The area of the region enclosed by the petal of a rose curve r = sin2θ in the first quadrant is π/8 square units
What is integration?It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
We know the area in the polar coordinates is given by:
[tex]\rm A =\int\limits^a_b {\dfrac{1}{2}r^2} \, d\theta[/tex]
We have r = sin2θ
Here the quadrant is not given, so we are assuming we need to find the area in the first quadrant.
Put this value in the above integration and limit 0 to π/2
[tex]\rm A =\int\limits^{\dfrac{\pi}{2}}_0 {\dfrac{1}{2}(sin^22\theta)} \, d\theta[/tex]
After solving the above integration, we get:
[tex]\rm A = \dfrac{\pi}{8}[/tex]
Thus, the area of the region enclosed by the petal of a rose curve r = sin2θ in the first quadrant is π/8 square units
Learn more about integration here:
brainly.com/question/18125359
#SPJ4
Calculate the price of melons if melons cost $2.35 a pound and the melon on the scale weighs 2.2 pounds, making sure to round your answer to the nearest cent.
A conservationist determines that a particular beach is eroding at a rate of 1.1% each year. when writing an explicit formula to represent the amount of beach remaining each year, which value should she use as the common ratio? 0.011 0.089 0.989 1.011
Using exponential function concepts, it is found that the common ratio would be given by 0.989.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.1 - r, also as a decimal, is the common ratio.In this problem, the amount decays 1.1% a year, hence:
r = 0.011.1 - r = 1 - 0.011 = 0.989.The common ratio would be given by 0.989.
More can be learned about exponential function concepts at https://brainly.com/question/25537936
#SPJ4
Answer: C
Step-by-step explanation:
Trust
Which of these equations shows the correct relationship between x and y?
X+y = 90
x + y = 180
x=y
x + 50 = y
Miriam has 2 yellow tea cups and 5 brown teacups. Which ratio compares the number of brown tea cups to the total number of teacups?
A. 5:2
B. 2 to 7
C. 5 to 7
D. 2/5
F. 5:7
D. 5/7
The answer is 5:2 ration, it's already fully simplified
Thirty-five students passed the test. If that’s 70% of the class how many students is in the class?
Answer:
50
Step-by-step explanation:
fr the question,
35 students----------------70%
x students-------------------100%
cross multiplying
x ×70 = 35×100
dividing bothsides by 70
x = 3500/70
x=50 students
therefore,
there are 50 students in the class
help i need the answer
Answer:
Step-by-step explanation:
The ratio of width to length for an American flag is 10 to 19. How wide is a flag that is 66 cm long
Answer:
35cm
Step-by-step explanation:
The ratio of width:length is 10/19. Since the given length is 66cm long, we multiply by the ratio to get 66 x 10/19 = 34.7 = 35cm
Please help asap! I don’t understand it
Step-by-step explanation:
From given graph
f(-3)= (-3)
f(1)=1
Answer:
f(-3) = -3
f(1) = 1
Step-by-step explanation:
f(x) means the "function of x".
Therefore, the number in the bracket after the letter f is the value of x.
f(-3) means find the value of the function (y-value) when x = -3
f(1) means find the value of the function (y-value) when x = 1
To find f(-3), find x = -3 on the x-axis.
Now trace vertically until you meet the line. Read the value of y at this point.
⇒ f(-3) = -3
To find f(1), find x = 1 on the x-axis.
Now trace vertically until you meet the line. Read the value of y at this point.
⇒ f(1) = 1
Help please! Thank you
Answer:
A I might be wrong do
Step-by-step explanation:
The table shows the amount of money in your bank account over a period of 5
5
weeks. You plan to keep saving at the same rate until you have $800
$
800
in the account. Which equation could you use to find the number of weeks,
n
, it would take to reach your goal?
Math item stem image
CLEAR CHECK
100·=800
100
·
n
=
800
35·+100=800
35
·
n
+
100
=
800
100·+35=800
100
·
n
+
35
=
800
35·+800=100
The linear function that you could use to find the number of weeks it would take to reach your goal is:
35n + 100 = 800.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.From the table, we have that:
The intercept is the initial balance of 100.The slope is the rate of change of 35.Hence the balance after n weeks is given by:
B(n) = 100 + 35n.
You will have $800 when B(n) = 800, hence the equation is:
35n + 100 = 800.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
The table shows the ratio of people who ate a certain type of lunch to the total number of people who ate lunch. Lunch Type of Lunch Ratio to the Total Turkey sandwich 1 3 1 Vegetarian sandwich 6 4. Chicken sandwich 15 Salad 7 30 A total of 840 people ate lunch. Which statement is true? A Half as many people ate a turkey sandwich as ate a vegetarian sandwich. B One-fourth as many people ate a vegetarian sandwich as ate a salad. C There were 56 more people who ate a turkey sandwich than ate a chicken sandwich. с D There were 28 more people who ate a salad than ate a chicken sandwich.
Using proportions, it is found that the correct statement is given by:
C There were 56 more people who ate a turkey sandwich than ate a chicken sandwich.
What is a proportion?A proportion is a fraction of a total amount.
In this problem, one third out of 840 people ate Turkey Sandwich, hence the number is given by:
nT = 840/3 = 280.
One sixth ate Vegetarian Sandwich, hence the number is given by:
nV = 840/6 = 140.
4/15 ate Chicken Sandwich, hence the number is given by:
nC = 4 x 840/15 = 224.
7/30 ate Salad, hence the number is given by:
nS = 7 x 840/30 = 196.
Thus, option C is correct.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Jamal is painting his room. He determines that 1/2 gallon container of paint will cover 1/6 of a wall. How many gallons of paint are needed to cover an entire wall (assuming there are no windows or doors)? Enter your answer in the box below, do NOT include units.
Answer:
3 gallons
Step-by-step explanation:
1/6+1/6=2/6=1/3
1/3x3=3/3=1
Select the correct answer.
Which statement describes a relationship between these equations?
equation 1: y= 3x - 7
equation 2: y=-4x-7
O A.
The equations have the same y-intercept.
B.
The equations have the same slope.
OC.
Each equation represents a line that decreases from left to right.
OD.
Each equation represents a line that increases from left to right.
Answer:
A. Yes they do. Both equations have their opposing set of y-intercept. Where equation one has a y-intercept of +7, and equation two, +7.
B. No they do not. Equation one has a slope of +3, while equation 2 has a slope of -4.
C. Yes they do. Equation one represents that of a positive increasing graph, while equation two the opposite, decreasing.
Step-by-step explanation:
You can use the slope formula to identify and graph each equation simply by using y = mx + b. Where y is the the y coordinate, x is the x coordinate, m is the slope, and b is the y-intercept. With this you can start plotting by marking the y-intercept by putting the x as zero and seeing what number you get. In this case, 3x0-7 = -7. Meaning that would be the y-intercept. For the slope, depending on what the x coordinate is, that's how much the graph will increase or decrease whenever the x coordinate changes. Say the x coordinate is 1, so 3x1-7 = 3-7 = -4. Meaning your coordinate would be (1, -4) where you can keep doing this formula on and on to find the y coordinate for what x coordinate you want to find, or make it easier to graph with a ruler on paper once you have enough points.
The volume of a right cone is 3975\piπ units^3 3 . If its radius measures 15 units, find its height.
If its radius measures 15 units. Then the height of the cone will be 53 units.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
The volume of a right cone is 3975π cubic units.
If its radius measures 15 units.
Then the height of the cone will be
The volume of the cone is given as
Volume = 1/3 x π x r² x h
Then we have
3975π = 1/3 x π x 15² x h
11925 = 225 x h
h = 53 units
More about the geometry link is given below.
https://brainly.com/question/7558603
#SPJ1
OMG PLS HELP ME!!!!! WILL GIVE BRAINLIEST
Step-by-step explanation:
I made the added things green so you can understand better what I did to get the right answer. If you have any questions you may text me
Answer:
1. 62 ( 8X8 ) -2
2. 13 ( 10 + 3)
3. 6 ( 4 + 2 )
4. 18 (22 - 4)
5. 3 ( 6/2)
6. 14 (7+7)
Step-by-step explanation:
Next question pls !
It just plain simple add , multiplication , division and subtraction
Pls Do what as you written ! Mark me as Brainly for 100% correct !! Alr helped
3(2x + 8) = 0 what is x
Answer: Heyaa!
The Answer, x= −4
Step-by-step explanation:
Divide both sides by the numeric factor on the left side, then solve.
Hopefully this helps you~
- Matthew :)
have an amazing day <3
Answer:
X = - 4
Step-by-step explanation:
3(2x+8) =0
6x + 24 = 0
6x = 0 - 24
6x = - 24
X = - 24/6
X = - 4
Hope this helpssssss
50 points for whoever could someone please assist me with this question
The first step to the proof is ∠QRS + ∠STQ = 180°
What is a cyclic Quadrilateral?A cyclic quadrilateral is a quadrilateral circumscribed by a circle in which all the vertices of the quadrilateral touch the circle.
Analysis:
Join line Qx and Sx together.
2∠QRS = reflex ∠QxS ( twice angle at the circumference is that at center)
2∠STQ = ∠QxS( twice angle at circumference is that at the center)
Also ∠QXS + reflex ∠QXS = 360(angle at a point)
2∠QRS + 2∠STQ = 360
2(∠QRS + ∠STQ) = 360
∠QRS + ∠STQ = 180°
In conclusion, ∠QRS + ∠STQ = 180°
Learn more about cyclic quadrilateral: brainly.com/question/24142962
#SPJ1
Find the area of this circle. Use
3.14 for i.
72 in.
..
in.2
The area of the circle is about
(Round to the nearest hundredth as needed.)
Answer:
4,069.44 in squared
Step-by-step explanation:
pir^2
72/2 = 36
36^2 = 1,296pi
1,296*3.14 = 4,069.44
(1+5²) –16 (1/2)³
Please help please and Thank you
Answer:
the answer simplified is 24
Step-by-step explanation:
If 10% of a number is 16, find 5% of that number.
Answer:
5% = 8
Step-by-step explanation:
Since 10% of a number is 16, multiply that by 10 to get 160. In order to get 5%, divide 10% (16) by 2 to get 8, which is 5% of 160.
PLEASE HELP ASAP WILL GIVE BRAINLIEST AND 5 STARS
Someone help me I send a question on my profile
And this my question
Step-by-step explanation:
A=X AB=ZX
B=Z. AC=XY
C=Y. BC=YZ
Traingle BCA = Traingle ZYX
Guys, I beg you! How do you do these factoring quadratic equations!
Which is a solution to (x − 2)(x + 10) = 13
======================================================
Explanation:
There are at least three ways to solve this.
----------------------------------------------
Method 1:
We could graph y = (x-2)(x+10) using a tool like Desmos. Graph y = 13 as well which is a horizontal line.
Check out the screenshot shown below.
The parabola in red and the horizontal line in blue intersect at the locations (-11, 13) and (3, 13)
We only focus on the x coordinates of the intersection points.
Therefore, the two solutions are x = -11 and x = 3
The order of the solutions doesn't matter.
----------------------------------------------
Method 2:
Expand things out and get everything to one side
(x-2)(x+10) = 13
x^2 + 10x - 2x - 20 = 13
x^2 + 8x - 20 - 13 = 0
x^2 + 8x - 33 = 0
From here we can use the quadratic formula
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-8\pm\sqrt{(8)^2-4(1)(-33)}}{2(1)}\\\\x = \frac{-8\pm\sqrt{64+132}}{2}\\\\x = \frac{-8\pm\sqrt{196}}{2}\\\\x = \frac{-8\pm14}{2}\\\\x = \frac{-8+14}{2} \ \text{ or } \ x = \frac{-8-14}{2}\\\\x = \frac{6}{2} \ \text{ or } \ x = \frac{-22}{2}\\\\x = 3 \ \text{ or } \ x = -11\\\\[/tex]
----------------------------------------------
Method 3:
Instead of using the quadratic formula, we could factor.
To factor x^2+8x-33, we need to find two numbers that
Multiply to -33Add to 8Through trial and error, you should get 11 and -3
11 times -3 = -3311 plus -3 = 8So,
x^2+8x-33 = 0
(x+11)(x-3) = 0
x+11 = 0 or x-3 = 0
x = -11 or x = 3
helpppppppppppppppppp 100 points
Answer:
Range = 4Mode = 3Step-by-step explanation:
The range is the difference between the maximum and minimum values:
5 - 1 = 4The mode is the most repeated value of the data set
This is 3 (repeated 5 times)Answer:
I attached a screen shot of the answer
Step-by-step explanation:
Find the length of the hypotenuse
What is the volume of this cone?
Answer:
201.06193
Step-by-step explanation:
Write the following phrase as an algebraic expression. Use n for "a number."
three increased by the quotient of a number and two
a.
3+ n
2
b.
22
3 + -
2
C.
3(2 + 2)
d.
3 + 222
Please select the best answer from the choices provided
A
B
C
Answer:
3+(n/2) i think that is a? i cant rlly tell
Step-by-step explanation:
What is the first step when rewriting y = 3x2 + 9x – 18 in the form y = a(x – h)2 + k?
3 must be factored from 3x2 + 9x
x must be factored from 3x2 + 9x
9 must be factored from 9x – 18
3 must be factored from 3x2 – 18
Answer:
(a) 3 must be factored from 3x^2 + 9x
Step-by-step explanation:
The first step when rewriting a quadratic from standard form to vertex form is to factor out the leading coefficient from the variable terms.
__
y = 3x^2 +9x -18 . . . . . . given
y = 3(x^2 +3x) -18 . . . . . leading coefficient factored out
y = 3(x^2 +3x +2.25) -18 -3(2.25) . . . . . complete the square
y = 3(x +1.5)^2 -24.75 . . . . . simplify to vertex form
Answer:
3rd one
Step-by-step explanation: I am pretty sure becuase the other ones don't sound right hope this helps :)
pls help i will give brainliest and 5 stars
Answer:
See attached diagram
Step-by-step explanation:
See attached picture....I assumed -3% was really just -3
A square has an area of square inch what is [tex]18x^{2}[/tex] the length of one of its sides
Answer:
18x
Step-by-step explanation:
18x times 18x
so the side is 18x because it was squared
