The triple integral that is bounded by a paraboloid x = 4y2 4z2 given as 16.762
Parabloid, x = 4y² + 4z²
plane x = 4
x = 4y² + 4z²
x = 4
4 = 4y² + 4z²
4 = 4 (y² + z² )
1 = y² + z²
from polar coordinates
y = r cos θ
z = r sin θ
r² = y² + z²
The limits of the integral0 ≤ θ ≤ 2π
4r² ≤ x ≤ 4
0 ≤ r ≤ 1
[tex]\int\limits\int\limits\int\limits {x} \, dV = \int\limits^1_0\int\limits^a_b\int\limits^c_d {x} \, dx ( rdrdz)[/tex]
where
a = 4
b = 4r²
c = 2r
d = 0
The first integral using limits c and d gives:
[tex]2pi\int\limits^1_0\int\limits^a_b {xr} \, dx[/tex]
The second integral using limits a and b
[tex]pi\int\limits^1_0 {16 } } \, rdr - pi\int\limits^1_0 {16r^{5} \, dx[/tex]
[tex]16pi\int\limits^1_0 { } } \, rdr - 16pi\int\limits^1_0 {r^{5} \, dx[/tex]
[tex]16pi\int\limits^1_0 { } } \, [r-r^{5}]dr[/tex]
The third integral using limits 1 and 0 gives: 16.762
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The triple integral that is bounded by a paraboloid x = 4y2 4z2 given as 16.762
What is integration?Integration is defined as adding small parts to form a new significant part.
Parabloid, x = 4y² + 4z²
plane x = 4
x = 4y² + 4z²
x = 4
4 = 4y² + 4z²
4 = 4 (y² + z² )
1 = y² + z²
from polar coordinates
y = r cos θ
z = r sin θ
r² = y² + z²
The limits of the integral
0 ≤ θ ≤ 2π
4r² ≤ x ≤ 4
0 ≤ r ≤ 1
[tex]\int\int\intxdV = \int_0_1\int_b_a\int_d_cxdx(rdrdz)[/tex]
where
a = 4
b = 4r²
c = 2r
d = 0
The first integral using limits c and d gives:
[tex]2\pi\int_0^1\int_b^axydx[/tex]
The second integral using limits a and b
[tex]\pi \int_0^116rdr-\pi\int_0^116r^5dx[/tex]
[tex]16\pi \int_0^1rdr-16\pi\int_0^1 r^5dx[/tex]
[tex]16\pi\int_0^1[r-r^5]dr[/tex]
The third integral using limits 1 and 0 gives: 16.762
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if y=5x-3, find the value of y when x=0
Answer: [tex]Y=-3[/tex]
Step-by-step explanation:
[tex]Y=5x-3[/tex]
[tex]Y=5 * (x) -3[/tex]
Then replace x by 0
[tex]Y=5 * (0) -3[/tex] or [tex]Y= 5(0) -3[/tex]
[tex]Y=0 -3[/tex]
[tex]Y=-3[/tex]
Find the area of a triangle
Answer:
240 feet
Step-by-step explanation:
The formula for finding the area of a triangle is: [tex]\frac{1}{2}bh[/tex], where [tex]b[/tex] stands for the base and [tex]h[/tex] stands for the height.
In this case, 20 is our height, and 24 is our base. Let's plug that into the formula.
[tex]1/2(20)(24)\\1/2(480)\\240[/tex]
Therefore, the area of the triangle is 240 feet.
#LearnWithBrainly
PLEASE HELP!! 100 POINTS
Consider this dilation.
(a) Is the image of the dilation a reduction or an enlargement of the original figure? Explain.
(b)What is the scale factor? Explain and show your work.
The red figure is the original and the green the dilation. We know this because the dilated points are marked with '.
Therefore, we can see that the dilation is a reduction of the original figure. The figure got smaller in size after the dilation.
To find the scale factor, we'll need to look at a few of the points before and after the dilation.
A = (-4, 4)
A' = (-2, 2)
C = (0, 4)
C' = (0, 2)
---The scale factor will be the same on all the points, which is why I have selected only 2 sets of points to look at.
Now, we can figure out the scale factor by thinking about how -4 got to -2, how 4 got to 2. In this case, it is simply dividing by 2. The scale factor must be in multiplication, so we cannot use division in reporting the scale factor, it must be a fraction.
2 / 4 = 1 / 2
The scale factor, therefore, is 1/2.
Hope this helps!
Answer:
a) A reduction.
b) 0.5 or 1/2
Step-by-step explanation:
a) The new points are indicated by the ' next to the letters. By observing the graph, we can see that new points have lessened, and therefore shrank the dialtion, so it is a reduction.
b) On each point, it is reducted by 0.5.
Point A went down from 4 to 2, which is half of 4.
Point B went down from -2 to -1, which is half of -2.
Point C went down from 4 to 2, which is half of 4.
Point D went down from 8 to 4, which is half of 8.
hope this helps!
The charge of an atom is the sum of the charges of its protons, neutrons, and electrons.
• Each proton has a charge of e.
• Each neutron has a charge of 0.
Each electron has a charge of -e.
An atom consists of 6 protons, 10 neutrons, and 4 electrons.
How many electrons would need to be added to make the charge of the atom 0?
Answer:
2 electrons
Step-by-step explanation:
2 electrons is the answer
If u need explanation do mention in comments
Answer:
*2 electrons more*
Explanation:
In an atom the number of electron and protons must be same.Otherwise, it will have charge and form ions. [ ignore the neutrons ]
Here,
protons: 6electrons: 4The electron and proton is unbalanced, In order to make them same.
2 more electrons need to be added to make total 6 electrons.
Which of the following represents 5 + 10? Mark all that apply.
Can someone please help with this? I'll give brainliest. I don't understand this... or the explanation it gives... the page before was just teaching how to solve simple problems to put on graphs what's an asymptote?
Step-by-step explanation:
Hello!
I'd love to help you learn.
I see the formula attached is [tex]4*(\frac{1}{2})^{x} =-2^{x}-1\\[/tex]
This problem is explaining you to graph, since algebraically it's a little more harder to try and find the solution.
Since they're both equal to each other, we can assign a variable like y, so we can make them into two individual lines.
You can use your scientific calculator to graph lines like this, or otherwise there are online sources (Desmos helps alot!) which can graph two equations as so.
Now that we have the corresponding system of equations, we can graph both.
[tex]y=4*(\frac{1}{2})^x\\ y=-2^x-1[/tex]
Let's graph them on Desmos on the same plane. The answers are attached. Red is the first equation, blue is the second.
What determines the solutions of a system of equations?
-No solution: the two lines will never intersect/does not intersect ever, which means that there are no set point where it satisfies both equations.
-One solution: the two lines intersect once and only once, meaning that there is that one set point where the x and y values both satisfy both equations.
-Multiple solutions: the two lines will intersect each other multiple times, meaning there are multiple set points where the x and y values satisfy both equations. You usually will not have to worry about these problem sets.
-Infinite solutions: the two lines are both the same line, which means every x and y value will satisfy both equations.
Looking at the solution attached, we can see that there are no places where a system of equations intersect, therefore ruling it that they have no solution.
And to answer your last question, an asymptote is a imaginary line in which a equation can approach closely and closely, but will never touch that imaginary line. Think of a line at y=[tex]\frac{1}{x}[/tex]. When you graph it, you can see that the two lines never ever EVER intersect the y-axis, or x=0; giving that x=0 as a vertical asymptote.
Which function is a quadratic function? u(x) = –x 3x2 – 8 v(x) = 2x2 8x3 9x y(x) = x2 3x5 4 z(x) = 7x2 2x3 – 3.
The function [tex]u(x)=-x+3x^{2} -8[/tex] is a quadratic function due to the highest exponent being 2.
Given functions are:
[tex]u(x)=-x+3x^{2} -8[/tex]
[tex]v(x)=2x^{2} +8x^3+9x[/tex]
[tex]y(x)=x^{2} +3x^5+4[/tex]
[tex]z(x) =7x^{2} +2x^3-3[/tex]
What is a quadratic function?A function of the form [tex]f(x)=ax^{2} +bx+c[/tex] with [tex]a\neq 0[/tex] is called a quadratic function means the highest exponent of polynomial should be 2.
Let us check one by one.
[tex]u(x)=-x+3x^{2} -8[/tex]
Highest exponent =2
The function is also of form [tex]f(x)=ax^{2} +bx+c[/tex] so u(x) is a quadratic function.
The functions v(x), y(x), and z(x) are having highest exponents as 3,5, and 3 respectively so they are not quadratic functions.
Hence, the function [tex]u(x)=-x+3x^{2} -8[/tex] is a quadratic function due to the highest exponent being 2.
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hi anyone can help me :) i have no idea how to do it . pls help me thx
Explanation:
The first column is nothing but "2"s.
The second column has the sequence 2, 1, 0 from top to bottom. If the pattern keeps up, then the next value in the second column should be -1 since we're counting down by 1. Use a number line to see this.
So we have 2-(-1) = 2+1 = 3 or 2-(-1) = 3 as the next line. I think keeping it as 2-(-1) rather than 2+1 is beneficial so that the minus signs line up.
The result of 3 helps confirm that the final column of values (0,1,2) is incrementing by 1.
5. A box contains 4 white balls and 6 yellow balls. A ball is drawn at random from the box and is not replaced. What is the probability that both balls are white?
8/45
3/25
4/25
2/15
Answer:
2/15
Step-by-step explanation:
Given:
A box contains 4 white balls and 6 yellow balls. A ball is drawn at random from the box and is not replaced. What is the probability that both balls are white?
8/45
3/25
4/25
2/15
Solve:
Knowing that total = 10 { 4 white balls and 6 yellow balls}
P(first white)=4/10=2/5 { 4 out of 10 balls are white}
P(second white)=3/9=1/3 { 3 out of 9 balls are white; Since no replaced}
P(both white)=2/5 × 1/3=2/15
Hence, Answer = 2/15
Lenvy~
Use the image below to find the missing side lengths.
Answer:
Step-by-step explanation:
your dog weighs 18 kilograms. the medication dosage is 1 milliliter per every 10 pounds. rounded to the nearest milliliter, how many milliliters of medication should you give your dog? 1 kilogram = 2.2 pounds
A) 2mL
B) 3mL
C) 4mL
D) 5mL
Answer:4mL
Step-by-step explanation: if you multiply 18 by 2.2 you would get 39.6, you would divide by 10 to get 3.96, then you would round to the nearest whole number so you’d get 4.
By using a change of units, we will see that the dog needs 4 mL of medication.
How many milliliters of medication should you give your dog?
Here we need to see how many pounds are in 18 kilograms, using the relation:
1kg = 2.2lb
We get:
18 kg = 18*(2.2lb) = 39.6 lb
Now, for each 10 lb, we add 1mL of medication, then we need to divide the mass of the dog by 10lb, we get:
M = (39.6 lb)/(10 lb) = 3.96
Rounding to the next whole number we get 4, so the dog needs 4 mL of medication.
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HURRY PLEASE SOLVE will give brainliest!!!
2
x-9 = -5
2=x 2+x + 4-2=2 2-6+
-4
2
X
+2= 4 + 62 =66 +9 = 75Lashonda reads a book at a rate of 12 chapters per hour. How many chapters does she read in 3 hours?
Answer:
12×3=36
Step-by-step explanation:
hope ththis helped :))
What are the linear equations for the lines passing through the following points (3,4) and (5,8)
Answer:
The equation of the line is y = 2x + 2
Step-by-step explanation:
Given:The two points are (3, 4) and (5, 8)To find:- Equation of a linear line Solution:-
Equation of a linear line can be placed in the format:
y = mx + cFormula for finding the slope(m):
[tex] \sf{}m = \frac{x- x_1}{y - y_1} = \frac{y_2 - y_1}{x_2 - x_1} \\ \\ \sf{}m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex] \sf{}m = \frac{8 - 4}{5 - 3} = \cancel \frac{4}{2} = 2[/tex]
Form the intermediate equation:
y = mx + c
[tex] \mathtt{y = 2x + c}[/tex]
Find the y-intercept:
Substitute (3,4) into the equation
[tex] : \longrightarrow \: \mathtt{y = 2x + c} \\ \\ : \longrightarrow \:\mathtt{4 = 2(3) + c} \\ \\ : \longrightarrow \: \mathtt{4 = 6 + c} \\ \\ : \longrightarrow \: \mathtt{c = 6 - 4} \\ \\ : \longrightarrow \: \mathtt{c = 2}[/tex]
Form the equation:
[tex]: \longrightarrow \: \mathtt{y = 2x + c} \: \\ \\ \mathtt{putting \: values \: of \: c} \\ \\ : \longrightarrow \: \mathtt{y = 2x + 2}[/tex]
The equation of the line is [tex]\underline\mathfrak\red{{{y = 2x + 2}}}[/tex]
I WILL GIVE BRAINLEIST(I NEED THIS RIGHT OR I HAVE TO START OVER)
Answer:
It’s irrational hope this is correct
Step-by-step explanation:
Answer:
rational
Step-by-step explanation:
Convert both to decimals
[tex]\\ \rm\Rrightarrow x=0.147147\dots [/tex]
[tex]\\ \rm\Rrightarrow 1000x=147.147..[/tex]
Hence..
999x=147x=147/99On similar way we can get second one
So if
p/q and r/s [tex]\in [/tex]QThen
pr/qs also rationalQuestion 2 of 5
Which choice describes the shape of the data?
83 84 85 86 87 88 89 90 91 92
A. Symmetric; not bell-shaped
ОО o
B. Not symmetric; not bell-shaped
C. Symmetric, bell-shaped
o
D. Not symmetric, bell-shaped
2 2/3 - 1 1/2 - 4/5
what does it equal
Answer:
11/30
Step-by-step explanation:
Do you need an explanation?
Turn the written information into a equation (exponential function):
Common ratio of 4; horizontal shift right 6
Step-by-step explanation:
common ratio is usually used for geometric sequences.
every term is created by multiplying the previous term by a certain constant factor (= common ratio).
this factor or common ratio is in our case 4.
such a sequence is a function f(x) for x being whole numbers.
a0 = 1
a1 = a0×4 = 1×4 = 4
a2 = a1×4 = 4×4 = 16
...
an = 4^n
as general function that is then
f(x) = 4^x
a horizontal shift right by 6 units means that now the functional value of x is the same as it was for (x-6) before the shift.
e.g. f_new(6) = f_old(0)
so, the function is
f(x) = 4^(x - 6) or (4^x)/4⁶
rohana wants to find the volume of a sphere that has a radius of 10 feet. which equation can she use to solve for this value in cubic feet ?
The equation that can be used to determine the volume of the sphere is 4/3π10³
What is the volume of the sphere?A sphere is a three-dimensional object in which points from its center to its circumference is equidistant.
Volume of a sphere = 4/3πr³
Where:
π = pi = 22/7r = radiusTo learn more about the volume of a sphere, please check: https://brainly.com/question/13705125
HELP PLEASEE, ILL BRAINLIST!!
Answer:
(a) To find the missing angle, we would do inverse tan.
[tex]angle =tan^{-1}\frac{opp}{adj}[/tex]
[tex]angle = tan^{-1}\frac{17}{21}[/tex]
angle= 39.0 degrees or 0.7 radians
(b) To find the missing angle, we would do inverse sin.
[tex]angle= sin^{-1}\frac{opp}{hyp}[/tex]
[tex]angle= sin^{-1}\frac{12.7}{22.1}[/tex]
angle= 35.1 degrees or 0.6 radians
please help me write quadratic equation given the roots and the leading coefficient
Answer:
Example Question: f(x) = 2x^2 + 2x - 1
If the leading coefficient is positive, the graph will be opening up (U) if the leading coefficient is negative, the graph will be opening down (n)
Roots are the x-intercepts that help find the axis of symmetry (add the two roots together and divide the result by 2 to get the axis of symmetry)
To find the vertex, simply imput the axis of symmetry into the given equation.
And that’s about it.
Step-by-step explanation:
I don’t know what you’re asking for??
Philip is a football player who runs a pass route that takes a right angle bend as shown in the diagram below. Which do you think will have the greater magnitude; the average speed or the average velocity? explain why
Answer:
Average velocity
Step-by-step explanation:
The average speed is only different from average velocity because it has direction.
The average speed will be calculated with the hypotenuse A_C, but average velocity will be calculated with the two directions AB_BC.
The volume of this rectangular prism is 72 in³. What is the missing measurement for c?
What is the length of the shipping carton?
Enter your answer in the box.
c = in
[tex]\huge\fbox\purple{ANSWER} [/tex]
[tex] \mathsf\pink{v = l \times w \times h}[/tex]
[tex] \mathsf \purple{{72in}^{3} = c \times 4in \times 3in}[/tex]
[tex] \mathsf \pink{ {72in}^{3} = c \times 12 {in}^{2} }[/tex]
[tex] \mathsf \purple{ \frac{72 {in}^{3} }{ {12in}^{2} } = c \times \frac{12 {in}^{2} }{ {12in}^{2} } }[/tex]
[tex] \mathsf \pink{6in = c}[/tex]
[tex] \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }[/tex]
➣Given➣shipping carton basically shape is rectangular prism type➣its volume (shipping carton)=72in²➣its height =3in➣its width = 4in➣ assumption :- length "c"[tex] \boxed{ \pink✠\underline{ \boxed{ \sf{Volume \: of \: Rectangular \: prism=length × width × height.}}} \pink✠}[/tex]
[tex]\rule{80mm}{2.5pt}[/tex]
★ Let's substitute values according to given info[tex] \qquad \sf \: ➛ 72 = c \times 4 \times 3 \\ \qquad \sf \: ➛72 = c \times 12 \\ \qquad \sf \: ➛transporting \: 12 \: in \: divide \\ \qquad \sf \: ➛ \frac{72}{12} = c \\ \qquad \sf \: ➛ \cancel\frac{72}{12} = c \\ \qquad \sf \: ➛6 = c[/tex]
[tex]\rule{80mm}{2.5pt}[/tex]
★ Hence "c" (length) of Rectangular prism (shipping carton) is
[tex]\boxed{ \blue✜\underline{ \boxed{ \sf{length(c)= 6inch \green✓}}} \blue✜}[/tex]
Hope it helps !
help guys with this question
Answer:
slope: 2
points: (2, 4), (6, 12)slope:
[tex]\sf \dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\rightarrow \sf \dfrac{12-4}{6-2}[/tex]
[tex]\rightarrow \sf \dfrac{8}{4}[/tex]
[tex]\rightarrow 2[/tex]
what is the least common denominator of 1/3 and 1/6
Answer: 6. this is like 3rd grade math just multiply 1/3 and 1/6 to see
Answer:
1/2
Step-by-step explanation:
1/6/1/3=1/2or2
I the not understand the question properly
A collector has 210 magazines and 300 books. She wants to maintain
this ratio in her collection but she needs to sell some of her items. If
she sells 21 magazines, how many total items should she sell from
her collection?
Answer:
51 total items
Step-by-step explanation:
210 Magazine : 300 Books
21 Magazine : 30 Books
If She wants to sell 21 magazines, she would have to sell another 30 books in order to maintain the ratio.
21 + 30 = 51
What is the area of this figure?
Answer:
38.5
Step-by-step explanation:
to find the area of the triangle, you can do 11 x 3 ÷ 2 = 16.5
then you find the area of the triangles: 3 x 3 = 9
and 3 × 11 = 33
then you add them all to find a total area of 38.5
how do i get my math grade up
Answer:
just practice alot . .. ...........
Answer:
you could do all your work and try to ask the teacher for help
Step-by-step explanation:
(systems of equations word problem)
ms. arrington has been raising money to take her classroom to the zoo. she has raised $580. the zoo has allowed all the adults to enter the zoo at a flat rate of $75 for all. if each student ticket costs $8.50, what is the maximum number of students allowed to attend the field trip?
a 59 students
b 60 students
c 58. students
d 61 students
Answer:
C
Step-by-step explanation:
All you have to do is divide 580 by 8.50 to easily distribute the money to each student equally.
IMAGE BELOW I WIL GIVE BRANLIEST
Answer:
The scale factor is 2.
Step-by-step explanation:
From the coordiante plane, we can see that:
Point H(4) has been expanded to 4 {4 · 2 = 8}
Point G(1) has been expanded to 2 {1 · 2 = 2}
Point I(-2) has been expanded to -4 {-2 · 2 = -4}
hope this helps!