You mention circles, so I assume the missing symbols are plus signs.
The first circle has equation x² + y² = 64 = 8², so it's centered at the origin and has radius 8. In polar coordinates, we take x = r cos(θ) and y = r sin(θ). Then this circle's equation is
(r cos(θ))² + (r sin(θ))² = 64
r² (cos²(θ) + sin²(θ)) = 8²
r = 8
Complete the square in the second circle's equation to determine its center and radius:
x² - 8x + y² = x² - 8x + 16 + y² = 16 ⇒ (x - 4)² + y² = 4²
so the second circle is centered at (4, 0) with radius 4. In polar coordinates, this equation becomes
(r cos(θ) - 4)² + (r sin(θ))² = 16
r² (cos²(θ) + sin²(θ)) - 8r cos(θ) + 16 = 16
r² - 8r cos(θ) = 0
r - 8 cos(θ) = 0
r = 8 cos(θ)
Determine where these two circles intersect:
8 = 8 cos(θ)
cos(θ) = 1
θ = arccos(1) + 2nπ
θ = 2nπ
where n is any integer. So both circles intersect once at (8, 0), which means they are tangent to one another, and since the second circle's radius is smaller, it must lie completely within the larger one.
The region between the two circles is the set
R = {(r, θ) : 0 ≤ θ ≤ π/2 and 8 cos(θ) ≤ r ≤ 8}
The area of R is given by the double integral,
[tex]\displaystyle \iint_R dA = \int_0^{\frac\pi2} \int_{8\cos(\theta)}^8 r \, dr \, d\theta[/tex]
or the single integral
[tex]\displaystyle \iint_R dA = \frac12 \int_0^{\frac\pi2} \left(64 - 64\cos^2(\theta)\right) \, d\theta[/tex]
Recall the half-angle identity for cosine:
cos²(x/2) = (1 + cos(x))/2
Then the area is
[tex]\displaystyle \iint_R dA = 16 \int_0^{\frac\pi2} \left(1 - \cos(2\theta)\right) \, d\theta[/tex]
[tex]\displaystyle \iint_R dA = 16 \left(\theta - \frac12 \sin(2\theta)\right) \bigg|_0^{\frac\pi2}[/tex]
[tex]\displaystyle \iint_R dA = \boxed{8\pi}[/tex]
1. Which graphs could represent a proportional relationship? Explain how you decided.
A
B
y
у
5
5
5
10
x
5
10
х
С
D
У
5
5
5
10
ol
5
10
X
Step-by-step explanation:
What's the rule .
The line should be linear .i.e it should be a straight line on coordinate planeSo our answers are
A,C,DThe two graphs that represent proportional relationships are A and C.
What is a proportional relationship?
A proportional relationship is:
y = k*x
Where k is the constant of proportionality.
So, a proportional relationship is a linear equation that passes through the point (0, 0).
With that in mind, we can see that the two graphs that represent a proportional relationship are A and C.
If you want to learn about proportional relationships:
https://brainly.com/question/12242745
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Can someone PLEASE tell me the answer to this
Answer:
Explanation is
Step-by-step explanation:
PLEASE HELP ME OUT!!!!!!!!!!
Answer:
Exponential
Step-by-step explanation:
- Linear is a straight line no matter what.
- Quadratic lines makes a u or v shape that opens up, down, left, or right.
- Exponential is like a slanted 45° clockwise u and a bit stretched horizontally.
- Square root lines on a graph, looks more like a slanted L 90° clockwise.
- Inverse Variation would show its inverse, same as a mirror, it would be something similar to a hyperbola.
Hope This Helps!
Given A(0,-4), B(0,-9), and C(-2,-5). Find the length of BC.
1.5
4.5
5
2.2
Answer:
4.5
Step-by-step explanation:
B(0,-9)
C(-2,-5)
=> BC = [tex]\sqrt{(-2-0)^{2} -(-5+9)^{2} } = 4.4721[/tex]
The state fair is a popular field trip destination. This year the senior class at High School Aandthe senior class at High School B both planned trips there. The senior class at High School Arented and filled 9 vans and 7 buses with 457 students. High School B rented and filled 11vansand 7 buses with 473 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry? A) Van: 55, Bus: 8 B) Van: 8, Bus: 55
C) Van: 12, Bus: 38 D) Van: 10, Bus: 71
Answer:
B
Step-by-step explanation:
v = how many students fit into a van
b = how many students fit into a bus
School A:
9v+7b=457 (1)
School B:
11v+7b=473 (2)
(1)&(2) => v=8
b=55
B.
CO
Given right triangle ABC, what is the value of tan(A)?
o o
26
24
w/w with with wher
A
10
ОО
Answer:12/5 (3rd option)
Step-by-step explanation:
tangent is opposite over adjacent so take the side opposite the angle A and put it over the side that is adjacent to angle A
For Thanksgiving dinner, Josie purchased three cans of cranberry sauce that cost $0.78 each. She gave the cashier $10.00. How much change did she get back?
Answer:
$7.66
Step-by-step explanation:
[tex]0.78 \times 3 = 2.34[/tex]
[tex]10.00 - 2.34 = 7.66[/tex]
Answer:
$7.66
Step-by-step explanation:
1. Multiply $0.78 x 3. (you should get $2.34)
2. Subtract $10.00 from $2.34
Your final answer should be $7.66
K(x) k(-3) 2x^2-5x+3
Answer:
When k(x) is 2x² - 5x + 3, k(-3) = 36.
Step-by-step explanation:
k(x) = 2x² - 5x + 3
Substitute the input of x.
k(-3) = 2(-3)² - 5(-3) + 3
Square -3.
k(-3) = 2(9) - 5(-3) + 3
Multiply 2 and 9.
k(-3) = 18 - 5(-3) + 3
Multiply -5 and -3.
k(-3) = 18 + 15 + 3
Add 18 and 15.
k(-3) = 33 + 3
Add 33 and 3.
k(-3) = 36.
1. Find the quotient of 6.523 and 0.01.
Equation:
Solution:
Answer:
652.3
Step-by-step explanation:
Y-intercept of (-2,2) and (-5,4)
yes. yes.
yes, yes,
yes, yes,
Can anyone help me explain why
find the value of U.
It's given that WXYZ is a parallelogram. In a parallelogram, the adjacent angles sum up to 180°. Here, 2u - 2 & 3u + 12 together make 180° because they are adjacent angles.
2u - 2 + 3u + 12 = 180
2u + 3u - 2 + 12 = 180
5u + 10 = 180
5u = 170
u = 170/5
u = 34
_______
꧁✿ ᴿᴬᴵᴺᴮᴼᵂˢᴬᴸᵀ2222 ✬꧂
Joan descends down a
mountain 140 feet in 5
minutes. What was the change
in altitude per minute?
Answer:
28
Step-by-step explanation:
140 / 5 = 28
{y=10x+2
-5x+4y=-27
this is systems of equations
[tex]y = 10x +2~~....(i) \\\\-5x +4y = -27~~....(ii)\\\\\text{Substitute y =10x+2 in equation (ii):}\\\\\\-5x +4(10x+2) = -27 \\\\\implies -5x + 40x + 8 +27 =0\\\\\implies 35x +35=0\\\\\implies 35(x +1) =0\\\\\implies x +1 = 0 \implies x = -1\\\\\text{Substitute} ~x =-1 ~ \text{in equation (i):}\\\\y = 10(-1) +2 = -10+2 = -8 \\\\\\\text{Hence}~ (x,y) = (-1,-8)[/tex]
Answer:
(x, y) = (19/35, 52/7)
Step-by-step explanation:
When you have an expression for one of the variables, the "substitution" method of solution is a reasonable choice. Here, we have an expression for y that can be substituted into the second equation.
-5x +4(10x +2) = 27
35x +8 = 27 . . . . . . . simplify
35x = 19 . . . . . . . subtract 8
x = 19/35 . . . . divide by the coefficient of x
y = 10(19/35) +2 = 52/7
The solution is (x, y) = (19/35, 52/7).
The distance from Scott's house to school is 3/5 of a mile scott walked 2/3 of the way there before he stopped to pick up his friend. How far did Scott walk?
Answer:
2/5
Step-by-step explanation:
2/3 of 3/5 means to multiply the fractions to get 6/15
6/15 can be reduced by dividing by 3 to get 2/5
You are riding your bicycle and it takes you 15 minutes to go 3.5 miles. How fast are you
going in miles per hour (mph) ?
Answer:
14 miles per 1 hour (14m/1hr), I hope this helps :)
Derma roll 60 mg is ordered you have 75 mg per 1 mL on hand how many milliliters should you administer to the patient per dose
Answer:
75mg subtracts 60mg equals 15
Answer: 15mg per dose
Step-by-step explanation: 75mg - 60mg = 15mg per dose
Can someone help me with this, I don’t understand.
Answer:
the answer is after 5 hours.
6 times 67.............................................................................................................
Answer:
402
Step-by-step explanation:
Solve the problem.The world population of a certain species is evaluated at 5.1× 1010. By some projections, this population will be 3 times more important in 30 years. Express the population at that time in scientific notation.
Large population can be represented in scientific notations
The population in 30 years time is 1.53 * 10^11
The current population is given as:
[tex]\mathbf{Population = 5.1 \times 10^{10}}[/tex]
In 30 years time, the population would be 3 times more.
This means that, the population in 30 years time is: 3 multiplied by the current population.
So, we have:
[tex]\mathbf{New = 3 \times Population}[/tex]
So, we have:
[tex]\mathbf{New = 3 \times 5.1 \times 10^{10}}[/tex]
Multiply
[tex]\mathbf{New = 15.3 \times 10^{10}}[/tex]
Rewrite as:
[tex]\mathbf{New = 1.53 \times 10^{11}}[/tex]
Hence, the population in 30 years time is 1.53 * 10^11
Read more about scientific notations at:
https://brainly.com/question/1705769
Write a linear equation in point-slope form that satisfies the given set of conditions.
passes through (4, –1) and (8, 3)
local theatre has a goal this Friday to sell #200 worth of candy. If M&M's cost $1 and snickers $2, determine haw many M&Ms will need to be sold if 30,40, or 50 snickers are sold
Answer:
30 = 140 M&M's I 40 = 120 M&M's I 50 = 100 M&M's
Step-by-step explanation:
I have a question regarding trignometry
How does Sin(180°-θ) = Sinθ
and how does Cos(180°-θ) = -Cosθ
Step-by-step explanation:
If A is acute, cos (180 - A) = - cos A (because the coordinates would be in 2nd quadrant)
If A is right angle, cos (180 - 90) = cos 90 = 0
(because the coordinates would be on y-axis)
If A is obtuse, cos (180 - A) = + cos A (because the coordinates would be in 1st quadrant)
Given the diagram below, find the value of MQR.
Answer:
The answer is MQR= 48 degrees
Step-by-step explanation:
I got this answer from process of elimination. The first option was 48 degrees so I divided 48 by 3 and got 16 then I applied to (2x + 16): (2(16)+16) and got 48 which comfirmed my answer. Also I took the test and it was right so I know its correct.
I need help on 25 please and thank you
Answer:
hi, the answer is B or 1 :)
Answer:
1
Step-by-step explanation:
[tex](3^{2} +4^{2})*5^{-2}[/tex]
Simplify (remember [tex]a^{-n}=\frac{1}{a^{n} }[/tex]):
[tex](9+16)*\frac{1}{25} \\25*\frac{1}{25}\\\frac{25}{25} \\1[/tex]
Help on this question pls
100 points & brainliest!! ONLY IF U ANSWER CORRECTLY, IF YOU DONT ILL REPORT.
Total objects
As
[tex]\\ \sf\longmapsto Unit\:price=\dfrac{Sale\: Price}{No\:of\: units}[/tex]
[tex]\\ \sf\longmapsto Unit\:Price=\dfrac{D_2({E_2)}}{C_2}[/tex]
Or
[tex]\\ \sf\longmapsto Unit P=\dfrac{E_2(D_2)}{C_2}[/tex]
Answer:
= D2/E2Step-by-step explanation:
See attached
Number of units in cell E2, Total price in D2
The formula for unit price is:
= D2/E2PLZ HELP 500 POINTS AND BRAINLIEST
Answer:
26 meters
Step-by-step explanation:
Answer:
the answer is 20.
add up the length, and the hight,
then times it by 2.
BOOM
you get the answer :)
Step-by-step explanation:
What is the length of the indicated arc ?
A.
2π
B.
π
C.
1π
⁄
2
D.
4π
E.
None of the above
Answer:
Length of an Arc = θ × (π/180) × r
each bus for Philips elementary school transport 40 students to school there are 12 buses each day .how many students are transported to school each day by bus
Answer:
480 students
Step-by-step explanation:
if we know that each bus transports 40 students and there are 12 buses each day then we can just multiply 12 by 40 and we get 480
