In cylindrical coordinates, W is the set of points
W = {(r, θ, z) : 0 ≤ r ≤ 2 and 0 ≤ θ ≤ 2π and -2 ≤ z ≤ 5}
(A) Then the integral of f(x, y, z) over W is
[tex]\displaystyle\iiint_W(x^2+y^2+z^2)\,\mathrm dV = \int_0^{2\pi}\int_0^2\int_{-2}^5r(r^2+z^2)\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]
(B)
[tex]\displaystyle \int_0^{2\pi}\int_0^2\int_{-2}^5r(r^2+z^2)\,\mathrm dz\,\mathrm dr\,\mathrm d\theta = 2\pi \int_0^2\int_{-2}^5(r^3+rz^2)\,\mathrm dz\,\mathrm dr \\\\\\= 2\pi \int_0^2\left(zr^3+\frac13rz^3\right)\bigg|_{z=-2}^{z=5}\,\mathrm dr \\\\\\= 2\pi \int_0^2\left(\frac{133}3r+7r^3\right)\,\mathrm dr \\\\\\= 2\pi \left(\frac{133}6r^2+\frac74r^4\right)\bigg|_{r=0}^{r=2} \\\\\\= 2\pi \left(\frac{110}3\right) = \boxed{\frac{220\pi}3}[/tex]
evaluate the expression when c= -4 and x=5
x-4c
Answer:
21
Step-by-step explanation:
Fill in x into 5 and c into -4
5-4(-4)
21
Answer: -11
Step-by-step explanation:
x=5
and
c=4
the equation written in numbers is:
5-4x4 which simplified equals 5-16
this equals 5-5-11 so it should be -11
Mathematics I need help
what is equivalent to x-2(3x-1)=3x
Answer:
1/4 = x
Step-by-step explanation:
x - 2( 3x - 1 ) = 3x
Step 1 :- Distribute 2
x - 2 × 3x - 2 × 1 = 3x
x - 6x + 2 = 3x
Step 2:- Combine like terms
-5x + 2 = 3x
Step 3 :- Add 5x to both sides
-5x + 5x + 2 = 3x + 5x
2 = 8x
Step 4 :- Divide both side by 8
2/8 = 8x / 8
1/4 = x
Which of the following shows the graph of y = 4^x + 3?
The images of the graphs are missing and so i have attached them.
Answer:
Graph in option A
Step-by-step explanation:
y = 4^(x) + 3
Let's input some values of x and find the corresponding value of y and see if any of the graph matches the coordinates we get.
At x = 0;
y = 4^(0) + 3
y = 4
At x = 1;
y = 4^(1) + 3
y = 7
At x = 2;
y = 4^(2) + 3
y = 19
Looking at all the graphs, the only one with y = 4 when x = 0 is graph A
All I need is number two
in a board game you must roll two 6-sided number cubes. you can only start the game if you roll a 3on at least one of the number cubes.
Answer:
[tex]1-(5/6)^2[/tex]
31% chance
1 in 3.272727273 rolls
Step-by-step explanation:
XYZ ∆ where Angle Y =90° , XZ= 14 m , XY = 6 m . Find YZ ?
( Show all your workings )
[tex]4 \sqrt{10} [/tex]
Step-by-step explanation:
Use Pythagoras
A^2 + b^2 = c^2
(6)^2 + b^2 = (14)^2
36 + b^2 = 196
B^2 =160
[tex]b = \sqrt{160} [/tex]
[tex]b = 4 \sqrt{10} [/tex]
A pizza dough recipe calls for 6 1/2 cups of flour. The recipe makes 37 1/2 ounces of dough. How many ounces of dough does 1 cup of flour make?
Answer:
[tex]n = 5\frac{10}{13}[/tex]
Step-by-step explanation:
Given
[tex]Call = 6\frac{1}{2}[/tex] cups
[tex]Recipe = 37\frac{1}{2}[/tex] ounce
Required
Number of ounces per cup (n)
To do this, we simply divide the Recipe by the call
So, we have:
[tex]n = \frac{Recipe}{Call}[/tex]
[tex]n = 37\frac{1}{2} \div 6\frac{1}{2}[/tex]
Express as improper fraction
[tex]n = \frac{75}{2} \div \frac{13}{2}[/tex]
Rewrite as:
[tex]n = \frac{75}{2} * \frac{2}{13}[/tex]
[tex]n = \frac{75}{13}[/tex]
[tex]n = 5\frac{10}{13}[/tex]
You want to buy a $203,000 home. You plan to pay 10% as a down payment, and take out a 30 year loan for the rest. or a) How much is the loan amount going to be? $ b) What will your monthly payments be if the interest rate is 6%? $ c) What will your monthly payments be if the interest rate is 7%?
Answer:
The amount of the loan is going to be $ 182,700, and the monthly payments, if the interest is 6%, are going to be $ 537.95, while if the interest is 7%, are going to be $ 543.02.
Step-by-step explanation:
Given that you want to buy a $ 203,000 home, and you plan to pay 10% as a down payment, and take out a 30 year loan for the rest, for A) determine how much is the loan amount going to be, B) determine what will your monthly payments be if the interest rate is 6%, and C) determine what will your monthly payments be if the interest rate is 7%, the following calculations must be made:
A) 100 - 10 = 90
203,000 x 0.90 = X
182,700 = X
B) (182,700 x 1.06) / (30 x 12) = X
193,662 / 360 = X
537.95 = X
C) (182,700 x 1.07) / (30 x 12) = X
195,489 / 360 = X
543.025 = X
Therefore, the amount of the loan is going to be $ 182,700, and the monthly payments, if the interest is 6%, are going to be $ 537.95, while if the interest is 7%, are going to be $ 543.02.
find the HCF by prime factorization method 60 and 75
HCF=15
Hope it helps you...
Isch is taking a class where people say that everyone fails the first exam; however, he got a 93%. Instead of being proud, he thought, It must have been a fluke. Based on this, what can you conclude about Isch
Answer:
is a smart guy and also don't want others to hate him
She uses a scale of 1 centimeter to 6 inches
the scale drawing of the front face is
Answer:
change inches into centimeter and then divide it
hope this help
Happy buys 5 litres of milk on Monday and uses a fifths of it. On Tuesday she uses
half of what is left. How many millilitres are left after Tuesday?
it is 2000 ml after she drank it on Tuesday
Answer:
2000 mL
Step-by-step explanation:
1. The amount of milk left after 1/5 is drank is 4 litres, which is 4000 mL.
2. She drinks half of that, so divide 4000 mL by two.
2000 mL are left after tuesday
A die is rolled 5 times and a 5 or 6 is considered a success. Find the peobability of no success
Answer:
0.1317 = 13.17% probability of no successes.
Step-by-step explanation:
For each toss, there are only two possible outcomes. Either there is a success, or there is not. The probability of a success on a toss is independent of any other toss, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A die is rolled 5 times.
This means that [tex]n = 5[/tex]
5 or 6 is considered a success.
2 out of 6 sides are successes, so:
[tex]p = \frac{2}{6} = 0.3333[/tex]
Find the probability of no success:
This is P(X = 0). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.3333)^{0}.(0.6667)^{5} = 0.1317[/tex]
0.1317 = 13.17% probability of no successes.
Test 21,753 for divisibility by 2,3,5,9 and 10
Answer:
Step-by-step explanation:
21,753
at unit place=3 not an even number,not equal to 5 and not equal to 0
so 21,753 is not divisible by 2,5 and 10
again
2+1+7+5+3=18 divisible by 3 and 9.
so 21,753 is divisible by 3 and 9.
2(5 – 9x) = -3(x - 2)
Answer:
[tex]x=\frac{4}{15}[/tex]
Step-by-step explanation:
1. Distributive Property[tex]10-18x=-3x+6[/tex]
2. Solving for x[tex]10-6=-3x+18x\\4=15x\\\frac{4}{15} =x[/tex]
Hope this helped! Please mark brainliest :)
Which line is parallel to the line that passes through the points (1,7) and (-3, 4)? A. y=--x-5 B. y=+*+1 y=-x-8 O c. D. 11 v==x+3 4
Answer:
B
Step-by-step explanation:
because
If 2x^2 + 3x + 3 = Kx - K has real roots, find the possible values of k.
Answer:
Step-by-step explanation:
Dd
Write an equation that expresses the following relationship.
d varies directly with w and inversely with p.
In your equation, use k as the constant of proportionality.
9514 1404 393
Answer:
d = kw/p
Step-by-step explanation:
When d varies directly with w, the equation is ...
d = kw
When d varies inversely with p, the equation is ...
d = k/p
When d does both, the equation is ...
d = kw/p
Which of the following is result of using the remainder theorem to find F(3) for the polynomial function F(x) = x^3 - 9x^2 + 5x - 2
A. -32
B. 11
C. -59
D. -41
-41
Step-by-step explanation:The remainder theorem states that when a polynomial F(x) is divided by (x - k) the remainder is F(k). In other words, the remainder when f(x) is divided by (x-k) is calculated by simply calculating F(k).
Given:
F(x) = x³ - 9x² + 5x - 2 -----------------(i)
To calculate F(3), substitute x = 3 into equation (i) as follows;
F(3) = (3)³ - 9(3)² + 5(3) - 2
F(3) = 27 - 81 + 15 - 2
F(3) = -41
This means that if the polynomial F(x) = x³ - 9x² + 5x - 2 is divided by x - 3, the remainder will be -41.
The first five terms of an arithmetic sequence are shown below:
20, 17, 14, 11, 8, . . .
Let n represent the term number and f(n) the term in the sequence.
Choose a function that represents the sequence.
The answer to this question is f(n) = -3 + 23
Now my question is, how do you find the solution? I was taught the explicit formula is f(n) = m(n) + b, but no matter how many times I've tried to plug in the numbers I cannot seem to get the right answer. Please help me and do show the entire process and the steps.
Answer:
The function represents the sequence is - 3 n + 23.
Step-by-step explanation:
20. 17, 14, 11, 8,......
Here, the first term is
a = 20
Common difference, d = -3
Let the nth term is Tn.
Tn = a + (n -1) d
Tn = 20 + (n -1) x (-3)
Tn = 20 - 3 n + 3
Tn = 23 - 3 n = - 3 n + 23
So, the function represents the sequence is - 3 n + 23.
Answer:
Y'all know what it is already, but I want points, so: f(n) = -3n + 23
What is the slope of the line that passes through (17, −13) and (17, 8)?
(also can you try to explain ive been having trouble with these types of question)
Answer:
Slope is undefined. Line parallel to y-axis.
Step-by-step explanation:
By Analytic Geometry, we can determine the slope of a line by knowing two distinct lines and using the definition of secant line:
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] (1)
Where:
[tex](x_{1}, y_{1})[/tex] - Coordinates of the initial point.
[tex](x_{2}, y_{2})[/tex] - Coordinates of the final point.
[tex]m[/tex] - Slope.
If we know that [tex](x_{1}, y_{1}) = (17, -13)[/tex] and [tex](x_{2}, y_{2}) = (17, 8)[/tex], then the slope of the line is:
[tex]m = \frac{8-(-13)}{17-17}[/tex]
[tex]m = \frac{21}{0}[/tex]
The slope is undefined, which means that line is parallel to y-axis.
PLEASE HELP!!!! WILL GIVE BRAINLIEST!!!!
Answer:
9
[tex]3^{\frac{4}{2} }[/tex] = [tex]3^{2} =9[/tex]
Step-by-step explanation:
Omgg please help right now
Answer:
64in^3
Step-by-step explanation:
6×3 = 18
18×2 = 36
4×7 = 28
36+28 = 64
Hope this helps! :)
what is g(x)? please help
Answer:
It's the 4th answer: g(x) = 1/4 x - 3
Step-by-step explanation:
Switch x and y and solve for y
x=4y+12
-4y=-x+12
y = 1/4 x - 3
I need help on this graphing question if anyone can, please help me
Answer/Step-by-step explanation:
Given:
f(x) = 2x + 2
Domain = {-5, -1, 2, 3}
To write the range of f using set notation, substitute each domain value into f(x) = 2x + 2 to get each corresponding range value that will make up the set.
Thus:
✔️f(-5) = 2(-5) + 2
= -10 + 2
f(-5) = -8
✔️f(-1) = 2(-1) + 2
= -2 + 2
f(-1) = 0
✔️f(2) = 2(2) + 2
= 4 + 2
f(-1) = 6
✔️f(3) = 2(3) + 2
= 6 + 2
f(3) = 8
Range of f using set notation = {-8, 0, 6, 8}
✔️Graph f by plotting the domain values on the x-axis against the corresponding range values on the y-axis as shown in the attachment below:
*See attachment for the graph of f
find the angle between following linesroot 3x-y=2,x-root 3y=7
Answer:
where I find? where is the directions
Find the solution to the system
of equations.
y = 2x + 3
([?], [ ]
2
بیر
2 3 4
-4 -3 -2 -1
-1
-2
3
-4
y=-x
Enter
Answer:
The two lines meet at (-1,1)
Please Help NO LINKS
Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by
y
=
x
2
,
y
=
0
, and
x
=
9
,
about the
y
-axis.
V
=
Answer:
[tex]\displaystyle V = \frac{6561 \pi}{2}[/tex]
General Formulas and Concepts:
Algebra I
FunctionsFunction NotationGraphingCalculus
Integrals
Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Shell Method: [tex]\displaystyle V = 2\pi \int\limits^b_a {xf(x)} \, dx[/tex]
[Shell Method] 2πx is the circumference[Shell Method] 2πxf(x) is the surface area[Shell Method] 2πxf(x)dx is volumeStep-by-step explanation:
Step 1: Define
y = x²
y = 0
x = 9
Step 2: Identify
Find other information from graph.
See attachment.
Bounds of Integration: [0, 9]
Step 3: Find Volume
Substitute in variables [Shell Method]: [tex]\displaystyle V = 2\pi \int\limits^9_0 {x(x^2)} \, dx[/tex][Integrand] Multiply: [tex]\displaystyle V = 2\pi \int\limits^9_0 {x^3} \, dx[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle V = 2\pi \bigg( \frac{x^4}{4} \bigg) \bigg| \limits^9_0[/tex]Evaluate [Integration Rule - FTC 1]: [tex]\displaystyle V = 2\pi \bigg( \frac{6561}{4} \bigg)[/tex]Multiply: [tex]\displaystyle V = \frac{6561 \pi}{2}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Applications of Integration
Book: College Calculus 10e
Factorize 5b2-11b+6=0
Answer:
5b^2-(5+6)b+6=0
5b^2-5b-6b+6=0
5b(b-1)-6(b-1)=0
(5b-6)(b-1)=0
either
(5b-1)=0
5b=1
b=1/5
or
b-1=0
b=1
Step-by-step explanation:
firstly find out the mid term factor i e in above qn 11 should be break down so that its multiple should be coefficient of b and constant and additiqn should be equals to 11 .so we find out 5 and 6