \dfrac{ \dfrac{ - 27}{2} + 7}{ \dfrac{ - 27}{2} - 6} = \dfrac{1}{3}}}[/tex]
[tex] \implies{\sf{ \dfrac{ \dfrac{ - 27 + 14}{2}}{ \dfrac{ - 27 - 12}{2} } = \dfrac{1}{3}}}[/tex]
[tex] \implies{\sf{ \dfrac{ \dfrac{ - 13}{2}}{ \dfrac{ - 39}{2} } = \dfrac{1}{3}}}[/tex]
[tex] \implies{\sf{ \dfrac{ - 13}{2} \times \dfrac{2}{ - 39} = \dfrac{1}{3}}}[/tex]
[tex] \implies{\sf{ \dfrac{ - 13}{\cancel{2}} \times \dfrac{\cancel{2}}{ - 39} = \dfrac{1}{3}}}[/tex]
[tex] \implies{\sf{ \dfrac{ - 13}{ - 39} = \dfrac{1}{3}}}[/tex]
[tex] \implies{\sf{ \cancel{\dfrac{ - 13}{ - 39}} = \dfrac{1}{3}}}[/tex]
[tex] \implies{\sf{ \dfrac{1}{3} = \dfrac{1}{3}}}[/tex]
[tex]\implies{\sf{\underline{\underline{\red{LHS = RHS}}}}}[/tex]
Hence Verified!
[tex]\underline{\rule{220pt}{3pt}}[/tex]
Suppose that $ 700 is invested at 5.42% compounded continuously. How much is in the account after 18 years? Round your answer to the nearest cent. Write only a number as your answer. Do not write any units.
Answer:
Hello!
This word problem uses the common equation called; [tex]A=Pe^{rt}[/tex]
A = Pe^rt
P=700
e= e
r = 0.0542
t = 18
This is what you get when you plug in the according information.
700e^(0.0542*18)
700e^0.9756
=1856.9308
We need to put this into the nearest cent.
=1856.93
Have a great day!
I hope this helps you!
14. A triangle has vertices at A(4,2), B(-4,-2), and
C(2, 4). If the triangle is dilated with respect to the
origin using a scale factor of 172, what will the
coordinates for the new vertices be?
A A' (2.1). B' (-2,-1), and C (1.-2)
B. A (8.4), B (-8,-4). and C (4. - 8)
C. A' (1,2), B (-1,-2), and C (-2. - 1)
D. A (-2,-1), B' (-2,-1), and C° (-1,2)
Answer:
A
Step-by-step explanation:
Each coordinate of the triangle will have to dilate by 1/2 in order for the triangle to be fully dilated. Let's check each option to see which one has the correctly dilated points.
First, we'll look at A. A(4, 2) goes to A'(2, 1)... which is looking good so far! Half of 4 is 2, and half of 2 is 1, so the right dilation was applied. Next, let's check out B. B(-4, -2) goes to B'(-2, -1), which is still looking okay. Half of -4 is -2, and half of -2 is -1. Finally, we'll check the point C. If this one is correctly dilated, option A is the right option. C(2, -4) goes to C'(1, -2), and we can now be sure that option A is correct. Half of 2 is 1, and half of -4 is -2.
So, option A is the one to select. Hopefully that's helpful! :)
what is an equation of the line that passes through the points 0,-2and 0,-5
Answer:
Any equation with a slope of 3 will work. You can use any y-intercept. This equation will work: y = 3x+1
Step-by-step-explanation:
3x says that the slope is 3, and on a coordinate plane, 2 is 3 places above 5, and since the slope is 3, it will go 3 spots up, and run into (0,2)
what does a discrete quantitative variable mean?
Answer:
A discrete quantitative variable is one that can only take specific numeric values (rather than any value in an interval)
Step-by-step explanation:
A discrete quantitative variable is one that can only take specific numeric values (rather than any value in an interval), but those numeric values have a clear quantitative interpretation. Examples of discrete quantitative variables are number of needle punctures, number of pregnancies and number of hospitalizations.
What is the value of y?
Answer:
80° because 50° 60° 70° and 80°
Simplify the expression.
−6−7
Answer:
-13
Step-by-step explanation:
subtract 7 from -6
Answer: -13
Step-by-step explanation: When you have two numbers with negative signs, you add them but you keep the negative sign.
Therefore, -6-7 = -13
For the future, know these rules for signs when adding, subtracting, dividing and multiplying:
When adding two negative numbers, you add but keep the negative sign like in the above problem.
When adding a positive and negative, you subtract but keep the sign of the highest number. Example: -4+9 = 5 or -11+3 = -8.
When multiplying two negatives or positives numbers, the answer will be positive. When multiplying negatives x positive = negative.
The same applies to division. (-)/(+) = (-) or (+)/(-) = (-)
(-)/(-) = (+)
Hope this explanation and rules help.
A student has a savings account with $475 in it.
She deposits $125 of her paycheck into the account
every week. Her goal is to save $7,000 for college.
How long will it be before she has $1350?
Answer: 7 weeks
Step-by-step explanation:
Let x represent number of weeks
Let y represent the total amount
Amount = Paycheck deposited * number of weeks + Initial amount
y = 125x + 475
Number of weeks until she has $1350
1350 = 125x + 475
125x+475-475=1350-475
125x=875
x=7
Therefore, the student will have $1350 in her bank account after 7 weeks
Inequality word problem
Step by step and explanation pls do the problem or report
Answer:
34 hours or more
Step-by-step explanation:
If h is the number of hours Jack works, then his earnings will total 15h. He wants that to be at least 500. The appropriate inequality is ...
15h ≥ 500
h ≥ 33 1/3 . . . . . divide by 15
Jack needs to work 34 hours or more to earn at least $500.
Round 512.45 to the nearest ones place.
The answer would be 512.
i need help with number 5
Find the x and y intercepts of y=-x-8
Answer:
anyone wants to have fun with indian girl ?
Help pelsss thank you math sucks
Answer:
103
Step-by-step explanation:
180-77=103
Consider the circle centered at the origin and passing through the point (0, 2).
(a) Give the equation of the circle.
(b) For each point, decide whether or not it is on the circle. Is the point on the circle? (look at the image I attached)
Answer:
x^2+y^2=4, yes, no, yes, no
Step-by-step explanation:
a) It's centered at the origin, which means that the equation is x^2+y^2=r^2, right? Then since point (0,2) is on the circle, its radius can be solved using Pythagoras theory, r=sqrt(0^2+2^2)=2, so the equation is x^2+y^2=4.
b) You plug the points into the equation and if the equation is true, they're on the circle. I'll give you an example of the first two.
([tex]\sqrt{3},1[/tex]): so x=[tex]\sqrt{3}[/tex], y=1. When you bring that into the equation you got in (a), it would be 3+1=4, which is true, which means that the point is on the circle.
(4,0): so x=4, y=0. When you bring that into the equation you got in (a), it would be 16+0=4, which is not true, which means the point isn't on the circle.