The region outside the circle r = 3 and inside the circle r = - 6cos θ is given below.
[tex]\rm Area = \dfrac{12\pi - 9\sqrt3 }{2}[/tex]
What is an area bounded by the curve?When the two curves intersect then they bound the region is known as the area bounded by the curve.
The region outside the circle r = 3 and inside the circle r = - 6cos θ
Then the value of the θ will be
[tex]\begin{aligned} -6\cos \theta &= 3\\\\\cos \theta &= -\dfrac{1}{2}\\\\\theta &= -\dfrac{2\pi}{3}, \dfrac{2\pi}{3} \end{aligned}[/tex]
Then the area will be given as
[tex]\rm Area = \dfrac{1}{2} \int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}} [-6 \cos \theta)^2 - 3^2 ] d \theta \\\\\\Area = \dfrac{1}{2} \int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}} [18 (2\cos ^2 \theta ) - 9]d \theta \\\\\\Area = \dfrac{9}{2} \int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}} [2(1 + \cos 2\theta ) - 1] d \theta \\\\\\Area = \dfrac{9}{2} \int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}} [2 \cos 2\theta ) + 1] d \theta \\\\[/tex]
[tex]\rm Area = \dfrac{9}{2} [ \sin 2\theta + \theta ] _{-\frac{2\pi}{3}}^{\frac{2\pi}{3}} \\\\\\ Area = \dfrac{9}{2} [ \sin 2( \frac{2\pi}{3}) +\frac{2\pi}{3} - \sin 2 (\frac{2\pi}{3}) - \frac{2\pi}{3}] \\\\\\[/tex]
On simplifying, we have
[tex]\rm Area = \dfrac{12\pi - 9\sqrt3 }{2}[/tex]
More about the area bounded by the curve link is given below.
https://brainly.com/question/24563834
#SPJ4
What is size of
angle p?°
Answer:
A) 75°
Step-by-step explanation:
It is the property of a polygon that the sum of the external angles is equal to 360°.
===============================================================
Solving :
⇒ p + 55 + 30 + 75 + 55 + 70 = 360
⇒ p + 85 + 130 + 70 = 360
⇒ p + 285 = 360
⇒ p = 360 - 285
⇒ ∠p = 75°
Answer :
A) 75°
because the property of polygon is equal to 360° the sum of external angles.
Hope it will help you
Please someone help me with this
Answer: I believe I answered this on a later post.
Step-by-step explanation:
I did.
There are 5 blue blocks, 7 red blocks, 2 yellow blocks, and 12 green blocks. What is the ratio of yellow blocks to total blocks?
Answer:
2:26.
Step-by-step explanation:
There are 26 blocks total, and compared to the yellow blocks, there are only two. So that would be 2:26.
Answer:
2:26
Step-by-step explanation:
A ratio is just a mathematical way to show a relationship between things. I wrote it with a colon (:), but you can write it as a fraction or words "x to b."
Most of the time in math, the order of how the question is asked doesn't matter. When it's a ratio, it does matter. Because they ask about the yellow blocks first, that has to be the first part of the ratio.
There are 2 yellow blocks.
Next, it asks for the total. That will be the other part. Add all the total blocks together: 5+7+2+12= 26.
There are 26 total blocks.
Technically, we can simplify this down to 1:13, but it's not asking to simplify it, so let's just leave it as 2:26.
can yall tell me what im doing wrong? for 50 points.
Crackdown result: DFBG
[tex]\sf slope \ (m): \dfrac{y_2-y_1}{x_2-x_1}[/tex]
1)
[tex]\rightarrow \sf m = \dfrac{-13-19}{-1-3}[/tex]
simplify
[tex]\rightarrow \sf m=8[/tex]
2) take two points: (-1,-1), (0, 1)
[tex]\rightarrow \sf m = \dfrac{1-(-1)}{0-(-1)}[/tex]
simplify
[tex]\rightarrow \sf m = 2[/tex]
3) take two points: (1, -8), (2, -16)
[tex]\rightarrow \sf m = \dfrac{-16-(-8)}{2-1}[/tex]
simplify
[tex]\rightarrow \sf m = -8[/tex]
4)
[tex]\rightarrow \sf m = \dfrac{8-(-10)}{0-9}[/tex]
simplify
[tex]\rightarrow \sf m = -2[/tex]
#1
(3,19)(-1,-13)Slope
m=-13-19/-1-3=-32/-4=8D#2
(0,1)(-1,-1)Slope:-
m=-1-1/-1=2F#3
(1,-8)(2,-16)Slope
m=-16+8/2-1=-8B#4
(9,-10)(0,8)Slope:-
m=8+10/0-9m=18/-9m=-2GCode is
DFBGWrite an equation to represent the following statement. 51 5151 divided by 3 33 is k kk
Answer:
[tex]k \: kk \: = \frac{515151}{333} [/tex]
By the end of year 8, demarco and tanya would have to pay a final payout of $120,887. $130,900. $143,152. $154,768.
If a person invests $50 in a business and gets a percentage increase of 10%, then he would have $55 as his final payout.
What is an Investment?This refers to the financial activity where a person puts money or an asset into a business or venture to gain profit after a period of time.
Hence, we can see that since your question is incomplete as it does not include the initial amount of both Demarco and Tanya, then a final payout cannot be found.
Read more about investments here:
https://brainly.com/question/25300925
#SPJ4
Answer:
143,152
Step-by-step explanation:
5/6 + 5/6 = ?
? = 10/6
10/6= 5/3
Answer:
10/6 = 10/6
↓
1 4/6 = 10/6
Step-by-step explanation:
5/6 + 5/6 = 10/6
↓
1 4/6
10/6 ÷ 2 = 5/3
10/6 = 10/6
1 4/6 = 10/6
Which is NOT a property of all similar triangles?
A The corresponding angles are congruent.
B The perimeters are in the same ratio as the corresponding sides.
CThe corresponding sides are congruent.
D) The altitudes are in the same ratio as the corresponding sides.
Answer:
C) The corresponding sides are congruent.
Step-by-step explanation:
Option C is the correct answer.
Hope it helps you in your learning process.
A punch recipe calls for 4 cups of lemonade to 3 cups of sparkling juice. If Sara is making 42 cups of punch, the how many cups of lemonade does she need/
A.) Greg says that she needs 16 cups of lemonade
B.) Grace says that she needs 24 cups of lemonade
Answer:
Grace is correct. She needs 24 cups of lemonade.
Step-by-step explanation:
With the current ratio 4:3, if you were to have 24 cups of lemonade, then you would have 18 cups of sparkling juice. 24 + 18 = 42 total cups of punch.
if 45% of an item 75.00 what is the original price
Answer: 157.5
Step-by-step explanation:
I would add 45 % again and you'd get 90 % or
150.00 the find 10 % of 75 which is 10*75/100 or 7.5
then add 150.00+ 7.5 = 157.5
The diameter of a circle is 25 m. Find its area to the nearest whole number.
Answer:
Answer down below
Step-by-step explanation:
Which equation is y = 6x2 12x – 10 rewritten in vertex form? y = 6(x 1)2 – 11 y = 6(x 1)2 – 10 y = 6(x 1)2 – 4 y = 6(x 1)2 – 16
The vertex form of the given quadratic equation is:
[tex]y = 6*(x + 1)^2 - 16[/tex]
How to rewrite the equation in vertex form?We have the quadratic equation:
[tex]y = 6x^2 + 12x -10[/tex]
First, we need to find the vertex. The x-value of the vertex is:
h = -12/2*6 = -1
To get the y-value of the vertex, we need to evaluate the function in h, so we get:
y = 6 - 12 - 10 = -16
Then the vertex is (-1, -16)
This means that the vertex form is:
[tex]y = 6*(x + 1)^2 - 16[/tex]
If you want to learn more about quadratic equations:
https://brainly.com/question/1214333
#SPJ4
Answer:
y = 6(x + 1)2 – 16. D ON EDGE
Step-by-step explanation:
find the value of each variable
x=
y=
z=
Answer:
Step-by-step explanation:
A 45 degree angle in a right triangle produces 2 equal sides. In this case z and the perpendicular line are equal. So that's were we'll start. Then you move on to the 60 degree angle to get x and y.
Finding z
z^2 + z^2 = (24√2) Combine the left
2z^2 = 24^2 * 2 Divide both sides by 2
2z^2/2 = 24^2/2
z^2 = 24^2 Take the square root of both sides
√z^2 = √24^2
z = 24
Finding x and y
The perpendicular = 24. Because it is a 60 degree angle that's given, we can do this without a calculator.
Tan 60 = opposite over adjacent
sqrt(3) = Perpendicular / z Multiply both sides by z
z*sqrt(3) = perpendicular
The above calculation tells us the perpendicular is 24
z*sqrt(3) = 24 Divide by sqrt 3
z = 24/√3
z = 24/1.73
z = 8√3
Finding x
Use Pythagoras to determine x
Perpendicular^2 + (8√3)^2 = x^2
24^2 + 8^2*3 = x^2
576 + 192 = x^2
768 = x^2
√x^2 = √768
x = 27.71
please help, i will mark brainliest :))
Answer: 6x and 18y.
x x x x x x= 6x
30y - 12= 18y
A number is greater than 8. The same number is less than 10. The inequalities x greater-than 8 and x less-than 10 represent the situation. Which best explains the number of possible solutions to the inequality?
There is one solution because 9 is the only number between 8 and 10. There are a three solutions because 8, 9, and 10 are possible solutions.
There are a three solutions because 8, 9, and 10 are possible solutions
There are a few solutions because there are some fractions and decimals between 8 and 10.
There are infinite solutions because there is always another number between any two numbers.
Answer:
There are a few solutions because there are some fractions and decimals between 8 and 10.
Step-by-step explanation:
Have a great day! Hope this helps!!
Is the line of best fit accurate for the data shown?
(A) Yes, because it touches the y-axis
(B) Yes, because there are about the same number of points above the line as below it
(C) No, because the line does not touch any points
(D) No, because the line should touch every point
Simplify the expression. Write your answer as a power.
(-3)⁴/(-3)¹
The simplified expression is
Answer:
[tex](-3)^3[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{(-3)^4}{(-3)^1}=(-3)^{4-1}=(-3)^3[/tex]
PLEASE HELP ASAP! ANSWER GETS BRAINLIEST!
The following data set represents the population growth or decay in the past 5 years. (attachment below)
Determine which value is the independent value and the dependant value. Create a set of ordered pairs for the relation.
Answer:
it goes up 80 in every column in this problem except the 6,. so the answer is 6,591 423
I hope I help
901334 x 2368 = ? I WILL GIVE BRAINLIEST TO A CORRECT ANSWER PLEASE HURRY
Answer:
901334 x 2368 = 2134358912 is the correct answer
Step-by-step explanation:
I hope this helps you :)
can someone help me with this? Thank you!
Answer:
384
Step-by-step explanation:
W x L x 2 + H x L x 2 + W x H x 2 = Formula for Surface area of a rectangular prism
9x12x2=216, 4x12x2=96, 9x4x2=72 Then add them all up
216+96+72=384
Brainly would help, thank you and have a good day.
FYI I did not copy this took ten minutes to do pls no report... thanks
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Surface area of a rectangular prism is ~
[tex]\qquad \sf \dashrightarrow \: 2(lb + bh + lh)[/tex]
l = Length = 12 ftb = width = 9 fth = height = 4 ft[tex]\qquad \sf \dashrightarrow \: 2 \{(12 \times 9)+ (9 \times 4) +( 12 \times 4) \}[/tex]
[tex]\qquad \sf \dashrightarrow \: 2 \{(108)+ (36) +( 48) \}[/tex]
[tex]\qquad \sf \dashrightarrow \: 2 \{192\}[/tex]
[tex]\qquad \sf \dashrightarrow \:384 \: \: ft {}^{2} [/tex]
Evaluate each expression.
a. 7 + 2³
b. 9 • 3¹
c. 20 - 2⁴
d. 2 • 6²
e. 8 • (1/2)²
f. 1/3 • 3³
g. (1/5 • 5)⁵
Answer:
The answers are
→ a. 15
→ b. 27
→ c. 4
→ d. 72
→ e. 2
→ f. 9
→ g. 1
Step-by-step explanation:
Given expressions:
a. 7 + 2³
b. 9 • 3¹
c. 20 - 2⁴
d. 2 • 6²
e. 8 • (1/2)²
f. 1/3 • 3³
g. (1/5 • 5)⁵
Solve:a. 7 + 2³
[tex]7+2^3[/tex]
[tex]2^3 = 8[/tex]
[tex]8 + 7 = 15[/tex]
Hence, 15 is your answer.
b. 9 • 3¹
[tex]9*3^1[/tex]
⇒ [tex]9*(3)[/tex]
⇒ [tex]27[/tex]
Hence, 27 is your answer.
c. 20 - 2⁴
[tex]20 - 2^4[/tex]
[tex]2^4 = 16[/tex]
[tex]20-16 = 4[/tex]
Hence, 4 is your answer.
d. 2 • 6²
[tex]2 * 6^2[/tex]
⇒ [tex]2*6^2[/tex]
⇒ [tex]2*(6*6)[/tex]
⇒ [tex]72[/tex]
Hence, 72 is your answer.
e. 8 • (1/2)²
[tex]8 * (\frac{1}{2})^2[/tex]
⇒ [tex]8*((\frac{1}{2})*(\frac{1}{2}))[/tex]
⇒ [tex]2[/tex]
Hence, 2 is your answer.
f. 1/3 • 3³
[tex]\frac{1}{3} * 3^3[/tex]
⇒ [tex]9[/tex]
Hence, 9 is your answer.
g. (1/5 • 5)⁵
[tex](\frac{1}{5} * 5)^5[/tex]
⇒ [tex]1*1*1*1*1[/tex]
⇒ [tex]1[/tex]
Hence, 1 is your answer.
- ✨7272033Alt✨(angles) please help ASAP.
The angle k will be 100 in the triangle KJL and the side HI will be 4.
What is triangle?
A triangle is a plane figure formed by the three sides having sum of the angles 180 degree.
Here in triangle KJL we can see that it is a isosceles triangle So the angle j and angle L will be 40.
Now we can solve
[tex]\angle L + \angle J + \angle K=180\\\\\\40+40+\angle K=180\\\\\\\angle k=180-80\\\\\\\angle k=100[/tex]
Now the side HI in the triangle HGI
We can see that the triangle HGI is the equilateral triangle so the all sides will be equal so
[tex]HI=IG=GH=4\[/tex]
Hence the angle k will be 100 in the triangle KJL and the side HI will be 4.
To know more about Triangles follow
https://brainly.com/question/2644832
#SPJ1
the top of a ladder rest at a height of 20 feet against the side of the house if the base of the ladder is 7 feet from the house what is the length of the ladder
let the length of the ladder be x Using Pythagoras theorem, |hyp|^2=|opp|^2+|adj|^2
x^2=20^2+7^2
x^2= 400+49
x^2= 449
Square root of both sides:
√x^2= √449
x= 21.19ft
Thus, the length of the ladder is 21.19feet.
Which of the following can sine squared theta over the quantity 1 plus cosine theta end quantity be simplified to?
The simplified value of the given function [tex]\dfrac{Sin^2\theta}{1+Cos^2\theta}[/tex] will be equal to 1.
What is trigonometry?The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle are termed trigonometry.
The given function is:-
[tex]=\dfrac{Sin^2\theta}{1+Cos^2\theta}\\\\\\=\dfrac{Sin^2\theta}{Sin^2\theta}\\\\\\\ = 1[/tex]
Hence the simplified value of the given function [tex]\dfrac{Sin^2\theta}{1+Cos^2\theta}[/tex] will be equal to 1.
To know more about Trigonometry follow
https://brainly.com/question/24349828
#SPJ1
587×6543÷285{32+65}= ? HELP
Answer:
1307199.57
Step-by-step explanation:
Follow BEDMAS (brackets first, then exponents, then multiplication and division, then addition and subtraction)
587x6543÷285(32+65)
32+65=97
587 x 6543 ÷ 285 x 97
= 3840741 ÷ 285 x 97
= 13476.2842 x 97
= 1307199.57
a car travels at 49 km/hour how far does it travel in a 12 hour day
Answer: 2.88 km.
Step-by-step explanation:
We will discuss here how to find the distance when speed and time are given.
When speed and time are given, the distance travelled is calculated by using the formula:
Distance = Speed × Time
The unit of time in speed should be the same as that of the given time.
Solved examples to calculate distance when speed and time are given:
1. How much distance will be covered in 5 hrs at a speed of 55 km per hour?
Solution:
Distance covered in 1 hour = 55 km.
We know, Distance = Speed × Time
Distance covered in 5 hrs = 55 × 5
= 275 km.
Therefore, distance covered in 5 hrs = 275 km.
2. A bus travels at a speed of 45 km/hour. How far will it travel in 36 minutes?
Solution:
Speed = 45 km/hour
Time = 36 minutes
= 36/60 Hour (Since we know, 1 hour = 60 minutes)
= 3/5 hour
Distance = speed × time
= 45 × (3/5) km
= (45 × 3)/5 km
= 27 km.
3. How much distance will be covered in 7 hrs at a speed of 62 km per hour?
Solution:
Distance covered in 1 hour = 62 km.
We know, Distance = Speed × Time
Distance covered in 7 hrs = 62 × 7
= 434 km.
Therefore, distance covered in 7 hrs = 434 km.
4. Mike drives his car at a speed of 70 km per hour. How much distance will he cover in 3 hours 30 minutes?
Solution:
Speed of the car = 70 km/hr
Time taken = 3 hours 30 minutes
= 3 ½ hours.
Distance covered in 1 hour = 70 km
Distance covered in 3 ½ hour = 70 × 3 ½ km
= 70 × 7/2 km
= 245 km.
5. How much distance will be covered in 1 ½ hour at a speed of 32 m per minute?
Solution:
[1 ½ hr = (60 + 30) minutes = 90 minutes].
Distance covered in 1 minute = 32 metres.
Distance covered in 90 minutes = 32 × 90 = 2880 m.
We know, 1 m = 1/1000 km.
= 2880/1000 km.
= 2.88 km.
Hope this helps!
I NEED THIS ASAP its geometry ( look at picture).
Answer:
-1.118 is the required value of tan theta
Benjamin drives 5 miles in 10 minutes. If he drove one hour in total at the same rate, how far did he go?
Answer:
30 miles because:
Step-by-step explanation:
10 x 6 = 60/1min
5 x 6 = 30miles
a bike path is 3 miles long. there are distance markers every 1/4 mile to the end of the path. which number line correctly models this situation and the total number of distance markers?
Answer:
12
Step-by-step explanation:
i assume theres supposed to be an image along with the question but just choose the numberline that has 12 marks on it, with each mark being every 1/4
Can anyone solve this correctly?
Answer:
5.32 inches
Step-by-step explanation:
It is given that 1 inch represents 50 feet, or 1 in = 50 feet.
The actual dome is 266 feet. To find the amount of inches, divide 266 with 50:
266 total feet/50 feet per inch = 5.32 inches.
The scale model in inches, therefore, would be 5.32 inches.
~
Answer:
her model will be 5.32 inches
Step-by-step explanation:
use the butterfly proportions method
Make a table of inches to feet. then cross multiply to find 'y' and boom. watch me solve it for a better understanding. Its not as difficult as it seems
inches feet
1 50
y 266
266 x 1 = 50y
266 ÷ 50 = y
y = 5.32
her model will be 5.32 inches