In polar coordinates, the inequality changes to
[tex]x^2+y^2\le4x\implies r^2\le4r\cos\theta\implies r\le4\cos\theta[/tex]
which is a circle of radius 2 and centered at (2, 0). The set D is then
[tex]D=\left\{(r,\theta)\mid0\le r\le4\cos\theta\land0\le\theta\le\pi\right\}[/tex]
The integral is then
[tex]\displaystyle\iint_D\frac{y^2}{x^2+y^2}\,\mathrm dx\,\mathrm dy=\int_0^\pi\int_0^{4\cos\theta}\frac{r^2\sin^2\theta}{r^2}r\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\int_0^\pi\int_0^{4\cos\theta}r\sin^2\theta\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\frac12\int_0^\pi((4\cos\theta)^2-0^2)\sin^2\theta\,\mathrm d\theta[/tex]
[tex]=\displaystyle8\int_0^\pi\cos^2\theta\sin^2\theta\,\mathrm d\theta[/tex]
There are several ways to compute the remaining integral; one would be to invoke the double-angle formula,
[tex]\sin(2\theta)=2\sin\theta\cos\theta[/tex]
so that the integral is
[tex]=\displaystyle8\int_0^\pi\frac{\sin^2(2\theta)}4\,\mathrm d\theta[/tex]
[tex]=\displaystyle2\int_0^\pi\sin^2(2\theta)\,\mathrm d\theta[/tex]
Then invoke another double-angle formula,
[tex]\sin^2\theta=\dfrac{1-\cos(2\theta)}2[/tex]
to change the integral to
[tex]=\displaystyle\int_0^\pi1-\cos(4\theta)\,\mathrm d\theta[/tex]
[tex]=(\pi-\cos(4\pi))-(0-\cos0)=\boxed{\pi}[/tex]
During the calendar year of 1971 a total of 171 deaths were caused by influenza in a city of 450,000 persons. The temporal distribution of these deaths was as follows: First Quarter, 54; Second Quarter, 43; Third Quarter, 35; and Fourth Quarter, 39. Calculate the annual and quarterly mortality rates per 100,000 population.
Answer and Step-by-step explanation:
The computation of annual and quarterly mortality rates per 100,000 population is shown below:-
Quarterly mortality rates are
[tex]= \frac{Deaths}{Population\ in\ the\ city}\times Population[/tex]
For the first quarter
[tex]= \frac{54}{450,000}\times 100,000[/tex]
= 12 death per 100,000 population
For the second quarter
[tex]= \frac{43}{450,000}\times 100,000[/tex]
= 9.5 death per 100,000 population
For the third quarter
[tex]= \frac{35}{450,000}\times 100,000[/tex]
= 7.7 death per 100,000 population
For the fourth quarter
[tex]= \frac{39}{450,000}\times 100,000[/tex]
= 8.6 death per 100,000 population
Now the annual mortality is
[tex]= \frac{Deaths}{Population\ in\ the\ city}\times Population[/tex]
[tex]= \frac{171}{450,000}\times 100,000[/tex]
= 38 death per 100,000 population
Help asap giving branlist!!!
Answer:
D.
Step-by-step explanation:
So you know you have to have $62 as the base fee.
If you exceed 2 gigabytes, you subtract that by 2 because you want to find how many gigabytes you're going over. You then multiply it by 30 to find the cost.
You get C = 62 + 30(g - 2)
Answer:
anwser is d because it is write.
Step-by-step explanation:
A tree grows three feet per year. What happens to the growth of the
When the number of years increases, the number of feet decrea
When the number of years decreases, the number of feet stays
When the number of years increases, the number of feet increas
When the number of years decreases, the number of feet increa
Answer:
The answer is C :,)
Step-by-step explanation:
Answer:
The answer to your question is c
Step-by-step explanation:
Because the years have to increase for it to grow.
The perimeter of the rectangle is 28 units.
A rectangle with perimeter 28 units is shown. The length of the sides is w, and the length of the top and bottom sides are 2 w minus 1.
What is the value of w?
5 units
7 units
14 units
15 units
Answer:
5 units
Step-by-step explanation:
P=2(w)+2(2w-1)
28=2w+4w-2
30=6w
w=5
Answer:
5
Step-by-step explanation:
Write two trinomials that you can factor into two binomials. Factor each trinomial. Then write one trinomial that you cannot factor and explain why.
Answer:
- Trinomials that can be factored into two binomials are:
1. x² + 5x + 6
Factored to: (x + 3)(x + 2)
2. x² + x - 2
Factored to: (x - 1)(x + 2)
Example of a Trinomial that cannot be factored into two binomials:
x² + 5x + 1
Step-by-step explanation:
- A trinomial is a polynomial that consist of three terms. It is in the form:
ax² + bx + c.
- A binomial is a polynomial that consists of two terms. It is of the form:
bx + c.
A trinomial is said to be factorable if the can be written as a product of two binomials.
Example 1:
The expression: x² + 5x + 6
Can be rewritten as:
x² + 2x + 3x + 6
Grouping this, we have
(x² + 2x) + (3x + 6)
Which becomes
x(x + 2) + 3(x + 2)
Factoring (x + 2), we have
(x + 3)(x + 2)
Which is a product of two binomials as required.
Therefore, the expression is factorable.
Example 2:
The trinomial expression:
x² + x - 2
Can be written as:
x² + 2x - x - 2
= (x² + 2x) - (x + 2)
= x(x + 2) - (x + 2)
Factoring (x + 2), we have
(x - 1)(x + 2)
This a product of two binomials, hence, the tutorial is factorable.
Example 3:
Consider the trinomial:
x² + 5x + 1
This is not factorable, because the term 5x cannot be split into a sum or difference, in such a way that it has a common factor with x² and with 1.
Unlike in the case of Example 1.
x² + 5x + 6
5x was split into the sum of 2x and 3x
That is, x² + 5x + 6 = x² + 2x + 3x + 6
So that, 2x has a common factor, x with x², and 3x has a common factor, 3 with 6.
You are rolling two dice. When the two numbers (1-6) come up, you multiply the numbers
together. What is the probability of getting a product that is NOT divisible by 2?*
Answer:
1/4 probability of getting a product that isn't divisible by 2.
Step-by-step explanation:
These are all the possible outcomes
1 x 1 = 1 2 x 1 = 2 3 x 1 = 3 4 x 1 = 4 5 x 1 = 5 6 x 1 = 6
1 x 2 = 2 2 x 2 = 4 3 x 2 = 6 4 x 2 = 8 5 x 2 = 10 6 x 2 = 12
1 x 3 = 3 2 x 3 = 6 3 x 3 = 9 4 x 3 = 12 5 x 3 = 15 6 x 3 = 18
1 x 4 = 4 2 x 4 = 8 3 x 4 = 12 4 x 4 = 16 5 x 4 = 20 6 x 4 = 24
1 x 5 = 5 2 x 5 = 10 3 x 5 = 15 4 x 5 = 20 5 x 5 = 25 6 x 5 = 30
1 x 6 = 6 2 x 6 = 12 3 x 6 = 18 4 x 6 = 24 5 x 6 = 30 6 x 6 = 36
All of the outcomes that aren't divisible by 2 are in bold
There are 9 out of 36 possible outcomes that aren't divisible by 2
9/36 = 1/4
There are 390 students at Walker Elementary this year. This is a 30% increase from the previous year. How many students were at Walker Elementary last year?
Answer:
There were 300 students
Step-by-step explanation:
Original * 30 = increase
Add the increase to get the new number
original + increase = 308
original + original*30% = 390
Factor out original number
original ( 1+30%) = 390
Change to decimal form
original ( 1+.30) = 390
original ( 1.30) = 390
Divide by 1.3
original = 390/1.3
=300
if this net were to be folded into a cube which number would be opposite of the number 1?
Answer:
6
Step-by-step explanation:
When the cube is folded, 6 is the opposite of 1.
2 is the opposite of 4 and 5 is the opposite of 3.
When the given net is folded into a cube, the number that we will find opposite 1 is 6.
What number will be opposite 1?When the net is folded, two will be folded left and up with 3 being the base. 4 will be folded right with 5 being the top of the cube.
We will then observe the following pairs opposite each other:
5 and 3.4 and 2.1 and 6.This means that the number that we will see opposite 1 will be the number 6.
Find out more on folding nets at https://brainly.com/question/16670460.
#SPJ9
The function s(t) represents the position of an object at time t moving along a line. Suppose s(2)=69 and s(6)=141.Find the average velocity of the object over the interval of time [2,6 ].
Answer:
The average velocity of the object over the interval of time [2,6] is of 18 units of distance per unit of time.
Step-by-step explanation:
The average velocity can be calculated as the division of the position change by the time change.
Find the average velocity of the object over the interval of time [2,6 ].
6 - 2 = 4 units of time (t, min,...)
s(6) = 141, s(2) = 69
141 - 69 = 72 units of distance(m, km...)
72/4 = 18 u.d./u.t.
The average velocity of the object over the interval of time [2,6] is of 18 units of distance per unit of time.
Pablo created the bar model and equation after paying a $9.79 lunch bill with a $20 bill.
Answer:
It is c he revived 10.21
Step-by-step explanation:
Pamela is a college student. She pays tuition every semester and rent every month, and she uses cash daily for food. The expression 2x+12y+365z represents her yearly expenses. Which variable represents her rent?
Answer:
Variable y represent the rent of Pamela
Step-by-step explanation:
Given
Pamela pays tuition every semester and rent every month, and she uses cash daily for food.
lets understand what constitute semester , month and day in a year.
A semester consist of 6 months.
As a year has 12 months , a year will have 2 semester.
If one pays x for one semester then in a year one has to pay 2x .
As a year has two semester
Similarly
A year has 12 months .
If one pays y for one month then in a year one has to pay 12y .
As a A year has 12 months .
A year has 365 days
If one pays z for each month then in a year one has to pay 365z .
As a A year has 365 days.
__________________________________________
Based on above discussion , we can now safely assume that the we have to look at the coefficient of expression 2x+12y+365z to find the which variable represent which type of bill.
As we have to find variable for rent and rent is paid monthly.
so for a year total bill will have 12 months and hence going by expression variable y represent the rent of Pamela.
A survey asks teachers and students whether they would like the new school
mascot to be a shark or a moose. This table shows the results. Which
statement is true?
Will pick brainliest! Please help with the attached file!
Answer:
25 degrees
Step-by-step explanation:
The value of an exterior angle is the difference between the two arcs that it forms divide by two. Therefore:
[tex]x+10=\dfrac{146-(6x+6)}{2}[/tex]
Multiply both sides by 2:
[tex]2x+20=146-6x-6[/tex]
Move all of the x's to one side:
[tex]8x+20=146-6[/tex]
Combine all of the constants on the other side:
[tex]8x=120[/tex]
Divide both sides by 8:
[tex]x=15[/tex]
Therefore, ECB=x+10=15+10=25 degrees.
Hope this helps!
3(5 − 2 x) = −2(6 – 3 x) − 10 x
Answer:
15-6x= -12-4x
15-2x= -12
-2x= -27
x= -13.5
Step-by-step explanation:
HELP...it has timer
Answer:
lily has a larger ratio
Step-by-step explanation:
A spherical gemstone just fits inside a plastic cube with edges 12cm. a) calculate the volume of gemstone, to the nearest cubic centimeter. b) how much empty space is there.
Answer:
a) (V) = 904.78 of a sphere = 288pi diameter = 12
(V) = 1728cm^3 of a cube = face diagonal = 16.9cm
b) Difference Volume = 1728-904.78 = 823.22cm^3
Step-by-step explanation:
To find volume of an inscribed sphere within a square cube
We use 4 π/3 * r^3 for the equation
As Radius = 6 = 6cm this is the only thing plugged into the equation to create a division first then a multiplication square of radius and then a multiplication. 4pi /3 * 6^3
r^3 = 216
4pi/3 = 4.18
4.18 * 216 = 904.78
This means the answer is 288 pi cm^3.
Answer:
volume of gemstone = 905 cm^3
volume of empty space = 823 cm^3
Step-by-step explanation:
volume of cube = s^3, where s = length of edge
volume of sphere = (4/3)(pi)r^3, where r = radius of sphere
The cube has a 12-cm edge. The sphere fits tightly inside the cube, so the diameter, d, of the sphere is 12 cm. The radius is half the diameter, so radius = r = diameter/2 = 12 cm/2 = 6 cm.
a)
volume of sphere = (4/3)(pi)r^3
volume of sphere = (4/3)(3.14159)(6 cm)^3
volume of sphere = 905 cm^3
b)
The empty space is the difference between the volume of the cube and the volume of the sphere.
volume of cube = s^3
volume of cube = (12 cm)^3
volume of cube = 1728 cm^3
empty space = volume of cube - volume of sphere
empty space = 1728 cm^3 - 905 cm^3
empty space = 823 cm^3
Solve the following system of equations using the elimination method. 5x – 5y = 10 6x – 4y = 4
Answer:
11×-9y=14
Step-by-step explanation:
123hsvwjwjbe
Answer:
(-2,-4)
Step-by-step explanation:
add the equations in order to solve the first variable. put the value into the other equations in order to solve the other variables.
What’s the correct answer for this question?
Answer: 3/20
Step-by-step explanation:
p(A)=the day selected in Monday =1/5
p(B)=student is absent
P(A∩B)=it is Monday AND a student is absent =3/100
Events A and B are independent so
P(A∩B) = P(A) · P(B)
3/100=1/5*p(B)
p(B)=3/20
Florian ran 1.2 miles and walked 4.8 laps around the path at the park for a total distance of 3.6 miles. Which shows the correct equation and value of x, the distance of 1 lap around the path at the park? 3.6 x + 1.2 = 4.8; x = 1 mile 4.8 x + 1.2 = 3.6; x = 1 mile 3.6 x + 1.2 = 4.8; x = 0.5 mile 4.8 x + 1.2 = 3.6; x = 0.5 mile
Answer:
The correct answer would be D) 4.8x + 1.2 = 3.6; x = 0.5 mile
Step-by-step explanation:
This is because laps would be the dependent variable, so we know the number of them (4.8) would be multiplied by the variable (x). We also know that 1.2 is the constant. Now we can solve to make sure this is the right equation.
4.8x + 1.2 = 3.6
4.8x = 2.4
x = 0.5
Answer:
D) 4.8x + 1.2 = 3.6; x = 0.5 miles
y = c1 cos(5x) + c2 sin(5x) is a two-parameter family of solutions of the second-order DE y'' + 25y = 0. If possible, find a solution of the differential equation that satisfies the given side conditions. The conditions specified at two different points are called boundary conditions. (If not possible, enter IMPOSSIBLE.) y(0) = 1, y'(π) = 9
Answer:
y = 2cos5x-9/5sin5x
Step-by-step explanation:
Given the solution to the differential equation y'' + 25y = 0 to be
y = c1 cos(5x) + c2 sin(5x). In order to find the solution to the differential equation given the boundary conditions y(0) = 1, y'(π) = 9, we need to first get the constant c1 and c2 and substitute the values back into the original solution.
According to the boundary condition y(0) = 2, it means when x = 0, y = 2
On substituting;
2 = c1cos(5(0)) + c2sin(5(0))
2 = c1cos0+c2sin0
2 = c1 + 0
c1 = 2
Substituting the other boundary condition y'(π) = 9, to do that we need to first get the first differential of y(x) i.e y'(x). Given
y(x) = c1cos5x + c2sin5x
y'(x) = -5c1sin5x + 5c2cos5x
If y'(π) = 9, this means when x = π, y'(x) = 9
On substituting;
9 = -5c1sin5π + 5c2cos5π
9 = -5c1(0) + 5c2(-1)
9 = 0-5c2
-5c2 = 9
c2 = -9/5
Substituting c1 = 2 and c2 = -9/5 into the solution to the general differential equation
y = c1 cos(5x) + c2 sin(5x) will give
y = 2cos5x-9/5sin5x
The final expression gives the required solution to the differential equation.
What’s the correct answer for this ? Two chords AB and CD intersect at E. If AE = 2cm, EB =4, and CE = 2.5 cm, find the length of ED
Answer:
ED = 3.2 cm
Step-by-step explanation:
According to chord-chord power theorem,
(AE)(EB) = (CE)(ED)
2*4 = 2.5 *ED
8/2.5 = ED
ED = 3.2 cm
The supreme choice pizza at Pizza Paradise contains 2 different meats and 4 different vegetables. The customer can select any one of 5 types of crust. If there are 4 meats and 9 vegetables to choose from, how many different supreme choice pizzas can be made?
Answer:
756
Step-by-step explanation:
This is a combination problem. Combination has to do with selection.
If we are to select r objects out of a oiil of n objects, this can be done in nCr number of ways as shown;
nCr = n!/(n-r)!r!
From the question, there are 4 meats and 9 vegetables to choose from. If the customer is to select 2 different meats and 4 different vegetables from the available ones, this can be done as shown
4C2 (selection of 2 different meats from 4meats) and 9C4(selection of 4 different vegetables from 9 total vegetables)
The total number of ways this can be done is 4C2 × 9C4
= 4!/(4-2)!2! × 9!/(9-4)!4!
= 4!/2!2! × 9!/5!4!
= 4×3×2!/2!×2 × 9×8×7×6×5!/5!×4×3×2
= 6 × 9×7×2
= 756ways
This means 756 different supreme choice pizzas can be made.
Please answer this correctly as soon as possible.I have to finish this today. A triangular prism is 19 yards long and has a triangular face with a base of 12 yards and a height of 8 yards. The other two sides of the triangle are each 10 yards. What is the surface area of the triangular prism?
total SA = 764 yd²
A triangular prism is 13 yards long and has a triangular face with a base of 12 yards and a height of 8 yards. The other two sides of the triangle are each 10 yards. What is the surface area of the triangular prism?
See attachment.
if length = 13 yards then total SA = 512 yd²
if length = 19 yards then total SA = 764 yd²
select the statements and number line that can represent the inequality.
Answer:
every equivalent to 6 ≤ x
Step-by-step explanation:
We can subtract 5+11/6x to get ...
7 ≤ -(11/6)x +3x = (7/6)x
Multiplying by 6/7 gives ...
6 ≤ x
__
When x is in the set of real numbers, x in any real number that is 6 or more.
When x is in the set of integers, x is any integer that is 6 or more: {6, 7, 8, ...}.
When no set is specified, the solution is simply ...
6 ≤ x
Exactly one pair of opposite sides is parallel
Answer:
Yeah btw is this a question?
Can you help me with this one don’t get it
PLEASE HELP ALGEBRA PROBLEM!!! 20 POINTS ANSWER A-D
Answer:
A. 1.5 seconds
B. 36 feet
C. 0 feet
D. After 3 seconds
Step-by-step explanation:
I graphed it on desmos.
A=(-2,-7) B=(-6,4) C=(-2,7) D=(2,4) What is the perimeter?
[tex]\displaystyle\bf\\AB=\sqrt{\Big(-6-(-2)\Big)^2+\Big(4-(-7)\Big)^2}\\\\AB=\sqrt{\Big(-6+2\Big)^2+\Big(4+7\Big)^2}\\\\AB=\sqrt{\Big(-4\Big)^2+\Big(11\Big)^2}\\\\AB=\sqrt{16+121}\\\\\boxed{\bf AB=\sqrt{137}}[/tex]
.
[tex]\displaystyle\bf\\BC=\sqrt{\Big(-2-(-6)\Big)^2+\Big(7-4\Big)^2}\\\\BC=\sqrt{\Big(-2+6\Big)^2+\Big(7-4\Big)^2}\\\\BC=\sqrt{\Big(4\Big)^2+\Big(3\Big)^2}\\\\BC=\sqrt{16+9}\\\\BC=\sqrt{25}\\\\\boxed{\bf BC=5}[/tex]
.
[tex]\displaystyle\bf\\CD=\sqrt{\Big(2-(-2)\Big)^2+\Big(4-7\Big)^2}\\\\CD=\sqrt{\Big(2+2\Big)^2+\Big(4-7\Big)^2}\\\\CD=\sqrt{\Big(4\Big)^2+\Big(-3\Big)^2}\\\\CD=\sqrt{16+9}\\\\CD=\sqrt{25}\\\\\boxed{\bf CD=5}[/tex]
.
[tex]\displaystyle\bf\\AD=\sqrt{\Big(2-(-2)\Big)^2+\Big(4-(-7)\Big)^2}\\\\AD=\sqrt{\Big(2+2\Big)^2+\Big(4+7\Big)^2}\\\\AD=\sqrt{\Big(4\Big)^2+\Big(11\Big)^2}\\\\AD=\sqrt{16+121}\\\\\boxed{\bf AD=\sqrt{137}}[/tex]
.
[tex]\displaystyle\bf\\P=AB+BC+CD+AD=\sqrt{137}+5+5+\sqrt{137}\\\\\boxed{\bf P=10+2\sqrt{137}}[/tex]
What is the point-slope form of a line with slope 3 that contains the point
(2, 1)?
Answer:
y-1 = 3(x-2)
Step-by-step explanation:
The point slope form of a line is
y-y1 = m(x-x1)
where m is the slope and (x1,y1) is a point on the line
y-1 = 3(x-2)
Solve 5(2x-3a)+2b=3ax-4, for x
Answer:
10x-15a
Step-by-step explanation: