Answer:
26 po hahahahahahahahahahaha
Compute the integral Z Z Z U y dV , where U is the part of the ball of radius 2, centered at (0, 0, 0), that lies in the 1st octant. Recall that the first octant is the part of the 3d space where all three coordinates x, y, z are nonnegative. (Hint: You may use cylindrical or spherical coordinates for this computation, but note that the computation with cylindrical coordinates will involve a trigonometric substitution - so spherical cooridnates should be preferable.)
As the hint suggests, convert to spherical coordinates using
x = p cos(u) sin(v)
y = p sin(u) sin(v)
z = p cos(v)
dV = dx dy dz = p² sin(v) dp du dv
Then U is the set
[tex]U = \left\{ (p,u,v) \mid 0\le p\le2 \text{ and } 0\le u\le \dfrac{\pi}2 \text{ and } 0\le v\le\dfrac{\pi}2\right\}[/tex]
and the integral of y over U is
[tex]\displaystyle \iiint_U y \, dV = \iiint_U p\sin(u)\sin(v) \cdot p^2 \sin(v) \, dV[/tex]
[tex]\displaystyle \iiint_U y \, dV = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \int_0^2 p^3 \sin(u) \sin^2(v) \, dp \, du \, dv [/tex]
[tex] \displaystyle \iiint_U y \, dV = \frac{2^4-0^4}4 \int_0^{\frac\pi2} \int_0^{\frac\pi2} \sin(u) \sin^2(v) \, du \, dv [/tex]
[tex]\displaystyle \iiint_U y \, dV = 4 \cdot \left(-\cos\left(\frac\pi2\right) + \cos(0)\right) \int_0^{\frac\pi2} \sin^2(v) \, dv [/tex]
[tex]\displaystyle \iiint_U y \, dV = 4 \cdot \frac12 \int_0^{\frac\pi2} (1-\cos(2v)) \, dv [/tex]
[tex]\displaystyle \iiint_U y \, dV = 2 \left(\left(\frac\pi2 - \frac12 \sin\left(2\cdot\frac\pi2\right)\right) - \left(0 - \frac12 \sin\left(2\cdot0\right)\right) \right)[/tex]
[tex]\displaystyle \iiint_U y \, dV = \pi - \sin(\pi) = \boxed{\pi}[/tex]
Mary is doing research on bird migration. Last week she counted 12 migration birds in her yard. This week she counted 10. What was the percent decrease in birds this week?
Ms. April likes for the twenty students in her
class to have a carton of milk each day at break
time. She sends three of her students down to
the cafeteria to ask for the cartons of milk, but
she likes to mix things up a bit and wants to
send a different group of students down every
day. Will she have enough different groups of
three students in her class of twenty students to
send a different group every day of the school year? (There are 180 days in the school year)
Answer:
Ms. April will not have enough students.
Step-by-step explanation:
This is because 180 days of the year divided by 3 students per day = 60 students per year. The class only has 20 students, therefore, there is not enough students needed to collect milk.
Answer:
Ms. April will not have enough students.
Step-by-step explanation:
This is because 180 days of the year divided by 3 students per day = 60 students per year. The class only has 20 students, therefore, there is not enough students needed to collect milk.
Miss Jurkovac went to Costa Rica for 6 days and saw 42 monkeys. If she saw 84 monkeys, how many days was she there?__________ days
Answer:
Step-by-step explanation:
6 times 2 is 12
42 multiplied by 2 is 84
therefore the answer is 12 days.
A patient is prescribed Coreg 12.5 mg by mouth twice a day. How many tablets should the patient
receive for one dose if the medication available is 6.25 mg/tablet?
Answer:
yes...
Step-by-step explanation:
k
The area of a rectangle is 50 ft, and the length of the rectangle is 5 ft less than three times the width. Find the dimensions of the rectangle.
Answer:
L - 10 . W - 5
Step-by-step explanation:
Length = 3*width - 5
area = length * width
50 = (3w-5)* w
50 = 3w^2-5w
0 = 3w^2 - 5w -50
0= (3w+10)(w-5)
w = 5 , w can't equal -10/3 because width can't be negative
width is 5
Length = 3 * 5 - 5
Length = 10 , width = 5
Answer:
first lets say w is the width
50(area)=w(idth)+3(w-5)
50=w+3w+15
50=4w+15
35=4w
8.75=w
w equals 8 3/4
Hope This Helps!!!
Solve for x and y. (Geometry)
Step-by-step explanation:
All angles of the ∆ are same. So it's a equilateral ∆ . So all sides will also be equal .
16 + y = 46
y = 46 -16 = 30
And ,
60 + x + (180-80) = 180
-20 +x = 0
x = 0 +20
x = 20°
NEED HELP I DONT REMEBER DIS
Answer:
a. ΔMNK =Δ [tex]PRT[/tex]
b. TR=MN
c. [tex]x=7[/tex]
Step-by-step explanation:
I hope this help you
Which is a recursive formula for this geometric sequence? -320, -80, -20, -5, . . .
The recursive formula for the geometric sequence is:
[tex]f(n) = \frac{1}{4}f(n - 1), f(1) = -320[/tex]
What is a geometric sequence?A geometric sequence is a sequence in which the coefficient of consecutive terms is always the same, called common ratio q.The recursive equation for a geometric sequence is:
[tex]f(n) = qf(n - 1)[/tex]
With f(1) as the first term.In this problem, the sequence is: {-320, -80, -20, -5, . . .}
The first term is [tex]f(1) = -320[/tex].The common ratio is [tex]q = \frac{-80}{-320} = \frac{1}{4}[/tex]Hence, the recursive equation is:
[tex]f(n) = \frac{1}{4}f(n - 1), f(1) = -320[/tex]
You can learn more about geometric sequence at https://brainly.com/question/11847927
The required recursive formula is expressed as [tex]a_{n-1}=-320(\frac{1}{4} )^n[/tex]
Geometric progressionThe required recursive formula is expressed as [tex]a_{n-1}=-320(\frac{1}{4} )^n[/tex]
n the following sequence -320, -80, -20, -5,...
The The required recursive formula is expressed as [tex]a_{n-1}=-320(\frac{1}{4} )^n[/tex]is given as:
r = -80/-320 = -20/-80 = 1/4The first term = -320The required recursive formula is expressed as [tex]a_{n-1}=-320(\frac{1}{4} )^n[/tex]
Learn more on geometric functions here: https://brainly.com/question/222209
What is the rectangular form of theta = 3pi/4?
Please answer this question if you 100% know this answer.
a. x - y = 0
b. x - y = 1
c. x + y = 0
d. x + y = 1
The answer was not a.
Answer:
c. x + y = 0
Step-by-step explanation:
The terminal ray of the angle θ = 3π/4 extends to the upper left through the 2nd quadrant with a slope of -1. It lies on the line ...
y = -x
x + y = 0 . . . . . . add x to get this standard form equation
Jorge wants to find the height of the house, help him find it.
Answer:
:)
Step-by-step explanation:
:)
What is the slope and y intercept form of -5x + 3y =-9.
What is the slope and y intercept form of -x +2y =-20
fast help.
Answer:
y = 5/3x - 3 and y = 1/2x - 10
Step-by-step explanation:
A. -5x + 3y = -9
In order to go from standard to slope-intercept form, we want to isolate y on the left side. We start by adding 5x to both sides:
3y = -9 + 5x
Next, we divide both sides by 3:
y = (-9 + 5x)/3
And then distribute:
y = -9/3 + 5x/3
And finally simplify:
[tex]y = -3 + \frac{5}{3}x[/tex]
And move the numbers on the right to fit the form y = mx + b:
[tex]y = \frac{5}{3}x-3[/tex]
B. -x + 2y = -20
In order to go from standard to slope-intercept form, we want to isolate y on the left side. We start by adding x to both sides:
2y = -20 + x
Next, we divide both sides by 2:
y = (-20 + x)/2
And then distribute:
y = -20/2 + x/2
And finally simplify:
[tex]y = -10 + \frac{1}{2}x[/tex]
And move the numbers on the right to fit the form y = mx + b:
[tex]y = \frac{1}{2}x - 10[/tex]
which has one solution:
2x + 2y = 180
0.1x + 7y = 78
What is the average rate of change between: x = 1 and x = 2? x = 2 and x = 3? x = 3 and x = 4? x y 1 2 3 4 5 4 8 12
Answer:
The average rate of change between x = 1 to x = 2 is 2, from x = 2 to x = 3 is 4 and from x = 3 to x = 4 is 8.
Step-by-step explanation:
-
4. 3x² - 2x - 1 = 0
What is -3/2 as a decimal
Answer:
-1.5
Step-by-step explanation:
To convert a fraction to a decimal number divide the numerator (-3) by denominator (2)
Answer:
-1.5
Step-by-step explanation:
Solve the system of linear equations using any method you choose:
-6x + 3y = 18
10x - y = 4
9514 1404 393
Answer:
(x, y) = (1.25, 8.5)
Step-by-step explanation:
I choose to put these equations into reduced general form, then use the "cross multiplication method" to solve.
2x -y +6 = 0
10x -y -4 = 0
d1 = 2(-1) -10(-1) = 8
d2 = -1(-4) -(-1)(6) = 10
d3 = 6(10) -(-4)(2) = 68
Solutions are ...
x = d2/d1 = 10/8 = 1.25
y = d3/d1 = 68/8 = 8.5
The solution is (x, y) = (1.25, 8.5).
_____
Additional comment
I like a graphing calculator for a quick and easy solution. When the values are not integers, I like an algebraic solution to see what the exact values are.
__
The "cross multiplication method" is similar to Cramer's rule in that determinants of pairs of coefficients are computed. If you look up this method, videos will show you a variation that is slightly different. Here, we determined d1, d2, and d3 as the 2×2 determinant of the coefficients in adjacent columns of the array you get from the general form equations with the first column repeated:
[tex]\begin{array}{cccc}2&-1&6&2\\10&-1&-4&10\end{array}[/tex]
In each pair, the determinant is the difference between the product of numbers on the down-diagonal and the product of numbers on the up-diagonal.
The determinants relate to the x- and y-values by ...
1/d1 = x/d2 = y/d3 ⇒ x = d2/d1, y = d3/d1
There is a Vedic solution method for linear equations that is similar to this, but starts from equations in standard form. As a consequence, the cross-differences are done in a different order.
__
Standard form: ax +by = c
General form: ax +by +c = 0
A line that passes through (3, 1) and (0, -3)
how many feet in 13 miles, 176 yards?
30x^8-4x^7+6x^4/-6x^3 perform division
Answer:
[tex]-\frac{x(15x^4-2x^3+3)}{3}[/tex]
Step-by-step explanation:
[tex]\frac{30x^8-4x^7+6x^4}{-6x^3}[/tex]
The first thing I would do is to factor the numerator. All coefficients there are divisible by 2, and all variables are divisible by x⁴. I'll also move the negative sign to the left.
[tex]-\frac{2x^4(15x^4-2x^3+3)}{6x^3}[/tex]
Next, you can simplify 2/6 to 1/3:
[tex]-\frac{x^4(15x^4-2x^3+3)}{3x^3}[/tex]
Finally, the last thing you can do is simplify x⁴/x³ to x/0:
[tex]-\frac{x(15x^4-2x^3+3)}{3}[/tex]
That's as simplified as it gets.
Does anyone know the answer.With explanation plz.
Answer: He sold 1,800 merchandise
Step-by-step explanation: 426 - 300 = 126 ÷0.07 = 1,800
I dont know if im right though
Please Help me Solve this question
Answer:
Step-by-step explanation:
Correct Answer: C
We can rely on the guess and check method to easily solve this problem. Let’s first pick arbitrary values of x and y to eliminate some answer choices.
Let’s consider the case where |x| and let x = 3 and y = -10.
Because x/y = -3/10 < 1, answer choice A is incorrect.
Because |x|2 = (3)2 = 9 and |-10| = 10, we have that |x|2 < y, so answer choice B is also incorrect.
Because x2 + 1= (3)2 + 1 = 10 and y2 + 1 = (10)2 + 1 = 101, we have that x2 + 1 < y2 + 1, so answer choice D is also incorrect.
Now, let’s consider the case where |x|>|y| and let x = 3 and y = -2.
Then, x-2 = 1/x2 = 1/9 and y-2 = 1/y2 = 1/4. This means that x-2 < y-2 , so answer choice E is also incorrect.
This means that answer choice C is correct. We can manipulate the inequality to see why this is true: (x/3 – 5) > (y/3 – 5)
We add 5 to both sides: x/3 > y/3
We multiply both sides by 3: x > y.
We know this is true since we are given that x > 1 > -1 > y, which simplifies to x > y.
The total age of a cat, dog, monkey is 4 year 2 month. The dog is twice as old as the cat. The monkey is twice as old as the dog. How old is the monkey?
28 years
Step-by-step explanation:
Co-relating their ages:Let's say, the cat is x years old.The dog is twice as old as the cat
That makes the dog 2x years old.The monkey is twice as old as the dog.
That is, 2 × (2x) = 4x years old- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Calculating the total:Their total age is 4 years 2 months.
1 year has 12 months
=> 4 years have (4 × 12)
= 48 months
Since, the total age is 4 years 2 months, we can express it in "months" by adding "48" and "2".
= 50 months
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solving for x:Sum of their ages = 50 months
=> x + 2x + 4x = 50
=> 7x = 50
=>x = 50/ 7 months
If we write this in mixed fractions the whole number will represent the number of years.
=
[tex] \mathsf{7 \frac{1}{7} \: \: months}[/tex]
[tex] = \mathsf{7 \: years \: \frac{1}{7} \: \: months}[/tex]
The value of 1/ 7 is really small,I.e., 0.1428...
So, we can ignore the fraction while rounding off the term that makes it
[tex] \mathsf{x = 7yrs.(approx.)}[/tex]
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Recall:x is the age of the cat.
The monkey's age is "4x"
= 4 × 7
= 28 years.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Answer:So, the monkey's age is approximately 28 years
Write an equation of the line in slope-intercept form.
Answer:
y = x + 4
Step-by-step explanation:
From point (-1, 3) to point (0, 4), go up 1 (rise = 1) and go right 1 (run = 1).
slope = m = rise/run = 1/1 = 1
The y-intercept is b = 4
y = mx + b
y = x + 4
a meal came to $16.41 without tax. calculate the 6% sales tax, and then calculate the 15% tip based on the sum of the meal and the tax. what is the total cost of the meal?
Answer:
$20
Step-by-step explanation:
correct me if im wrong(┬┬﹏┬┬)
What is the y-intercept of the graph of the equation [tex]y=x(1/4) - 2/3[/tex]
A. -2/3
B. 2/3
C. -1/4
D. 1/4
Answer:
A
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{1}{4}[/tex] x - [tex]\frac{2}{3}[/tex] ← is in slope- intercept form
with y- intercept c = - [tex]\frac{2}{3}[/tex] → A
A 13 foot ladder is placed
5 feet away from a wall
How many feet up the wall
will the ladder reach?
Answer: 12 feet up
Step-by-step explanation:
This problem models a right triangle, in which the ladder is the hypotenuse and the distance away from the wall is one of the legs. Thus, you may use the Pythagorean Theorem (a^2 + b^2 = c^2)
[tex]a^2+b^2=c^2\\5^2+b^2=13^2\\25+b^2=169\\b^2=144\\b=12[/tex]
N.B. There are some very useful sets of numbers that can help you with this unit.
They are called Pythagorean triplets, and they are the sets of whole numbers that make right triangles. The important ones are 3, 4, 5, and 5, 12, 13 (And their multiples, like 6, 8, 10(3,4,5 *2))
Hope it helps :) and let me know if you want me to elaborate further.
Solve this system of linear equations. Separate
the x- and y-values with a comma.
-20x = -16 - 9y
- 14x = -22 - 9y
Answer:
(x, y)
(-1, -4)
Step-by-step explanation:
[tex]-20x=-16-9y\\-14x=-22-9y[/tex]
Solve by elimination, subtract the 2nd row from the 1st row:
[tex](-20x-(-14x))=(-16-(-22))+(-9y-(-9y))\\(-20x+14x)=(-16+22)+(-9y+9y)\\-6x=6[/tex]
Solve for x in the equation above
[tex]-6x=6\\x=-1[/tex]
Now we have the value of X, substitute it into any of the 2 original equations:
[tex]-20x=-16-9y\\-20(-1)=-16-9y[/tex]
Solve for y:
[tex]-20(-1)=-16-9y\\20=-16-9y\\36=-9y\\-4=y\\y=-4[/tex]
Please mark brainliest if this answer helps you. I can provide more information if needed.
please help me with this sum I will mark you as brainest
Answer:
6/8 × 6 = 9/22/5 × 4 = 8/59/3 × 9 = 277/4 × 8 = 148/6 × 2 = 8/34/9 × 7 = 28/93/8 × 3 = 9/87/2 × 4 = 146/3 × 6 = 12 8/9 × 3 = 8/3Hope It's Help
thanks in advance ill mark brainliest
Answer:
100º
Step-by-step explanation:
Cooresponding angles are congruent
11x + 1 = 10x + 10
Subtract 10x from both sides
x + 1 = 10
subtract 1 from both sides
x = 9
θ = 11x + 1
θ = 11(9) + 1
θ = 99 + 1
θ = 100º