The area of one petal of the polar curve r = 5 sin 2θ would be 25π/4.
How to find the area of a region?Supposing that there is no direct formula available for deriving the area, we can derive the area of that region by dividing it into smaller pieces, whose area can be known directly.
Then summing all those pieces' area gives us the area of the main big region.
The polar curve r = 5sin 2θ
When r = 0, θ = 0, π/2 which corresponds to one loop.
We need the limits to provide r=0 or cos(5x) =0 so:
Therefore the area of the region enclosed by this curve is
[tex]A = \dfrac{1}{2} \int\limits^a_b {r^{2} } \, d\theta \\\\\\A = \dfrac{1}{2} \int\limits^{\pi /2}_0 {25sin^{2}2\theta } \, d\theta \\\\\\A = \dfrac{1}{2} \times 25\int\limits^{\pi /2}_0 {sin^{2}2\theta } \, d\theta \\\\\\A = \dfrac{1}{2} \times 25\int\limits^{\pi /2}_0 \dfrac {1-cos^{2}4\theta } {2}\, d\theta\\ \\\\A = \dfrac{25}{2}( \theta - \dfrac {sin4\theta} {2})\, d\theta |^{\pi /2}_0\\\\\\A = \dfrac{25}{2} \times \dfrac{\pi }{2} \\\\\\A = \dfrac{25\pi }{4}[/tex]
Thus, the area of one petal of the polar curve r = 5sin 2θ would be 25π/4.
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Please and thank you?
Let's learn the relationship
Area=Length×BreadthSo Area is directly proportional to length
The Garden B has largest area
But hang on this is incorrect it's rectangle other side might be too long .
Spare way(Accurate and correct)We can calculate also
For garden A
2(L+B)=1202(25+B)=120.25+B=60B=35Area
LB
35(25)875ft²For garden B
2(50+B)=12050+B=60B=10Area
50(10)500ft²Surprisingly assumption at first turned right
Garden A has highest area not Garden B
Answer:
Garden A
Step-by-step explanation:
Formula
Perimeter of a rectangle = 2(w + l)Area of a rectangle = w × l(where w is the width and l is the length)
Garden AGiven:
Perimeter = 120 ftOne side length = 25 ftUsing the formula for the perimeter to calculate the missing side length:
Perimeter = 2(w + l)
⇒ 120 = 2(25 + l)
⇒ 120 = 50 + 2l
⇒ 2l = 70
⇒ l = 35 ft
Therefore, the dimensions of Garden A are:
width = 25 ftlength = 35ftArea = w × l
⇒ Area of Garden A = 25 × 35
= 875 ft²
Garden BGiven:
Perimeter = 120 ftOne side length = 50 ftUsing the formula for the perimeter to calculate the missing side length:
Perimeter = 2(w + l)
⇒ 120 = 2(w + 50)
⇒ 120 = 2w + 100
⇒ 2w = 20
⇒ w = 10 ft
Therefore, the dimensions of Garden B are:
width = 10 ftlength = 50 ftArea = w × l
⇒ Area of Garden B = 10 × 50
= 500 ft²
ConclusionAs 875 > 500, Garden A has the largest area.
Select the correct answer.
Based on the data in this two-way table, which statement is true?
Type of Flower/Color Red Pink Yellow Total
Rose 40 20 45 105
Hibiscus 80 40 90 210
Total 120 60 135 315
A. A flower being pink and a flower being a rose are independent of each other.
B. A flower being pink is dependent on a flower being a rose.
C. A flower being a rose is dependent on a flower being pink.
D. A flower being pink and a flower being a rose are the same.
Answer: The answer would be A. A flower being pink and a flower being a rose are independent of each other.
Step-by-step explanation:took the test and it was correct on edmentun!!
Find the sum or type "impossible" [3 -8]+[4 -5 -6]
Algebra 2 (On Acellus)
The sum of the given expression will be equal to -12.
What is an Algebra?
Algebra is the study of mathematical symbols and the rules for manipulating them in formulas; it is a common thread that runs through practically all of mathematics.
The solution of the given expression will be:-
= [ 3 - 8 ] + [ 4 - 5 - 6 ]
= [ -5 ] + [ -7 ]
= [ -12 ]
Therefore the sum of the given expression will be equal to -12.
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What is the difference? startfraction 2 x 5 over x squared minus 3 x endfraction minus startfraction 3 x 5 over x cubed minus 9 x endfraction minus startfraction x 1 over x squared minus 9 endfraction startfraction (x 5) (x 2) over x cubed minus 9 x endfraction startfraction (x 5) (x 4) over x cubed minus 9 x endfraction startfraction negative 2 x 11 over x cubed minus 12 x minus 9 endfraction startfraction 3 (x 2) over x squared minus 3 x endfraction
The difference of the expression [tex]\frac{2x^5}{x^2 - 3x} - \frac{3x^5}{x^3 - 9x}[/tex] is [tex]\frac{2x^5(x + 3) - 3x^5}{x(x - 3)(x + 3)}[/tex]
How to determine the difference?The expression is given as:
[tex]\frac{2x^5}{x^2 - 3x} - \frac{3x^5}{x^3 - 9x}[/tex]
Factor the denominators of the expressions:
[tex]\frac{2x^5}{x(x - 3)} - \frac{3x^5}{x(x^2 - 9)}[/tex]
Apply the difference of two squares to x² - 9
[tex]\frac{2x^5}{x(x - 3)} - \frac{3x^5}{x(x - 3)(x + 3)}[/tex]
Take LCM
[tex]\frac{2x^5(x + 3) - 3x^5}{x(x - 3)(x + 3)}[/tex]
Hence, the difference of the expression [tex]\frac{2x^5}{x^2 - 3x} - \frac{3x^5}{x^3 - 9x}[/tex] is [tex]\frac{2x^5(x + 3) - 3x^5}{x(x - 3)(x + 3)}[/tex]
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Answer:
A
Step-by-step explanation:
on Edge 2022
pls help!!!
math
what the value??
--
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: \sqrt{ - 25} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{ - 1 \times 25} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt{ {i}^{2} \times 25} [/tex]
[tex]\qquad \sf \dashrightarrow \: 5i[/tex]
so, correct choice is D
[tex] \sqrt{ - 25} [/tex]
To find:The equivalent value from the given options.
Solution:[tex] \sqrt{ - 25} [/tex]
[tex] = \sqrt{ - 1\times 25} [/tex]
[tex] = \sqrt{ {i}^{2} \times 25 } [/tex]
[tex] = 5i[/tex]
Therefore, the correct answer is option D
PLS HELP ASAP FIRST CORRECT ANSWER GETS BRAINLIEST
When a shape has 4 inside angles, the sum of the angles need to equal 360 degrees. This shape has 2 90 degree angles.
Angle DAB = 360 - 90-90 -155 = 25
Answer: 25 degrees,
Answer:
I got u, maybe.
In a triangle, all angles add up to 180, so it might be 180, you already got 155.
Step-by-step explanation:
calculate the volume of a cone whose base radius is 3 and half cm and vertical height 24cm
The volume of a cone whose radius is 3 1 / 2 cm and vertical height is 24 cm is 307.72 cm³
Volume of a coneThe volume of a cone can be represented as follows:
volume = 1 / 3 πr²h
where
r = radiush = heightTherefore,
r = 3 1 / 2 cm = 7 / 2 cm
h = 24 cm
Hence,
volume = 1 / 3 × π × (7 / 2 )² × 24
volume of a cone = 1 / 3 × π × 49 / 4 × 24
volume of the cone = 1 / 3 × π × 1176 / 4
volume of the cone = 1176 / 12 π
volume of the cone = 98π
volume of the cone = 307.72 cm³
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What is a probability if the youngest four members of a 15-member choir being randomly selected for a group of four singers
The point P has coordinates (5, 7) The point Q has coordinates (-1,-1) Find the length of the line segment PQ.
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{5}~,~\stackrel{y_1}{7})\qquad Q(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PQ=\sqrt{[-1 - 5]^2 + [-1 - 7]^2}\implies PQ=\sqrt{(-6)^2 + (-8)^2} \\\\\\ PQ=\sqrt{36+64}\implies PQ=10[/tex]
5 units to the right of -6 is
Answer:
-1
Step-by-step explanation:
To solve the problem, it is suggested to use a number line.
~Please look at image attached
We know the following:
If the change is going to the right of the initial point, the change is a positive integer, and the initial point will be added by the change.If the change is going to the left of the initial point, the change is a negative integer and the initial point will be subtracted by the change.Statement: 5 units to the right of -6.
Therefore, we know the following:
Initial starting point: -6Change: +5Ending point: -6 + 5 = -1
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Number line:Calculate the portion of each mix that is peanuts, again expressing your answer as a percent. Which recipe has the greatest concentration of peanuts?
Answer:
Recipie A has a higher percentage of chocolate chips and Recipie B has a higher percentage of peanuts.
Step-by-step explanation:
Chocolate Chunks:
Recipie A calls for a total of ten cups. So 3 cups of chocolate chips are used in Recipe A. The percentage of chocolate chips in the mix is given by 3/10, which can be written as 30%. Recipie B now has a total of 20 cups. So in Recipe B 5/20, which can be written in percentages as 25%. Recipe C now has a total of 25 cups. So 6 cups of chocolate chips are used in the recipe. The percentage of chocolate chips in the mix is given by 6/25, which can be written as 24 percent. Recipie A has the highest percentage of chocolate chips of the three recipes.
Peanuts:
Recipie A calls for a total of ten cups. So, according to the recipe, A 2 cups are peanuts. The amount of peanuts in the mixture is given by 2/10, which can be written as a percentage of 20%. Recipie B calls for 20 cups. So there are 7 cups of peanuts in the recipe. The percentage of peanuts in the mix is given by 7/20, which can be written as 35%. Recipie C has a total of 25 cups, so there are 7 cups of peanuts in the recipe. The percentage of peanuts in the mix is given by 7/25, which is equivalent to 28 percent in percentages. The recipie b contains the highest percentage of peanuts of the three.
As a result, Recipie A has a higher percentage of chocolate chips and Recipie B has a higher percentage of peanuts.
The diameter of a circle is 10 ft. Find the circumference to the nearest tenth to the nearest tenth. (Urgent)
Answer:
31.42ft
Step-by-step explanation:
diameter = 10
radius = diameter ÷ 2
r = 10 ÷ 2
r= 5
Circumference = 2(pie)(r)
= 2(22÷7)(5)
= 31.42ft
Answer:
C ≈ 31.4 ft
Step-by-step explanation:
the circumference (C) of a circle is calculated as
C = πd ( d is the diameter ) , then
C = π × 10 = 10π ≈ 31.4 ft ( to the nearest tenth )
Which term best describes the expression 5x4y8 ?
O Polynomial
Binomial
O Monomial
O Trinomial
Answer: Binomial
Step-by-step explanation: There are two variables here, x and y. 5x^4y^8 is a binomial since it involves 2 variables.
Answer:
Monomial
Step-by-step explanation:
A monomial is 1 term. 5x4y8 is one term, and nothing is getting added to it.
6cm
5cm
20cm
4cm
5cm
4cm
12cm
6cm
4cm
Answer:
SA = 788cm^2
Step-by-step explanation:
pink one:
length- 5
width- 6
height- 20
surface area- 500
purple one:
length- 4
width- 6
height- 12
surface area- 288
total surface area:
500 + 288 = 788
SA = 788cm^2
GOOD LUCK!!!! You'll do amazing <3
The total surface area of the composite figure will be 788 cm².
What is surface area?The total area occupied by an object's surface is referred to as its surface area. Varying 3D forms have different surface areas in geometry, which may be simply estimated using calculations.
The given pink cuboid has :
The length = 5
The width = 6
The height = 20
The surface area of pink cuboid = 500 cm²
The given purple cuboid has :
The length = 6
The width = 4
The height = 12
The surface area of purple cuboid = 288 cm²
Total surface area = The surface area of pink cuboid + The surface area of purple cuboid
Total surface area = 500 + 288 = 788 cm²
SA = 788 cm²
Thus, the total surface area of the composite figure will be 788 cm².
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Simplify the following expression
-2x^2 + 4 + 5x^2 - 11 - 12x
Show the steps on how to solve this
Answer:
3x² - 12x - 7
Step-by-step explanation:
Subtract the numberS
-2x²+4+5x²-11 - 12x
-2x²-7+5x² - 12x
Combine like terms
-2x²-7+5x² - 12x
3x²-7-12x
Rearrange terms
3x²-7-12x
3x²-12x-7
Solution
3x² - 12x - 7
Answer:
3x² - 12x - 7
Step-by-step explanation:
-2x² + 4 + 5x² - 11 - 12x3x² - 12x - 7Please someone help me with this
Answer:Around 14.7 minutes
Step-by-step explanation:
if q= the amount of time, and p=18 you do 12*18 is 216 and radical 216 is 14.6969, (nice). Please let me know if i am inncorrect i am not 100% sure.
Find the value of x
Answer:
x = 6
Step-by-step explanation:
(-6, 2), (6, 2), (3, 1), (6, 1)
Pls help me this is hard!!
Answer:
27.5
Step-by-step explanation:
<DAC is an inscribed angle that subtends a half circle, so m<DAC = 90°.
Triangle DAC is a right triangle.
CD = 30
AD = 12
(AC)² + (AD)² = (CD)²
(AC)² + 144 = 900
AC = √756
AC = 27.5
Grace is considering purchasing a phone plan. The phone plan
costs $20 per month plus ten cents for each text message sent.
Write and solve an equation to determine how many text
messages were sent if her monthly bill totals $41.10. (5 points - 1
for defining a variable, 1 for correct equation, 1 for work, 1
for answer, 1 for label)
Answer:
211 text messages
Step-by-step explanation:
20+(m•0.10)=41.10
41.1-20=21.1÷0.1=211
Scott and Huong each improved their yards by planting daylilies and ivy. They bought their
supplies from the same store. Scott spent $91 on 7 daylilies and 1 pot of ivy. Huong spent $105
on 7 daylilies and 3 pots of ivy. What is the cost of one daylily and the cost of one pot of ivy?
Answer:
daylilies - $12; ivy - $7
Step-by-step explanation:
one way to answer this question is by using two equations
first write your let statements
let d be daylilies and let i be ivy
7d + i = 91
7d + 3i = 105
then you can subtract the equations
you get -2i = -14
then divide eveything by -2
i = 7
ivy costs $7
lastly plug this into an equation
7d + 7 = 91
7d = 84
d = 12
daylilies cost $12
What is angle M in degrees?
What is the probabillity ?
Answer: the chance that a given event will occur
Step-by-step explanation:
Carla worked 13 1/4 hours making $9.75 per hour. Daniel earned $10.50 per hour and worked 11 3/4 hours. What was the total amount of money earned?
Answer:
$252.5625
Step-by-step explanation:
9.75×53/4+10.50×47/4
129.1875+123.375
=252.5625
hope it helpsss
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a steel drum is shaped like a cylinder and it has a height of 3 feet and a base radius of one what is the volume of the steel drum in cubic feet
If the height of the cylinder is 3 feet and the base radius of the cylinder is 1 foot. Then the volume of the cylinder will be 9.43 cubic feet.
What is a cylinder?A cylinder is a closed solid with two parallel circular bases and a curving surface connecting them.
A steel drum is shaped like a cylinder and it has a height of 3 feet and a base radius of one.
Then the volume of the cylinder will be
The volume of the cylinder is given as
Volume = πr²h
where r is the radius and h is the height of the cylinder.
We have
h = 3 ft
r = 1 ft
Then the volume of the cylinder will be
Volume = π x 1² x 3
Volume = π x 3
Volume = 9.4247
Volume ≅ 9.43 cubic ft
Then the volume of the cylinder will be 9.43 cubic feet.
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if sin x =cos 60° what is the value of x
Use the following data set to answer question 8:
13, 19, 7, 12, 21, 18, 15 8.
Predict how the mean will change if the 7 is deleted from the data set. Calculate the new mean. Round to the nearest tenth.
Answer:
15.1 to nearest tenth.
Step-by-step explanation:
The 7 is the lowest number so the mean would increase if taken away.
New mean = (8 + 12 + 13 + 15 + 18 + 19+21) / 7
= 106 / 7
= 15.14
2)
8q+6=4q-14
What is The answer ?
Answer:
q=-5
Step-by-step explanation:
8q+6=4q-14
Remove q from one side
8q+6=4q-14
-4q -4q
4q+6=-14
Remove 6 from both sides
4q+6=-14
-6 -6
4q=-20
Divide 4 to isolate q
4q/4=-20/4
q=-5
Which inequality describes the graph?
The graph is a linear inequality, and the inequality that describes the graph is y < 2x - 1
How to determine the inequality?From the graph, we have the following features:
y-intercept, b = -1It passes through the points (0,-1) and (1,1)The line is a dotted line and the lower region are shaded; so, we make use of the < inequalityNext, we calculate the slope using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{1 + 1}{1 - 0}[/tex]
m = 2
The inequality is then calculated using:
y < mx + b
This gives
y < 2x - 1
Hence, the inequality that describes the graph is y < 2x - 1
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Build a number line to show 4/3
The number line with the number 4/3 graphed can be seen at the end of the answer.
How to show the number in a number line?
A number line is something that we use to show the order of the numbers.
Here, we want to show the number 4/3.
Notice that we can write this as:
4/3 = 3/3 + 1/3 = 1 + 1/3
So we need to identify the 1 in the number line, and then move 1/3 to the right. Below you can see a image where the number 4/3 is graphed on the shown number line.
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Fiona can type 60 words a minute.
How many words can be typed in 10.5 minutes?
Answer:
630 word
10.5 minute: 10×60+0.5×60=600+30=630 second
60 word 60second
? word 630 second
?=630
Step-by-step explanation:
630 words !?! Because 10.5×60=630
